Fusion model construction method and health assessment method

Abstract

The application provides a fusion model construction method and a health assessment method, and relates to the technical field of metal material life prediction. The fusion model construction method comprises: performing multiple independent random assignments on crack growth parameters to obtain multiple first expressions of each failure mechanism model; performing Bayesian updating on the prior probability of each first expression according to first measured data; calculating a second expression of each failure mechanism model according to the multiple first expressions and the posterior probability of each first expression; performing Bayesian updating on the prior probability of each second expression according to second measured data; and calculating a fusion model according to the multiple second expressions and the posterior probability of each second expression. The method of the application solves the problem that the inherent uncertainty of different failure mechanism models superimposed on the parameters of metal materials makes it difficult to ensure the accuracy of the fatigue life prediction method relying on the failure mechanism model.

Description

Technical Field

[0001] This application relates to the field of life prediction of metallic materials, and in particular to a method for integrating model construction and health assessment. Background Technology

[0002] During service, fatigue failure is the dominant failure mechanism for metallic materials in mechanical structures. This failure mode is insidious and dangerous because even if the cyclic load amplitude of the metallic material is generally lower than its yield strength threshold, fatigue damage can still accumulate unnoticed, eventually leading to a sudden failure event. Therefore, conducting accurate health assessments of metallic materials to prevent fatigue failure is particularly important.

[0003] In existing technologies, health assessments of metallic materials are primarily based on measured data. However, historical measured data for metallic materials typically reflects conditions before failure, with limited data available for materials nearing or already experiencing fatigue failure. Therefore, conducting health assessments based solely on measured data is challenging and cannot achieve high accuracy. Consequently, it is necessary to combine measured data with failure mechanism models to conduct health assessments of metallic materials.

[0004] However, the selection of failure mechanism models is highly dependent on the professional insights and accumulated experience of technical personnel, essentially belonging to a methodology system that deeply relies on domain knowledge. Differences in the depth of technical personnel's understanding of failure mechanisms, as well as differences in their experience in recognizing failure modes, directly affect the selection and application of failure mechanism models. The inherent uncertainties in the parameters of metallic materials, coupled with different failure mechanism models, make it difficult to guarantee the accuracy of health assessment methods based on failure mechanism models. Summary of the Invention

[0005] This application provides a method for integrating model construction and health assessment to address the problem that the accuracy of health assessment methods based on failure mechanism models is difficult to guarantee due to the inherent uncertainty of the parameters of metallic materials when different failure mechanism models are superimposed.

[0006] A first aspect of this application provides a method for constructing a fusion model, the method comprising:

[0007] Multiple crack growth parameters of each of the preset failure mechanism models are independently and randomly assigned multiple times to obtain the first expression of each failure mechanism model after each random assignment.

[0008] First measured data of the first fatigue crack in the target metallic material are obtained, and based on the first measured data, the prior probability of each preset first expression is updated using Bayesian method to obtain the posterior probability of each first expression; wherein, the first measured data is used to indicate the crack propagation of the first fatigue crack, and the prior probability and posterior probability of each first expression are used to indicate the ability of the corresponding first expression to describe the crack propagation.

[0009] Based on the multiple first expressions of each failure mechanism model and the posterior probability of the corresponding first expressions, the second expression of each failure mechanism model is calculated.

[0010] The second measured data of the second fatigue crack of the target metal material is obtained, and based on the second measured data, the prior probability of each preset second expression is updated by Bayes to obtain the posterior probability of each second expression.

[0011] Based on the second expression of each failure mechanism model and the posterior probability of the corresponding second expression, a fusion model is calculated to predict the fatigue life of the target metallic material.

[0012] In one possible design, the first measured data includes: the measured crack size of the target metal material in each of multiple first preset cycles, where the first target cycle is any one of the multiple first preset cycles; the first target expression is any one of multiple first expressions of the target failure mechanism model, where the target failure mechanism model is any one of multiple failure mechanism models;

[0013] For the first objective loop and the first objective expression, based on the first measured data, a Bayesian update is performed on the pre-defined prior probability of each first expression to obtain the posterior probability of each first expression, including:

[0014] Based on the first measured data, the first measured crack size of the target metal material in the first target cycle is obtained, and based on the first target expression, the first predicted crack size of the target metal material in the first target cycle is obtained.

[0015] Based on the error between the first predicted crack size and the first measured crack size, the first likelihood function of the first objective expression in the first objective loop is obtained;

[0016] Based on the first likelihood function, a Bayesian update is performed on the prior probability of the first objective expression in the first objective loop to obtain the posterior probability of the first objective expression in the first objective loop.

[0017] In one possible design, the prior probabilities of the multiple first expressions of the target failure mechanism model in the first loop follow a mean distribution; the likelihood functions of the multiple first expressions of the target failure mechanism model in the first target loop follow a normal distribution.

[0018] For the first target cycle and the target failure mechanism model, after performing a Bayesian update on the prior probability of the first target expression in the first target cycle based on the first likelihood function to obtain the posterior probability of the first target expression in the first target cycle, the method further includes:

[0019] The posterior probabilities of the multiple first expressions of the target failure mechanism model in the first target loop are normalized.

[0020] In one possible design, for a target failure mechanism model, based on multiple first expressions of each failure mechanism model and the posterior probability of the corresponding first expressions, a second expression for each failure mechanism model is calculated, including:

[0021] Based on the posterior probabilities of the multiple first expressions of the target failure mechanism model, the multiple crack growth parameters of each first expression of the target failure mechanism model are weighted and calculated to obtain the calculated value of each crack growth parameter.

[0022] Based on the calculated values ​​of multiple crack growth parameters, the second expression of the target failure mechanism model is obtained.

[0023] In one possible design, after calculating the second expression of each failure mechanism model based on multiple first expressions of each failure mechanism model and the posterior probability of the corresponding first expressions, the method further includes:

[0024] Obtain the third measured data for each of the multiple third fatigue cracks in the target metallic material; wherein the sampling time and / or sampling location of each third fatigue crack are different from those of the first fatigue crack;

[0025] Based on multiple third-party measured data, the parameters of the second expression for each failure mechanism model are updated.

[0026] In one possible design, the second measured data includes: the measured crack size of the target metal material in each of the multiple second preset cycles, where the second target cycle is any one of the multiple second preset cycles;

[0027] For the second objective loop, based on the second measured data, a Bayesian update is performed on the prior probability of each preset second expression to obtain the posterior probability of each second expression, including:

[0028] Based on the second measured data, the second measured crack size of the target metal material in the second target cycle is obtained, and based on multiple second expressions, the second predicted crack size of the target metal material in the second target cycle is obtained as predicted by each second expression.

[0029] Based on the error between each second predicted crack size and the second measured crack size, the second likelihood function of each second expression in the second objective loop is obtained;

[0030] Based on the second likelihood function of each second expression in the second objective loop, a Bayesian update is performed on the prior probability of each second expression in the second objective loop to obtain the posterior probability of each second expression in the second objective loop.

[0031] In one possible design, the prior probabilities of the multiple second expressions in the first loop follow a mean distribution; the errors of the multiple second expressions in the second target loop follow a normal distribution.

[0032] Based on the second likelihood function of each second expression in the second objective loop, and after performing a Bayesian update on the prior probability of each second expression in the second objective loop, the method further includes:

[0033] The posterior probabilities of the multiple second expressions in the second objective loop are normalized.

[0034] In one possible design, a fusion model is calculated based on the second expression of each failure mechanism model and the posterior probability of the corresponding second expression, including:

[0035] For the second objective loop, the segmented fusion model of the second objective loop is obtained by weighted calculation based on multiple second expressions and the posterior probability of the corresponding second expressions in the second objective loop.

[0036] A fusion model is obtained by fitting the segmented fusion model based on the segmented fusion model of each second preset cycle.

[0037] A second aspect of this application provides a health assessment method, the method comprising:

[0038] Obtain the fourth measured data of the fourth fatigue crack in the target metallic material; wherein, the fourth measured data includes: the initial crack size of the fourth fatigue crack;

[0039] Based on the fourth measured data and the pre-set fusion model, at least one of the multiple health assessment indicators of the target metallic material is evaluated; wherein, the fusion model is a model constructed by any of the fusion model construction methods in the first aspect; the multiple health assessment indicators include: fatigue life, reliability and crack size.

[0040] In one possible design, the evaluation results include: the predicted crack size of the target metallic material in each cycle;

[0041] Based on the fourth measured data and a pre-set fusion model, after evaluating at least one of multiple health assessment indicators of the target metallic material, the method further includes:

[0042] Based on the predicted crack size of the target metal material in each cycle and the preset prediction confidence level, a confidence interval is obtained; wherein, the confidence interval includes: the upper confidence crack size and the lower confidence crack size of the target metal material in each cycle.

