A fault physical model parameter identification method based on adaptive parameter range iteration

Abstract

The present application relates to the technical field of fault physical model parameter identification, and particularly relates to a fault physical model parameter identification method based on adaptive parameter range iteration, comprising: setting a parameter value range of a model parameter, and sampling the model parameter; obtaining a parameter sensitivity index value sequence; obtaining a global sensitivity index value sequence; obtaining a target parameter value range when the sorting results of the parameter sensitivity index value sequence and the global sensitivity index value sequence meet consistency; and obtaining an optimal model parameter. The present application improves the stability, precision and calculation efficiency of parameter identification.

Description

Technical Field

[0001] This invention relates to the field of fault physical model parameter identification technology, and specifically to a fault physical model parameter identification method based on adaptive parameter range iteration. Background Technology

[0002] As electronic packaging structures evolve towards high-density integration and complex service environments, reliability modeling methods based on Physics of Failure (PoF) are gradually becoming important tools for lifetime prediction and failure analysis. PoF models typically describe the response behavior of structures under multi-physics coupling by establishing material constitutive relations and damage evolution mechanisms; their prediction accuracy largely depends on the accuracy of the model parameters. However, PoF models generally have characteristics such as a large number of parameters, strong nonlinearity, and complex coupling relationships.

[0003] For the Anand viscoplastic constitutive model, its parameters involve multiple physical processes such as material thermal activation behavior, strain rate sensitivity, and internal state variable evolution. For this type of multi-parameter model, the following problems usually exist in the actual parameter identification process: (1) Large parameter search space: that is, the model parameters are usually derived from literature experience, theoretical estimation or experimental fitting range, resulting in a wide initial parameter range, which in turn causes the parameter search space to be high-dimensional and wide-ranging, which not only significantly increases the computational cost, but also reduces the accuracy of parameter identification. (2) Unstable parameter sensitivity analysis results: that is, in the high-dimensional parameter space, the sensitivity ranking results obtained under different sampling methods or sample sizes are prone to fluctuation, resulting in inconsistent key parameter identification results, affecting the reliability of subsequent parameter identification. (3) Strong parameter coupling, and the identification process is prone to getting trapped in local optima: that is, there is usually a significant nonlinear coupling relationship between model parameters. When using traditional optimization methods for parameter search, it is easy to get trapped in local extrema in the complex objective function space, thereby reducing the accuracy of identification.

[0004] In summary, all the aforementioned problems are closely related to the setting of the parameter search range. An excessively large parameter range will introduce a large number of invalid search regions, increasing computational complexity and reducing identification efficiency; an unreasonable parameter range will lead to increased fluctuations in sensitivity analysis results, affecting the stability of key parameter selection and further amplifying the coupling effect between parameters, making the optimization process more prone to getting trapped in local optima. Therefore, how to achieve adaptive optimization and dynamic shrinkage of the parameter space during parameter identification becomes a key issue in improving the accuracy and efficiency of fault physics model parameter identification.

[0005] Therefore, a fault physical model parameter identification method based on adaptive parameter range iteration is needed to solve the above problems. Summary of the Invention

[0006] To address the problems of insufficient parameter identification accuracy and unstable sensitivity analysis results caused by excessively large parameter spaces in existing technologies, this invention provides a fault physical model parameter identification method based on adaptive parameter range iteration to solve the existing problems.

[0007] The first aspect of this invention provides a fault physical model parameter identification method based on adaptive parameter range iteration, employing the following technical solution, including: Determine the model parameters of the physical model of the fault, and set the parameter value range for each model parameter; The model parameter set is obtained by sampling the model parameters based on the parameter value range; Correlation analysis was performed on the equivalent stress values ​​output by each model parameter in the model parameter set and the fault physical model to obtain the Spearman rank correlation coefficient corresponding to each model parameter. The Spearman rank correlation coefficient was used as the parameter sensitivity index value, and the parameter sensitivity index value sequence was obtained. The model parameters corresponding to the absolute values ​​of parameter sensitivity indexes that are greater than a preset threshold are taken as key model parameters, and a set of key model parameters is obtained. Sobol sequence sampling is performed on the key model parameters in the set of key model parameters, and the global sensitivity index values ​​of the key model parameters are obtained by combining variance decomposition, and a global sensitivity index value sequence is obtained. The system determines the consistency between the sorting results of the parameter sensitivity index value sequence and the global sensitivity index value sequence. If the sorting results are consistent, the current parameter value range is used as the target parameter value range. If the sorting results are inconsistent, the parameter value range is adaptively shrunk to obtain an updated parameter value range. The updated parameter value range is used in the next iteration until the sorting results of the parameter sensitivity index value sequence and the global sensitivity index value sequence are consistent. Then, the updated parameter value range is used as the target parameter value range. The strain test values ​​are input into the fault physical model to obtain the equivalent stress prediction value. An objective function is constructed based on the equivalent stress prediction value and the equivalent stress test value. Model parameters are selected within the range of objective parameter values. The model parameters are optimized using a global optimization method with the objective function as the goal. The model parameters corresponding to the minimum objective function are taken as the optimal model parameters.

[0008] A further technical solution of the present invention is that the model parameters of the fault physics model include: initial value of deformation impedance, activation energy term, exponential function coefficient, stress multiplier, strain rate sensitivity index, deformation impedance evolution coefficient, deformation impedance saturation coefficient, and strain rate sensitivity index of deformation impedance evolution.

