DETAILED ACTION
This Office action is responsive to the claims filed on June 23, 2026. Claims 12-18, 10-22, and 25-26 are pending.
Claim 14 is objected to for lack of antecedence.
Claims 12-18, 20-22, and 25-26 are rejected under 35 USC 101 as being ineligible.
Claims 14-17 are rejected under 35 USC 103 as obvious over Roux in view of Moore and Danielson.
Claims 12-13, 18, and 20-22 are rejected under 35 USC 103 as obvious over Roux in view of Li, Moore, and Danielson.
Claims 12-13 and 20-23 are rejected under 35 USC 103 as obvious over Roux in view of Li.
Claim 25 is rejected under 35 USC 103 as obvious over Roux in view of Li, Moore, Danielson, and NCORR.
Claim 26 is rejected under 35 USC 103 as obvious over Roux in view of Li, Moore, Danielson, and Terzic.
Response To Amendments/Arguments
Drawing Objections: The Applicant’s arguments and amendments have been considered and are persuasive.
35 USC 112(a): The Applicant’s arguments and amendments have been considered and are persuasive. The rejection is withdrawn.
35 USC 112(b): The Applicant’s arguments and amendments have been considered and are persuasive. The rejections are withdrawn.
35 USC 101: The Applicant’s amendments and arguments have been considered but are not persuasive. The Applicant’s arguments will be addressed in the order they were presented in the response.
The Applicant argues that the claim recites a practical application by the newly amended feature introduced to the independent claims,
wherein the target structure is a shrink-fit part of a retention ring shrink-fitted to a rotor core at an end of a rotor of a rotary electric machine, and the shape of the target structure is represented in a cylindrical coordinate system.
Specifically, the Applicant states that the claim identifies faulty components prior to failure. However, the claim does not recite this potential additional limitation. Further, mere detection of a potential failure without reciting a corresponding responsive action with a mechanism is likely insufficient as a mere apply it limitation under MPEP 2106.05(f)(1), so it would not qualify as an additional limitation that integrates the abstract idea into a practical application. The claim fails to recite the application the Applicant asserts, let alone an application that is sufficient to satisfy MPEP 2106.05(f)(1). More importantly, the claims fail to recite any additional limitations that confer eligibility at Step 2A, Prong 2 or at Step 2B.
Accordingly, the rejections are maintained.
Art Rejections: The Applicant’s arguments and amendments have been considered and are persuasive with respect to claims 12-18, 20-22, and 25-26. The prior rejections have been replaced with new rejections that rely on new art.
The Applicant argues in the response that the inverse matrix in Roux is used to calculate noise and asserts that this means that the claims allegedly fail to teach the feature, “outputs, as an estimation model for estimating a state of the crack occurrence plane from a state of the observation plane, an inverse matrix of a matrix that associates, with each other, the state of the crack occurrence plane and the state of the observation plane.” However, the Matrix in Roux used to determine the noise, which is an element for determining the “state of the crack occurrence,” is the inverse of the Mmn matrix that relates the image to the crack, as shown on Page 7, Equation 7 of Roux, as follows:
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Accordingly, the Applicant’s assertion that the Roux reference fails to teach the claimed matrix is incorrect. The new rejections are the result of the incorporation of the features from canceled claim 19 into the independent claims.
Claim Objections
Claim 14 is objected to because of the following informalities:
Claim 14 recites, “while analysis under the sequentially set boundary condition is sequentially performed by the numerical analyzer.” However, claim 14 does not provide primary antecedence for the numerical analyzer, an element that has been canceled from the claim.
Appropriate correction is required.
Claim Rejections - 35 USC § 101
35 U.S.C. 101 reads as follows:
Whoever invents or discovers any new and useful process, machine, manufacture, or composition of matter, or any new and useful improvement thereof, may obtain a patent therefor, subject to the conditions and requirements of this title.
Claims 12-24 are rejected under 35 U.S.C. 101 because the claimed invention is directed to an abstract idea without significantly more.
Independent Claims
Claim 12 (Statutory Category – Machine)
Step 2A – Prong 1: Judicial Exception Recited?
Yes, the claims recite a mental process and a mathematical concept, which are abstract ideas.
Claim 12 recites (Claim language in bold italic):
determines a shape model of a target structure to be inspected, and a crack occurrence plane and an observation plane in the shape model; (Mental Evaluation, Mental Process – Estimating features of a crack including by determining a shape model of a target structure that includes a crack occurrence plane and an observational plane is an evaluation practically performable in the mind or with the aid of a pen, paper, and/or a calculator. This is a mental process, an abstract idea.)
outputs, as an estimation model for estimating a state of the crack occurrence plane from a state of the observation plane, an inverse matrix of a matrix that associates, with each other, the state of the crack occurrence plane and the state of the observation plane, obtained through numerical analysis of a structural analysis model generated from the shape model; and (Mental Evaluation, Mental Process; Mathematical Calculation; Mathematical Concept – Calculating an inverse matrix is an evaluation practically performable in the mind or with the aid of a pen, paper, and/or a calculator. This is a mental process, an abstract idea. Additionally, this recites an inverse matrix operation, a mathematical calculation, a mathematical concept, an abstract idea.)
estimates a state of a crack at the crack occurrence plane on the basis of the estimation model and a measurement value for the target structure actually measured at the observation plane, (Mental Evaluation, Mental Process – Estimating a state of a crack and estimating a measurement value are evaluations practically performable in the mind or with the aid of a pen, paper, and/or a calculator. These are mental processes, an abstract idea.)
Claim 14 (Statutory Category – Machine)
Step 2A – Prong 1: Judicial Exception Recited?
Yes, the claims recite a mental process and a mathematical concept, which are abstract ideas.
Claim 14 recites (Claim language in bold italic):
determines a shape model of a target structure to be inspected, and a crack occurrence plane and an observation plane in the shape model; (Mental Evaluation, Mental Process – Determining a model of a structure that includes a crack occurrence plane and an observation plane is an evaluation practically performable in the mind or with the aid of a pen, paper, and/or a calculator. This is a mental process, an abstract idea.)
outputs an estimation model for estimating a state of the crack occurrence plane from a state of the observation plane, on the basis of a matrix that associates, with each other, the state of the crack occurrence plane and the state of the observation plane, obtained through numerical analysis of a structural analysis model generated from the shape model; and (Mental Evaluation, Mental Process; Mathematical Calculation; Mathematical Concept – Calculating an inverse matrix is an evaluation practically performable in the mind or with the aid of a pen, paper, and/or a calculator. This is a mental process, an abstract idea. Additionally, this recites an inverse matrix operation, a mathematical calculation, a mathematical concept, an abstract idea.)
estimates a state of a crack at the crack occurrence plane on the basis of the estimation model and a measurement value for the target structure actually measured at the observation plane and to provide the estimated state of the crack and the measurement value to a display device, wherein the estimation data calculator includes (Mental Evaluation, Mental Process – Estimating a state of a crack and estimating a measurement value are evaluations practically performable in the mind or with the aid of a pen, paper, and/or a calculator. These are mental processes, an abstract idea.)
divides each of the crack occurrence plane and the observation plane into unit planes and performs numerical analysis of the structural analysis model on the basis of a boundary condition for the divided unit planes, (Mental Evaluation, Mental Process; Mathematical Calculation; Mathematical Concept – Performing numerical analysis of a structural analysis model based on a boundary condition for specified planes is an evaluation practically performable in the mind or with the aid of a pen, paper, and/or a calculator. This is a mental process, an abstract idea. Additionally, this recites a numerical analysis, a mathematical calculation, a mathematical concept, an abstract idea.)
generates the structural analysis model from the shape model, sequentially sets such a boundary condition for the structural analysis model that a crack occurs at the crack occurrence plane, while analysis under the sequentially set boundary condition is sequentially performed by the numerical analyzer, […] (Mental Evaluation, Mental Process; Mathematical Calculation; Mathematical Concept – Generating a structural analysis model from a shape model, sequentially setting boundary conditions for a model, and performing numerical analysis of a structural analysis model based on a boundary condition for specified planes are evaluations practically performable in the mind or with the aid of a pen, paper, and/or a calculator. These are mental processes, abstract elements of an abstract idea. Additionally, this recites a numerical analysis, a mathematical calculation, a mathematical concept, an abstract idea.)
calculates a forward coefficient matrix for mapping a crack occurrence plane matrix in which the analysis result of the crack occurrence plane stored in the storage device is represented as a matrix, to an observation plane matrix in which the analysis result of the observation plane stored in the storage device is represented as a matrix, and outputs an inverse matrix of the forward coefficient matrix as the estimation model. (Mental Evaluation, Mental Process; Mathematical Calculation; Mathematical Concept – Calculating a forward coefficient matrix for output is an evaluation practically performable in the mind or with the aid of a pen, paper, and/or a calculator. This is a mental process, an abstract idea. Additionally, this recites a matrix calculation, a mathematical calculation, a mathematical concept, an abstract idea.)
Claim 20 (Statutory Category – Process)
Step 2A – Prong 1: Judicial Exception Recited?
Yes, the claims recite a mental process and a mathematical concept, which are abstract ideas.
Claim 20 recites (Claim language in bold italic):
A crack estimation method comprising the steps of: inputting a shape model of a target structure to be inspected, and a crack occurrence plane and an observation plane in the shape model; outputting, as an estimation model for estimating a state of the crack occurrence plane from a state of the observation plane, an inverse matrix of a matrix that associates, with each other, the state of the crack occurrence plane and the state of the observation plane in a structural analysis model generated from the shape model; and (Mental Evaluation, Mental Process; Mathematical Calculation; Mathematical Concept – Calculating an inverse matrix is an evaluation practically performable in the mind or with the aid of a pen, paper, and/or a calculator. This is a mental process, an abstract idea. Additionally, this recites an inverse matrix operation, a mathematical calculation, a mathematical concept, an abstract idea.)
estimating a state of a crack at the crack occurrence plane on the basis of the estimation model and a measurement value for the target structure actually measured at the observation plane. (Mental Evaluation, Mental Process – Estimating a state of a crack and estimating a measurement value are evaluations practically performable in the mind or with the aid of a pen, paper, and/or a calculator. These are mental processes, an abstract idea.)
Claims 12, 14, and 20 recite abstract ideas.
Step 2A – Prong 2: Integrated into a Practical Application?
No.
The Additional limitations:
{stores an analysis result of the crack occurrence plane and an analysis result of the observation plane […], and } (Claim 14)
Storing data is insignificant extra-solution activity similar to the MPEP 2106.05(g) examples: “v. Consulting and updating an activity log” “iii. Selecting information, based on types of information and availability of information in a power-grid environment, for collection, analysis and display” “ii. Printing or downloading generated menus.” Because the limitation is insignificant extra-solution activity, under MPEP 2106.05(g), the limitation fails to integrate the abstract idea into a practical application at Step 2A, Prong 2.
{A crack estimation device comprising a processor that […]
[…] a data determination circuit […]
[…] shape model […]
[…] estimation model […]
[…] structural analysis model […]
[…] and to provide the estimated state of the crack and the measurement value to a display device for display […]} (Claim 12)
{[…] A crack estimation device comprising: a process that[…]
[…] shape model […]
[…] estimation model […]
[…] the processor further […]
[…] structural analysis model […]
[…] storage device […]
[…] and to provide the estimated state of the crack and the measurement value to a display device for display […]} (Claim 14)
{[…] shape model […]
[…] estimation model […]
[…] structural analysis model […]
[…] and providing the estimated state of the crack and the measurement value to a display device for display […]} (Claim 20)
Should it be found that any of these elements are not elements of the abstract idea (e.g., as software components), these elements recite generic computing components/code at a high level and, under MPEP 2106.05(f), fail to integrate the abstract idea into a practical application at Step 2A, Prong 2.
wherein the target structure is a shrink-fit part of a retention ring shrink-fitted toa rotor core at an end of a rotor of a rotary electric machine, and the shape of the target structure is represented in a cylindrical coordinate system.
Any specific details about the parameters the data recited represent, the parameters merely limit the abstract idea to a particular technological environment and, under MPEP 2106.05(h), fail to integrate the abstract idea into a practical application at Step 2A, Prong 2.
Claims 12, 14, and 20 fail to provide any additional limitations that integrate the abstract idea into a practical application.
Claims 12, 14, and 20 are directed to the abstract idea.
Step 2B: Claim provides an Inventive Concept?
No.
The Additional limitations:
{stores an analysis result of the crack occurrence plane and an analysis result of the observation plane […], and } (Claim 14)
The store step is well-understood, routine, and conventional activity similar to the MPEP 2106.05(d) examples: “i. Receiving or transmitting data over a network,” “iii. Electronic recordkeeping” “iv. Storing and retrieving information in memory” “i. Determining the level of a biomarker in blood by any means” (sensors) “vi. Arranging a hierarchy of groups, sorting information, eliminating less restrictive pricing information and determining the price.” Because the store step is WURC and, as previously demonstrated, insignificant extra-solution activity, under MPEP 2106.05(d) and MPEP 2106.05(g), the step fails to combine with other elements of the claim to provide significantly more that would confer an inventive concept at Step 2B.