[0043] A third aspect of this application provides a fusion model building apparatus, the apparatus comprising:

[0044] The random assignment module is used to perform multiple independent random assignments on multiple crack growth parameters of each of the preset failure mechanism models, so as to obtain the first expression of each failure mechanism model after each random assignment.

[0045] The first update module is used to acquire the first measured data of the first fatigue crack of the target metal material, and to perform Bayesian update on the prior probability of each preset first expression based on the first measured data to obtain the posterior probability of each first expression; wherein, the first measured data is used to indicate the crack propagation of the first fatigue crack, and the prior probability and posterior probability of each first expression are used to indicate the ability of the corresponding first expression to describe the crack propagation.

[0046] The first calculation module is used to calculate the second expression of each failure mechanism model based on multiple first expressions of each failure mechanism model and the posterior probability of the corresponding first expressions.

[0047] The second update module is used to acquire the second measured data of the second fatigue crack of the target metal material, and based on the second measured data, to perform Bayesian update on the prior probability of each preset second expression to obtain the posterior probability of each second expression.

[0048] The second calculation module is used to calculate the fusion model based on the second expression of each failure mechanism model and the posterior probability of the corresponding second expression, so as to predict the fatigue life of the target metallic material based on the fusion model.

[0049] A fourth aspect of this application provides a health assessment device, the device comprising:

[0050] The data acquisition module is used to acquire the fourth measured data of the fourth fatigue crack of the target metallic material; wherein, the fourth measured data includes: the initial crack size of the fourth fatigue crack;

[0051] The life prediction module is used to evaluate at least one of multiple health assessment indicators of the target metallic material based on the fourth measured data and the pre-set fusion model; wherein, the fusion model is a model constructed by the health assessment device of the third aspect; the multiple health assessment indicators include: fatigue life, reliability and crack size.

[0052] A fifth aspect of this application provides an electronic device, including: a memory, and a memory communicatively connected to a processor;

[0053] The memory stores the instructions that the computer executes;

[0054] When the processor executes computer execution instructions stored in memory, it is used to implement the fusion model construction method of any one of the first aspects, or the health assessment method of any one of the second aspects.

[0055] The sixth aspect of this application provides a computer-readable storage medium storing computer-executable instructions, which, when executed by a processor, are used to implement the fusion model construction method of any one of the first aspects, or the health assessment method of any one of the second aspects.

[0056] The seventh aspect of this application provides a computer program product, including a computer program, which, when executed by a processor, is used to implement the fusion model construction method of any one of the first aspects, or the health assessment method of any one of the second aspects.

[0057] This application provides a fusion model construction method and a health assessment method. The fusion model construction method includes: assigning multiple independent random values ​​to crack growth parameters to obtain multiple first expressions for each failure mechanism model; performing Bayesian updates on the prior probabilities of each first expression based on first measured data; calculating a second expression for each failure mechanism model based on the multiple first expressions and their posterior probabilities; performing Bayesian updates on the prior probabilities of each second expression based on second measured data; and calculating a fusion model based on the multiple second expressions and their posterior probabilities. This achieves the following technical effects: performing Bayesian updates on the prior probabilities of the multiple first expressions for each failure mechanism model solves the problem of uncertainty in multiple crack growth parameters of the failure mechanism model; performing Bayesian updates on the prior probabilities of the second expressions for each of the multiple failure mechanism models solves the problem that different failure mechanism models cannot be accurately applied to various objects and scenarios; and determining the likelihood function expression form through measured data and updating the parameters of the failure mechanism model through Bayesian updates improves the accuracy of fatigue life prediction. Attached Figure Description

[0058] To more clearly illustrate the technical solutions in this application 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 some embodiments of this application. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0059] Figure 1 A schematic diagram of a through-crack;

[0060] Figure 2 A schematic diagram of a multi-sided surface crack;

[0061] Figure 3 This is a schematic diagram of a crack with a single-sided surface crack.

[0062] Figure 4 A flowchart illustrating the fusion model construction method provided in this application embodiment. Figure 1 ;

[0063] Figure 5 A flowchart illustrating the fusion model construction method provided in this application embodiment. Figure 2 ;

[0064] Figure 6 A schematic diagram of the curve cluster of the Paris-Erdogan model provided in the embodiments of this application;

[0065] Figure 7 The prior cumulative probability distribution provided for the embodiments of this application Figure 1 ;

[0066] Figure 8 A comparison diagram of the posterior probability distribution and the state before the update provided in this application embodiment;

[0067] Figure 9 Comparison of post-hoc reliability with that before the update provided for embodiments of this application Figure 1 ;

[0068] Figure 10 A flowchart illustrating the fusion model construction method provided in this application embodiment. Figure 3 ;

[0069] Figure 11 A comparison chart of the fusion model, prediction model, and measured data provided in the embodiments of this application;

[0070] Figure 12 A schematic flowchart illustrating the health assessment method provided in this application embodiment;

[0071] Figure 13 A schematic diagram of the confidence intervals provided in the embodiments of this application;

[0072] Figure 14 The prior cumulative probability distribution provided for the embodiments of this application Figure 2 ;

[0073] Figure 15 A posterior probability distribution diagram provided for embodiments of this application;

[0074] Figure 16 Comparison of post-hoc reliability with that before the update provided for embodiments of this application Figure 2 . Detailed Implementation

[0075] Exemplary embodiments will now be described in detail, examples of which are illustrated in the accompanying drawings. When the following description relates to the drawings, unless otherwise indicated, the same numbers in different drawings denote the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with this application. Rather, they are merely examples of apparatuses and methods consistent with some aspects of this application as detailed in the appended claims.

[0076] In this application, the terms "first" and "second" are used to distinguish identical or similar items with substantially the same function and effect. Those skilled in the art will understand that the terms "first" and "second" do not limit the quantity or execution order, nor do they necessarily imply difference. It should be noted that in this application, the terms "exemplary" or "for example" are used to indicate examples, illustrations, or explanations. Any embodiment or design scheme described as "exemplary" or "for example" in this application should not be construed as being more preferred or advantageous than other embodiments or design schemes. Specifically, the use of "exemplary" or "for example" is intended to present the relevant concepts in a concrete manner. In this application, "at least one" means one or more, and "more than one" means two or more.

[0077] It should be noted that the phrase "at the moment when..." in this application can refer to the instant at which a certain situation occurs, or to a period of time after the occurrence of a certain situation; this application does not impose a specific limitation on this. Furthermore, the fusion model construction method and health assessment method provided in this application are merely examples, and the fusion model construction method and health assessment method may include more or less content.

[0078] To facilitate a clear description of the technical solution of this application, some of the terms and technologies involved in this application are briefly introduced below:

[0079] Fatigue failure refers to the phenomenon where the metallic materials of a mechanical structure, under cyclic loading below their yield strength, suddenly fracture or experience a significant decline in performance after prolonged cumulative damage. This failure mode is often difficult to detect in a timely manner, thus possessing both insidiousness and danger.

[0080] Failure mechanism model: This refers to a mathematical model or theoretical framework used to describe and predict fatigue failure of metallic materials under specific conditions. Based on factors such as the material's microstructure, mechanical properties, and loading conditions, the failure mechanism model can simulate and analyze the development process of fatigue damage, thereby predicting the material's fatigue life.

[0081] Domain knowledge refers to the professional knowledge, theories, methods, and experience accumulated within a specific discipline or professional field. Domain knowledge includes a deep understanding of the properties of metallic materials, fatigue damage mechanisms, failure analysis, and related experimental techniques and data processing methods.

[0082] Bayesian update is a method for updating the probability of an event or hypothesis after new information or data has been provided. Based on Bayesian inference, Bayesian update calculates the posterior probability by combining the prior probability with the likelihood function of the new information.

[0083] The likelihood function is a function that describes the probability of model parameters taking specific values ​​given observed data. It is commonly used to estimate model parameters by maximizing the likelihood function to find the parameter values ​​that best match the observed data.

[0084] The technical solutions of this application will be described in detail below with reference to specific embodiments. These specific embodiments can be combined with each other, and the same or similar concepts or processes may not be described again in some embodiments. The application will be described below with reference to the accompanying drawings. In order to clearly understand the technical solutions of this application, the solutions of the prior art will be described in detail first.