[0009] A further technical solution of the present invention is that the step of sampling model parameters based on the parameter value range to obtain a model parameter set is as follows: Based on the parameter value range, the initial model parameter set is obtained by sampling the model parameters using LHS sampling; IQR is used to detect outliers in the initial model parameter set to remove outlier model parameters and obtain the final model parameter set.

[0010] A further technical solution of the present invention is to use the Spearman rank correlation coefficient method to perform correlation analysis on the equivalent stress values ​​output by each model parameter in the model parameter set and the fault physical model to obtain the Spearman rank correlation coefficient corresponding to each model parameter.

[0011] A further technical solution of the present invention is that the step of adaptively shrinking the parameter value range to obtain the updated parameter value range is as follows: Obtain the interval span ratio corresponding to the parameter value range of each model parameter; Based on the interval span ratio and the span ratio threshold, the model parameters are divided into large span parameters and regular span parameters; When the model parameters are conventional span parameters, the arithmetic center of the parameter value range corresponding to the conventional span parameter is used as the contraction center; the interval span of the parameter value range corresponding to the conventional span parameter is the difference between the upper limit and the lower limit of the parameter value range; When the model parameter is a large-span parameter, the parameter value range of the large-span parameter is mapped to the logarithmic space, and the geometric center is used as the contraction center of the parameter value range corresponding to the large-span parameter; the interval span of the parameter value range of the large-span parameter is the difference between the logarithm of the upper limit and the logarithm of the lower limit of the parameter value range. A contraction factor is introduced, and the updated parameter value range is obtained based on the contraction factor, the contraction center, and the interval span of the parameter value range of each model parameter.

[0012] A further technical solution of the present invention is that, based on the interval span ratio and the span ratio threshold, the model parameters are divided into large-span parameters and regular-span parameters as follows: If the interval span ratio is greater than the span ratio threshold, the model parameters will be treated as large span parameters; If the interval span ratio is less than or equal to the span ratio threshold, the model parameters will be used as regular span parameters.

[0013] A further technical solution of the present invention is that the step of obtaining the updated parameter value range based on the contraction factor, the contraction center, and the interval span of the parameter value range of each model parameter is as follows: The updated range of values ​​for the standard span parameter is as follows:

[0014]

[0015] In the formula, Indicates the standard span parameter in The range of parameter values ​​during the next iteration; Indicates the first The contraction center corresponding to the conventional span parameter under round iteration; Indicates the first The interval width corresponding to the conventional span parameter under round iteration; Indicates the first The interval width corresponding to the conventional span parameter under round iteration; The updated parameter value range for the large span is as follows:

[0016]

[0017] In the formula, Indicates the large span parameter in The range of parameter values ​​during the next iteration; Indicates the first The contraction center corresponding to the model parameters being large-span parameters; The parameter range for the large span parameter is within The interval span at the next iteration; The parameter range for the large span parameter is within The interval span during the next iteration.

[0018] A further technical solution of the present invention is that the expression of the objective function is:

[0019] In the formula, Represents the objective function value; This represents the total number of samples in the experiment. Indicating the first in the test data One equivalent stress test value; Indicates the first One equivalent stress prediction value.

[0020] A further technical solution of the present invention is that the global optimization method adopts the Bayesian optimization algorithm.

[0021] A second aspect of the present invention provides a fault physical model parameter identification system based on adaptive parameter range iteration, comprising: The model parameter set module is used to determine the model parameters of the fault physical model and set the parameter value range for each model parameter; the model parameters are sampled based on the parameter value range to obtain the model parameter set; The parameter sensitivity index value sequence module is used to perform correlation analysis between each model parameter in the model parameter set and the equivalent stress value output by the fault physical model to obtain the Spearman rank correlation coefficient corresponding to each model parameter, and use the Spearman rank correlation coefficient as the parameter sensitivity index value to obtain the parameter sensitivity index value sequence. The global sensitivity index value sequence module is used to identify the model parameters corresponding to the absolute values ​​of parameter sensitivity index values ​​that are greater than a preset threshold as key model parameters and obtain a set of key model parameters; it performs Sobol sequence sampling on the key model parameters in the set of key model parameters and combines it with variance decomposition to obtain the global sensitivity index values ​​of the key model parameters and obtain the global sensitivity index value sequence. The parameter value range update module is used to determine the consistency between the sorting results of the parameter sensitivity index value sequence and the global sensitivity index value sequence. If the sorting results are consistent, the current parameter value range is used as the target parameter value range. If the sorting results are inconsistent, the parameter value range is adaptively shrunk to obtain the updated parameter value range. The updated parameter value range is used for the next iteration until the sorting results of the parameter sensitivity index value sequence and the global sensitivity index value sequence are consistent. Then, the updated parameter value range is used as the target parameter value range. The model parameter optimization module is used to input strain test values ​​into the fault physics model to obtain equivalent stress prediction values, construct an objective function based on the equivalent stress prediction values ​​and equivalent stress test values, select model parameters within the range of objective parameter values, optimize the model parameters with the objective function as the goal and a global optimization method, and take the model parameters corresponding to the minimum objective function as the optimal model parameters.