{A crack estimation device comprising a processor that […]
[…] a data determination circuit […]
[…] shape model […]
[…] estimation model […]
[…] structural analysis model […]
[…] and to provide the estimated state of the crack and the measurement value to a display device for display […]} (Claim 12)
{[…] A crack estimation device comprising: a process that[…]
[…] shape model […]
[…] estimation model […]
[…] the processor further […]
[…] structural analysis model […]
[…] storage device […]
[…] and to provide the estimated state of the crack and the measurement value to a display device for display […]} (Claim 14)
{[…] shape model […]
[…] estimation model […]
[…] structural analysis model […]
[…] and providing the estimated state of the crack and the measurement value to a display device for display […]} (Claim 20)
Should it be found that any of these elements are not elements of the abstract idea (e.g., as software components), these elements recite generic computing components/code at a high level of generality and, under MPEP 2106.05(f), fail to combine with other elements of the claim to provide significantly more that would confer an inventive concept at Step 2B.
wherein the target structure is a shrink-fit part of a retention ring shrink-fitted toa rotor core at an end of a rotor of a rotary electric machine, and the shape of the target structure is represented in a cylindrical coordinate system.
Any specific details about the parameters the data recited represent, the parameters merely limit the abstract idea to a particular technological environment and, under MPEP 2106.05(h), fail to combine with other elements of the claim to provide significantly more that would confer an inventive concept at Step 2B.
The additional limitations of claims 12, 14, and 20 fail to combine with the other elements of their respective claims to provide significantly more than the abstract idea that would confer an inventive concept at Step 2B.
Claims 12, 14, and 20 are ineligible.
Dependent Claims
The dependent claims fail to provide any additional limitations that would confer eligibility at Step 2A, Prong 2 and Step 2B.
NOTE: For all of the dependent claims, the parameters the data represents merely limit the abstract idea to a particular technological field and fail to confer eligibility under MPEP 2106.05(g). Also, all recited computing elements or the use thereof are recited at a high level of generality and represent generic computing processes, so, under MPEP 2106.05(f), these fail to confer eligibility.
Claim 13
wherein the matrix that associates the state of the crack occurrence plane and the state of the observation plane with each other in the estimation data calculator is a matrix that associates, with each other, a matrix in which the state of the crack occurrence plane is arranged in a predetermined order for each shape of the crack and a matrix in which the state of the observation plane is arranged in a predetermined order for each shape of the crack.
This merely characterizes an element of the mental process and the mathematical concept, so it is an element of the abstract idea. Therefore, the limitation does not provide any additional limitations that confer eligibility.
Should it be found otherwise, these merely characterize what the data represent and merely limit the abstract idea to a particular field of technology, and under MPEP 2106.05(h), fail to confer eligibility at Step 2A, Prong 2 and Step 2B.
Claim 13 fails to provide any additional limitations that confer eligibility at Step 2A, Prong 2, and Step 2B.
Claim 13 is ineligible.
Claim 15
wherein an input boundary condition which is the boundary condition for the structural analysis model is that, in the crack occurrence plane, connection between the divided unit planes of the crack occurrence plane is disconnected or displacement of the crack occurrence plane is changed to a shape or a boundary condition equal to a case where a crack has occurred.
Using a particular boundary condition is merely an element of the mental processes and mathematical concepts recited in the claim(s) from which this claim depends, an element of the abstract idea.
Claim 15 fails to provide any additional limitations that confer eligibility at Step 2A, Prong 2, and Step 2B.
Claim 15 is ineligible.
Claim 16
wherein the analysis result of the observation plane is represented as a vector based on any of displacement change, strain change, and angle change in the observation plane.
Outputting a specific format of solution from an evaluation is an element of the evaluation, a mental process, an abstract idea.
Claim 16 fails to provide any additional limitations that confer eligibility at Step 2A, Prong 2, and Step 2B.
Claim 16 is ineligible.
Claim 17
wherein the analysis result of the crack occurrence plane is represented as a vector based on displacement change or load change in the crack occurrence plane.
Outputting a specific format of solution from an evaluation is an element of the evaluation, a mental process, an abstract idea.
Claim 17 fails to provide any additional limitations that confer eligibility at Step 2A, Prong 2, and Step 2B.
Claim 17 is ineligible.
Claim 18
wherein the processor calculates a displacement vector of the crack occurrence plane, from the inverse matrix and a deformation vector of the observation plane generated from a result of deformation of the target structure actually measured at the observation plane, and estimates a position and a size of a crack at the crack occurrence plane on the basis of the displacement vector.
The calculation of a displacement vector and position estimation are evaluations practically performable in the mind or with the aid of a pen, paper, and/or a calculator. This is an element of the abstract idea and provides no additional limitations that confer eligibility.
As demonstrated, the processor is a generic computing element that fails to confer eligibility under MPEP 2106.05(f).
Claim 18 fails to provide any additional limitations that confer eligibility at Step 2A, Prong 2, and Step 2B.
Claim 18 is ineligible.
Claim 21
wherein the matrix that associates the state of the crack occurrence plane and the state of the observation plane with each other is a matrix that associates, with each other, a matrix in which the state of the crack occurrence plane is arranged in a predetermined order for each shape of the crack and a matrix in which the state of the observation plane is arranged in a predetermined order for each shape of the crack.
This describes the nature of the matrix in the evaluations of the independent claim, which is an element of the mental process, an abstract idea, and an element of the mathematical concept, an abstract idea. Therefore, this claim fails to provide an additional limitation.
Claim 21 fails to provide any additional limitations that confer eligibility at Step 2A, Prong 2, and Step 2B.
Claim 21 is ineligible.
Claim 22
wherein the step of outputting, as the estimation model includes (This was already addressed in a rejection of claim 20.)
a step of performing numerical analysis while sequentially setting such a boundary condition for the structural analysis model that a crack occurs at every node between the divided unit planes of the crack occurrence plane, and
Performing a numerical analysis while considering boundary conditions and generating an analysis result for storage is practically performable in the mind or with the aid of pen, paper, and/or a calculator. This is a mental process, an abstract idea. Further, the numerical analysis is a mathematical calculation, a mathematical concept, an abstract idea.
storing an analysis result of the crack occurrence plane and an analysis result of the observation plane obtained through the numerical analysis, in a storage device, and
The storage is insignificant extra-solution activity and WURC for the same reasons as the store step of claim 14, so this feature fails to confer eligibility at Step 2A, Prong 2, and Step 2B.
a step of calculating a crack occurrence plane matrix in which the crack occurrence plane is represented as a matrix and an observation plane matrix in which the observation plane is represented as a matrix from the analysis results stored in the storage device, calculating a forward coefficient matrix for mapping the crack occurrence plane matrix to the observation plane matrix, and outputting an inverse matrix of the forward coefficient matrix as the estimation model.
Calculating a plane and a forward coefficient matrix and configuring the evaluation for outputting an inverse matrix as an estimation model are practically performable in the mind or with the aid of a pen, paper, and/or a calculator. This is a mental process, an abstract idea. Further, the calculations are mathematical calculations, mathematical concepts, an abstract idea.
Claim 22 fails to provide any additional limitations that confer eligibility at Step 2A, Prong 2, and Step 2B.
Claim 22 is ineligible.
Claim 25
wherein the displacement is used as the state of the crack occurrence plane, strain is used as the state of the observation plane, and the estimation model represents the relationship therebetween by the inverse matrix.
This merely characterizes the data which merely limits the abstract idea to a technological environment and fails to confer eligibility under MPEP 2106.05(h).
Claim 25 fails to provide any additional limitations that confer eligibility at Step 2A, Prong 2, and Step 2B.
Claim 25 is ineligible.
Claim 26
wherein displacement change or force change is used as the state of the crack occurrence plane, and displacement change or angle change is used as the state of the observation plane, and the estimation model represents the relationship therebetween by the inverse matrix.
This merely characterizes the data which merely limits the abstract idea to a technological environment and fails to confer eligibility under MPEP 2106.05(h).
Claim 26 fails to provide any additional limitations that confer eligibility at Step 2A, Prong 2, and Step 2B.
Claim 26 is ineligible.
Claim Rejections - 35 USC § 103
The following is a quotation of 35 U.S.C. 103 which forms the basis for all obviousness rejections set forth in this Office action:
A patent for a claimed invention may not be obtained, notwithstanding that the claimed invention is not identically disclosed as set forth in section 102, if the differences between the claimed invention and the prior art are such that the claimed invention as a whole would have been obvious before the effective filing date of the claimed invention to a person having ordinary skill in the art to which the claimed invention pertains. Patentability shall not be negated by the manner in which the invention was made.
Claim(s) 14-17: Roux, Moore, and Danielson
Claim 14-17 are rejected under 35 U.S.C. 102(a)(1)/(a)(2) as being anticipated by NPL “Digital Image Correlation and Fracture: An Advanced Technique for Estimating Stress Intensity Factors of 2D and 3D Cracks” by Roux et al. (Roux) in view of NPL: “Damage Mechanisms Found in Generator Rotor 18Mn18Cr Retaining Rings.” by Moore (Moore) and NPL: “Three-dimensional finite element analysis in cylindrical coordinates for nonlinear solid mechanics problems” by Danielson et al. (Danielson).
Claim 14
Regarding claim 14, Roux teaches;
A crack estimation device comprising: a processor that determines a shape model of a target structure to be inspected, and a crack occurrence plane and an observation plane in the shape model; (Roux Abstract “Because of its remarkable sensitivity, it is not only possible to detect cracks with sub-pixel opening, which would not be visible, but also to provide accurate estimates of stress intensity factors. For this purpose suitable tools have been devised to minimize the sensitivity to noise. Working with digital images allows the experimentalist to deal with a wide range of scales from atomistic to geophysical one with the same tools.” Page 15, Third Paragraph “It is interesting to observe that the problem still remains linear in ω, even if it is somewhat more computer resource demanding.” – A crack estimation device comprising a processor for performing the steps of calculation. Page 4, Last Paragraph – Page 5, Second Paragraph “To monitor phenomena within opaque materials, X-Ray Computed MicroTomography (XCMT) is a very powerful way of imaging material microstructures in a nondestructive manner [46]. In particular, cracks can be observed [47, 48], their closure [49], and CODs measured by manually tracking particles [50]. When the crack morphology is determined, X-FEM techniques allow for the evaluation of surface vs. bulk propagation features [51]. Global correlation techniques [52] were used recently to measureCODs [53]. Enriched kinematics are also implemented (i.e., it corresponds to eXtendedDigital Image Correlation to measure 3D displacements, or X3D-DIC [54]). This procedure allows one to bridge the gap between 3D pictures and numerical models [55]. In Section 2, the principles of DIC are introduced. Various strategies are discussed to deal with the measurement of displacement fields, which is an ill-posed problem. This feature has consequences on the measurement uncertainties that are evaluated. Surface measurements are performed in the presence of cracks in Section 3 and the different strategies introduced above are illustrated. One key quantity in fracture mechanics is the SIF, which may be deduced from the knowledge of measured displacements. Different approaches are followed in Section 4. Last, cracks can also be analyzed in the bulk of opaque materials by resorting to 3D imaging techniques such as XCMT, and then 3D-DIC (Section 5). […] Digital image correlation consists in analyzing a series of images, from which displacement fields are measured so as to match either a first image considered as a reference one (typically the unloaded stage) and each subsequent image, or (if displacement amplitudes are too large) consecutive pairs of images. In the latter case, the displacement from the reference image is reconstructed as a sum of elementary displacements taking into account non-linearities induced by large displacements. We thus focus here on the analysis of image pairs, one being the “reference” image, while the second is the “deformed” image (Figure 1).” – The tomography (shape) of the crack is determined. The determination is based on determining a correlation between a surface image and a deformed image, 2-dimensional images (surface and crack occurrence planes) that are related by the digital image correlation (DIC). Page 33, First Paragraph “Recent software developments allow such DIC computations for 1 Mpixel-images to be performed mostly on Graphical Processing Units of PCs in 0.05 s [80] instead of 50 s when implemented in Matlab [81]. This opens the way for much faster and more complex control strategies.” – Roux teaches the use of GPUs, which when executing the methods of the claim, act as the circuits recited in the claim. This will cover all of the circuits of the claims.)
outputs an estimation model for estimating a state of the crack occurrence plane from a state of the observation plane, on the basis of a matrix that associates, with each other, the state of the crack occurrence plane and the state of the observation plane, obtained through numerical analysis of a structural analysis model generated from the shape model; and (Roux Page 4, Last Paragraph – Page 5, Third Paragraph “To monitor phenomena within opaque materials, X-Ray Computed MicroTomography (XCMT) is a very powerful way of imaging material microstructures in a nondestructive manner [46]. In particular, cracks can be observed [47, 48], their closure [49], and CODs measured by manually tracking particles [50]. When the crack morphology is determined, X-FEM techniques allow for the evaluation of surface vs. bulk propagation features [51]. Global correlation techniques [52] were used recently to measureCODs [53]. Enriched kinematics are also implemented (i.e., it corresponds to eXtendedDigital Image Correlation to measure 3D displacements, or X3D-DIC [54]). This procedure allows one to bridge the gap between 3D pictures and numerical models [55]. In Section 2, the principles of DIC are introduced. Various strategies are discussed to deal with the measurement of displacement fields, which is an ill-posed problem. This feature has consequences on the measurement uncertainties that are evaluated. Surface measurements are performed in the presence of cracks in Section 3 and the different strategies introduced above are illustrated. One key quantity in fracture mechanics is the SIF, which may be deduced from the knowledge of measured displacements. Different approaches are followed in Section 4. Last, cracks can also be analyzed in the bulk of opaque materials by resorting to 3D imaging techniques such as XCMT, and then 3D-DIC (Section 5). […] Digital image correlation consists in analyzing a series of images, from which displacement fields are measured so as to match either a first image considered as a reference one (typically the unloaded stage) and each subsequent image, or (if displacement amplitudes are too large) consecutive pairs of images. In the latter case, the displacement from the reference image is reconstructed as a sum of elementary displacements taking into account non-linearities induced by large displacements. We thus focus here on the analysis of image pairs, one being the “reference” image, while the second is the “deformed” image (Figure 1).” – The model presented as the original image is converted to a model that accounts for displacement measurement fields. Page 8, Second Paragraph and Eqs. (6)-(8) “As soon as more complex à functions are used the cross-correlation property cannot be used directly as a global search algorithm, but rather through an iterative minimization procedure. A strategy that is quite performing consists in assuming that the sought displacement is small enough to allow for a Taylor expansion up to first order of the functional to minimize [61]. This hypothesis then transforms the problem into a simple quadratic minimization, and hence an elementary linear system is to be solved
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with
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- The M matrix is a correlation matrix between images/planes.