[0085] In recent years, with the development of science and technology, the application of mechanical structures in various industries has become widespread. Many complex tasks in real life require the cooperation of mechanical structures and technicians, or the mechanical structure itself, to complete the task. In such cases, the requirements for the reliability and lifespan of mechanical structures are becoming increasingly stringent. Especially for mechanical structures operating in extreme environments, with harsh operating conditions, difficult maintenance and support, complex functional structures, and diverse operating conditions, these structures are prone to functional or performance degradation, and may even lead to failure with serious consequences. Therefore, how to conduct health status assessments for mechanical structures is currently a key research focus.

[0086] Metallic materials in mechanical structures are one research area. During service, fatigue failure is the dominant failure mechanism for metallic materials. This failure mode is insidious and dangerous because even if the cyclic load amplitude of the metallic material is generally below its yield strength threshold, fatigue damage can still accumulate unnoticed, eventually leading to a sudden failure event. Therefore, conducting accurate health assessments of metallic materials—that is, predicting the number of stress or strain cycles experienced before fatigue failure, the crack size under operating loads, and the current reliability level—is particularly important.

[0087] Based on the health assessment method of failure mechanism model, and with the help of condition monitoring, condition evaluation and measured data of metallic materials, it is possible to comprehensively judge the current health status of metallic materials, and further predict key indicators such as the evolution trend of their structural performance, the time of failure initiation, the remaining service life and the level of reliability.

[0088] In existing technologies, health assessments of metallic materials are primarily based on measured data. However, historical measured data for metallic materials typically reflects conditions before failure, with limited data available for materials nearing or already experiencing fatigue failure. Therefore, conducting health assessments based solely on measured data is challenging and cannot achieve high accuracy. Consequently, it is necessary to combine measured data with failure mechanism models to conduct health assessments of metallic materials.

[0089] A fault prediction and maintenance planning method based on global Bayesian update includes the following steps:

[0090] S101. Establish a lifetime prediction model based on nonlinear Wiener processes;

[0091] S102. Based on the parameters in the global Bayesian life prediction model, establish a dynamic predictive maintenance strategy for the equipment.

[0092] S103. Calculation of the cost rate function based on the renewal-return theory;

[0093] S104. Optimization solution of the prediction and maintenance model based on genetic algorithm, that is, using the Genetic Algorithm (GA) toolbox in MATLAB to solve for the lowest expected cost rate and the optimal combination of model parameters.

[0094] However, this method has the following problems: The parameter update step requires historical information and real-time monitoring data to derive online and offline parameters. This necessitates that technicians possess certain practical experience, such as how to select sensor models, how to deploy sensors on experimental equipment, and how to send and process sensor data.

[0095] Another method for assessing the health of alloy materials based on crack propagation rate includes the following steps:

[0096] S201. Use a continuous piecewise log-linear crack propagation rate model to describe the crack propagation rate data of the alloy.

[0097] S202. Introduce the Herveside step function and the magnitude of the transformation stress intensity factor into the classical Paris model to establish a continuous piecewise model;

[0098] S203. Crack propagation experiments were conducted on titanium alloy materials manufactured by electric arc additive manufacturing to obtain crack propagation rate data of alloy material specimens.

[0099] S204. Perform statistical analysis on the experimental results to verify the accuracy of the model's prediction results.

[0100] However, this method has the following problems: When used for fatigue life prediction of titanium alloys, the material manufacturing process requires technicians to have sufficient physical background knowledge of the analyzed object. Furthermore, using the damage tolerance method for fatigue life prediction and improving a single mechanism model is affected by manufacturing process parameters, meaning a single mechanism model cannot fully describe the actual crack propagation. Therefore, health assessment methods relying on failure mechanism models depend on the professional insights and experience of technicians, essentially belonging to a methodological system deeply dependent on domain knowledge. Differences in the depth of technicians' understanding of failure mechanisms and their experience in recognizing failure modes directly affect the selection and application of failure mechanism models. For example, when predicting the fatigue life of metallic materials, upon detecting an initial crack, the geometric and stress characteristics of the cracked structure and the crack propagation can be analyzed based on the damage location determined by the initial crack, and a suitable structural damage mechanism model, such as the Paris-Erdogan model, the Trantina-Johnson model, or the Forman model, can be selected. Then, using prior knowledge and measured data, the parameters of the selected failure mechanism model are updated and corrected in real time. Real-world engineering structures are typically complex, involving multiple stages such as raw material selection, processing and manufacturing, and installation and commissioning. Numerous parameters are involved, requiring consideration of the uncertainties inherent in the parameters of the metallic materials themselves. Furthermore, different metallic materials exhibit different fatigue behaviors and corresponding fatigue mechanisms, making it impossible for a single failure mechanism model to encompass all crack propagation scenarios. Therefore, existing technologies suffer from the problem of combining different failure mechanism models with the inherent uncertainties of the metallic material's parameters, leading to difficulties in guaranteeing the accuracy of health assessment methods based on failure mechanism models.

[0101] Therefore, to address the aforementioned technical problems, this research found that a multi-model fusion approach can be applied to fatigue life prediction, proposing a health assessment method based on a fusion model. Specifically, based on the aforementioned multiple failure mechanism models and measured data, a fusion model that closely approximates or matches the measured data is constructed, and this model is used to handle various uncertainties in fatigue life prediction. The fusion model can output a prediction curve that conforms to actual crack propagation, provide predictions of crack size distribution under corresponding cycles, and life prediction results with corresponding confidence limits.

[0102] Based on the above-mentioned inventive discovery, the technical solution of this application is proposed.

[0103] The following section introduces the application scenarios of the fusion model construction method and health assessment method provided in this application.

[0104] The fusion modeling and health assessment methods are applied to predict center cracks in finite-width plates. Based on Bayesian inference and failure mechanism models, various uncertainties in fatigue life prediction can be addressed. Taking the classic Paris-Erdogan model as an example, the crack propagation rate of the Paris-Erdogan model is shown in the following equation:

[0105]

[0106] Where a is the crack size, N is the number of cycles, Δk is the stress intensity factor, and c and m are crack growth parameters. Randomization of c and m reflects the inherent uncertainty of the metallic material, the initial crack size a0 reflects the uncertainty of the initial crack measurement, and randomization of Δk reflects the uncertainty of the load. The formula for calculating Δk is:

[0107]

[0108] Where β is a correction factor, and the formula for calculating β differs for different crack locations and stresses; Δσ k This represents the change in stress acting on a plate of finite width.

[0109] Figure 1 This is a schematic diagram of a through-crack. (Example) Figure 1 As shown, a penetrating crack is a crack that runs through the entire thickness of a finite-width plate. This type of crack is generally considered a serious defect because it severely affects the strength and durability of the component. When the crack is a penetrating crack, the formula for calculating β is:

[0110]

[0111] Among them, β=1.00 (a<<h), σ=6M / bh 2 b is the plate thickness, and h is half the plate width.

[0112] Figure 2 This is a schematic diagram of a multi-sided surface crack. (Example) Figure 2 As shown, multi-sided surface cracks refer to cracks that appear on multiple surfaces of a finite-width plate. These cracks do not completely penetrate the finite-width plate in the thickness direction, but may connect or be close to each other on multiple sides. When the crack is a multi-sided surface crack, the formula for calculating β is:

[0113]

[0114] Among them, β=1.12 (a<<h).

[0115] Figure 3 This is a schematic diagram of a crack with a single-sided surface crack. (Example:) Figure 3 As shown, a one-sided surface crack refers to a crack that appears only on one surface of a finite-width plate, and this type of crack does not completely penetrate the finite-width plate in the thickness direction. When the crack is a one-sided surface crack, the formula for calculating β is:

[0116]

[0117] Among them, β=1.12 (a<<h).

[0118] Given the initial crack size a0 and the measured crack size a N When the loop count N is reached, the formula for calculating the corresponding number of loops is:

[0119]

[0120] Crack size a corresponding to the number of cycles N N The calculation formula is:

[0121]

[0122] The embodiments of this application are described below with reference to the accompanying drawings.

[0123] Figure 4 A flowchart illustrating the fusion model construction method provided in this application embodiment. Figure 1 .like Figure 4 As shown in the embodiments of this application, the executing entity can be a fusion model building device, which can be located in an electronic device, and this device can be a data processing server. The fusion model building method provided in the embodiments of this application includes the following steps:

[0124] S301. For each of the preset multiple failure mechanism models, multiple crack growth parameters are independently and randomly assigned multiple times to obtain the first expression of each failure mechanism model after each random assignment.

[0125] Specifically, in experimental settings, the crack growth parameters c and m of the failure mechanism model are typically measured under experimental conditions. However, due to the differences between actual use of mechanical structures and experimental environments, the c and m obtained from experimental settings cannot fully reflect the actual situation and contain uncertainties. Therefore, c and m are assigned multiple independent random values.