[0022] The beneficial effects of this invention are: This invention obtains parameter sensitivity index value sequences and global sensitivity index value sequences through various sensitivity analysis methods. Based on these sequences, a parameter space convergence criterion based on sensitivity ranking consistency is constructed. This enables adaptive iterative shrinkage and dynamic updating of parameter value ranges based on the ranking consistency results. Furthermore, by combining experimental data and a global optimization algorithm, model parameters are efficiently searched and identified, thereby improving the stability, accuracy, and computational efficiency of parameter identification. Attached Figure Description

[0023] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0024] Figure 1 This is a flowchart illustrating a fault physical model parameter identification method based on adaptive parameter range iteration according to the present invention. Figure 2 This is a data distribution diagram of the model in an embodiment of the present invention; Figure 3 This is a graph showing the variation of the Spearman rank correlation coefficient with the number of samples in an embodiment of the present invention. Figure 4 This is a graph showing the relative difference of the Spearman rank correlation coefficient as a function of the sampling quantity in an embodiment of the present invention. Figure 5 This is a graph showing the results of Spearman global sensitivity analysis in an embodiment of the present invention; Figure 6 This is a graph showing the variation of the global sensitivity index value of Sobol with the number of samples in an embodiment of the present invention; Figure 7 This is a schematic diagram illustrating the interaction effects between key model parameters of the Anand model in this embodiment of the invention. Figure 8 This is a graph showing the uniaxial tensile test data of SAC305 under 125℃ conditions in an embodiment of the present invention. Figure 9 This is a schematic diagram of the iterative convergence process of the objective function under 125℃ conditions in an embodiment of the present invention; Figure 10 This is a comparison chart of predicted and experimental values ​​under the 125℃ operating condition in an embodiment of the present invention; Figure 11 This is a schematic diagram illustrating the prediction accuracy of the Anand model under a 125℃ operating condition in an embodiment of the present invention. Detailed Implementation

[0025] 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 embodiments of the present invention, and not all embodiments. 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.

[0026] An embodiment of the fault physical model parameter identification method based on adaptive parameter range iteration of the present invention is as follows: Figure 1 As shown, it includes: S1. Set the range of values ​​for the model parameters and sample the model parameters; Specifically, the model parameters of the fault physical model are determined, and the parameter value range of each model parameter is set; the model parameters are sampled based on the parameter value range to obtain the model parameter set.

[0027] For example, in one specific embodiment, model parameters are defined based on the meaning of model parameters and physical properties of the fault physical model, namely: The deformation impedance, an internal variable in the Anand model of fault physics, reflects the isotropic average resistance of the material to macroscopic plastic flow. It is related to effects such as dislocation density and grain coarsening, and is proportional to the equivalent stress, i.e.: (1) In the formula, This refers to the equivalent stress during plastic flow. It is the deformation impedance; Material parameters ( <1), Material parameters are related to temperature and strain rate, and the expression for material parameters is: (2) In the formula, For plastic strain rate, The coefficients are those of the exponential function. To activate energy, The strain rate sensitivity index For stress multipliers, It is the gas constant (8.314 J / (mol·K)). The absolute temperature. Under constant temperature and constant strain rate conditions, when plastic flow reaches its full potential, the equivalent plastic strain rate is approximately equal to the strain rate applied in the experiment, i.e. The Anand model unifies creep and rate-dependent plastic behavior through flow and evolution equations, and its flow equation can be expressed as: (3) In equation (3), note that the internal variables appear as the denominator in the stress term, and the relationship between strain rate and temperature satisfies the Arrhenius form. The evolution equation of the internal variables can be written in the following form: (4) (5) In the formula, the function The dynamic processes of strain hardening and recovery are defined; The deformation impedance evolution coefficient is used to control the deformation impedance. Towards saturation value The rate of evolution; The strain rate sensitivity index for deformation impedance evolution ( >1); Deformation resistance at constant temperature and strain rate saturation value; The deformation resistance saturation coefficient; The strain rate sensitivity is the saturation value; where, Deformation resistance The initial values ​​under the initial plastic strain condition, i.e. the initial values ​​of the deformation impedance, are used as the initial conditions for solving the internal variable evolution equation.

[0028] Under test conditions of given temperature and strain rate, the magnitude of the stress at which the deformation of a material reaches a steady state is defined as the saturation stress. That is, the plastic deformation rate is consistent with the loading rate, and at this time the deformation resistance is... Reaching saturation value Substituting equations (2) and (5) into equation (1), we can obtain the strain rate-saturation stress equation as follows: (6) Assuming saturation stress Taking the maximum value during the steady-state phase, then saturation stress and current stress Substituting into formula (4), we get: (7) Under constant temperature and constant strain rate test conditions, material parameters Since is a constant, substituting the above equation into formula (1) yields: (8) Integrating equation (8) yields the strain-stress relationship: (9) Material constants of the Anand model The expression (2) and saturation stress Substituting expression (6) into the inelastic strain-true stress relationship expression (9), we obtain the complete stress response formula, and the Anand model expression is: (10) Based on the mathematical expression of the Anand model, its complete set of parameters can be represented as: The response output of the Anand model is the equivalent stress. With plastic strain rate Constitutive relations between them, temperature As key environmental variables controlling material response under different temperature conditions, the model parameters determined in this embodiment are as follows: These nine parameters together determine the mechanical behavior of the solder during viscoplastic deformation.