Page 14, First Paragraph “and the full correlation matrix of the error in ω reads
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The latter result is quite interesting, as it allows one to estimate the uncertainty level
due to the image noise on the displacement directly from the inverse of the matrix [M]
to be computed for DIC. Moreover, it can be used to design robust determinations of
derived quantities, such as SIFs for cracks (see Section 4.1).” – The model accounts for noise and develops SIFs using the inverse of the correlation matrix between the planes.)
estimates a state of a crack at the crack occurrence plane on the basis of the estimation model and a measurement value for the target structure actually measured at the observation plane and to provide the estimated state of the crack and the measurement value to a display device for display, wherein (Roux Page 16, Second Paragraph “The first extension of the finite-element DIC for cracks concerns a specific enrichment that consists in introducing a discontinuity across the crack faces in addition to the regular finite-element description. This technique is widely used in computational mechanics, and is known under the name of X-FEM (for eXtended Finite Element Method [31, 32]). Its image correlation counter-part is referred to as X-DIC [33, 34, 36]. In addition to the displacement discontinuity, the enrichment may also contain stress and strain singular contributions to describe the displacement in the vicinity of the crack tip. The main advantage of this technique is that most of the analysis remains unchanged but only a local refinement is included. Page 30, Second-Third Paragraphs “To confirm the validity of the present procedure, a full three dimensional linear elastic finite element simulation was carried out on the actual geometry of the specimen and crack. Kinematic boundary conditions extracted from the DIC analysis were also prescribed on the top and bottom sides. Stress intensity factors for all three modes were computed all along the front. In Figure 21, these estimates are reported as curves while the measured estimates are shown as symbols for two load levels. An excellent general agreement is obtained between those estimates, for all modes, and a slight discrepancy for mode I under the highest load presumably because of a rather large plastic process zone developing over the remaining ligament (based on the elastic simulation, half of the ligament area exceeds the yield stress). A number of developments are yet to be performed for refining these tools, and in particular a totally automated procedure would be welcome to extract SIFs.” – An extended finite element method/module is applied to eliminate errors and estimate the state of the crack. A three-dimensional linear elastic finite element mode of the cracks, is generated based on the finite element methods and the DIC. The image taken of the surface is an actual measurement. Pages 29-31, Figures 19, 20, and 21 (shown below) – Roux teaches that the data is prepared for display, as shown in the figures below)
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the processer further: divides each of the crack occurrence plane and the observation plane into unit planes and performs numerical analysis of the structural analysis model on the basis of a boundary condition for the divided unit planes, (Roux Page 4, Last Paragraph – Page 5, Second Paragraph “To monitor phenomena within opaque materials, X-Ray Computed MicroTomography (XCMT) is a very powerful way of imaging material microstructures in a nondestructive manner [46]. In particular, cracks can be observed [47, 48], their closure [49], and CODs measured by manually tracking particles [50]. When the crack morphology is determined, X-FEM techniques allow for the evaluation of surface vs. bulk propagation features [51]. Global correlation techniques [52] were used recently to measureCODs [53]. Enriched kinematics are also implemented (i.e., it corresponds to eXtendedDigital Image Correlation to measure 3D displacements, or X3D-DIC [54]). This procedure allows one to bridge the gap between 3D pictures and numerical models [55]. In Section 2, the principles of DIC are introduced. Various strategies are discussed to deal with the measurement of displacement fields, which is an ill-posed problem. This feature has consequences on the measurement uncertainties that are evaluated. Surface measurements are performed in the presence of cracks in Section 3 and the different strategies introduced above are illustrated. One key quantity in fracture mechanics is the SIF, which may be deduced from the knowledge of measured displacements. Different approaches are followed in Section 4. Last, cracks can also be analyzed in the bulk of opaque materials by resorting to 3D imaging techniques such as XCMT, and then 3D-DIC (Section 5). […] Digital image correlation consists in analyzing a series of images, from which displacement fields are measured so as to match either a first image considered as a reference one (typically the unloaded stage) and each subsequent image, or (if displacement amplitudes are too large) consecutive pairs of images. In the latter case, the displacement from the reference image is reconstructed as a sum of elementary displacements taking into account non-linearities induced by large displacements. We thus focus here on the analysis of image pairs, one being the “reference” image, while the second is the “deformed” image (Figure 1).” – The tomography (shape) of the crack is determined. The determination is based on determining a correlation between a surface image and a deformed image, 2-dimensional images (surface and crack occurrence planes) that are related by the digital image correlation (DIC). Page 30, Second Paragraph “To confirm the validity of the present procedure, a full three dimensional linear elastic finite element simulation was carried out on the actual geometry of the specimen and crack. Kinematic boundary conditions extracted from the DIC analysis were also prescribed on the top and bottom sides. Stress intensity factors for all three modes were computed all along the front.” – Structural analysis is performed using kinematic boundary conditions on the images/planes.)
generates the structural analysis model from the shape model, sequentially sets such a boundary condition for the structural analysis model that a crack occurs at the crack occurrence plane, while analysis under the sequentially set boundary condition is sequentially performed by the numerical analyzer, and stores an analysis result of the crack occurrence plane and an analysis result of the observation plane in a storage device, and (Roux Page 16, Second Paragraph “The first extension of the finite-element DIC for cracks concerns a specific enrichment that consists in introducing a discontinuity across the crack faces in addition to the regular finite-element description. This technique is widely used in computational mechanics, and is known under the name of X-FEM (for eXtended Finite Element Method [31, 32]). Its image correlation counter-part is referred to as X-DIC [33, 34, 36]. In addition to the displacement discontinuity, the enrichment may also contain stress and strain singular contributions to describe the displacement in the vicinity of the crack tip. The main advantage of this technique is that most of the analysis remains unchanged but only a local refinement is included. Page 30, Second-Third Paragraphs “To confirm the validity of the present procedure, a full three-dimensional linear elastic finite element simulation was carried out on the actual geometry of the specimen and crack. Kinematic boundary conditions extracted from the DIC analysis were also prescribed on the top and bottom sides. Stress intensity factors for all three modes were computed all along the front. In Figure 21, these estimates are reported as curves while the measured estimates are shown as symbols for two load levels. An excellent general agreement is obtained between those estimates, for all modes, and a slight discrepancy for mode I under the highest load presumably because of a rather large plastic process zone developing over the remaining ligament (based on the elastic simulation, half of the ligament area exceeds the yield stress). A number of developments are yet to be performed for refining these tools, and in particular a totally automated procedure would be welcome to extract SIFs.” – FEA is conducted to determine the values for all parameters in the volume of the model, e.g., including at both planes/images that are related by the correlation matrix. An extended finite element method/module is applied to eliminate errors and estimate the state of the crack. A three-dimensional linear elastic finite element mode of the cracks, is generated based on the finite element methods and the DIC. Page 30, Second Paragraph “To confirm the validity of the present procedure, a full three dimensional linear elastic finite element simulation was carried out on the actual geometry of the specimen and crack. Kinematic boundary conditions extracted from the DIC analysis were also prescribed on the top and bottom sides. Stress intensity factors for all three modes were computed all along the front. In Figure 21, these estimates are reported as curves while the measured estimates are shown as symbols for two load levels. An excellent general agreement is obtained between those estimates, for all modes, and a slight discrepancy for mode I under the highest load presumably because of a rather large plastic process zone developing over the remaining ligament (based on the elastic simulation, half of the ligament area exceeds the yield stress).” – The boundary conditions are applied sequentially (e.g., an element by element basis for the calculations across the m X n cells for each image/plane. Page 15, Third Paragraph “even if it is somewhat more compute resource demanding” Page 32, “DIC may also be used to drive an experiment [78]. Because of heavy image processing and relatively lengthy image storage, the overall working frequency is about 1 Hz.” Page 33, First Paragraph “Recent software developments allow such DIC computations for 1 Mpixel-images to be performed mostly on Graphical Processing Units of PCs in 0.05 s [80] instead of 50 s when implemented in Matlab [81]. This opens the way for much faster and more complex control strategies.” – Roux teaches computerization of the method. All parameters and corresponding values are stored in computer memory as a matter of course in the computerized method.)
calculates a forward coefficient matrix for mapping a crack occurrence plane matrix in which the analysis result of the crack occurrence plane stored in the storage device is represented as a matrix, to an observation plane matrix in which the analysis result of the observation plane stored in the storage device is represented as a matrix, and outputs an inverse matrix of the forward coefficient matrix as the estimation model, (Roux Page 4, Last Paragraph – Page 5, Second Paragraph “To monitor phenomena within opaque materials, X-Ray Computed MicroTomography (XCMT) is a very powerful way of imaging material microstructures in a nondestructive manner [46]. In particular, cracks can be observed [47, 48], their closure [49], and CODs measured by manually tracking particles [50]. When the crack morphology is determined, X-FEM techniques allow for the evaluation of surface vs. bulk propagation features [51]. Global correlation techniques [52] were used recently to measureCODs [53]. Enriched kinematics are also implemented (i.e., it corresponds to eXtendedDigital Image Correlation to measure 3D displacements, or X3D-DIC [54]). This procedure allows one to bridge the gap between 3D pictures and numerical models [55]. In Section 2, the principles of DIC are introduced. Various strategies are discussed to deal with the measurement of displacement fields, which is an ill-posed problem. This feature has consequences on the measurement uncertainties that are evaluated. Surface measurements are performed in the presence of cracks in Section 3 and the different strategies introduced above are illustrated. One key quantity in fracture mechanics is the SIF, which may be deduced from the knowledge of measured displacements. Different approaches are followed in Section 4. Last, cracks can also be analyzed in the bulk of opaque materials by resorting to 3D imaging techniques such as XCMT, and then 3D-DIC (Section 5). […] Digital image correlation consists in analyzing a series of images, from which displacement fields are measured so as to match either a first image considered as a reference one (typically the unloaded stage) and each subsequent image, or (if displacement amplitudes are too large) consecutive pairs of images. In the latter case, the displacement from the reference image is reconstructed as a sum of elementary displacements taking into account non-linearities induced by large displacements. We thus focus here on the analysis of image pairs, one being the “reference” image, while the second is the “deformed” image (Figure 1).” – The tomography (shape) of the crack is determined. The determination is based on determining a correlation between a surface image and a deformed image, 2-dimensional images (surface and crack occurrence planes) that are related by the digital image correlation (DIC). Page 30, Second Paragraph “To confirm the validity of the present procedure, a full three dimensional linear elastic finite element simulation was carried out on the actual geometry of the specimen and crack. Kinematic boundary conditions extracted from the DIC analysis were also prescribed on the top and bottom sides. Stress intensity factors for all three modes were computed all along the front.” – Structural analysis is performed using kinematic boundary conditions on the images/planes. Page 8, Second Paragraph and Eqs. (6)-(8) “As soon as more complex à functions are used the cross-correlation property cannot be used directly as a global search algorithm, but rather through an iterative minimization procedure. A strategy that is quite performing consists in assuming that the sought displacement is small enough to allow for a Taylor expansion up to first order of the functional to minimize [61]. This hypothesis then transforms the problem into a simple quadratic minimization, and hence an elementary linear system is to be solved
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Page 14, First Paragraph “and the full correlation matrix of the error in ω reads
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The latter result is quite interesting, as it allows one to estimate the uncertainty level due to the image noise on the displacement directly from the inverse of the matrix [M] to be computed for DIC. Moreover, it can be used to design robust determinations of derived quantities, such as SIFs for cracks (see Section 4.1).” – The model accounts for noise and develops SIFs using the inverse of the correlation matrix between the planes. At some point, the models output the forward matrix M that represents the correlation between the images and its inverse used for error correction. Page 15, Third Paragraph “even if it is somewhat more compute resource demanding” – Roux teaches computerization of the method. All parameters and corresponding values are stored in computer memory as a matter of course in the computerized method.)
Roux does not appear to teach, but Roux in view of Moore teaches:
wherein the target structure is a shrink-fit part of a retention ring shrink-fitted to a rotor core at an end of a rotor of a rotary electric machine, (Moore Background “Generator rotor retaining rings are one of the most highly stressed components in the generator rotor. Additionally, some retaining ring materials such as 18Mn5Cr, have been susceptible to Stress Corrosion Cracking (SCC). 18Mn18Cr retaining ring material has been used to replace older 18Mn5Cr material rings with great success. The 18Mn18Cr material has been found to be resistant to SCC in the presence of moisture.”