[0126] Taking a failure mechanism model as an example, each random assignment of values ​​to c and m yields a first expression for the model; performing n independent random assignments yields n first expressions for the model. Correspondingly, for multiple failure mechanism models, performing n independent random assignments yields ∑n first expressions.

[0127] S302. Obtain the first measured data of the first fatigue crack in the target metallic material.

[0128] Specifically, the first measured data is used to indicate the crack propagation of the first fatigue crack. Based on this first measured data, the initial crack size of the first fatigue crack can be determined. Based on the initial crack size, ∑n fatigue life prediction curves, i.e., aN curves, can be obtained for each of the first expressions. Bayesian inference assumes that the uncertainties of c and m both follow a certain probability distribution, thus making the prediction more accurate. In existing technologies, the determination of prior data is usually based on experimental tests, past statistical data, and the professional insights and experience of technical personnel. When sufficient measured data is lacking, a uniform distribution can be assumed. Then, for each failure mechanism model, the probability that each aN curve is the actual crack growth curve is equal, all being 1 / n. These ∑n aN curves constitute the prior data for Bayesian inference; therefore, based on the first measured data, Bayesian updates can be performed on these prior data.

[0129] S303. Based on the first measured data, perform Bayesian update on the prior probability of each preset first expression to obtain the posterior probability of each first expression.

[0130] Specifically, for each aN curve, the Bayesian inference calculation formula is as follows:

[0131]

[0132] Wherein, P(aN) is the prior probability of each aN curve, and its value is 1 / n in the first loop; P(measured data | aN curve) is the likelihood function, P(measured data) is a constant term closely related to the first measured data; P(aN | measured data) is the posterior probability of each aN curve. The prior and posterior probabilities of each first expression are used to indicate the ability of the corresponding first expression to describe the crack propagation.

[0133] For each failure mechanism model, the sum of the probabilities that the multiple aN curves of the model are the actual crack propagation curves is equal to 1. Therefore, P (measured data) is a constant related to the first measured data and does not need to be calculated to a specific value. When the prior probability (i.e., 1 / n) of the aN curve is known, the first measurement is performed to obtain the initial crack size. The posterior probability of the aN curve can be obtained by Bayesian update.

[0134] When conducting another test, the first posterior probability of the aN curve can be used as the prior probability of the second test. A Bayesian update then yields the posterior probability of the second test. By continuously conducting tests and updating the aN curve with Bayesian methods, the probability of actual crack propagation can be continuously increased, resulting in a more reasonable fatigue prediction.

[0135] S304. Based on the multiple first expressions of each failure mechanism model and the posterior probability of the corresponding first expressions, calculate the second expression of each failure mechanism model.

[0136] Specifically, after performing a Bayesian update to obtain the posterior probability of each aN curve, the mean μ of c can be calculated. c , and the mean μ of m m The calculation formula is:

[0137] μ c =∑cP(c)

[0138] μ m =∑mP(m)

[0139] Where P(c) and P(m) represent the posterior probabilities of c and m for each aN curve, respectively. The μ of each failure mechanism model... c c, as the second expression of the model, and μ of each failure mechanism model m , where m is the second expression of the model, can be used to obtain the second expression of each failure mechanism model.

[0140] S305. Obtain the second measured data of the second fatigue crack in the target metallic material.

[0141] Specifically, the second measured data is used to indicate the crack propagation of the second fatigue crack. Based on the second measured data, the initial crack size of the second fatigue crack can be determined. The sampling time and / or sampling location of the second fatigue crack are different from those of the first fatigue crack.

[0142] Based on the initial crack size from the second measured data, aN curves for multiple second expressions can be obtained. These aN curves constitute the prior data for Bayesian inference. The higher the prior probability of the second expression, the better the corresponding failure mechanism model describes the actual crack propagation. The prior probability of the failure mechanism model is determined by the actual environment; each model has a different application environment and applicable stage, resulting in different prior probabilities. In fatigue life prediction, due to uncertainties in crack location, stress deformation mode, crack size, etc., it is difficult to determine which model is more applicable; therefore, it can only be assumed that all models have equal probability. Thus, based on the second measured data, Bayesian updates can be performed on the prior data of each second expression.

[0143] S306. Based on the second measured data, perform Bayesian update on the prior probability of each preset second expression to obtain the posterior probability of each second expression.

[0144] Specifically, for each aN curve, the Bayesian update calculation formula is as follows:

[0145]

[0146] Where i≤k, Pr(M) k ) represents the k-th failure mechanism model M among multiple failure mechanism models M. k The prior probability, k is a positive integer; L(D|M) k ( ) is the second measured data D, M k The likelihood function of M. k The magnitude of the likelihood function value reflects M k Compared to other failure mechanism models, M's ability to describe actual crack propagation is superior. k The likelihood function value is high, indicating its strong ability to describe actual crack propagation compared to other failure mechanism models; M k The likelihood function value is low, indicating that it is less capable of describing actual crack propagation compared to other failure mechanism models. Since the prior probabilities of all models are equal in fatigue life prediction, the likelihood function becomes the only metric that can distinguish the ability of each model to describe actual crack propagation.

[0147] S307. Based on the second expression of each failure mechanism model and the posterior probability of the corresponding second expression, a fusion model is calculated so as to predict the fatigue life of the target metallic material based on the fusion model.

[0148] Specifically, the uncertainty in the selection of failure mechanism models can be quantified by introducing model probabilities. The impact of this uncertainty on fatigue life prediction can be addressed through model fusion. This method probabilistically quantifies the ability of a set of deterministic failure mechanism models to describe fatigue life prediction, and then combines multiple models into a single fusion model by adjusting the posterior model probabilities of each failure mechanism model to predict fatigue life.

[0149] The method for obtaining the fusion model is essentially a probabilistic and weighted approach. First, it is assumed that each failure mechanism model has the same ability to describe the actual crack propagation, i.e., equal prior probabilities. Then, the posterior probabilities of each failure mechanism model are updated using second measured data. That is, the weights of each failure mechanism model are adjusted based on the second measured data, and the weighted fusion model describes the crack propagation.

[0150] This application provides a method for constructing a fusion model, which includes: assigning multiple independent random values ​​to crack growth parameters to obtain multiple first expressions for each failure mechanism model; performing Bayesian updates on the prior probabilities of each first expression based on first measured data; calculating a second expression for each failure mechanism model based on the multiple first expressions and their posterior probabilities; performing Bayesian updates on the prior probabilities of each second expression based on second measured data; and calculating a fusion model based on the multiple second expressions and their posterior probabilities. This method achieves the following technical effects: performing Bayesian updates on the prior probabilities of the multiple first expressions for each failure mechanism model solves the problem of uncertainty in multiple crack growth parameters of the failure mechanism model; performing Bayesian updates on the prior probabilities of the second expressions for each of the multiple failure mechanism models solves the problem that different failure mechanism models cannot be accurately applied to various objects and scenarios; and determining the likelihood function expression form through measured data and updating the parameters of the failure mechanism model through Bayesian updates improves the accuracy of fatigue life prediction.

[0151] Figure 5 A flowchart illustrating the fusion model construction method provided in this application embodiment. Figure 2 ,like Figure 5 As shown, the fusion model construction method provided in this application embodiment is... Figure 4Based on the fusion model construction method provided in the embodiment, further refinement is made. The first measured data includes: the measured crack size of the target metal material in each of multiple first preset cycles, where the first target cycle is any one of the multiple first preset cycles; the first target expression is any one of multiple first expressions of the target failure mechanism model, where the target failure mechanism model is any one of multiple failure mechanism models; for the first target cycle and the first target expression, S303 includes:

[0152] S401. Based on the first measured data, obtain the first measured crack size of the target metal material in the first target cycle.

[0153] Specifically, due to the lack of sufficient experimental information and previous statistical data, the first measured crack size of the target metallic material in the first target cycle can be obtained based on the first measured data.

[0154] S402. Based on the first target expression, obtain the first predicted crack size of the target metal material in the first target cycle.

[0155] It should be noted that there is no specific execution order for S401 and S402. It can be that S401 is executed first and then S402, as provided in the embodiments of this application; or it can be that S402 is executed first and then S401; or it can be that S401 and S402 are executed simultaneously.

[0156] S403. Based on the error between the first predicted crack size and the first measured crack size, obtain the first likelihood function of the first objective expression in the first objective loop.