[0029] For example, in one specific embodiment, this embodiment takes SAC305 material as the research object, and the parameters of each model are determined based on existing literature data and material test results as shown in Table 1.

[0030] Table 1

[0031] The parameter value ranges for the Anand model, as determined in Table 1, are shown in Table 2.

[0032] Table 2

[0033] For example, in one specific embodiment, the step of sampling model parameters based on the parameter value range to obtain a model parameter set is as follows: based on the parameter value range, the model parameters are sampled using LHS (Latin Hypercube Sampling) to obtain an initial model parameter set; outlier detection is performed on the initial model parameter set using IQR to remove outlier model parameters to obtain the final model parameter set. Specifically, in this embodiment, the sampling number k is set to [200, 400, 800, 1600, 3200, 6400, 12800, 25600, 51200]. The LHS sampling method is used to sample the model parameters of the Anand model of SAC305 solder within the parameter value range in Table 2, and the equivalent stress output by the Anand model is calculated. Taking a sampling number k=6400 as an example, the distribution of the model output equivalent stress prediction values ​​is as follows: Figure 2 As shown, the IQR-based data cleaning method cleans the samples obtained at various sampling sizes, effectively removing outliers caused by extreme parameter combinations or numerical simulation anomalies, ultimately yielding the parameter statistical distribution under different sampling times. Taking a sampling time k = 6400 as an example, the distribution range of the Anand model parameters is reasonable, with no obvious skewness or outlier concentration.

[0034] At this point, the model parameter set can be obtained.

[0035] S2. Obtain the parameter sensitivity index value sequence; Specifically, a correlation analysis is performed on the equivalent stress values ​​output by each model parameter in the model parameter set and the fault physical model to obtain the Spearman rank correlation coefficient corresponding to each model parameter. The Spearman rank correlation coefficient is then used as the parameter sensitivity index value, and a sequence of parameter sensitivity index values ​​is obtained. For example, in one specific embodiment, based on the model parameter set obtained in S2, the Spearman rank correlation coefficient method is used to calculate the correlation between each model parameter in the model parameter set and the equivalent stress value output by the fault physical model, so as to obtain the Spearman rank correlation coefficient corresponding to each model parameter. The Spearman rank correlation coefficient is used as the parameter sensitivity index value, and the parameter sensitivity index value sequence can be obtained by sorting it in descending order.

[0036] Specifically, in this embodiment, based on the results at different sampling numbers k, the output Spearman rank correlation coefficient changes with the number of sampling numbers as follows: Figure 3 As shown. The difference in Spearman rank correlation coefficient between adjacent sampling numbers is defined as one group. The output shows the relative differences in the Spearman rank correlation coefficients for a total of 8 groups, as shown below. Figure 4 As shown in the figure. Based on the Spearman rank correlation coefficient calculation results, it can be seen that when the number of samplings k=6400 and the number of sampling groups is 6, the fluctuation range of the Spearman rank correlation coefficients of each parameter significantly decreases, and the relative differences all tend to be in a smaller range. Therefore, the convergent sampling number is determined to be 6400. The Spearman rank correlation coefficient under this sampling number is output as the parameter sensitivity index value of the Anand model, as shown in the figure. Figure 5 As shown, sorting the Spearman rank correlation coefficients in descending order yields the parameter sensitivity index value sequence of the model parameters. for: .

[0037] S3. Obtain the global sensitivity index value sequence; Specifically, the model parameters corresponding to the absolute values ​​of parameter sensitivity indexes that are greater than a preset threshold are taken as key model parameters, and a set of key model parameters is obtained. Sobol sequence sampling is performed on the key model parameters in the set of key model parameters, and the global sensitivity index values ​​of the key model parameters are obtained by combining variance decomposition, and a global sensitivity index value sequence is obtained.

[0038] For example, in one specific embodiment, the step of selecting the model parameters corresponding to the absolute values ​​of parameter sensitivity indexes that are greater than a preset threshold as key model parameters and obtaining the set of key model parameters is as follows: In this embodiment, the preset threshold is 0.1, that is, within the absolute value of the parameter sensitivity index... When the model parameters and output are at a certain statistical correlation, the impact of changes in the model parameters on the model response exceeds the range of random fluctuations. Therefore, the model parameters at this point are identified as the key model parameters, and the set of key model parameters is as follows: .

[0039] For example, in one specific embodiment, the steps of sampling key model parameters in the key model parameter set using Sobol sequences, obtaining global sensitivity index values ​​of key model parameters by combining variance decomposition, and obtaining the global sensitivity index value sequence are as follows: For the key model parameter set... The Sobol sequence sampling method was used for sampling, and the global sensitivity index of the key model parameters was calculated based on the variance decomposition method. The global sensitivity index was then sorted in descending order to obtain the global sensitivity index value sequence of the key model parameters. .

