A method for assigning parameters for creep curve fitting using the θ method and related apparatus

Abstract

This invention discloses a method and related apparatus for assigning parameters to a creep curve fitting using the θ method, comprising: acquiring creep test data; plotting a creep curve based on the creep test data, identifying the boundary point t0 between the second and third stages of the creep curve; determining the slope θ1 of the linear segment of the second stage; extending the extension line of the creep curve in the reverse direction to intersect the ε-axis at point y0; and determining the detection endpoint t of the third stage. end According to the detection endpoint t of Phase III end Calculate the deformation degree θ2 in stage III; determine the rate θ3 in stage III based on the deformation degree θ2 in stage III. This method and related devices improve the stability and accuracy of fitting, and overcome the defects of traditional θ-method fitting, such as initial parameters relying on experience and poor convergence.

Description

Technical Field

[0001] This invention belongs to the field of material performance testing and analysis technology, and relates to a method for assigning parameters for θ-method creep curve fitting and related devices. Background Technology

[0002] The θ method is an important method for predicting the creep life of materials, and its core formula is: ε=θ1t+θ2(e tθ3 1)(1) Where θ1 is the creep rate in stage II (slope of the linear segment), θ2 is the deformation degree in stage III, θ3 is the creep rate in stage III, ε is the strain, and t is the time. Since stage I creep accounts for a very small proportion of the entire creep life, it can often be ignored in the fitting. However, the following problems exist when performing nonlinear fitting in practice: 1. Traditional methods rely on manual experience to assign initial parameters, which can easily lead to convergence failure or getting trapped in local optima, thus reducing the accuracy of lifetime prediction. 2. In equation (1), when t=0, ε=0. However, in actual fitting, the creep stage I is often not considered. The linear trend extension line of the creep curve stage II often does not pass through the origin. That is, when t=0, ε≠0 in the actual fitting segment. This leads to a large deviation in the fitting curve in stage II (linear segment) when using equation 1 for fitting, which seriously affects the subsequent calculation accuracy of θ2 and θ3 and the life prediction results.

[0003] Therefore, there is an urgent need for a scientific and efficient method for initial parameter assignment and adjustment to improve fitting stability and accuracy. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of the prior art and provide a method and related apparatus for assigning parameters for θ-method creep curve fitting. This method and apparatus improve the stability and accuracy of fitting and overcome the defects of traditional θ-method fitting, such as initial parameters relying on experience and poor convergence.

[0005] To achieve the above objectives, this invention discloses a method for assigning parameters to a creep curve fitting curve using the θ method, comprising: Obtain creep test data; Based on the creep test data, a creep curve is plotted, and the boundary point t0 between stage II and stage III of the creep curve is identified. Determine the slope θ1 of the linear segment in the second stage; Extend the extension of the creep stage II curve in the opposite direction to intersect the ε axis at point y0; Determine the endpoint t of Phase III testing. end According to the detection endpoint t of Phase III end Calculate the deformation degree θ2 in stage III; The rate θ3 of stage III is determined based on the degree of deformation θ2 of stage III.

[0006] Furthermore, the creep test data includes time and its corresponding strain.

[0007] Furthermore, θ2≈ε' end ,ε' end =ε end -θ1t end , ε end For the end strain of stage III, t end This is the end time of Phase III.

[0008] Furthermore, by substituting the deformation degree θ2 of stage III into equation (6), the rate θ3 of stage III is calculated; θ3(6) Where, ε'=θ2(e tθ3 1).

[0009] Furthermore, it also includes: To evaluate the quality of the fit, if the residual distribution is discrete, perform the following operations: When the fitting deviation is large in the low t interval, then fine-tune θ1 to minimize the sum of squared residuals in the linear segment; When the fitting deviation is large in the high t interval, first adjust θ2 to correct the degree of deformation, and then adjust θ3 to correct the acceleration rate.

[0010] Furthermore, the fit quality is evaluated using the residual plots from Origin.

[0011] This invention discloses a parameter assignment system for θ-method creep curve fitting, comprising: The acquisition module is used to acquire creep test data; The identification module is used to draw a creep curve based on the creep test data and identify the boundary point t0 between stage II and stage III of the creep curve. The first determining module is used to determine the slope θ1 of the linear segment in the second stage; The extension module is used to extend the extension line of the creep stage II curve in the opposite direction to the intersection point y0 with the ε axis; The calculation module is used to determine the detection endpoint t in stage III. end According to the detection endpoint t of Phase III end Calculate the deformation degree θ2 in stage III; The second determining module is used to determine the rate θ3 of stage III based on the deformation degree θ2 of stage III.