[0157] Specifically, according to Bayesian inference, the posterior probability of the first objective expression in the first objective cycle is proportional to the product of the first likelihood function and the prior probability of the first objective cycle. The determination of the first likelihood function is related to the first measured data. Here, it is assumed that the first likelihood function follows a normal distribution, and the formula for calculating the first likelihood function is:

[0158]

[0159] Among them, a h Let be the actual crack size of the first target cycle, 'a' be the first predicted crack size of the first target cycle, and 's' be the variance. The value of 's' is related to the first measured data; in this embodiment, the value of 's' can be 1. According to the above formula, the magnitude of the first likelihood function depends on 'a'. h The error between a and 'a' is such that when the error is small, the value of the first likelihood function is large, with a maximum value of 1, meaning that a... h Consistent with 'a'; when the error is large, the value of the first likelihood function is small, and the maximum value is approximately 0, meaning that 'a'... hThe difference from 'a' is significant. Therefore, the first likelihood function can be viewed as the weight of each first expression being the actual expression. The smaller the error, the larger the value of the first likelihood function, and the greater the probability that the first expression is the actual expression.

[0160] S404. Based on the first likelihood function, perform a Bayesian update on the prior probability of the first objective expression in the first objective loop to obtain the posterior probability of the first objective expression in the first objective loop.

[0161] It should be noted that the calculation method for the posterior probability is similar for other first preset loops outside the first target loop, and for other first expressions outside the first target expression, and will not be repeated in this embodiment.

[0162] In one possible design, the prior probabilities of the multiple first expressions of the target failure mechanism model in the first loop each follow a mean distribution; the likelihood functions of the multiple first expressions of the target failure mechanism model in the first target loop each follow a normal distribution; for the first target loop and the target failure mechanism model, after S404, the fusion model construction method also includes:

[0163] S405. Normalize the probability of each of the first expressions of the target failure mechanism model in the first target loop for their respective posterior probabilities.

[0164] Specifically, the sum of the probabilities of the aN curves of the multiple first expressions being the actual crack propagation curves must equal 1, meaning that the posterior probabilities of each of the multiple first expressions must be summed to 1. Therefore, after obtaining the posterior probability of each first expression, probability normalization must be performed.

[0165] In one possible design, for the target failure mechanism model, S304 includes:

[0166] Based on the posterior probabilities of the multiple first expressions of the target failure mechanism model, the multiple crack growth parameters of each first expression of the target failure mechanism model are weighted and calculated to obtain the calculated value of each crack growth parameter.

[0167] Based on the calculated values ​​of multiple crack growth parameters, the second expression of the target failure mechanism model is obtained.

[0168] Specifically, in the above embodiments, the mean μ of c is calculated. c , and the mean μ of m m This is equivalent to a weighted calculation. Furthermore, it can also be based on μ. c The variance σ of c is calculated. c And according to μ m The variance σ of m is calculated. m The calculation formula is:

[0169] σ c =∑(c-μ c ) 2 P(c)

[0170] σ m =∑(m-μ m ) 2 P(m)

[0171] Where, σ c and σ m The degree of discreteness of the second expression used to represent the target failure mechanism model.

[0172] It should be noted that the calculation method of the second expression for other failure mechanism models besides the target failure mechanism model is similar, and will not be repeated in this embodiment.

[0173] In one possible design, following S304, the fusion model construction method also includes:

[0174] Obtain the third measured data for each of the multiple third fatigue cracks in the target metallic material.

[0175] Based on multiple third-party measured data, the parameters of the second expression for each failure mechanism model are updated.

[0176] Specifically, the sampling time and / or sampling location of each third fatigue crack differs from that of the first fatigue crack. Due to measurement errors in the testing equipment, the initial crack size detected also has uncertainty. Therefore, for crack initiation points, crack sizes, and other information obtained from actual measurements at different sampling times and / or sampling locations, the above steps are repeated to obtain real-time updates to the target failure mechanism model for each key part of the target metallic material, and to revise the model accordingly. The technical effect is that it enables more accurate and reliable crack size predictions and remaining life assessments compared to before the update.

[0177] The following will provide a detailed explanation, with reference to specific embodiments, of how to derive the second expression of the Paris-Erdogan model from multiple first expressions of the Paris-Erdogan model.

[0178] Taking the penetrating crack on the fuselage panel as an example, according to the first measured data, a0 = 10mm; in addition, according to the parameter table of the target metal material, the limiting crack size a can be obtained. c =25.6mm. The parameter table of the target metallic material is shown in Table 1.

[0179] Table 1:

[0180] parameter Physical meaning value / range unit Distribution type <![CDATA[a0]]> Initial crack size 10 mm constant value β Correction coefficient 1 constant value <![CDATA[△σ h ]]> stress 78.6 MPa constant value c Failure parameters <![CDATA[U(2.1×10 -10 ,4.1×10 -10 )]]> random variable m Failure parameters U(3.32，3.52) random variable <![CDATA[a c ]]> Limiting crack size 25.6 mm constant value <![CDATA[△K th ]]> Threshold value 1.39 <![CDATA[MPam 0.5 ]]> constant value

[0181] For the prior distribution, the first expression of the Paris-Erdogan model is obtained by sampling from the probability distributions of c and m. If the sample size is large enough, the set of all first expressions can reflect the actual crack propagation. To illustrate this method more concisely, a Bayesian update is performed using 10 samples as an example. The 10 samples [m, c] are: [3.35, 2.1 × 10^3 m ... -10 ]、[3.35,2.5×10 -10 ]、[3.35,3×10 -10 ]、[3.35,3.5×10 -10 ]、[3.35,4.1×10 -10 ]、[3.45,2.1×10 -10 ]、[3.45,2.5×10 -10 ]、[3.45,3×10 -10 ]、[3.45,3.5×10 -10 [3.45, 4.1×10] and [3.45, 4.1×10] -10 ]. Figure 6 This is a schematic diagram of the aN curve cluster of the Paris-Erdogan model provided in an embodiment of this application. The aN curves for each of these 10 sample groups [m, c] are shown below. Figure 6 As shown.

[0182] The prior information for these 10 aN curves is shown in Table 2.

[0183] Table 2:

[0184]

[0185] From Table 2 and Figure 6 It can be seen that before the 1879th cycle, no aN curve predicted a crack size exceeding a. c ; In the 2000th iteration, only [3.45, 4.1 × 10] -10 The predicted crack size exceeds a c The corresponding fatigue life is 1879 cycles, so the prior reliability of the target metal material at 2000 cycles is 0.9. At 3000 cycles, there are 5 groups [3.35, 3.5×10]. -10 ]、[3.35,4.1×10 -10 ]、[3.45,3×10 -10 ]、[3.45,3.5×10 -10 [3.45, 4.1×10] and [3.45, 4.1×10] -10 The predicted crack size exceeds a cTherefore, the prior reliability of the target metal material at 3000 cycles is 0.5. The predicted crack size of all aN curves will exceed a after 4875 cycles. c . Figure 7 The prior cumulative probability distribution provided for the embodiments of this application Figure 1 ,like Figure 7 As shown, the prior probability distribution of crack size can be obtained for 250, 1000, 2000 and 3000 cycles.

[0186] Next, a Bayesian update is performed on the prior probability to obtain the posterior probability. The formula for calculating the posterior probability is:

[0187]

[0188] Where p(c, m) is the prior probability, with a value of 0.1. After 250 cycles, the actual crack size detected was 11.2 mm, and the posterior probability can be obtained according to the above formula. The posterior information of these 10 aN curves is shown in Table 3.

[0189] Table 3:

[0190]

[0191] Tables 2 and 3 show the posterior cumulative probability distribution of predicted crack size and the posterior reliability of fatigue life compared with the previous values. Figure 8 A comparison diagram of the posterior probability distribution and the state before the update provided in this application embodiment; Figure 9 Comparison of post-hoc reliability with that before the update provided for embodiments of this application Figure 1 .like Figure 8 As shown, the posterior cumulative probability distribution of the predicted crack size is illustrated, compared with that before the update. Figure 9 As shown, the relationship between reliability R(t) and the number of cycles is illustrated, compared with the previous state. The posterior reliability of fatigue life is shown by the solid line in the figure, and the prior reliability is shown by the dashed line in the figure.

[0192] Finally, μ was calculated. c =3.37×10 -10 , σ c =0.466×10 -10 μ m =3.44, σ m =0.003359.

[0193] It should be noted that the above is only a simple introduction to the process of obtaining the second expression using 10 sets of samples as an example. When c and m are independently and randomly assigned multiple times, the aN curve at a given confidence level can be obtained.