[0040] Using the Sobol sequence sampling method and combined with variance decomposition, the global sensitivity index value is obtained as a function of the number of samplings, as shown below. Figure 6 As shown in the figure. Based on this, the interaction effects between key parameters of the output model are as follows. Figure 7 As shown. According to Figure 6 and Figure 7 The interaction effect analysis reveals that the key model parameters in the Anand constitutive model do not act independently, but rather exhibit complex nonlinear coupling relationships. Specifically, for SAC305 lead-free solder, the initial value of the deformation impedance... It is the core of the interaction, and it is related to the activation energy term. and stress multipliers The second-order interaction sensitivity indices reached 0.13 and 0.11, respectively, indicating that there is a strong nonlinear cooperative mechanism among the parameters, and that the mechanical response is constrained by both temperature and stress parameters.

[0041] S4. Obtain the range of target parameter values ​​when the sorting results of the parameter sensitivity index value sequence and the global sensitivity index value sequence are consistent. Specifically, the consistency between the sorting results of the parameter sensitivity index value sequence and the global sensitivity index value sequence is determined. If the sorting results are consistent, the current parameter value range is taken as the target parameter value range. If the sorting results are inconsistent, the parameter value range is adaptively shrunk to obtain the updated parameter value range. The updated parameter value range is used in the next iteration until the sorting results of the parameter sensitivity index value sequence and the global sensitivity index value sequence are consistent. Then, the updated parameter value range is taken as the target parameter value range.

[0042] For example, in one specific embodiment, the step of determining the consistency of the sorting results of the parameter sensitivity index value sequence and the global sensitivity index value sequence is as follows: by comparing the consistency of the sorting results of the parameter sensitivity index value sequence obtained by the Spearman method in step S3 and the global sensitivity index value sequence obtained by the Sobol method in step S4, the consistency of the sorting results is used as the parameter space convergence criterion; when the sorting results are consistent, i.e. When the sorting results are consistent, the parameter space converges. If the sorting results are inconsistent, the parameter space has not converged. It should be noted that in this embodiment, when comparing consistency, only the sorting of key model parameters is compared.

[0043] For example, in one specific embodiment, the step of adaptively shrinking the parameter value range to obtain the updated parameter value range is as follows: obtaining the interval span ratio corresponding to the parameter value range of each model parameter; dividing the model parameters into large-span parameters and regular-span parameters according to the interval span ratio and the span ratio threshold; when the model parameter is a regular-span parameter, using the arithmetic center of the parameter value range corresponding to the regular-span parameter as the shrinkage center; the interval span of the parameter value range corresponding to the regular-span parameter is the difference between the upper limit and the lower limit of the parameter value range; When the model parameters are large-span parameters, the parameter value range of the large-span parameter is mapped to the logarithmic space, and the geometric center is used as the contraction center of the parameter value range corresponding to the large-span parameter; the interval span of the parameter value range of the large-span parameter is the difference between the logarithm of the upper limit and the logarithm of the lower limit of the parameter value range; a contraction factor is introduced, and the updated parameter value range is obtained based on the contraction factor, the contraction center, and the interval span of the parameter value range of each model parameter.

[0044] Among them, if At that time, with the first Current range of model parameters Taking adaptive shrinkage adjustment as an example: No. The ratio of the range of values ​​for each model parameter is: (11) Set the span ratio threshold as When the first The upper and lower limits of the parameter ranges for each model are relatively close, i.e. At that time, it was believed that the first The model parameters belong to the conventional span parameters, and the range of values ​​for these conventional span parameters can be approximated linearly within the original parameter space; when At that time, it was believed that the first The model parameters are large-span parameters, with values ​​spanning multiple orders of magnitude. If a uniform linear shrinkage is applied in the original space, it can easily lead to imbalance in interval shrinkage and even cause a shift in the effective search region of the parameters. Therefore, two update methods are used for the parameter value ranges of the two types of model parameters: linear space shrinkage and logarithmic space shrinkage, respectively, to balance shrinkage efficiency and numerical stability.

[0045] In the When each model parameter is a regular span parameter, the arithmetic center of its current parameter value range is taken as the contraction center, that is: (12) In the formula, Indicates the first The contraction center corresponding to the conventional span parameter under round iteration; Indicates the first The upper limit of the range of values ​​for each model parameter when it is a conventional span parameter; Indicates the first The lower limit of the parameter value range when each model parameter is a conventional span parameter. The width of the range of values ​​for the standard span parameter is: (13) In the formula, Indicates the first The interval width corresponding to the conventional span parameter under round iteration; Introducing contraction factor If the standard span parameter is a key model parameter, then For regular span parameters that are not critical model parameters, then... This allows us to focus on a more representative region within the parameter's value range. Therefore, the updated interval width is: (14) In the formula, Indicates the first The interval width corresponding to the conventional span parameter under round iteration; Then the first The parameter range for the conventional model under round iteration is: (15) In the formula, Indicates the standard span parameter in The range of parameter values ​​during the next iteration; In the When a model parameter is a large-span parameter, the geometric center of its current parameter value range is taken as the contraction center, that is: (16) In the formula, Indicates the first The contraction center corresponding to the large span parameter under round iteration.

[0046] The width of the logarithmic space interval is defined as: (17) The updated logarithmic space width is: (18) Thus, the first t Parameter range under +1 iteration: (19) In the formula, in the formula, Indicates the large span parameter in The range of parameter values ​​during the next iteration; Indicates the first The contraction center corresponding to the model parameters being large-span parameters; The parameter range for the large span parameter is within The interval span during the next iteration.