It would have been obvious to a person of ordinary skill in the art before the effective filing date of the claims to modify the crack model of Roux to be a model of a crack in a retaining ring of a rotor of Moore because a person of ordinary skill in the art would be motivated to by the statement in Roux that “Working with digital images allows the experimentalist to deal with a wide range of scales from atomistic to geophysical one with the same tools. Various examples are shown at different scales, as well as some recent extensions to three dimensional cracks based on X-ray Computed micro-tomographic images” to look to Moore which identified retention rings of a generator rotor for crack analysis, which has a different shape and scale relative to the Roux model. (Roux Abstract “Digital image correlation is a measurement technique that allows one to retrieve displacement fields “separating” two digital images of the same sample at different stages of loading. Because of its remarkable sensitivity, it is not only possible to detect cracks with sub-pixel opening, which would not be visible, but also to provide accurate estimates of stress intensity factors. For this purpose suitable tools have been devised to minimize the sensitivity to noise. Working with digital images allows the experimentalist to deal with a wide range of scales from atomistic to geophysical one with the same tools. Various examples are shown at different scales, as well as some recent extensions to three dimensional cracks based on X-ray Computed micro-tomographic images.”; Moore Background “Generator rotor retaining rings are one of the most highly stressed components in the generator rotor. Additionally, some retaining ring materials such as 18Mn5Cr, have been susceptible to Stress Corrosion Cracking (SCC). 18Mn18Cr retaining ring material has been used to replace older 18Mn5Cr material rings with great success. The 18Mn18Cr material has been found to be resistant to SCC in the presence of moisture. Recently, one OEM (Original Equipment Manufacturer) called for inspections of 18Mn18Cr rings, despite its reliable performance in the industry. Although resistant to SCC, some 18Mn18Cr rings have been found with cracks and other damage. The author’s company felt that it would be of value to go back through past job records with rotors that were identified to have 18Mn18Cr retaining rings, and review those records and report on the results of ring inspections due to damage. The author’s company typically rewinds dozens of rotors per year, with many of the rings manufactured from 18Mn18Cr. As part of a rewind, rings are disassembled and inspected. Of course, many rewinds are done because of failures, mostly related to the field winding. An XRF (X-Ray Fluorescence) analyzer is used to determine a ring’s composition.”)
Roux in view of Moore does not appear to explicitly teach but Roux in view of Moore and Danielson teaches:
and the shape model of the target structure is represented in a cylindrical coordinate system. (Danielson Abstract “A formulation for three-dimensional nonlinear finite element analysis in cylindrical coordinates in presented. The elements are isoparametric with the same interpolation functions used to represent the geometry and the physical displacement components. The elements can be used for general three-dimensional analysis, but they are most effective for cases when the geometry and the response are best described in cylindrical coordinates. In contrast to formulations in Cartesian coordinates, the foregoing formulation allows the exact representation of a circular shape. For structures with circular geometries, the improved accuracy of the elements can provide better finite element predictions and reduce the number of elements needed in the circumferential direction. The reduction in the number of elements can result in a significant reduction in computer resources needed for large three-dimensional analyses, particularly in the presence of nonlinearities.”– The coordinate system is cylindrical because the shape (e.g., of a rotor) is cylindrical. This simplifies the calculations by better representing the system.)
It would have been obvious to a person of ordinary skill in the art before the effective filing date of the claims to modify the crack model of Roux of the rotor in Moore by the use of cylindrical coordinates in modeling as presented in Danielson because Roux expresses an aim to expedite the modeling process and, unlike the rectangular prismatic shape of the modeled region in Roux, for which Cartesian coordinates are taught, Moore presents a rotor and its retention ring, which have circular geometries or cylindrical symmetry, and, the person of ordinary skill in the art would be motivated to use cylindrical coordinates to evaluate the rotor of Moore using the processes of Roux, as taught in Danielson to practically model cracks within a cylindrical shape and reduce the number of elements and, hence, the computer resources needed. (Roux Page 33, First Paragraph “It is envisioned that a real-time system is feasible when the pictures are not stored and computations optimized. The same type of procedure may be applied to other types of displacement fields (e.g., in the presence of cracks [79]). Recent software developments allow such DIC computations for 1 Mpixel-images to be performed mostly on Graphical Processing Units of PCs in 0.05 s [80] instead of 50 s when implemented in Matlab [81]. This opens the way for much faster and more complex control strategies.” Also, see Figures 18, 19, and 20 for use of cartesian coordinates with a rectangular prismatic volume.; Moore Background “Generator rotor retaining rings are one of the most highly stressed components in the generator rotor.”; Danielson Abstract “We consider the impact of a ring crack within a rotating hollow cylinder of fixed height under axisymmetric (torsion) loading. The form of the displacement is obtained from the equation of motion using the Fourier sin transform. The displacement jump over the crack is obtained from the boundary condition on the tangential stress, formulated as a singular integral equation which is solved by the method of orthogonal polynomials. The stress intensity factors on the opposing crack surfaces are calculated. The dependence of the crack extension on the problem geometry is investigated, including the impact of the crack’s location, cylinder’s height, torsion loading and rotation frequency. Possible extensions of the model to cover fatigue cracking are considered. A practical test to detect and locate cracks within a rotating cylinder is outlined.” Page 3, First Paragraph “We consider a hollow elastic cylinder containing a ring crack in cylindrical coordinates (see Fig. 1). The cylinders inner radius is a distance a0 from the origin, its outer radius a distance a1, and has height h. The ring crack is located at height d, with inner radius c0 and outer radius c1. The problem domain is therefore, in cylindrical coordinates”)
Claim 15
Regarding claim 15, Roux in view of Moore and Danielson teaches the features of claim 14 and further teaches:
wherein an input boundary condition which is the boundary condition for the structural analysis model is that, in the crack occurrence plane, connection between the divided unit planes of the crack occurrence plane is disconnected or displacement of the crack occurrence plane is changed to a shape or a boundary condition equal to a case where a crack has occurred. (Roux Page 4, Last Paragraph – Page 5, Second Paragraph “To monitor phenomena within opaque materials, X-Ray Computed MicroTomography (XCMT) is a very powerful way of imaging material microstructures in a nondestructive manner [46]. In particular, cracks can be observed [47, 48], their closure [49], and CODs measured by manually tracking particles [50]. When the crack morphology is determined, X-FEM techniques allow for the evaluation of surface vs. bulk propagation features [51]. Global correlation techniques [52] were used recently to measureCODs [53]. Enriched kinematics are also implemented (i.e., it corresponds to eXtendedDigital Image Correlation to measure 3D displacements, or X3D-DIC [54]). This procedure allows one to bridge the gap between 3D pictures and numerical models [55]. In Section 2, the principles of DIC are introduced. Various strategies are discussed to deal with the measurement of displacement fields, which is an ill-posed problem. This feature has consequences on the measurement uncertainties that are evaluated. Surface measurements are performed in the presence of cracks in Section 3 and the different strategies introduced above are illustrated. One key quantity in fracture mechanics is the SIF, which may be deduced from the knowledge of measured displacements. Different approaches are followed in Section 4. Last, cracks can also be analyzed in the bulk of opaque materials by resorting to 3D imaging techniques such as XCMT, and then 3D-DIC (Section 5). […] Digital image correlation consists in analyzing a series of images, from which displacement fields are measured so as to match either a first image considered as a reference one (typically the unloaded stage) and each subsequent image, or (if displacement amplitudes are too large) consecutive pairs of images. In the latter case, the displacement from the reference image is reconstructed as a sum of elementary displacements taking into account non-linearities induced by large displacements. We thus focus here on the analysis of image pairs, one being the “reference” image, while the second is the “deformed” image (Figure 1).” – The tomography (shape) of the crack is determined. The determination is based on determining a correlation between a surface image and a deformed image, 2-dimensional images (surface and crack occurrence planes) that are related by the digital image correlation (DIC). Page 30, Second Paragraph “To confirm the validity of the present procedure, a full three dimensional linear elastic finite element simulation was carried out on the actual geometry of the specimen and crack. Kinematic boundary conditions extracted from the DIC analysis were also prescribed on the top and bottom sides. Stress intensity factors for all three modes were computed all along the front.” – Structural analysis is performed using kinematic boundary conditions on the images/planes. Roux uses a boundary condition for elements where a crack (“equal to”) has occurred.)
Claim 16
Regarding claim 16, Roux in view of Moore and Danielson teaches the features of claim 14 and further teaches:
wherein the analysis result of the observation plane is represented as a vector based on any of displacement change, strain change, and angle change in the observation plane. (Roux Page 8, Second Paragraph and Eqs. (6)-(8) “As soon as more complex à functions are used the cross-correlation property cannot be used directly as a global search algorithm, but rather through an iterative minimization procedure. A strategy that is quite performing consists in assuming that the sought displacement is small enough to allow for a Taylor expansion up to first order of the functional to minimize [61]. This hypothesis then transforms the problem into a simple quadratic minimization, and hence an elementary linear system is to be solved
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Page 14, First Paragraph “and the full correlation matrix of the error in ω reads
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The latter result is quite interesting, as it allows one to estimate the uncertainty level due to the image noise on the displacement directly from the inverse of the matrix [M] to be computed for DIC. Moreover, it can be used to design robust determinations of derived quantities, such as SIFs for cracks (see Section 4.1).” – The model accounts for noise and develops SIFs using the inverse of the correlation matrix between the planes. At some point, the models output the forward matrix M that represents the correlation between the images and its inverse used for error correction. The matrix is a vector. Page 16, Second Paragraph “In addition to the displacement discontinuity, the enrichment may also contain stress and strain singular contributions to describe the displacement in the vicinity of the crack tip. The main advantage of this technique is that most of the analysis remains unchanged but only a local refinement is included.” – All parameters calculated are related by (“based on”) the algorithms in Roux to strain, stress, and displacement by the crack. Page 3, Last Paragraph – Page 4, First Paragraph “For instance, crack tip opening angles [25] or crack tip opening displacements [12, 19, 13] are measured with a very good accuracy by means of DIC. – Also angles.)
Claim 17
Regarding claim 17, Roux in view of Moore and Danielson teaches the features of claim 14 and further teaches:
wherein the analysis result of the crack occurrence plane is represented as a vector based on displacement change or load change in the crack occurrence plane. (Roux Page 8, Second Paragraph and Eqs. (6)-(8) “As soon as more complex à functions are used the cross-correlation property cannot be used directly as a global search algorithm, but rather through an iterative minimization procedure. A strategy that is quite performing consists in assuming that the sought displacement is small enough to allow for a Taylor expansion up to first order of the functional to minimize [61]. This hypothesis then transforms the problem into a simple quadratic minimization, and hence an elementary linear system is to be solved
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Page 14, First Paragraph “and the full correlation matrix of the error in ω reads
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The latter result is quite interesting, as it allows one to estimate the uncertainty level due to the image noise on the displacement directly from the inverse of the matrix [M] to be computed for DIC. Moreover, it can be used to design robust determinations of derived quantities, such as SIFs for cracks (see Section 4.1).” – The model accounts for noise and develops SIFs using the inverse of the correlation matrix between the planes. At some point, the models output the forward matrix M that represents the correlation between the images and its inverse used for error correction. The matrix is a vector. Page 16, Second Paragraph “In addition to the displacement discontinuity, the enrichment may also contain stress and strain singular contributions to describe the displacement in the vicinity of the crack tip. The main advantage of this technique is that most of the analysis remains unchanged but only a local refinement is included.” – All parameters calculated are related by (“based on”) the algorithms in Roux to strain, stress, and displacement by the crack. “Larger indices correspond to “subsingular” or higher order fields that may capture the remote heterogeneity of the loading, but do not affect the mechanical loading at the crack tip. This family of fields is thus the appropriate basis function to describe the displacement field for a traction free crack in an elastic solid.” – Roux also contemplates varying the load as a parameter to improve the model.)
Claims 12-13, 18, and 20-22: Roux, Li, Moore, and Danielson
Claim 24 is rejected under 35 U.S.C. 103 as being unpatentable over NPL “Digital Image Correlation and Fracture: An Advanced Technique for Estimating Stress Intensity Factors of 2D and 3D Cracks” by Roux et al. (Roux) in view of in view of NPL: “Modeling crack propagation with the extended scaled boundary finite element method based on the level set method” by Li et al. (Li), NPL: “Damage Mechanisms Found in Generator Rotor 18Mn18Cr Retaining Rings.” by Moore (Moore), and NPL: “Three-dimensional finite element analysis in cylindrical coordinates for nonlinear solid mechanics problems” by Danielson et al. (Danielson).