[0012] Furthermore, it also includes an adjustment module for evaluating the quality of the fit, which performs the following operations when the residual distribution is discrete: When the fitting deviation is large in the low t interval, then fine-tune θ1 to minimize the sum of squared residuals in the linear segment; When the fitting deviation is large in the high t interval, first adjust θ2 to correct the degree of deformation, and then adjust θ3 to correct the acceleration rate.

[0013] This invention discloses a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the steps of the θ-method creep curve fitting parameter assignment method.

[0014] The present invention discloses a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the steps of the θ-method creep curve fitting parameter assignment method.

[0015] The present invention has the following beneficial effects: In practical operation, the θ-method creep curve fitting parameter assignment method and related device described in this invention identify the boundary point t0 between the second and third stages of the creep curve; determine the slope θ1 of the linear segment of the second stage; extend the extension line of the second stage creep curve in the opposite direction to the intersection point y0 with the ε-axis; and determine the detection endpoint t of the third stage. end According to the detection endpoint t of Phase III end Calculate the deformation degree θ2 in stage III; determine the rate θ3 in stage III based on the deformation degree θ2 in stage III; calculate the initial parameters piecewise based on the physical meaning of the formula to avoid empirical errors, thereby improving the stability and accuracy of the fitting and overcoming the shortcomings of the traditional θ method fitting, which relies on experience for initial parameters and has poor convergence.

[0016] Furthermore, this invention combines the residual distribution interval to optimize the corresponding parameters in a targeted manner, thereby improving the stability and accuracy of the fitting. Attached Figure Description

[0017] To more clearly illustrate the technical solutions of the embodiments of this application, the drawings used in the description of the embodiments of this application will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0018] Figure 1 This is a typical creep curve characteristic diagram; Figure 2 The creep curve is fitted using equation (1); Figure 3The creep curve is fitted using the modified equation (2). Detailed Implementation

[0019] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0020] In the description of this invention, it should be understood that the terms "comprising" and "including" indicate the presence of the described features, integrals, steps, operations, elements and / or components, but do not exclude the presence or addition of one or more other features, integrals, steps, operations, elements, components and / or collections thereof.

[0021] It should also be understood that the terminology used in this specification is for the purpose of describing particular embodiments only and is not intended to limit the invention. As used in this specification and the appended claims, the singular forms “a,” “an,” and “the” are intended to include the plural forms unless the context clearly indicates otherwise.

[0022] It should also be further understood that the term "and / or" as used in this specification and the appended claims refers to any combination and all possible combinations of one or more of the associated listed items, and includes such combinations. For example, A and / or B can represent three cases: A alone, A and B simultaneously, and B alone. Additionally, the character " / " in this invention generally indicates that the preceding and following objects have an "or" relationship.

[0023] It should be understood that although terms such as first, second, third, etc., may be used in the embodiments of the present invention to describe the preset range, these preset ranges should not be limited to these terms. These terms are only used to distinguish the preset ranges from one another. For example, without departing from the scope of the embodiments of the present invention, the first preset range may also be referred to as the second preset range, and similarly, the second preset range may also be referred to as the first preset range.

[0024] Depending on the context, the word "if" as used here can be interpreted as "when," "when," "in response to determination," or "in response to detection." Similarly, depending on the context, the phrase "if determination" or "if detection (of the stated condition or event)" can be interpreted as "when determination," "in response to determination," "when detection (of the stated condition or event)," or "in response to detection (of the stated condition or event)."

[0025] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0026] The accompanying drawings illustrate various structural schematic diagrams according to embodiments disclosed in this invention. These drawings are not to scale, and some details have been enlarged for clarity, and some details may have been omitted. The shapes of the various regions and layers shown in the drawings, as well as their relative sizes and positional relationships, are merely exemplary and may deviate from reality due to manufacturing tolerances or technical limitations. Furthermore, those skilled in the art can design regions / layers with different shapes, sizes, and relative positions as needed.

[0027] Example 1 The method for assigning parameters for creep curve fitting using the θ method described in this invention includes the following steps: 1) Fitting model correction; In actual fitting, since the first stage of creep accounts for a very small proportion of the entire creep life, it can often be ignored in the fitting. When using equation (1), in order to solve the problem that ε≠0 at t=0, equation (1) is modified as follows: ε=θ1t+θ2(e tθ3 1)+y0(2) Where ε is strain, t is time, θ1 is the creep rate in stage II, θ2 is the deformation degree in stage III, θ3 is the rate in stage III, and y0 is the intercept.