[0194] Figure 10 A flowchart illustrating the fusion model construction method provided in this application embodiment. Figure 3 ,like Figure 10 As shown, the fusion model construction method provided in this application embodiment is... Figure 4 Based on the embodiment, further refinement is provided. The second measured data includes: the measured crack size of the target metal material in each of the multiple second preset cycles, where the second target cycle is any one of the multiple second preset cycles; for the second target cycle, S306 includes:

[0195] S501. Based on the second measured data, the second measured crack size of the target metal material in the second target cycle is obtained.

[0196] S502. Based on multiple second expressions, obtain the second predicted crack size of the target metal material in the second target cycle, as predicted by each second expression.

[0197] S503. Based on the error between each second predicted crack size and the second measured crack size, obtain the second likelihood function of each second expression in the second target loop.

[0198] Specifically, the prior probability of the failure mechanism model in the second objective cycle is the model's ability to describe crack propagation. If the model can completely describe crack propagation, the prior probability of the model is 1. Assuming there are multiple failure mechanism models that can be used to describe crack propagation, and there is a second set of measured data D, then the prior probability of the model can be updated using Bayesian inference.

[0199] Since the failure mechanism model is only an approximation of the actual crack propagation, errors inevitably exist between each predicted crack size and the actual crack size. These errors are unknown until the actual measured data is obtained. Unknown errors are generally described using the uncertainty principle. More specifically, the uncertainty of this error is usually described by a probability distribution. In statistics, this error is usually assumed to follow a normal distribution with a mean of 0 and a constant variance.

[0200] The formula for calculating the error between each second predicted crack size and the second measured crack size is as follows:

[0201] y = f k +ε k

[0202] ε k ~N(0, σ k 2 )

[0203] Where y is the second measured crack size, f kM is a failure mechanism model describing y. k The second predicted crack size, ε k It is y and f k The error between them, ε k It follows a pattern with a mean of 0 and a variance of σ. k 2 It follows a normal distribution. Introducing ε k The purpose is to describe the uncertainty difference between the second predicted crack size and the second measured crack size. When ε k When the mean is 0, M remains unchanged. k f k M k This is the actual model. This also reflects that each failure mechanism model, when established, assumes that its second predicted crack size most likely reflects the second measured crack size. ε k Reflects M k The mathematical relationship between y and M is such that, according to the formula, y also follows a normal distribution. k The prior distribution is:

[0204]

[0205] ε kn =d n -f kn

[0206] Where, d n The second measured data is D = {d1, ..., d...} N A measured crack size. kn It is M k Corresponding to d n The predicted crack size. ε kn To conform to a mean of 0 and a standard deviation of σ k The random variable is normally distributed. Assuming that the measured data are independent, the likelihood function L(D|σ) is given. k M k L(d) is the likelihood function of D. n |σ k M k The product of ) is L(D|σ) k M k This can be represented as:

[0207]

[0208] Then the second likelihood function L(D|M) k ) can be derived from L(D|σ) k M k The marginal distribution obtained by integrating over the parameters is calculated using the following formula:

[0209] L(D|M k ) = ∫L(D|σ k , M k )g(σ k |M k )dσ k

[0210] where g(σ k |M k ) is the conditional distribution of the unknown parameter σ k given M k . For a given D and M k , σ k can be obtained using the principle of maximum likelihood.

[0211] S504. Update the prior probability of each second expression in the second target loop based on the second likelihood function of each second expression in the second target loop to obtain the posterior probability of each second expression in the second target loop.

[0212] Specifically, the simplest way to estimate model parameters using the likelihood function is to find a set of parameters that maximize the value of the likelihood function. This estimation method is called Maximum Likelihood Estimation (MLE). MLE makes the occurrence probability of the observed data the highest. From the perspective of computational simplicity, we usually take the logarithm of the likelihood function first and then maximize it. The parameter estimates obtained by these two methods are the same. The logarithmic form of the likelihood function is called the log-likelihood function. The log-likelihood function is the sum of the logarithms of the probability densities of each observed value, while the likelihood function is the product of the sampling probability densities of each observed value.

[0213] σ k 's maximum likelihood estimate is clearly the maximum possible value for D to be detected, and can be obtained by setting the logarithm of L(d n |σ k , M k ) equal to 0 with respect to σ k . The calculation formula is:

[0214]

[0215] Solving gives the expression for σ k 2 as:

[0216]

[0217] where σ k 2 is a parameter obtained by fitting the second measured data, and can also be denoted as σ' k2 σ k 2 Substituting the maximum likelihood estimate into L(D|σ) k M k From the expression for ), we can obtain L(D|M) k The expression for ) is:

[0218]

[0219] It should be noted that this expression holds true only if the errors are independent and follow a normal distribution.

[0220] Assuming that the prior probability follows a uniform distribution, meaning that each failure mechanism model can completely describe the second measured data, the formula for calculating the posterior probability in the second expression can be obtained as follows:

[0221]

[0222] It should be noted that the calculation method for the posterior probability is similar for other second preset loops besides the second target loop, and will not be repeated in this embodiment.

[0223] In one possible design, the prior probabilities of multiple second expressions in the first loop follow a mean distribution; the errors of multiple second expressions in the second objective loop follow a normal distribution; therefore, after S504, the fusion model construction methods also include:

[0224] S505. Normalize the probability of each of the multiple second expressions in the second objective loop.

[0225] Specifically, the sum of the prior and posterior probabilities of all failure mechanism models is 1. Therefore, after obtaining the posterior probabilities of all failure mechanism models each time, probability normalization processing must be performed.

[0226] In one possible design, S307 includes:

[0227] For the second objective loop, the segmented fusion model of the second objective loop is obtained by weighted calculation based on multiple second expressions and the posterior probability of the corresponding second expressions in the second objective loop.

[0228] A fusion model is obtained by fitting the segmented fusion model based on the segmented fusion model of each second preset cycle.

[0229] Specifically, during the construction of the fusion model, only the first predicted crack size distribution under the preset number of cycles of the failure mechanism model is fused. This is a probabilistic treatment that does not involve physical mechanisms and does not obtain an analytical model. The posterior probability of the second expression essentially reflects the influence magnitude of each failure mechanism model in the fusion model, that is, the weight. The greater the posterior probability of the model, the higher the weight. Therefore, the analytical expression of the fusion model can be expressed as:

[0230] f(y丨D)=∑Pr(M k 丨D)f(y丨M k ,D)

[0231] where f(y丨M k ,D) is the prediction of the second measured data by M k under the premise of obtaining D, and Pr(M k 丨D) is the posterior probability of M k after obtaining D, which is the weight coefficient of M k relative to other models. According to this expression, the expression for the fusion model to describe the crack growth situation can be obtained as:

[0232] g(y丨D)=∑Pr(M k 丨D)g(y丨M k ,D)

[0233] where g(y丨M k ,D) is the prediction of the second measured data by M k under the premise of obtaining D.

[0234] If g(y丨M k ,D) has a mean E(y丨D) and a variance Var(y丨D), then the formulas for the mean and variance of the fusion model g(y丨D) are:

[0235] E(y丨D)=∑Pr(M k 丨D)E(y丨M k ,D)

[0236] Var(y丨D)

[0237] =∑Pr(M k 丨D)Var(y丨M k ,D)

[0238] +∑Pr(M k 丨D)[E(M k 丨D)-E(M k 丨D)] 2

[0239] where ∑Pr(M k|D)Var(y|M k , D) is the within-model variance, which reflects the uncertainty level of each failure mechanism model. Pr(M k |D)[E(M k |D) - E(M k |D)] 2 is the between-model variance, which reflects the uncertainty of the model form, that is, the uncertainty level of the target failure mechanism model relative to the fusion model.

[0240] Since g(y|M k , D) follows a normal distribution, the linear combination g(y|D) of g(y|M k , D) also follows a normal distribution. The distribution expression of the fusion model g(y|D) is:

[0241] g(y|D) = N{∑Pr(M k |D)f k , ∑Pr(M k |D)σ′ k 2 , ∑Pr(M k |D)[f k - E(y|D)] 2}

[0242] Next, specific embodiments will be combined to further elaborate on obtaining the fusion model according to multiple second expressions.