Claim 12
Regarding claim 12, Roux teaches:
A crack estimation device comprising: (Roux Abstract “Because of its remarkable sensitivity, it is not only possible to detect cracks with sub-pixel opening, which would not be visible, but also to provide accurate estimates of stress intensity factors. For this purpose suitable tools have been devised to minimize the sensitivity to noise. Working with digital images allows the experimentalist to deal with a wide range of scales from atomistic to geophysical one with the same tools.” – A crack estimation device.)
a data determinator circuit which determines a shape model of a target structure to be inspected, and a crack occurrence plane and an observation plane in the shape model; (Roux Abstract “Because of its remarkable sensitivity, it is not only possible to detect cracks with sub-pixel opening, which would not be visible, but also to provide accurate estimates of stress intensity factors. For this purpose suitable tools have been devised to minimize the sensitivity to noise. Working with digital images allows the experimentalist to deal with a wide range of scales from atomistic to geophysical one with the same tools.” Page 4, Last Paragraph – Page 5, Second Paragraph “To monitor phenomena within opaque materials, X-Ray Computed MicroTomography (XCMT) is a very powerful way of imaging material microstructures in a nondestructive manner [46]. In particular, cracks can be observed [47, 48], their closure [49], and CODs measured by manually tracking particles [50]. When the crack morphology is determined, X-FEM techniques allow for the evaluation of surface vs. bulk propagation features [51]. Global correlation techniques [52] were used recently to measure CODs [53]. Enriched kinematics are also implemented (i.e., it corresponds to eXtended Digital Image Correlation to measure 3D displacements, or X3D-DIC [54]). This procedure allows one to bridge the gap between 3D pictures and numerical models [55]. In Section 2, the principles of DIC are introduced. Various strategies are discussed to deal with the measurement of displacement fields, which is an ill-posed problem. This feature has consequences on the measurement uncertainties that are evaluated. Surface measurements are performed in the presence of cracks in Section 3 and the different strategies introduced above are illustrated. One key quantity in fracture mechanics is the SIF, which may be deduced from the knowledge of measured displacements. Different approaches are followed in Section 4. Last, cracks can also be analyzed in the bulk of opaque materials by resorting to 3D imaging techniques such as XCMT, and then 3D-DIC (Section 5). […] Digital image correlation consists in analyzing a series of images, from which displacement fields are measured so as to match either a first image considered as a reference one (typically the unloaded stage) and each subsequent image, or (if displacement amplitudes are too large) consecutive pairs of images. In the latter case, the displacement from the reference image is reconstructed as a sum of elementary displacements taking into account non-linearities induced by large displacements. We thus focus here on the analysis of image pairs, one being the “reference” image, while the second is the “deformed” image (Figure 1).” – The tomography (shape) of the crack is determined. The determination is based on determining a correlation between a surface image and a deformed image, 2-dimensional images (surface and crack occurrence planes) that are related by the digital image correlation (DIC). Page 33, First Paragraph “Recent software developments allow such DIC computations for 1 Mpixel-images to be performed mostly on Graphical Processing Units of PCs in 0.05 s [80] instead of 50 s when implemented in Matlab [81]. This opens the way for much faster and more complex control strategies.” – Roux teaches the use of GPUs, which when executing the methods of the claim, act as the circuits recited in the claim. This will cover all of the circuits of the claims.)
an estimation data calculator circuit which outputs, as an estimation model for estimating a state of the crack occurrence plane from a state of the observation plane, an inverse matrix of a matrix that associates, with each other, the state of the crack occurrence plane and the state of the observation plane, obtained through numerical analysis of a structural analysis model generated from the shape model, ; and (Roux Page 4, Last Paragraph – Page 5, Third Paragraph “To monitor phenomena within opaque materials, X-Ray Computed MicroTomography (XCMT) is a very powerful way of imaging material microstructures in a nondestructive manner [46]. In particular, cracks can be observed [47, 48], their closure [49], and CODs measured by manually tracking particles [50]. When the crack morphology is determined, X-FEM techniques allow for the evaluation of surface vs. bulk propagation features [51]. Global correlation techniques [52] were used recently to measureCODs [53]. Enriched kinematics are also implemented (i.e., it corresponds to eXtendedDigital Image Correlation to measure 3D displacements, or X3D-DIC [54]). This procedure allows one to bridge the gap between 3D pictures and numerical models [55]. In Section 2, the principles of DIC are introduced. Various strategies are discussed to deal with the measurement of displacement fields, which is an ill-posed problem. This feature has consequences on the measurement uncertainties that are evaluated. Surface measurements are performed in the presence of cracks in Section 3 and the different strategies introduced above are illustrated. One key quantity in fracture mechanics is the SIF, which may be deduced from the knowledge of measured displacements. Different approaches are followed in Section 4. Last, cracks can also be analyzed in the bulk of opaque materials by resorting to 3D imaging techniques such as XCMT, and then 3D-DIC (Section 5). […] Digital image correlation consists in analyzing a series of images, from which displacement fields are measured so as to match either a first image considered as a reference one (typically the unloaded stage) and each subsequent image, or (if displacement amplitudes are too large) consecutive pairs of images. In the latter case, the displacement from the reference image is reconstructed as a sum of elementary displacements taking into account non-linearities induced by large displacements. We thus focus here on the analysis of image pairs, one being the “reference” image, while the second is the “deformed” image (Figure 1).” – The model presented as the original image is converted to a model that accounts for displacement measurement fields. Page 8, Second Paragraph and Eqs. (6)-(8) “As soon as more complex à functions are used the cross-correlation property cannot be used directly as a global search algorithm, but rather through an iterative minimization procedure. A strategy that is quite performing consists in assuming that the sought displacement is small enough to allow for a Taylor expansion up to first order of the functional to minimize [61]. This hypothesis then transforms the problem into a simple quadratic minimization, and hence an elementary linear system is to be solved
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Page 14, First Paragraph “and the full correlation matrix of the error in ω reads
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due to the image noise on the displacement directly from the inverse of the matrix [M]
to be computed for DIC. Moreover, it can be used to design robust determinations of
derived quantities, such as SIFs for cracks (see Section 4.1).” – The model accounts for noise and develops SIFs using the inverse of the correlation matrix between the planes.)
a crack estimator circuit which estimates a state of a crack at the crack occurrence plane on the basis of the estimation model and a measurement value for the target structure actually measured at the observation plane and to provide the estimated state of the crack and the measurement value to a display device for display. (Roux Page 16, Second Paragraph “The first extension of the finite-element DIC for cracks concerns a specific enrichment that consists in introducing a discontinuity across the crack faces in addition to the regular finite-element description. This technique is widely used in computational mechanics, and is known under the name of X-FEM (for eXtended Finite Element Method [31, 32]). Its image correlation counter-part is referred to as X-DIC [33, 34, 36]. In addition to the displacement discontinuity, the enrichment may also contain stress and strain singular contributions to describe the displacement in the vicinity of the crack tip. The main advantage of this technique is that most of the analysis remains unchanged but only a local refinement is included. – An extended finite element method/module is applied to eliminate errors and estimate the state of the crack. Pages 29-31, Figures 19, 20, and 21 (shown below) – Roux teaches that the data is prepared for display, as shown in the figures below)
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Roux suggests the use of sequential methods for modeling crack propagation (Roux Page 4, Fourth Paragraph “In all the previous identification analyses, the measurement and identification steps are performed sequentially, namely, displacements are first measured and subsequently post-processed to determine SIFs or even J-integrals.”) does not appear to explicitly teach, but Roux in view of Li teaches:
the matrix being generated by sequentially setting a boundary condition for each of a plurality of nodes in the crack occurrence plane such that a crack is assumed to occur at each node; (Li Page 58, 3. Numerical examples, results and discussion “There is an initial edge crack from (0.0, 1.0) to (7.0, 1.0) on a square plate with x 2ð0;16Þ and y 2ð8;8Þ. The geometry and boundary conditions of the square plate are shown in Fig. 7. The plate is under uniform tension T on its top and bottom edges. In this example, we compare the SIFs and coordinates of the crack tip for 5 propagation steps and three mesh densities, 30 30;100 100 and 200 200. At each step in the iteration n, the crack increment is Da ¼ 0:5. The crack propagation direction is determined by the maximum circumferential stress criterion. […] Fig. 9 shows the crack propagation path on a 100 100mesh. During the propagation process, as long as we set the core at the crack tip and take a certain distance as the radius, the SBFEM nodes can be searched, and the super-element at the crack tip can be formed from potential FEM boundary elements.” – The models deal with nodes sequentially as they appear. Page 51, 2. The extended scaled boundary finite element method (X-SBFEM) “The core of the X-SBFEM [28,29] is to substitute the semi analytical SBFEM for the crack tip enrichment function to simulate the nonsmooth behavior around the crack tip while the Heaviside enrichment function is used to represent the jump across the dis continuity surface in the split element. The key is in how the algorithm addresses the boundary conditions at the joint. This method creates four types of elements in the domain: (1) general elements (named E0) with no enriched nodes; (2) mixed elements (named E1) with some enriched nodes; (3) split elements (named E2) with all nodes enriched; and (4) the SBFEM super-element (named E3). Fig. 1 shows a typical finite element mesh and a zone diagram depicting the different element types near an arbitrary crack used in the X-SBFEM. Nodes designated by hollow squares have the number of degrees of freedom of a generalized node, which is used to construct the displacement field in the form of a jump between neighboring elements. Hollow circles are used to designate the nodes that are in SBFEM elements.” Pages 51-52 (SEE THE COPIED IMAGES WITH THE EQUATIONS (2)-(8) – Each time, the data is loaded sequentially into the matrices, as demonstrated in the equations in the following images. As is taught, this can be done in a single plane of a crack, as in the claim.
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It would have been obvious to a person of ordinary skill in the art before the effective filing date of the claims to substitute the closed form Dirichlet crack determination of Roux with the sequential, iterative expansion using SBFEM of Li because the person of ordinary skill in the art would be motivated by the suggestion in Roux that sequential methods, such as the one in Li that predicts crack trajectories accurately, are effective substitutes for closed form solutions, and because Roux explicitly states an aim of producing accurate crack estimation results. This is an express suggestion from Roux. See MPEP 2144.06(II) (Roux Page 4, Fourth Paragraph “In all the previous identification analyses, the measurement and identification steps are performed sequentially, namely, displacements are first measured and subsequently post-processed to determine SIFs or even J-integrals.” Page 3, Last Paragraph – Page 4, First Paragraph “In the following, the discussion will focus on the analysis of cracks by means of DIC. The use of full field measurements is of particular interest when dealing with (strong) discontinuities induced by the presence of cracks. Fracture mechanics has benefited from DIC results [23, 24]. For instance, crack tip opening angles [25] or crack tip; opening displacements [12, 19, 13] are measured with a very good accuracy by means of DIC.; Li Abstract “[…] The results show that the proposed X-SBFEM is capable of calculating the stress intensity factors of cracks and predicting crack trajectories and load–displacement relations accurately. An analysis of the sensitivity of the parameters is employed to demonstrate that various mesh densities and crack propagation step lengths led to consistent results.”)
Roux does not appear to teach, but Roux in view of Moore teaches:
wherein the target structure is a shrink-fit part of a retention ring shrink-fitted to a rotor core at an end of a rotor of a rotary electric machine, (Moore Background “Generator rotor retaining rings are one of the most highly stressed components in the generator rotor. Additionally, some retaining ring materials such as 18Mn5Cr, have been susceptible to Stress Corrosion Cracking (SCC). 18Mn18Cr retaining ring material has been used to replace older 18Mn5Cr material rings with great success. The 18Mn18Cr material has been found to be resistant to SCC in the presence of moisture.”
It would have been obvious to a person of ordinary skill in the art before the effective filing date of the claims to modify the crack model of Roux to be a model of a crack in a retaining ring of a rotor of Moore because a person of ordinary skill in the art would be motivated to by the statement in Roux that “Working with digital images allows the experimentalist to deal with a wide range of scales from atomistic to geophysical one with the same tools. Various examples are shown at different scales, as well as some recent extensions to three dimensional cracks based on X-ray Computed micro-tomographic images” to look to Moore which identified retention rings of a generator rotor for crack analysis, which has a different shape and scale relative to the Roux model. (Roux Abstract “Digital image correlation is a measurement technique that allows one to retrieve displacement fields “separating” two digital images of the same sample at different stages of loading. Because of its remarkable sensitivity, it is not only possible to detect cracks with sub-pixel opening, which would not be visible, but also to provide accurate estimates of stress intensity factors. For this purpose suitable tools have been devised to minimize the sensitivity to noise. Working with digital images allows the experimentalist to deal with a wide range of scales from atomistic to geophysical one with the same tools. Various examples are shown at different scales, as well as some recent extensions to three dimensional cracks based on X-ray Computed micro-tomographic images.”; Moore Background “Generator rotor retaining rings are one of the most highly stressed components in the generator rotor. Additionally, some retaining ring materials such as 18Mn5Cr, have been susceptible to Stress Corrosion Cracking (SCC). 18Mn18Cr retaining ring material has been used to replace older 18Mn5Cr material rings with great success. The 18Mn18Cr material has been found to be resistant to SCC in the presence of moisture. Recently, one OEM (Original Equipment Manufacturer) called for inspections of 18Mn18Cr rings, despite its reliable performance in the industry. Although resistant to SCC, some 18Mn18Cr rings have been found with cracks and other damage. The author’s company felt that it would be of value to go back through past job records with rotors that were identified to have 18Mn18Cr retaining rings, and review those records and report on the results of ring inspections due to damage. The author’s company typically rewinds dozens of rotors per year, with many of the rings manufactured from 18Mn18Cr. As part of a rewind, rings are disassembled and inspected. Of course, many rewinds are done because of failures, mostly related to the field winding. An XRF (X-Ray Fluorescence) analyzer is used to determine a ring’s composition.”)
Roux in view of Moore does not appear to explicitly teach but Roux in view of Moore and Danielson teaches:
and the shape model of the target structure is represented in a cylindrical coordinate system. (Danielson Abstract “A formulation for three-dimensional nonlinear finite element analysis in cylindrical coordinates in presented. The elements are isoparametric with the same interpolation functions used to represent the geometry and the physical displacement components. The elements can be used for general three-dimensional analysis, but they are most effective for cases when the geometry and the response are best described in cylindrical coordinates. In contrast to formulations in Cartesian coordinates, the foregoing formulation allows the exact representation of a circular shape. For structures with circular geometries, the improved accuracy of the elements can provide better finite element predictions and reduce the number of elements needed in the circumferential direction. The reduction in the number of elements can result in a significant reduction in computer resources needed for large three-dimensional analyses, particularly in the presence of nonlinearities.”– The coordinate system is cylindrical because the shape (e.g., of a rotor) is cylindrical. This simplifies the calculations by better representing the system.)