[0028] 2) Data preprocessing and feature extraction; Input data: Import creep test data from Excel, including creep test time t and strain ε; Data segmentation: Based on the creep test data, a creep curve is plotted. Based on the characteristics of the creep curve (initial stage, stage II, stage III), the boundary point t0 between stage II (approximately linear segment) and stage III (acceleration segment) is identified using Origin's "data smoothing" and "derivative analysis" functions.

[0029] 3) Initial parameter assignment method; θ1 assignment: The creep rate in stage II is the slope of the linear segment. Using Origin, a linear fit is performed on the data from the start time of stage II creep up to t < t0. The slope θ1 is: θ1=Δε / Δt(3) Extend the extension of the creep stage II curve in the opposite direction to intersect the ε-axis at point y0.

[0030] Assigning values ​​to θ2 and θ3: For the data in stage III where t > t0, the correction formula is transformed into: ε-θ1t-y0= θ2(e tθ3 1)(4) Let ε' = ε - θ1t, then the above equation simplifies to: ε'=θ2(e tθ3 1) (5) Taking the logarithm of both sides, we get: θ3(6) First, estimate θ2: Take the detection endpoint t of stage III. end ,ε' end =ε end -θ1t end Then θ2≈ε' end ( ).

[0031] Substituting the estimated θ2 into equation (6), we obtain the initial value of θ3.

[0032] 4) Nonlinear fitting and dynamic parameter adjustment; Initial fitting: In Origin, select "Nonlinear Curve Fit", input equation (2), and substitute the initial parameters obtained in step 2).

[0033] Residual analysis: The quality of fit is evaluated using Origin's "Residual Plot". When the residual distribution is discrete (R²), the quality of fit is assessed. 2 If the value is less than 0.99, the following adjustment rules will be applied: 41) If the fitting deviation is large in the low t interval (t≤t0): then fine-tune θ1 to minimize the sum of squared residuals in the linear segment; 42) If the fitting deviation is large in the high t interval (t>t0): first adjust θ2 to correct the degree of deformation, and then adjust θ3 to correct the acceleration rate.

[0034] Convergence verification: Repeat the adjustment until iterative convergence (R) 2 (>0.99), the final output is the optimized parameters θ1, θ2, θ3 and y0.

[0035] Confirmatory Experiment This embodiment uses Origin data analysis software to fit the creep curve of a certain heat-resistant steel. The specific operation steps are as follows: 1) Data preprocessing and feature segmentation; 11) Data import: Import the "time strain" data collected in the experiment into the analysis software.

[0036] 12) Creep Curve Stage Boundary Point Identification: Using derivative analysis, identify the boundary point t0 between stage II (approximately linear segment) and stage III (acceleration segment) of the creep curve.

[0037] 13) Set the criterion: when the instantaneous creep rate deviates from the average rate of stage II by more than 5%, the corresponding time is t0.

[0038] 14) This divides the data into: the low t interval (t≤t) 0， It mainly includes linear creep and high t interval (t>t0, mainly includes accelerated creep).

[0039] Combining the above methods, the calculated t0≈2115h for the data example.

[0040] 2) Physical calculation and assignment of initial parameters; To avoid blind iteration, the initial values ​​of each parameter are calculated based on their physical meaning: 21) Determine the linear slope θ1: 211) Select data from the low t interval (500h~2115h) for linear fitting; 212) Directly read the slope of the fitted curve, θ1≈9.53×10 -6 This is the initial assignment of θ1.

[0041] 22) Determine the initial strain compensation value y0: 221) Problem identification: If Equation 1 is used directly for fitting, when the fitted curve t=0, ε≠0, which leads to a large fitting deviation in the second stage of the creep curve. Therefore, the modified Equation (2) is used for fitting. 222) Calculation method: Extend the fitted line of stage II in step 1) in the opposite direction to intersect the ε axis, and read the intercept as y0. y0≈0.00025, which is the initial value of y0.

[0042] 23) Estimate the nonlinear parameters θ2 and θ3: 231) Select the last data point of the third stage (ε) end , t end ), that is (0.089, 3640.3); 232) Based on equation (5), calculate θ2, θ2≈5.63×10 -2This is the initial value assigned to θ2; 233) Calculate θ3 based on equation (6), θ3≈1.9×10 -4 This is the initial value assigned to θ3.