[0243] In the above embodiment, only the Paris-Erdogan model is used to describe fatigue crack growth, but the Paris-Erdogan model does not consider the influence of the stress intensity factor threshold on crack growth. Here, two fatigue growth models, the Paris-Erdogan model and the Trantina-Johnson model, are comprehensively considered to obtain the fusion model. Among them, the expression of the Trantina-Johnson model is:

[0244]

[0245] Assume that c and m follow a uniform distribution and are independent of each other, and take c = 4.1×10 -10 , m = 3.49. Then the a-N curves of the Paris-Erdogan model and the Trantina-Johnson model, as well as the measured crack curves, are as Figure 11 shown, Figure 11 This is a comparison diagram of the fusion model, prediction model, and measured data provided by the embodiment of the present application. Among them, the a-N curve of the fusion model is shown as the dashed line in the figure, and the a-N curve of the measured data is shown as the dotted line in the figure. From Figure 11It is evident that when using a single failure mechanism model to describe fatigue crack propagation, the predicted curve is not accurate enough. Each failure mechanism model can only partially describe the fatigue crack propagation phenomenon. The Paris-Erdogan model can well describe the actual fatigue crack propagation phenomenon at low cycle counts, approximately below 1000 cycles. However, at high cycle counts, the crack grows exponentially, becoming too fast, and the error between the predicted curve and the curve obtained from the second measured data increases significantly. Furthermore, the predicted curve of the Trantina-Johnson model is lower than the actual fatigue crack propagation curve.

[0246] By using Bayesian inference and combining it with the second set of experimental data, a fusion model combining the Paris-Erdogan and Trantina-Johnson models can be obtained. The mean curve of the fusion model is fitted using the formula for its mean E(y|D) and compared with both the Paris-Erdogan and Trantina-Johnson models. When the two models are combined using Bayesian inference with the second set of experimental data, they become complementary, thus improving the accuracy of the fusion model.

[0247] Next, the posterior probability of the fusion model was calculated. According to the formula for calculating the posterior probability of fusion, the posterior probability of the Paris-Erdogan model is 0.9029, and the posterior probability of the Trantina-Johnson model is 0.0971. The comparison of the Paris-Erdogan model, the Trantina-Johnson model, and the fusion model is shown in Table 4.

[0248] Table 4

[0249]

[0250] Based on the posterior probabilities of the Paris-Erdogan and Trantina-Johnson models, the expression for the fusion model can be obtained as follows:

[0251]

[0252] Figure 12 This is a schematic flowchart illustrating the health assessment method provided in an embodiment of this application. Figure 12 As shown in the embodiments of this application, the executing entity can be a health assessment device, which can be located in an electronic device, and this device can be a data processing server. The health assessment method provided in the embodiments of this application includes the following steps:

[0253] S601. Obtain the fourth measured data of the fourth fatigue crack in the target metallic material.

[0254] The fourth measured data includes: the initial crack size of the fourth fatigue crack.

[0255] S602. Based on the fourth measured data and the pre-set fusion model, evaluate at least one of the multiple health assessment indicators of the target metallic material.

[0256] The fusion model is the model constructed using the fusion model construction method described in the above embodiments. Multiple health assessment indicators include fatigue life, reliability, and crack size. The prediction of fatigue life and crack size of the target metallic material is similar to that described in the above embodiments, and will not be repeated in this application.

[0257] After predicting the fatigue life and crack size of the target metallic material, the reliability of the prediction results can be verified based on the fourth set of measured data.

[0258] Specifically, the fusion model comprehensively considers multiple failure mechanism models, combining the advantages of each to more fully describe the actual fatigue crack propagation phenomenon. However, model fusion only considers the differences between models; the parameters within each model reflect its understanding of fatigue crack propagation, which the fusion model does not. Furthermore, the fusion model, and the confidence intervals derived from it, are entirely mathematically derived, detached from the physical essence, exhibiting excessive dispersion and negative values. Therefore, it is necessary to perform a Bayesian update on the prior probabilities of the fusion model to obtain its posterior probabilities.

[0259] In one possible design, the evaluation results include: the predicted crack size of the target metallic material in each cycle;

[0260] Following S602, health assessment methods also include:

[0261] S603. Based on the predicted crack size of the target metal material in each cycle and the preset prediction confidence level, obtain the confidence interval.

[0262] Specifically, for fatigue life prediction of a target metallic material, a confidence interval is needed to reflect its reliability. The confidence interval includes the upper and lower confidence crack sizes of the target metallic material in each cycle. Assuming a prediction confidence level of 95%, the expression for the confidence interval is:

[0263]

[0264] Figure 13 This is a schematic diagram illustrating the confidence intervals provided in an embodiment of this application. According to... Figure 13As can be seen, the aN curve of the fusion model is shown as the solid line in the figure, the aN curve of the confidence interval is shown as the dashed line in the figure, and the aN curve of the measured data is shown as the dotted line in the figure. The confidence interval with a confidence level of 95% completely includes the actual fatigue crack propagation curve, and the accuracy is improved compared with the single failure mechanism model.

[0265] Figure 14 The prior cumulative probability distribution provided for the embodiments of this application Figure 2 When the number of [m, c] is much greater than 10, for example, 1000, the prior reliability of the fusion model in 250, 1000, 2000, and 3000 iterations is as follows: Figure 14 As shown.

[0266] Based on the fourth measured data, the measured crack size of the fourth fatigue crack in each cycle is shown in Table 5.

[0267] Table 5

[0268]

[0269] Figure 15 A posterior probability distribution diagram provided for embodiments of this application; Figure 16 Comparison of post-hoc reliability with that before the update provided for embodiments of this application Figure 2 .like Figure 15 As shown, the posterior probability distribution for predicting crack size is illustrated; as... Figure 16 As shown, the relationship between reliability and cycle number is illustrated, compared with the previous state. The posterior reliability of fatigue life is represented by the solid line in the figure, and the prior reliability is represented by the dashed line in the figure.

[0270] In this embodiment, the fusion model building apparatus may be located in an electronic device. The fusion model building apparatus includes:

[0271] The random assignment module is used to perform multiple independent random assignments on multiple crack growth parameters of each of the preset failure mechanism models, so as to obtain the first expression of each failure mechanism model after each random assignment.

[0272] The first update module is used to acquire the first measured data of the first fatigue crack of the target metal material, and to perform Bayesian update on the prior probability of each preset first expression based on the first measured data to obtain the posterior probability of each first expression; wherein, the first measured data is used to indicate the crack propagation of the first fatigue crack, and the prior probability and posterior probability of each first expression are used to indicate the ability of the corresponding first expression to describe the crack propagation.

[0273] The first calculation module is used to calculate the second expression of each failure mechanism model based on multiple first expressions of each failure mechanism model and the posterior probability of the corresponding first expressions.

[0274] The second update module is used to acquire the second measured data of the second fatigue crack of the target metal material, and based on the second measured data, to perform Bayesian update on the prior probability of each preset second expression to obtain the posterior probability of each second expression.

[0275] The second calculation module is used to calculate the fusion model based on the second expression of each failure mechanism model and the posterior probability of the corresponding second expression, so as to predict the fatigue life of the target metallic material based on the fusion model.

[0276] In one possible design, the first measured data includes: the measured crack size of the target metal material in each of multiple first preset cycles, where the first target cycle is any one of the multiple first preset cycles; the first target expression is any one of multiple first expressions of the target failure mechanism model, where the target failure mechanism model is any one of multiple failure mechanism models;

[0277] For the first target loop and the first target expression, the first update module includes:

[0278] The first prediction module is used to obtain the first measured crack size of the target metal material in the first target cycle based on the first measured data, and to obtain the first predicted crack size of the target metal material in the first target cycle based on the first target expression.

[0279] The first error module is used to obtain the first likelihood function of the first objective expression in the first objective loop based on the error between the first predicted crack size and the first measured crack size.

[0280] The third update module is used to perform Bayesian updates on the prior probability of the first objective expression in the first objective loop based on the first likelihood function, so as to obtain the posterior probability of the first objective expression in the first objective loop.

[0281] In one possible design, the prior probabilities of the multiple first expressions of the target failure mechanism model in the first loop follow a mean distribution; the likelihood functions of the multiple first expressions of the target failure mechanism model in the first target loop follow a normal distribution.

[0282] For the first target cycle and target failure mechanism model, the fusion model construction device also includes:

[0283] The first normalization module is used to perform probability normalization processing on the posterior probabilities of the multiple first expressions of the target failure mechanism model in the first target loop.

[0284] In one possible design, for the target failure mechanism model, the first calculation module includes:

[0285] The first weighting module is used to perform weighted calculations on multiple crack growth parameters of each first expression of the target failure mechanism model based on the posterior probabilities of each of the multiple first expressions of the target failure mechanism model, so as to obtain the calculated value of each crack growth parameter.

[0286] The third calculation module is used to obtain the second expression of the target failure mechanism model based on the calculated values ​​of multiple crack growth parameters.

[0287] In one possible design, the fusion model building device also includes:

[0288] The first acquisition module is used to acquire the third measured data of each of the multiple third fatigue cracks in the target metallic material; wherein the sampling time and / or sampling location of each third fatigue crack are different from those of the first fatigue crack;

[0289] The fourth update module is used to update the parameters of the second expression of each failure mechanism model based on multiple third-party measured data.