It would have been obvious to a person of ordinary skill in the art before the effective filing date of the claims to modify the crack model of Roux of the rotor in Moore by the use of cylindrical coordinates in modeling as presented in Danielson because Roux expresses an aim to expedite the modeling process and, unlike the rectangular prismatic shape of the modeled region in Roux, for which Cartesian coordinates are taught, Moore presents a rotor and its retention ring, which have circular geometries or cylindrical symmetry, and, the person of ordinary skill in the art would be motivated to use cylindrical coordinates to evaluate the rotor of Moore using the processes of Roux, as taught in Danielson to practically model cracks within a cylindrical shape and reduce the number of elements and, hence, the computer resources needed. (Roux Page 33, First Paragraph “It is envisioned that a real-time system is feasible when the pictures are not stored and computations optimized. The same type of procedure may be applied to other types of displacement fields (e.g., in the presence of cracks [79]). Recent software developments allow such DIC computations for 1 Mpixel-images to be performed mostly on Graphical Processing Units of PCs in 0.05 s [80] instead of 50 s when implemented in Matlab [81]. This opens the way for much faster and more complex control strategies.” Also, see Figures 18, 19, and 20 for use of cartesian coordinates with a rectangular prismatic volume.; Moore Background “Generator rotor retaining rings are one of the most highly stressed components in the generator rotor.”; Danielson Abstract “We consider the impact of a ring crack within a rotating hollow cylinder of fixed height under axisymmetric (torsion) loading. The form of the displacement is obtained from the equation of motion using the Fourier sin transform. The displacement jump over the crack is obtained from the boundary condition on the tangential stress, formulated as a singular integral equation which is solved by the method of orthogonal polynomials. The stress intensity factors on the opposing crack surfaces are calculated. The dependence of the crack extension on the problem geometry is investigated, including the impact of the crack’s location, cylinder’s height, torsion loading and rotation frequency. Possible extensions of the model to cover fatigue cracking are considered. A practical test to detect and locate cracks within a rotating cylinder is outlined.” Page 3, First Paragraph “We consider a hollow elastic cylinder containing a ring crack in cylindrical coordinates (see Fig. 1). The cylinders inner radius is a distance a0 from the origin, its outer radius a distance a1, and has height h. The ring crack is located at height d, with inner radius c0 and outer radius c1. The problem domain is therefore, in cylindrical coordinates”)
Claim 13
Regarding claim 13, Roux in view of Li, Moore, and Danielson teaches the features of claim 12 and further teaches:
wherein the matrix that associates the state of the crack occurrence plane and the state of the observation plane with each other in the estimation data calculator is a matrix that associates, with each other, a matrix in which the state of the crack occurrence plane is arranged in a predetermined order for each shape of the crack and a matrix in which the state of the observation plane is arranged in a predetermined order for each shape of the crack. (Roux Page 8, Second Paragraph and Eqs. (6)-(8) “As soon as more complex à functions are used the cross-correlation property cannot be used directly as a global search algorithm, but rather through an iterative minimization procedure. A strategy that is quite performing consists in assuming that the sought displacement is small enough to allow for a Taylor expansion up to first order of the functional to minimize [61]. This hypothesis then transforms the problem into a simple quadratic minimization, and hence an elementary linear system is to be solved
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- The M matrix is a correlation matrix between images/planes. The matrix represents the special correlation of all m and n cells, as indicated by the subscript. Every quantity is determined in a predetermined order based on the special arrangement of the elements of the m x n matrix.)
Claim 18
Regarding claim 18, Roux in view of Li, Moore, and Danielson teaches the features of claim 12 and further teaches:
wherein the crack estimator circuit calculates a displacement vector of the crack occurrence plane, from the inverse matrix and a deformation vector of the observation plane generated from a result of deformation of the target structure actually measured at the observation plane, and estimates a position and a size of a crack at the crack occurrence plane on the basis of the displacement vector. (Roux Page 20, Third Paragraph “Since the displacement fields that correspond to a crack in an elastic solid are known, it is natural to use them as basis functions. […] The advantage of this procedure is that only very few degrees of freedom are used to describe the kinematics […] Hence small uncertainty levels are to be expected. [… Figure 13 shows the resulting displacement field for the SiC sample. Let us underline that this procedure can be seen as being along the same line as the regularize approach based on a finite-element penalization (XI-DIC [41]). – The system estimates magnitudes and directions (vectors) of displacement fields of the crack. Page 8, Second Paragraph and Eqs. (6)-(8) “As soon as more complex à functions are used the cross-correlation property cannot be used directly as a global search algorithm, but rather through an iterative minimization procedure. A strategy that is quite performing consists in assuming that the sought displacement is small enough to allow for a Taylor expansion up to first order of the functional to minimize [61]. This hypothesis then transforms the problem into a simple quadratic minimization, and hence an elementary linear system is to be solved
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- The M matrix is a correlation matrix between images/planes.
Page 14, First Paragraph “and the full correlation matrix of the error in ω reads
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The latter result is quite interesting, as it allows one to estimate the uncertainty level due to the image noise on the displacement directly from the inverse of the matrix [M] to be computed for DIC. Moreover, it can be used to design robust determinations of derived quantities, such as SIFs for cracks (see Section 4.1).” – The model accounts for noise and develops SIFs using the inverse of the correlation matrix between the planes. Overall, the system estimates the displacement vectors based on the inverse matric and a measure deformation vector as presented in the images. The image of the surface, is a surface measurement. All of these are used to estimate the position and size of the crack at the location of the crack (e.g., a crack occurrence plane) based on the displacement vector.
Claim 20
Regarding claim 20, Roux teaches:
A crack estimation method comprising the steps of: inputting a shape model of a target structure to be inspected, and a crack occurrence plane and an observation plane in the shape model; (Roux Abstract “Because of its remarkable sensitivity, it is not only possible to detect cracks with sub-pixel opening, which would not be visible, but also to provide accurate estimates of stress intensity factors. For this purpose suitable tools have been devised to minimize the sensitivity to noise. Working with digital images allows the experimentalist to deal with a wide range of scales from atomistic to geophysical one with the same tools.” – A crack estimation device to perform a crack estimation method. Page 4, Last Paragraph – Page 5, Second Paragraph “To monitor phenomena within opaque materials, X-Ray Computed MicroTomography (XCMT) is a very powerful way of imaging material microstructures in a nondestructive manner [46]. In particular, cracks can be observed [47, 48], their closure [49], and CODs measured by manually tracking particles [50]. When the crack morphology is determined, X-FEM techniques allow for the evaluation of surface vs. bulk propagation features [51]. Global correlation techniques [52] were used recently to measureCODs [53]. Enriched kinematics are also implemented (i.e., it corresponds to eXtendedDigital Image Correlation to measure 3D displacements, or X3D-DIC [54]). This procedure allows one to bridge the gap between 3D pictures and numerical models [55]. In Section 2, the principles of DIC are introduced. Various strategies are discussed to deal with the measurement of displacement fields, which is an ill-posed problem. This feature has consequences on the measurement uncertainties that are evaluated. Surface measurements are performed in the presence of cracks in Section 3 and the different strategies introduced above are illustrated. One key quantity in fracture mechanics is the SIF, which may be deduced from the knowledge of measured displacements. Different approaches are followed in Section 4. Last, cracks can also be analyzed in the bulk of opaque materials by resorting to 3D imaging techniques such as XCMT, and then 3D-DIC (Section 5). […] Digital image correlation consists in analyzing a series of images, from which displacement fields are measured so as to match either a first image considered as a reference one (typically the unloaded stage) and each subsequent image, or (if displacement amplitudes are too large) consecutive pairs of images. In the latter case, the displacement from the reference image is reconstructed as a sum of elementary displacements taking into account non-linearities induced by large displacements. We thus focus here on the analysis of image pairs, one being the “reference” image, while the second is the “deformed” image (Figure 1).” – The tomography (shape) of the crack is determined. The determination is based on determining a correlation between a surface image and a deformed image, 2-dimensional images (surface and crack occurrence planes) that are related by the digital image correlation (DIC).)
outputting, as an estimation model for estimating a state of the crack occurrence plane from a state of the observation plane, an inverse matrix of a matrix that associates, with each other, the state of the crack occurrence plane and the state of the observation plane in a structural analysis model generated from the shape model; and Roux Page 4, Last Paragraph – Page 5, Third Paragraph “To monitor phenomena within opaque materials, X-Ray Computed MicroTomography (XCMT) is a very powerful way of imaging material microstructures in a nondestructive manner [46]. In particular, cracks can be observed [47, 48], their closure [49], and CODs measured by manually tracking particles [50]. When the crack morphology is determined, X-FEM techniques allow for the evaluation of surface vs. bulk propagation features [51]. Global correlation techniques [52] were used recently to measureCODs [53]. Enriched kinematics are also implemented (i.e., it corresponds to eXtendedDigital Image Correlation to measure 3D displacements, or X3D-DIC [54]). This procedure allows one to bridge the gap between 3D pictures and numerical models [55]. In Section 2, the principles of DIC are introduced. Various strategies are discussed to deal with the measurement of displacement fields, which is an ill-posed problem. This feature has consequences on the measurement uncertainties that are evaluated. Surface measurements are performed in the presence of cracks in Section 3 and the different strategies introduced above are illustrated. One key quantity in fracture mechanics is the SIF, which may be deduced from the knowledge of measured displacements. Different approaches are followed in Section 4. Last, cracks can also be analyzed in the bulk of opaque materials by resorting to 3D imaging techniques such as XCMT, and then 3D-DIC (Section 5). […] Digital image correlation consists in analyzing a series of images, from which displacement fields are measured so as to match either a first image considered as a reference one (typically the unloaded stage) and each subsequent image, or (if displacement amplitudes are too large) consecutive pairs of images. In the latter case, the displacement from the reference image is reconstructed as a sum of elementary displacements taking into account non-linearities induced by large displacements. We thus focus here on the analysis of image pairs, one being the “reference” image, while the second is the “deformed” image (Figure 1).” – The model presented as the original image is converted to a model that accounts for displacement measurement fields. Page 8, Second Paragraph and Eqs. (6)-(8) “As soon as more complex à functions are used the cross-correlation property cannot be used directly as a global search algorithm, but rather through an iterative minimization procedure. A strategy that is quite performing consists in assuming that the sought displacement is small enough to allow for a Taylor expansion up to first order of the functional to minimize [61]. This hypothesis then transforms the problem into a simple quadratic minimization, and hence an elementary linear system is to be solved
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- The M matrix is a correlation matrix between images/planes.
Page 14, First Paragraph “and the full correlation matrix of the error in ω reads
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The latter result is quite interesting, as it allows one to estimate the uncertainty level
due to the image noise on the displacement directly from the inverse of the matrix [M]
to be computed for DIC. Moreover, it can be used to design robust determinations of
derived quantities, such as SIFs for cracks (see Section 4.1).” – The model accounts for noise and develops SIFs using the inverse of the correlation matrix between the planes.)