[0043] 3) Construction and execution of nonlinear fitting models; 31) Custom function construction: 311) Open "Nonlinear Fitting" in Origin and create a new custom function.

[0044] 312) The fitting formula is explicitly defined as: y=a*x +b*((exp(c*x))-1)+d, where x corresponds to t, y corresponds to ε, a corresponds to θ1, b corresponds to θ2, c corresponds to θ3, and d corresponds to y0.

[0045] 32) Preliminary parameter fitting; Input the calculated θ1, θ2, θ3, y0 from step 2) into the corresponding initial values ​​of a, b, c, d, and execute the iteration.

[0046] 4) Residual analysis and dynamic fine-tuning; 41) Observe the fitting effect: Check the degree of agreement between the fitted curve and the data curve; 42) Parameter Adjustment: If the fitted curve does not match the data curve well, you can manually fine-tune the relevant parameters while locking the corresponding parameters, and click "Iterate Once" to observe the curve changes until the fitted curve matches the data curve well. If the curve does not fit well in stage II, you can fine-tune parameters a and d; if the curve does not fit well in stage III, you can fine-tune parameters b and c.

[0047] 43) Output Results: Perform the final iteration to complete the curve fitting until the fitted curve matches the original data well, and the correlation coefficient R is [value missing]. 2 If the value is greater than 0.99, then a, b, c, and d are the optimal θ1, θ2, θ3, and y0 obtained from the fitting.

[0048] Example 2 The θ-method creep curve fitting parameter assignment system of the present invention includes: The acquisition module is used to acquire creep test data; The identification module is used to draw a creep curve based on the creep test data and identify the boundary point t0 between stage II and stage III of the creep curve. The first determining module is used to determine the slope θ1 of the linear segment in the second stage; The extension module is used to extend the extension line of the creep stage II curve in the opposite direction to the intersection point y0 with the ε axis; The calculation module is used to determine the detection endpoint t in stage III. endAccording to the detection endpoint t of Phase III end Calculate the deformation degree θ2 in stage III; The second determining module is used to determine the rate θ3 of stage III based on the deformation degree θ2 of stage III.

[0049] Furthermore, it also includes an adjustment module for evaluating the quality of the fit, which performs the following operations when the residual distribution is discrete: When the fitting deviation is large in the low t interval, then fine-tune θ1 to minimize the sum of squared residuals in the linear segment; When the fitting deviation is large in the high t interval, first adjust θ2 to correct the degree of deformation, and then adjust θ3 to correct the acceleration rate.

[0050] The module division in this embodiment is illustrative and represents only one logical functional division. In actual implementation, other division methods may be used. Furthermore, the functional modules in each embodiment of this application can be integrated into a single processor, exist as separate physical entities, or be integrated into a single module. The integrated modules described above can be implemented in hardware or as software functional modules.

[0051] Example 3 A computer device includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the steps of the θ-method creep curve fitting parameter assignment method, for example, including: acquiring creep test data; plotting a creep curve based on the creep test data; identifying the boundary point t0 between stage II and stage III of the creep curve; determining the slope θ1 of the linear segment of stage II; extending the extension line of stage II creep curve in the opposite direction to the intersection point y0 with the ε-axis; and determining the detection endpoint t of stage III. end According to the detection endpoint t of Phase III end Calculate the deformation degree θ2 of stage III; determine the rate θ3 of stage III based on the deformation degree θ2. The memory may include main memory, such as high-speed random access memory, or it may also include non-volatile memory, such as at least one disk storage device. The processor, network interface, and memory are interconnected via an internal bus, which can be an industry-standard architecture bus, a peripheral component interconnection standard bus, an extended industry-standard architecture bus, etc. The bus can be divided into address bus, data bus, control bus, etc. The memory is used to store programs; specifically, the program may include program code, which includes computer operation instructions. The memory may include main memory and non-volatile memory, and provides instructions and data to the processor.

[0052] Example 4 A computer-readable storage medium storing a computer program, which, when executed by a processor, implements the steps of the θ-method creep curve fitting parameter assignment method, for example including: acquiring creep test data; plotting a creep curve based on the creep test data; identifying the boundary point t0 between the second and third stages of the creep curve; determining the slope θ1 of the linear segment of the second stage; extending the extension line of the creep second stage curve in the opposite direction to the intersection point y0 with the ε-axis; and determining the detection endpoint t of the third stage. end According to the detection endpoint t of Phase III end Calculate the deformation degree θ2 in stage III; determine the rate θ3 in stage III based on the deformation degree θ2. Specifically, the computer-readable storage medium includes, but is not limited to, volatile memory and / or non-volatile memory. The volatile memory may include random access memory (RAM) and / or cache memory, etc. The non-volatile memory may include read-only memory (ROM), hard disk, flash memory, optical disk, magnetic disk, etc.