[0047] To ensure the effectiveness of the iterative process, a minimum width constraint is set based on the range of values ​​for each model parameter. That is, when the updated interval width is less than the width constraint. When that happens, stop further shrinking of the parameter and maintain its current parameter value range for subsequent sampling and analysis.

[0048] (20) The updated parameter value range is used in the next iteration. The process returns to the consistency of the sorting results of the parameter sensitivity index value sequence and the global sensitivity index value sequence until the parameter space convergence criterion is met. Then the target parameter value range that meets the space convergence criterion can be obtained.

[0049] The target parameter value range in this embodiment is shown in Table 3.

[0050] Table 3

[0051] S5. Obtain the optimal model parameters; Specifically, strain test values ​​are input into the fault physics model to obtain equivalent stress prediction values. An objective function is constructed based on the equivalent stress prediction values ​​and equivalent stress test values. Model parameters are selected within the range of objective parameter values. The model parameters are optimized using a global optimization method with the objective function as the goal. The model parameters corresponding to the minimum objective function are taken as the optimal model parameters.

[0052] For example, in one specific embodiment, the step of constructing the objective function is as follows: the root mean square error (RMSE) between the predicted equivalent stress value and the experimental equivalent stress value is used as the objective function, and the expression of the objective function is: (twenty one) In the formula, Represents the objective function value; This represents the total number of samples in the experiment. Indicating the first in the test data One equivalent stress test value; Indicates the first One equivalent stress prediction value.

[0053] For example, in this embodiment, under the constraint of the objective function, the model parameters are optimized using a global optimization method with the objective function as the minimum. The model parameters corresponding to the minimum objective function are taken as the optimal model parameters. The Anand model contains nine mutually coupled nonlinear model parameters used to describe the flow stress response, strain rate sensitivity, and internal state variable evolution of the solder. Its parameter identification belongs to a high-dimensional nonlinear parameter inversion problem. Since the model response is highly sensitive to changes in model parameters, and the objective function exhibits multi-peak characteristics, traditional gradient-based optimization methods are prone to getting trapped in local optima in this type of problem, making it difficult to obtain the global optimal solution. Therefore, in this embodiment, the global optimization method employs Bayesian optimization (BO) to achieve efficient global optimization of parameters within the optimized parameter space, improving the accuracy and stability of parameter identification.

[0054] This embodiment uses SAC305 lead-free solder as the research object. Mechanical response data under different temperatures and strain rates were obtained based on uniaxial tensile tests. The experimental data were then processed and analyzed to serve as input data for the Anand model parameter identification. Taking the 125℃ condition as an example, the uniaxial tensile curves under different strain rate conditions are shown below. Figure 8 As shown.

[0055] First, within the range of target parameter values, several sets of model parameters are generated using the LHS sampling method, and the objective function value of the Anand model based on these parameters is calculated to construct the initial parameter-error mapping relationship. In subsequent iterations, the algorithm continuously generates new combinations of model parameters based on the sampling function and gradually approximates the optimal solution by updating the posterior distribution. The convergence process of the objective function is as follows: Figure 9 As shown. By Figure 9As can be seen, in the initial stage (the first 100 iterations), the parameter values ​​fluctuate significantly, indicating that the algorithm mainly explores the global solution. After approximately 150-250 iterations, the parameters gradually stabilize, and the objective function value decreases rapidly. After approximately 350 iterations, both the parameters and the objective function reach a stable state, indicating that the algorithm has converged and obtained the global optimum. The optimal combination of model parameters for the Anand model is shown in Table 4.

[0056] Table 4

[0057] Substituting the model parameters from Table 4 under the 125℃ condition into the Anand model, numerical calculations were performed under the same temperature and strain rate conditions as the experiment to obtain the predicted equivalent stress values, which were then compared with the corresponding experimental equivalent stress values. Figure 10 As shown in the figure, the comparison results show that the equivalent stress predictions of the Anand model are in good agreement with the experimental equivalent stress values, and can accurately reflect the mechanical response characteristics of the material.

[0058] To further quantitatively evaluate the ability of the Anand model to describe the true stress-plastic strain relationship of SAC305 solder under different temperature and strain rate conditions, goodness of fit is introduced as an evaluation index, including goodness of fit under a single strain rate condition. and the overall goodness of fit for all operating conditions at the corresponding temperature .

[0059] Goodness of fit of single strain rate Defined as: (twenty two) In the formula, For the first Number of experimental data points under the strain rate group; For the first i Equivalent stress test values ​​at each sampling point; For the first Predicted equivalent stress values ​​for each sampling point; This is the arithmetic mean of the equivalent stress test values ​​in the equivalent stress test value curve.

[0060] Overall goodness of fit under all operating conditions Defined as: (twenty three) In the formula, M This represents the total number of strain rate groups at this temperature. This represents the global average stress value for all experimental data points at this temperature.

[0061] Used to determine the local performance of the model at a specific loading rate, avoiding local fitting bias caused by different data volumes; These are used to evaluate the model's overall ability to fit the viscoplastic behavior. The closer the values ​​of the two evaluation indicators mentioned above are to 1, the higher the consistency between the model's predictions and the experimental data, and the better the accuracy of the parameter identification results.

[0062] The goodness of fit of the single strain rate of SAC305 solder at 125℃ was calculated using formula (22). The results are shown in Table 5. The overall goodness of fit for all working conditions was calculated using formula (23). The result is as follows Figure 11 As shown.