estimating a state of a crack at the crack occurrence plane on the basis of the estimation model and a measurement value for the target structure actually measured at the observation plane and providing the estimated state of the crack and the measurement value to a display device for display. (Roux Page 16, Second Paragraph “The first extension of the finite-element DIC for cracks concerns a specific enrichment that consists in introducing a discontinuity across the crack faces in addition to the regular finite-element description. This technique is widely used in computational mechanics, and is known under the name of X-FEM (for eXtended Finite Element Method [31, 32]). Its image correlation counter-part is referred to as X-DIC [33, 34, 36]. In addition to the displacement discontinuity, the enrichment may also contain stress and strain singular contributions to describe the displacement in the vicinity of the crack tip. The main advantage of this technique is that most of the analysis remains unchanged but only a local refinement is included. Page 30, Second-Third Paragraphs “To confirm the validity of the present procedure, a full three dimensional linear elastic finite element simulation was carried out on the actual geometry of the specimen and crack. Kinematic boundary conditions extracted from the DIC analysis were also prescribed on the top and bottom sides. Stress intensity factors for all three modes were computed all along the front. In Figure 21, these estimates are reported as curves while the measured estimates are shown as symbols for two load levels. An excellent general agreement is obtained between those estimates, for all modes, and a slight discrepancy for mode I under the highest load presumably because of a rather large plastic process zone developing over the remaining ligament (based on the elastic simulation, half of the ligament area exceeds the yield stress). A number of developments are yet to be performed for refining these tools, and in particular a totally automated procedure would be welcome to extract SIFs.” – An extended finite element method/module is applied to eliminate errors and estimate the state of the crack. A three-dimensional linear elastic finite element mode of the cracks, is generated based on the finite element methods and the DIC. The image taken of the surface is an actual measurement. Pages 29-31, Figures 19, 20, and 21 (shown below) – Roux teaches that the data is prepared for display, as shown in the figures below)
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Roux suggests the use of sequential methods for modeling crack propagation (Roux Page 4, Fourth Paragraph “In all the previous identification analyses, the measurement and identification steps are performed sequentially, namely, displacements are first measured and subsequently post-processed to determine SIFs or even J-integrals.”) does not appear to explicitly teach, but Roux in view of Li teaches:
the matrix being generated by sequentially setting a boundary condition for each of a plurality of nodes in the crack occurrence plane such that a crack is assumed to occur at each node; (Li Page 58, 3. Numerical examples, results and discussion “There is an initial edge crack from (0.0, 1.0) to (7.0, 1.0) on a square plate with x 2ð0;16Þ and y 2ð8;8Þ. The geometry and boundary conditions of the square plate are shown in Fig. 7. The plate is under uniform tension T on its top and bottom edges. In this example, we compare the SIFs and coordinates of the crack tip for 5 propagation steps and three mesh densities, 30 30;100 100 and 200 200. At each step in the iteration n, the crack increment is Da ¼ 0:5. The crack propagation direction is determined by the maximum circumferential stress criterion. […] Fig. 9 shows the crack propagation path on a 100 100mesh. During the propagation process, as long as we set the core at the crack tip and take a certain distance as the radius, the SBFEM nodes can be searched, and the super-element at the crack tip can be formed from potential FEM boundary elements.” – The models deal with nodes sequentially as they appear. Page 51, 2. The extended scaled boundary finite element method (X-SBFEM) “The core of the X-SBFEM [28,29] is to substitute the semi analytical SBFEM for the crack tip enrichment function to simulate the nonsmooth behavior around the crack tip while the Heaviside enrichment function is used to represent the jump across the dis continuity surface in the split element. The key is in how the algorithm addresses the boundary conditions at the joint. This method creates four types of elements in the domain: (1) general elements (named E0) with no enriched nodes; (2) mixed elements (named E1) with some enriched nodes; (3) split elements (named E2) with all nodes enriched; and (4) the SBFEM super-element (named E3). Fig. 1 shows a typical finite element mesh and a zone diagram depicting the different element types near an arbitrary crack used in the X-SBFEM. Nodes designated by hollow squares have the number of degrees of freedom of a generalized node, which is used to construct the displacement field in the form of a jump between neighboring elements. Hollow circles are used to designate the nodes that are in SBFEM elements.” Pages 51-52 (SEE THE COPIED IMAGES WITH THE EQUATIONS (2)-(8) – Each time, the data is loaded sequentially into the matrices, as demonstrated in the equations in the following images. As is taught, this can be done in a single plane of a crack, as in the claim.
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It would have been obvious to a person of ordinary skill in the art before the effective filing date of the claims to substitute the closed form Dirichlet crack determination of Roux with the sequential, iterative expansion using SBFEM of Li because the person of ordinary skill in the art would be motivated by the suggestion in Roux that sequential methods, such as the one in Li that predicts crack trajectories accurately, are effective substitutes for closed form solutions, and because Roux explicitly states an aim of producing accurate crack estimation results. This is an express suggestion from Roux. See MPEP 2144.06(II) (Roux Page 4, Fourth Paragraph “In all the previous identification analyses, the measurement and identification steps are performed sequentially, namely, displacements are first measured and subsequently post-processed to determine SIFs or even J-integrals.” Page 3, Last Paragraph – Page 4, First Paragraph “In the following, the discussion will focus on the analysis of cracks by means of DIC. The use of full field measurements is of particular interest when dealing with (strong) discontinuities induced by the presence of cracks. Fracture mechanics has benefited from DIC results [23, 24]. For instance, crack tip opening angles [25] or crack tip; opening displacements [12, 19, 13] are measured with a very good accuracy by means of DIC.; Li Abstract “[…] The results show that the proposed X-SBFEM is capable of calculating the stress intensity factors of cracks and predicting crack trajectories and load–displacement relations accurately. An analysis of the sensitivity of the parameters is employed to demonstrate that various mesh densities and crack propagation step lengths led to consistent results.”)
Roux does not appear to teach, but Roux in view of Moore teaches:
wherein the target structure is a shrink-fit part of a retention ring shrink-fitted to a rotor core at an end of a rotor of a rotary electric machine, (Moore Background “Generator rotor retaining rings are one of the most highly stressed components in the generator rotor. Additionally, some retaining ring materials such as 18Mn5Cr, have been susceptible to Stress Corrosion Cracking (SCC). 18Mn18Cr retaining ring material has been used to replace older 18Mn5Cr material rings with great success. The 18Mn18Cr material has been found to be resistant to SCC in the presence of moisture.”
It would have been obvious to a person of ordinary skill in the art before the effective filing date of the claims to modify the crack model of Roux to be a model of a crack in a retaining ring of a rotor of Moore because a person of ordinary skill in the art would be motivated to by the statement in Roux that “Working with digital images allows the experimentalist to deal with a wide range of scales from atomistic to geophysical one with the same tools. Various examples are shown at different scales, as well as some recent extensions to three dimensional cracks based on X-ray Computed micro-tomographic images” to look to Moore which identified retention rings of a generator rotor for crack analysis, which has a different shape and scale relative to the Roux model. (Roux Abstract “Digital image correlation is a measurement technique that allows one to retrieve displacement fields “separating” two digital images of the same sample at different stages of loading. Because of its remarkable sensitivity, it is not only possible to detect cracks with sub-pixel opening, which would not be visible, but also to provide accurate estimates of stress intensity factors. For this purpose suitable tools have been devised to minimize the sensitivity to noise. Working with digital images allows the experimentalist to deal with a wide range of scales from atomistic to geophysical one with the same tools. Various examples are shown at different scales, as well as some recent extensions to three dimensional cracks based on X-ray Computed micro-tomographic images.”; Moore Background “Generator rotor retaining rings are one of the most highly stressed components in the generator rotor. Additionally, some retaining ring materials such as 18Mn5Cr, have been susceptible to Stress Corrosion Cracking (SCC). 18Mn18Cr retaining ring material has been used to replace older 18Mn5Cr material rings with great success. The 18Mn18Cr material has been found to be resistant to SCC in the presence of moisture. Recently, one OEM (Original Equipment Manufacturer) called for inspections of 18Mn18Cr rings, despite its reliable performance in the industry. Although resistant to SCC, some 18Mn18Cr rings have been found with cracks and other damage. The author’s company felt that it would be of value to go back through past job records with rotors that were identified to have 18Mn18Cr retaining rings, and review those records and report on the results of ring inspections due to damage. The author’s company typically rewinds dozens of rotors per year, with many of the rings manufactured from 18Mn18Cr. As part of a rewind, rings are disassembled and inspected. Of course, many rewinds are done because of failures, mostly related to the field winding. An XRF (X-Ray Fluorescence) analyzer is used to determine a ring’s composition.”)
Roux in view of Moore does not appear to explicitly teach but Roux in view of Moore and Danielson teaches:
and the shape model of the target structure is represented in a cylindrical coordinate system. (Danielson Abstract “A formulation for three-dimensional nonlinear finite element analysis in cylindrical coordinates in presented. The elements are isoparametric with the same interpolation functions used to represent the geometry and the physical displacement components. The elements can be used for general three-dimensional analysis, but they are most effective for cases when the geometry and the response are best described in cylindrical coordinates. In contrast to formulations in Cartesian coordinates, the foregoing formulation allows the exact representation of a circular shape. For structures with circular geometries, the improved accuracy of the elements can provide better finite element predictions and reduce the number of elements needed in the circumferential direction. The reduction in the number of elements can result in a significant reduction in computer resources needed for large three-dimensional analyses, particularly in the presence of nonlinearities.”– The coordinate system is cylindrical because the shape (e.g., of a rotor) is cylindrical. This simplifies the calculations by better representing the system.)
It would have been obvious to a person of ordinary skill in the art before the effective filing date of the claims to modify the crack model of Roux of the rotor in Moore by the use of cylindrical coordinates in modeling as presented in Danielson because Roux expresses an aim to expedite the modeling process and, unlike the rectangular prismatic shape of the modeled region in Roux, for which Cartesian coordinates are taught, Moore presents a rotor and its retention ring, which have circular geometries or cylindrical symmetry, and, the person of ordinary skill in the art would be motivated to use cylindrical coordinates to evaluate the rotor of Moore using the processes of Roux, as taught in Danielson to practically model cracks within a cylindrical shape and reduce the number of elements and, hence, the computer resources needed. (Roux Page 33, First Paragraph “It is envisioned that a real-time system is feasible when the pictures are not stored and computations optimized. The same type of procedure may be applied to other types of displacement fields (e.g., in the presence of cracks [79]). Recent software developments allow such DIC computations for 1 Mpixel-images to be performed mostly on Graphical Processing Units of PCs in 0.05 s [80] instead of 50 s when implemented in Matlab [81]. This opens the way for much faster and more complex control strategies.” Also, see Figures 18, 19, and 20 for use of cartesian coordinates with a rectangular prismatic volume.; Moore Background “Generator rotor retaining rings are one of the most highly stressed components in the generator rotor.”; Danielson Abstract “We consider the impact of a ring crack within a rotating hollow cylinder of fixed height under axisymmetric (torsion) loading. The form of the displacement is obtained from the equation of motion using the Fourier sin transform. The displacement jump over the crack is obtained from the boundary condition on the tangential stress, formulated as a singular integral equation which is solved by the method of orthogonal polynomials. The stress intensity factors on the opposing crack surfaces are calculated. The dependence of the crack extension on the problem geometry is investigated, including the impact of the crack’s location, cylinder’s height, torsion loading and rotation frequency. Possible extensions of the model to cover fatigue cracking are considered. A practical test to detect and locate cracks within a rotating cylinder is outlined.” Page 3, First Paragraph “We consider a hollow elastic cylinder containing a ring crack in cylindrical coordinates (see Fig. 1). The cylinders inner radius is a distance a0 from the origin, its outer radius a distance a1, and has height h. The ring crack is located at height d, with inner radius c0 and outer radius c1. The problem domain is therefore, in cylindrical coordinates”)
Claim 21
Regarding claim 21, Roux in view of Li, Moore, and Danielson teaches the features of claim 20 and further teaches:
the matrix that associates the state of the crack occurrence plane and the state of the observation plane with each other is a matrix that associates, with each other, a matrix in which the state of the crack occurrence plane is arranged in a predetermined order for each shape of the crack and a matrix in which the state of the observation plane is arranged in a predetermined order for each shape of the crack. (Roux Page 8, Second Paragraph and Eqs. (6)-(8) “As soon as more complex à functions are used the cross-correlation property cannot be used directly as a global search algorithm, but rather through an iterative minimization procedure. A strategy that is quite performing consists in assuming that the sought displacement is small enough to allow for a Taylor expansion up to first order of the functional to minimize [61]. This hypothesis then transforms the problem into a simple quadratic minimization, and hence an elementary linear system is to be solved
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- The M matrix is a correlation matrix between images/planes. The matrix represents the special correlation of all m and n cells, as indicated by the subscript. Every quantity is determined in a predetermined order based on the special arrangement of the elements of the m x n matrix.)
Claim 22
Regarding claim 22, Roux in view of Roux in view of Li, Moore, and Danielson teaches the features of claim 20 and further teaches:
wherein the step of outputting, as the estimation model includes a step of performing numerical analysis while sequentially setting such a boundary condition for the structural analysis model that a crack occurs at every node between the divided unit planes of the crack occurrence plane, and storing an analysis result of the crack occurrence plane and an analysis result of the observation plane obtained through the numerical analysis, in a storage device, and (Roux Page 16, Second Paragraph “The first extension of the finite-element DIC for cracks concerns a specific enrichment that consists in introducing a discontinuity across the crack faces in addition to the regular finite-element description. This technique is widely used in computational mechanics, and is known under the name of X-FEM (for eXtended Finite Element Method [31, 32]). Its image correlation counter-part is referred to as X-DIC [33, 34, 36]. In addition to the displacement discontinuity, the enrichment may also contain stress and strain singular contributions to describe the displacement in the vicinity of the crack tip. The main advantage of this technique is that most of the analysis remains unchanged but only a local refinement is included. Page 30, Second-Third Paragraphs “To confirm the validity of the present procedure, a full three-dimensional linear elastic finite element simulation was carried out on the actual geometry of the specimen and crack. Kinematic boundary conditions extracted from the DIC analysis were also prescribed on the top and bottom sides. Stress intensity factors for all three modes were computed all along the front. In Figure 21, these estimates are reported as curves while the measured estimates are shown as symbols for two load levels. An excellent general agreement is obtained between those estimates, for all modes, and a slight discrepancy for mode I under the highest load presumably because of a rather large plastic process zone developing over the remaining ligament (based on the elastic simulation, half of the ligament area exceeds the yield stress). A number of developments are yet to be performed for refining these tools, and in particular a totally automated procedure would be welcome to extract SIFs.” – FEA is conducted to determine the values for all parameters in the volume of the model, e.g., including at both planes/images that are related by the correlation matrix. An extended finite element method/module is applied to eliminate errors and estimate the state of the crack. A three-dimensional linear elastic finite element mode of the cracks, is generated based on the finite element methods and the DIC. Page 30, Second Paragraph “To confirm the validity of the present procedure, a full three dimensional linear elastic finite element simulation was carried out on the actual geometry of the specimen and crack. Kinematic boundary conditions extracted from the DIC analysis were also prescribed on the top and bottom sides. Stress intensity factors for all three modes were computed all along the front. In Figure 21, these estimates are reported as curves while the measured estimates are shown as symbols for two load levels. An excellent general agreement is obtained between those estimates, for all modes, and a slight discrepancy for mode I under the highest load presumably because of a rather large plastic process zone developing over the remaining ligament (based on the elastic simulation, half of the ligament area exceeds the yield stress).” – The boundary conditions are applied sequentially (e.g., an element by element basis for the calculations across the m X n cells for each image/plane. Page 15, Third Paragraph “even if it is somewhat more compute resource demanding” Page 32, “DIC may also be used to drive an experiment [78]. Because of heavy image processing and relatively lengthy image storage, the overall working frequency is about 1 Hz.” Page 33, First Paragraph “Recent software developments allow such DIC computations for 1 Mpixel-images to be performed mostly on Graphical Processing Units of PCs in 0.05 s [80] instead of 50 s when implemented in Matlab [81]. This opens the way for much faster and more complex control strategies.” – Roux teaches computerization of the method. All parameters and corresponding values are stored in computer memory as a matter of course in the computerized method.)