[0053] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0054] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0055] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1The function specified in one or more boxes.

[0056] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0057] Other embodiments of the invention will readily occur to those skilled in the art upon consideration of the specification and disclosure of the invention. This application is intended to cover any variations, uses, or adaptations of the invention that follow the general principles of the invention and include common knowledge or customary techniques in the art not disclosed herein. The specification and examples are to be considered exemplary only, and the true scope and spirit of the invention are indicated by the following claims.

[0058] It should be understood that the present invention is not limited to the precise structure described above and shown in the accompanying drawings, and various modifications and changes can be made without departing from its scope. The scope of the invention is limited only by the appended claims.

[0059] The above description is merely a preferred embodiment of the present invention and does not constitute any limitation on the present invention. Any simple modifications, alterations, or equivalent structural changes made to the above embodiments based on the technical essence of the present invention shall still fall within the protection scope of the present invention.

Claims

1. A method for assigning parameters for creep curve fitting using the θ method, characterized in that, include: Obtain creep test data; Based on the creep test data, a creep curve is plotted, and the boundary point t0 between stage II and stage III of the creep curve is identified. Determine the slope θ1 of the linear segment in the second stage; Extend the extension of the creep stage II curve in the opposite direction to intersect the ε axis at point y0; Determine the endpoint t of Phase III testing. end According to the detection endpoint t of Phase III end Calculate the deformation degree θ2 in stage III; The rate θ3 of stage III is determined based on the degree of deformation θ2 of stage III.

2. The method for assigning parameters for creep curve fitting using the θ method according to claim 1, characterized in that, The creep test data includes time and the corresponding strain.

3. The method for assigning parameters for creep curve fitting using the θ method according to claim 1, characterized in that, θ2≈ε' end ,ε' end =ε end -θ1t end , ε end For the end strain of stage III, t end This is the end time of Phase III.

4. The method for assigning parameters for creep curve fitting using the θ method according to claim 1, characterized in that, Substituting the deformation degree θ2 of stage III into equation (6), the rate θ3 of stage III is calculated; θ3(6) Where, ε'=θ2(e tθ3 1).

5. The method for assigning parameters for creep curve fitting using the θ method according to claim 1, characterized in that, Also includes: To evaluate the quality of the fit, if the residual distribution is discrete, perform the following operations: When the fitting deviation is large in the low t interval, then fine-tune θ1 to minimize the sum of squared residuals in the linear segment; When the fitting deviation is large in the high t interval, first adjust θ2 to correct the degree of deformation, and then adjust θ3 to correct the acceleration rate.

6. The method for assigning parameters for creep curve fitting using the θ method according to claim 5, characterized in that, The quality of the fit is assessed using residual plots from Origin.

7. A parameter assignment system for θ-method creep curve fitting, characterized in that, include: The acquisition module is used to acquire creep test data; The identification module is used to draw a creep curve based on the creep test data and identify the boundary point t0 between stage II and stage III of the creep curve. The first determining module is used to determine the slope θ1 of the linear segment in the second stage; The extension module is used to extend the extension line of the creep stage II curve in the opposite direction to the intersection point y0 with the ε axis; The calculation module is used to determine the detection endpoint t in stage III. end According to the detection endpoint t of Phase III end Calculate the deformation degree θ2 in stage III; The second determining module is used to determine the rate θ3 of stage III based on the deformation degree θ2 of stage III.

8. The θ-method creep curve fitting parameter assignment system according to claim 7, characterized in that, It also includes a tuning module for evaluating the quality of the fit, which performs the following operations when the residual distribution is discrete: When the fitting deviation is large in the low t interval, then fine-tune θ1 to minimize the sum of squared residuals in the linear segment; When the fitting deviation is large in the high t interval, first adjust θ2 to correct the degree of deformation, and then adjust θ3 to correct the acceleration rate.

9. A computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the steps of the θ-method creep curve fitting parameter assignment method as described in any one of claims 1-6.

10. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by the processor, it implements the steps of the θ-method creep curve fitting parameter assignment method as described in any one of claims 1-6.

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