[0063] Table 5

[0064] The fitting results show that the Anand model parameters obtained by the fault physics model parameter identification method based on adaptive parameter range iteration have a goodness of fit to a single strain rate under the 125℃ condition. and overall goodness of fit under all working conditions All parameters reached a high level (generally exceeding 0.95), indicating good consistency between the model predictions and experimental data. Comprehensive analysis shows that the identified parameters not only mathematically achieve an effective fit to the experimental data but also physically reasonably characterize the viscoplastic deformation behavior of the solder under different working conditions, including steady-state flow characteristics under high temperature and high strain rate conditions, and initial yielding and transient hardening processes under low temperature and low strain rate conditions. Therefore, the parameter identification method based on adaptive parameter range iteration proposed in this embodiment can effectively improve the accuracy and stability of parameter identification, reduce fitting deviation problems caused by unreasonable parameter search ranges, and verify the rationality and effectiveness of the method.

[0065] An embodiment of a fault physics model parameter identification system based on adaptive parameter range iteration includes: a model parameter set module, a parameter sensitivity index value sequence module, a global sensitivity index value sequence module, a parameter value range update module, and a model parameter optimization module. The model parameter set module determines the model parameters of the fault physics model and sets the parameter value range for each model parameter; it samples the model parameters based on the parameter value range to obtain a model parameter set. The parameter sensitivity index value sequence module performs correlation analysis between each model parameter in the model parameter set and the equivalent stress value output by the fault physics model to obtain the Spearman rank correlation coefficient corresponding to each model parameter, and uses the Spearman rank correlation coefficient as the parameter sensitivity index value, obtaining a parameter sensitivity index value sequence. The global sensitivity index value sequence module identifies the model parameters whose absolute values ​​of parameter sensitivity index values ​​are greater than a preset threshold as key model parameters, obtaining a set of key model parameters; and it performs Sob analysis on the key model parameters in the key model parameter set. The algorithm performs OL sequence sampling and variance decomposition to obtain global sensitivity index values ​​for key model parameters, and acquires a global sensitivity index value sequence. The parameter value range update module determines the consistency between the ranking results of the parameter sensitivity index value sequence and the global sensitivity index value sequence. If the ranking results are consistent, the current parameter value range is used as the target parameter value range. If the ranking results are inconsistent, the parameter value range is adaptively shrunk to obtain an updated parameter value range, which is used in the next iteration until the ranking results of the parameter sensitivity index value sequence and the global sensitivity index value sequence are consistent. Then, the updated parameter value range is used as the target parameter value range. The model parameter optimization module inputs strain test values ​​into the fault physics model to obtain equivalent stress prediction values. An objective function is constructed based on the equivalent stress prediction values ​​and equivalent stress test values. Model parameters are selected within the target parameter value range, and the model parameters are optimized using a global optimization method with the objective function as the minimum. The model parameters corresponding to the minimum objective function are taken as the optimal model parameters.

[0066] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for identifying fault physical model parameters based on adaptive parameter range iteration, characterized in that, include: Determine the model parameters of the physical model of the fault, and set the parameter value range for each model parameter; The model parameter set is obtained by sampling the model parameters based on the parameter value range; Correlation analysis was performed on the equivalent stress values ​​output by each model parameter in the model parameter set and the fault physical model to obtain the Spearman rank correlation coefficient corresponding to each model parameter. The Spearman rank correlation coefficient was used as the parameter sensitivity index value, and the parameter sensitivity index value sequence was obtained. The model parameters corresponding to the absolute values ​​of parameter sensitivity indexes that are greater than a preset threshold are taken as key model parameters, and a set of key model parameters is obtained. Sobol sequence sampling is performed on the key model parameters in the set of key model parameters, and the global sensitivity index values ​​of the key model parameters are obtained by combining variance decomposition, and a global sensitivity index value sequence is obtained. The system determines the consistency between the sorting results of the parameter sensitivity index value sequence and the global sensitivity index value sequence. If the sorting results are consistent, the current parameter value range is used as the target parameter value range. If the sorting results are inconsistent, the parameter value range is adaptively shrunk to obtain an updated parameter value range. The updated parameter value range is used in the next iteration until the sorting results of the parameter sensitivity index value sequence and the global sensitivity index value sequence are consistent. Then, the updated parameter value range is used as the target parameter value range. The strain test values ​​are input into the fault physics model to obtain the equivalent stress prediction value, and the objective function is constructed based on the equivalent stress prediction value and the equivalent stress test value. Model parameters are selected within the range of target parameter values. The objective function is minimized, and the model parameters are optimized using a global optimization method. The model parameters corresponding to the minimum objective function are taken as the optimal model parameters.

2. The fault physical model parameter identification method based on adaptive parameter range iteration according to claim 1, characterized in that, The model parameters of the fault physics model include: initial value of deformation impedance, activation energy term, exponential function coefficient, stress multiplier, strain rate sensitivity index, deformation impedance evolution coefficient, deformation impedance saturation coefficient, and strain rate sensitivity index of deformation impedance evolution.