a step of calculating a crack occurrence plane matrix in which the crack occurrence plane is represented as a matrix and an observation plane matrix in which the observation plane is represented as a matrix from the analysis results stored in the storage device, calculating a forward coefficient matrix for mapping the crack occurrence plane matrix to the observation plane matrix, and outputting an inverse matrix of the forward coefficient matrix as the estimation model. (Roux Page 4, Last Paragraph – Page 5, Second Paragraph “To monitor phenomena within opaque materials, X-Ray Computed MicroTomography (XCMT) is a very powerful way of imaging material microstructures in a nondestructive manner [46]. In particular, cracks can be observed [47, 48], their closure [49], and CODs measured by manually tracking particles [50]. When the crack morphology is determined, X-FEM techniques allow for the evaluation of surface vs. bulk propagation features [51]. Global correlation techniques [52] were used recently to measureCODs [53]. Enriched kinematics are also implemented (i.e., it corresponds to eXtendedDigital Image Correlation to measure 3D displacements, or X3D-DIC [54]). This procedure allows one to bridge the gap between 3D pictures and numerical models [55]. In Section 2, the principles of DIC are introduced. Various strategies are discussed to deal with the measurement of displacement fields, which is an ill-posed problem. This feature has consequences on the measurement uncertainties that are evaluated. Surface measurements are performed in the presence of cracks in Section 3 and the different strategies introduced above are illustrated. One key quantity in fracture mechanics is the SIF, which may be deduced from the knowledge of measured displacements. Different approaches are followed in Section 4. Last, cracks can also be analyzed in the bulk of opaque materials by resorting to 3D imaging techniques such as XCMT, and then 3D-DIC (Section 5). […] Digital image correlation consists in analyzing a series of images, from which displacement fields are measured so as to match either a first image considered as a reference one (typically the unloaded stage) and each subsequent image, or (if displacement amplitudes are too large) consecutive pairs of images. In the latter case, the displacement from the reference image is reconstructed as a sum of elementary displacements taking into account non-linearities induced by large displacements. We thus focus here on the analysis of image pairs, one being the “reference” image, while the second is the “deformed” image (Figure 1).” – The tomography (shape) of the crack is determined. The determination is based on determining a correlation between a surface image and a deformed image, 2-dimensional images (surface and crack occurrence planes) that are related by the digital image correlation (DIC). Page 30, Second Paragraph “To confirm the validity of the present procedure, a full three dimensional linear elastic finite element simulation was carried out on the actual geometry of the specimen and crack. Kinematic boundary conditions extracted from the DIC analysis were also prescribed on the top and bottom sides. Stress intensity factors for all three modes were computed all along the front.” – Structural analysis is performed using kinematic boundary conditions on the images/planes. Page 8, Second Paragraph and Eqs. (6)-(8) “As soon as more complex à functions are used the cross-correlation property cannot be used directly as a global search algorithm, but rather through an iterative minimization procedure. A strategy that is quite performing consists in assuming that the sought displacement is small enough to allow for a Taylor expansion up to first order of the functional to minimize [61]. This hypothesis then transforms the problem into a simple quadratic minimization, and hence an elementary linear system is to be solved
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- The M matrix is a correlation matrix between images/planes.
Page 14, First Paragraph “and the full correlation matrix of the error in ω reads
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The latter result is quite interesting, as it allows one to estimate the uncertainty level due to the image noise on the displacement directly from the inverse of the matrix [M] to be computed for DIC. Moreover, it can be used to design robust determinations of derived quantities, such as SIFs for cracks (see Section 4.1).” – The model accounts for noise and develops SIFs using the inverse of the correlation matrix between the planes. At some point, the models output the forward matrix M that represents the correlation between the images and its inverse used for error correction. Page 15, Third Paragraph “even if it is somewhat more compute resource demanding” – Roux teaches computerization of the method. All parameters and corresponding values are stored in computer memory as a matter of course in the computerized method.)
Claim 25: Roux, Li, Moore, Danielson, and NCORR
Claim 25 is rejected under 35 U.S.C. 103 as being unpatentable over NPL “Digital Image Correlation and Fracture: An Advanced Technique for Estimating Stress Intensity Factors of 2D and 3D Cracks” by Roux et al. (Roux) in view of in view of NPL: “Modeling crack propagation with the extended scaled boundary finite element method based on the level set method” by Li et al. (Li), NPL: “Damage Mechanisms Found in Generator Rotor 18Mn18Cr Retaining Rings.” by Moore (Moore), NPL: “Three-dimensional finite element analysis in cylindrical coordinates for nonlinear solid mechanics problems” by Danielson et al. (Danielson), and NPL: “DIC Algorithms” by NCORR (NCORR).
Claim 25
Regarding claim 25, Roux in view of Li, Moore, and Danielson teaches the features of claim 12 and further teaches:
wherein the estimation model represents the relationship therebetween by the inverse matrix. (Roux Page 8, Second Paragraph and Eqs. (6)-(8) “As soon as more complex à functions are used the cross-correlation property cannot be used directly as a global search algorithm, but rather through an iterative minimization procedure. A strategy that is quite performing consists in assuming that the sought displacement is small enough to allow for a Taylor expansion up to first order of the functional to minimize [61]. This hypothesis then transforms the problem into a simple quadratic minimization, and hence an elementary linear system is to be solved
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- The M matrix is a correlation matrix between images/planes.
Roux in view of Li, Moore, and Danielson suggests but does not expound on what the DIC relational matrix represents, however, Roux in view of Li, Moore, Danielson, and NCORR teaches:
wherein the displacement is used as the state of the crack occurrence plane, strain is used as the state of the observation plane, and the estimation model represents the relationship therebetween by the inverse matrix. (NCORR Page 2, First Paragraph “The overall goal of DIC is to obtain displacement and strain fields within a region of interest (ROI) for a material sample undergoing deformation. DIC uses image processing techniques in an attempt to solve this problem. Basically, images of a sample are taken as it deforms; these images are used as inputs to a DIC program. The idea is to somehow obtain a one-to-one correspondence between material points in the reference (initial undeformed picture) and current (subsequent deformed pictures) configurations. DIC does this by taking small subsections of the reference image, called subsets, and determining their respective locations in the current configuration. For each subset, we obtain displacement and strain information through the transformation used to match the location of the subset in the current configuration. Many subsets are picked in the reference configuration, often with a spacing parameter to reduce computational cost (also note that subsets typically overlap as well). The end result is a grid containing displacement and strain information with respect to the reference configuration, also referred to as Lagrangian displacements/strains. The displacement/strain fields can then either be reduced or interpolated to form a "continuous" displacement/strain field. These ideas will be made more precise in the following sections. – This describes the typical strain-displacement relationship reflected in the Roux matrix of strain and displacement fields to bridge between an external image and an internal crack plane.)
It would have been obvious to a person of ordinary skill in the art before the effective filing date of the claims to modify the generic explanation of the strain-displacement matrix of Roux by the general explanation of what these matrices represent in NCORR because the person of ordinary skill in the art would be motivated by the high level explanation that DIC as a measurement technique that, in implementation, relates strains and displacements in Roux to look to NCORR that establishes the basic groundwork of DIC to explain its fundamentals with an emphasis on implementation. (Roux Page 2, Second Paragraph “One of the popular measurement techniques using pictures [3] is Digital Image Correlation (DIC). The latter consists in comparing two images of the same scene, typically an object under load, and retrieving the displacement field that allows for the best match. In its spirit and even in some implementations, DIC is very similar to the corresponding tool very frequently used in fluid mechanics, which is known as “Particle Image Velocimetry” or PIV. DIC [4, 5, 6] appeared at about the same time as PIV [7, 8, 9, 10, 11]. However, because of the typical magnitude of strains and displacements that are usually much smaller in solid mechanics than in fluid flow analyses, its development was a bit slower since the demand was more challenging to meet. However, today it can be said that the common performances of such techniques allow one to use them in most instances of experimental mechanics.”; NCORR Page 22, 6 – Concluding Remarks “At this point, the basic groundwork has been established for obtaining displacement and strain fields from images of samples undergoing deformation. Overall, this writeup was intended to explain the fundamentals of DIC with an emphasis on implementation.”
Claim 26: Roux, Li, Moore, Danielson, and Terzic
Claim 26 is rejected under 35 U.S.C. 103 as being unpatentable over NPL “Digital Image Correlation and Fracture: An Advanced Technique for Estimating Stress Intensity Factors of 2D and 3D Cracks” by Roux et al. (Roux) in view of in view of NPL: “Modeling crack propagation with the extended scaled boundary finite element method based on the level set method” by Li et al. (Li), NPL: “Damage Mechanisms Found in Generator Rotor 18Mn18Cr Retaining Rings.” by Moore (Moore), NPL: “Three-dimensional finite element analysis in cylindrical coordinates for nonlinear solid mechanics problems” by Danielson et al. (Danielson), , and NPL: “Force-based Element vs. Displacement-based Element” by Terzic (Terzic).
Claim 26
Regarding claim 26, Roux in view of Li, Moore, and Danielson teaches the features of claim 12 and further teaches:
wherein displacement is used as the state of the crack occurrence plane, and [strain] is used as the state of the observation plane, and the estimation model represents the relationship therebetween by the inverse matrix. (Roux Page 8, Second Paragraph and Eqs. (6)-(8) “As soon as more complex à functions are used the cross-correlation property cannot be used directly as a global search algorithm, but rather through an iterative minimization procedure. A strategy that is quite performing consists in assuming that the sought displacement is small enough to allow for a Taylor expansion up to first order of the functional to minimize [61]. This hypothesis then transforms the problem into a simple quadratic minimization, and hence an elementary linear system is to be solved
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- The M matrix is a correlation matrix between images/planes.
Roux in view of Li, Moore, and Danielson suggests but does not expound on what the DIC relational matrix represents, however, Roux in view of Li, Moore, Danielson, and Terzic teaches:
wherein displacement change or force change is used as the state of the crack occurrence plane, and displacement change or angle change is used as the state of the observation plane, and the estimation model represents the relationship therebetween by the inverse matrix. (Terzic Page 3 “Contrary to concentrated plasticity models (elastic element with rotational springs at element ends) force-based element (FBE) and displacement based element (DBE) permit spread of plasticity along the element (distributed plasticity models).” Page 10 “Section forces are determined from the basic forces by interpolation within the basic system. - Interpolation comes from static equilibrium and provides constant axial force and linear distribution of bending moment in the absence of distributed element loads. Page 12:
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These demonstrate that the force-based techniques relate change in force to tangential/angular displacement.)
It would have been obvious to a person of ordinary skill in the art to modify the displacement-based techniques of Roux with the force-based techniques of Tervic because a person of ordinary skill in the art would be motivated by the aim to provide am accurate/noise-free relationship between the external image and the crack in Roux to look to Tervic, which provides force-based matrix determinations that generally improve global and local response without mesh refinement. (Roux Abstract “Because of its remarkable sensitivity, it is not only possible to detect cracks with sub-pixel opening, which would not be visible, but also to provide accurate estimates of stress intensity factors. For this purpose suitable tools have been devised to minimize the sensitivity to noise.”; Tervic Page 25 “FBE generally improves global and local response without mesh refinement.”)
Conclusion
The prior art made of record and not relied upon is considered pertinent to applicant's disclosure.
US 7016825 B1 to Tyron et al. (Teaches using FEM to predict a part failure)
NPL: “Geometrical identification of invisible defects in structural elements basing on digital image correlation data” by Apalkov (Teaches digital image correlation for determining structural defects)
NPL: “MARGINAL MAXIMUM LIKELIHOOD ESTIMATION OF ITEM PARAMETERS: APPLICATION OF AN EM ALGORITHM” by Bock et al. (Teaches FEM methods that are relevant)
NPL: “Ultrasonic Ply-by-Ply Detection of Matrix Cracks in Laminated Composites” by Kinra (Teaches comparison of planes for damage)
NPL: “H-matrix based fast direct finite-element methods for large-scale electromagnetic analysis” by Liu (Teaches using inverse matrices to solve FEM)
NPL: “Crack detection using image processing: A critical review and analysis” by Mohan et al. (Teaches using image analysis to detect cracks)
NPL: “Image Correlation for Shape, Motion and Deformation Measurements” by Sutton et al. (Teaches image correlation techniques for several applications)
NPL: “Development of digital image correlation method to analyse crack variations of masonry wall” by Tung et al. (Teaches using DIC to analyze cracks)
NPL: “Aircraft wing structural damage localization research based on RBF neural network” by Bao et al. (Teaches using neural networks to analyze cracks)
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