3. The fault physical model parameter identification method based on adaptive parameter range iteration according to claim 1, characterized in that, The steps for sampling model parameters based on their value range to obtain the model parameter set are as follows: Based on the parameter value range, the initial model parameter set is obtained by sampling the model parameters using LHS sampling; IQR is used to detect outliers in the initial model parameter set to remove outlier model parameters and obtain the final model parameter set.

4. The fault physical model parameter identification method based on adaptive parameter range iteration according to claim 1, characterized in that, The Spearman rank correlation coefficient method was used to analyze the correlation between each model parameter in the model parameter set and the equivalent stress value output by the fault physical model to obtain the Spearman rank correlation coefficient corresponding to each model parameter.

5. The fault physical model parameter identification method based on adaptive parameter range iteration according to claim 1, characterized in that, The steps to adaptively shrink the parameter value range to obtain the updated parameter value range are as follows: Obtain the interval span ratio corresponding to the parameter value range of each model parameter; Based on the interval span ratio and the span ratio threshold, the model parameters are divided into large span parameters and regular span parameters; When the model parameters are conventional span parameters, the arithmetic center of the parameter value range corresponding to the conventional span parameters is used as the contraction center; The range of values ​​for a standard span parameter is the difference between the upper and lower limits of that parameter's range. When the model parameter is a large-span parameter, the parameter value range of the large-span parameter is mapped to the logarithmic space, and the geometric center is used as the contraction center of the parameter value range corresponding to the large-span parameter. The range of values ​​for a large span parameter is the difference between the logarithm of the upper limit and the logarithm of the lower limit of the parameter's range. A contraction factor is introduced, and the updated parameter value range is obtained based on the contraction factor, the contraction center, and the interval span of the parameter value range of each model parameter.

6. The fault physical model parameter identification method based on adaptive parameter range iteration according to claim 5, characterized in that, The steps for dividing model parameters into large-span parameters and regular-span parameters based on the interval span ratio and span ratio threshold are as follows: If the interval span ratio is greater than the span ratio threshold, the model parameters will be treated as large span parameters; If the interval span ratio is less than or equal to the span ratio threshold, the model parameters will be used as regular span parameters.

7. The fault physical model parameter identification method based on adaptive parameter range iteration according to claim 1, characterized in that, The steps to obtain the updated parameter value range based on the contraction factor, contraction center, and the interval span of the parameter value range for each model parameter are as follows: The updated range of values ​​for the standard span parameter is as follows: In the formula, Indicates the standard span parameter in The range of parameter values ​​during the next iteration; Indicates the first The contraction center corresponding to the conventional span parameter under round iteration; Indicates the first The interval width corresponding to the conventional span parameter under round iteration; Indicates the first The interval width corresponding to the conventional span parameter under round iteration; The updated parameter value range for the large span is as follows: In the formula, Indicates the large span parameter in The range of parameter values ​​during the next iteration; Indicates the first The contraction center corresponding to the model parameters being large-span parameters; The parameter range for the large span parameter is within The interval span at the next iteration; The parameter range for the large span parameter is within The interval span during the next iteration.

8. The fault physical model parameter identification method based on adaptive parameter range iteration according to claim 1, characterized in that, The expression for the objective function is: In the formula, Represents the objective function value; This represents the total number of samples in the experiment. Indicating the first in the test data One equivalent stress test value; Indicates the first One equivalent stress prediction value.

9. The fault physical model parameter identification method based on adaptive parameter range iteration according to claim 1, characterized in that, The global optimization method employs the Bayesian optimization algorithm.

10. A fault physical model parameter identification system based on adaptive parameter range iteration, characterized in that, include: The model parameter set module is used to determine the model parameters of the fault physical model and set the parameter value range for each model parameter. The model parameter set is obtained by sampling the model parameters based on the parameter value range; The parameter sensitivity index value sequence module is used to perform correlation analysis between each model parameter in the model parameter set and the equivalent stress value output by the fault physical model to obtain the Spearman rank correlation coefficient corresponding to each model parameter, and use the Spearman rank correlation coefficient as the parameter sensitivity index value to obtain the parameter sensitivity index value sequence. The global sensitivity index value sequence module is used to identify the model parameters corresponding to the absolute values ​​of parameter sensitivity index values ​​that are greater than a preset threshold as key model parameters and obtain a set of key model parameters; it performs Sobol sequence sampling on the key model parameters in the set of key model parameters and combines it with variance decomposition to obtain the global sensitivity index values ​​of the key model parameters and obtain the global sensitivity index value sequence. The parameter value range update module is used to determine the consistency between the sorting results of the parameter sensitivity index value sequence and the global sensitivity index value sequence. If the sorting results are consistent, the current parameter value range is used as the target parameter value range. If the sorting results are inconsistent, the parameter value range is adaptively shrunk to obtain the updated parameter value range. The updated parameter value range is used for the next iteration until the sorting results of the parameter sensitivity index value sequence and the global sensitivity index value sequence are consistent. Then, the updated parameter value range is used as the target parameter value range. The model parameter optimization module is used to input strain test values ​​into the fault physics model to obtain equivalent stress prediction values, and to construct an objective function based on the equivalent stress prediction values ​​and equivalent stress test values. Model parameters are selected within the range of target parameter values. The objective function is minimized, and the model parameters are optimized using a global optimization method. The model parameters corresponding to the minimum objective function are taken as the optimal model parameters.

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