[0290] In one possible design, the second measured data includes: the measured crack size of the target metal material in each of the multiple second preset cycles, where the second target cycle is any one of the multiple second preset cycles;

[0291] For the second target loop, the second update module includes:

[0292] The second prediction module is used to obtain the second measured crack size of the target metal material in the second target cycle based on the second measured data, and to obtain the second predicted crack size of the target metal material in the second target cycle predicted by each of the multiple second expressions based on the second measured data.

[0293] The second error module is used to obtain the second likelihood function of each second expression in the second target loop based on the error between each second predicted crack size and the second measured crack size.

[0294] The fifth update module is used to perform Bayesian updates on the prior probability of each second expression in the second objective loop based on the second likelihood function of each second expression in the second objective loop, so as to obtain the posterior probability of each second expression in the second objective loop.

[0295] In one possible design, the prior probabilities of the multiple second expressions in the first loop follow a mean distribution; the errors of the multiple second expressions in the second target loop follow a normal distribution.

[0296] The fusion model building apparatus also includes:

[0297] The second normalization module is used to perform probability normalization on the posterior probabilities of multiple second expressions in the second target loop.

[0298] In one possible design, the second computing module includes:

[0299] The second weighting module is used to calculate the segmented fusion model of the second target loop by weighting multiple second expressions and the posterior probability of the corresponding second expressions in the second target loop.

[0300] The fourth calculation module is used to fit a fusion model based on the segmented fusion model of each second preset cycle.

[0301] The fusion model construction apparatus provided in this application embodiment can execute Figures 4 to 11 The technical solution of the method embodiment shown has the same implementation principle and technical effect as... Figures 4 to 11 The method embodiments shown are similar, and will not be described again in the embodiments of this application.

[0302] In this embodiment, the health assessment device may be located in an electronic device. The health assessment device includes:

[0303] The data acquisition module is used to acquire the fourth measured data of the fourth fatigue crack of the target metallic material; wherein, the fourth measured data includes: the initial crack size of the fourth fatigue crack;

[0304] The life prediction module is used to evaluate at least one of multiple health assessment indicators of the target metallic material based on the fourth measured data and a preset fusion model; wherein, the fusion model is a model constructed by the health assessment device of the above embodiment; the multiple health assessment indicators include: fatigue life, reliability and crack size.

[0305] In one possible design, the predicted fatigue life includes: the predicted crack size of the target metallic material in each cycle;

[0306] The health assessment device also includes:

[0307] The confidence interval module is used to obtain a confidence interval based on the predicted crack size of the target metal material in each cycle and the preset prediction confidence level; wherein, the confidence interval includes: the upper confidence crack size and the lower confidence crack size of the target metal material in each cycle.

[0308] The health assessment device provided in this application embodiment can perform... Figures 12 to 16 The technical solution of the method embodiment shown has the same implementation principle and technical effect as... Figures 12 to 16 The method embodiments shown are similar, and will not be described again in the embodiments of this application.

[0309] This application also provides an electronic device, which includes at least one processor and a memory. The electronic device further includes a communication component. The processor, memory, and communication component are connected via a bus.

[0310] In the specific implementation process, at least one processor executes computer execution instructions stored in memory, so that at least one processor is used to implement the fusion model construction method and health assessment method of the above embodiments.

[0311] The specific implementation process of the processor can be found in the above method embodiments, and its implementation principle and technical effect are similar. The embodiments of this application will not be repeated here.

[0312] In the above embodiments, it should be understood that the processor can be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), etc. The general-purpose processor can be a microprocessor or any conventional processor. The steps of the method disclosed in the application can be directly manifested as being executed by a hardware processor, or executed by a combination of hardware and software modules within the processor.

[0313] The memory may include high-speed RAM, and may also include non-volatile storage (NVM), such as at least one disk storage.

[0314] The bus can be an Industry Standard Architecture (ISA) bus, a Peripheral Component Interconnect (PCI) bus, or an Extended Industry Standard Architecture (EISA) bus, etc. Buses can be categorized as address buses, data buses, control buses, etc. For ease of illustration, the buses shown in the accompanying drawings are not limited to a single bus or a single type of bus.

[0315] The above description addresses the functions implemented by electronic devices and main control devices, and introduces the solutions provided in the embodiments of this application. It is understood that, in order to achieve the above functions, the electronic device or main control device includes hardware structures and / or software modules corresponding to the execution of each function. By combining the units and algorithm steps of the various examples described in the embodiments disclosed in this application, the embodiments of this application can be implemented in hardware or a combination of hardware and computer software. Whether a function is executed by hardware or by computer software driving hardware depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of the technical solutions of the embodiments of this application.

[0316] This application also provides a computer-readable storage medium storing computer-executable instructions. When executed by a processor, these instructions are used to implement the fusion model construction method and health assessment method described above. In the specific implementation of the aforementioned fusion model construction method and health assessment method, each module can be implemented as a processor.

[0317] The aforementioned readable storage medium can be implemented by any type of volatile or non-volatile storage device or a combination thereof, such as static random access memory (SRAM), electrically erasable programmable read-only memory (EEPROM), erasable programmable read-only memory (EPROM), programmable read-only memory (PROM), read-only memory (ROM), magnetic storage, flash memory, magnetic disk, or optical disk. The readable storage medium can be any available medium accessible to a general-purpose or special-purpose computer.

[0318] An exemplary readable storage medium is coupled to a processor, enabling the processor to read information from and write information to the readable storage medium. Of course, the readable storage medium can also be a component of the processor. The processor and the readable storage medium can reside in an application-specific integrated circuit (ASIC). Alternatively, the processor and the readable storage medium can exist as discrete components in an electronic device or a host device.

[0319] This application also provides a computer program product, including a computer program, which, when executed by a processor, is used to implement the fusion model construction method and health assessment method of the above embodiments.

[0320] The computer program is stored in a readable storage medium, and at least one processor can read the computer program from the readable storage medium and execute the computer program to perform the scheme provided in any of the above embodiments.

[0321] Those skilled in the art will understand that all or part of the steps of the above-described embodiments can be implemented by hardware related to program instructions. The aforementioned program can be stored in a computer-readable storage medium. When executed, the program performs the steps of the above-described method embodiments; and the aforementioned storage medium includes various media capable of storing program code, such as ROM, RAM, magnetic disks, or optical disks.

[0322] The technical solutions of this application have been described above with reference to the preferred embodiments shown in the accompanying drawings. However, it is readily understood by those skilled in the art that the scope of protection of this application is obviously not limited to these specific embodiments. The above embodiments are only used to illustrate the technical solutions of this application and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. These modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of this application.

Claims

1. A method for constructing a fusion model, characterized in that, The method includes: Multiple crack growth parameters of each of the preset failure mechanism models are independently and randomly assigned multiple times to obtain the first expression of each failure mechanism model after each random assignment. First measured data of the first fatigue crack in the target metallic material are obtained, and based on the first measured data, Bayesian updates are performed on the prior probabilities of each of the first expressions to obtain the posterior probabilities of each of the first expressions; wherein, the first measured data is used to indicate the crack propagation of the first fatigue crack, and the prior and posterior probabilities of each of the first expressions are used to indicate the ability of the corresponding first expression to describe the crack propagation. The target failure mechanism model is any one of the plurality of failure mechanism models; based on the posterior probabilities of the plurality of first expressions of the target failure mechanism model, the plurality of crack growth parameters of each first expression of the target failure mechanism model are weighted and calculated to obtain the calculated value of each crack growth parameter; based on the calculated values ​​of the plurality of crack growth parameters, the second expression of the target failure mechanism model is obtained. Second measured data of the second fatigue crack of the target metal material are obtained, and based on the second measured data, Bayesian update is performed on the prior probability of each of the second expressions to obtain the posterior probability of each of the second expressions. The second measured data includes: the measured crack size of the target metal material in each of multiple second preset cycles, wherein the second target cycle is any one of the multiple second preset cycles; for the second target cycle, a segmented fusion model of the second target cycle is obtained by weighted calculation based on multiple second expressions and the posterior probability of the corresponding second expressions in the second target cycle; the fusion model is fitted based on the segmented fusion model of each second preset cycle, so as to predict the fatigue life of the target metal material based on the fusion model.

2. The method according to claim 1, characterized in that, The first measured data includes: the measured crack size of the target metal material in each of multiple first preset cycles, where the first target cycle is any one of the multiple first preset cycles; and the first target expression is any one of multiple first expressions of the target failure mechanism model. For the first target loop and the first target expression, the step of performing a Bayesian update on the preset prior probability of each first expression based on the first measured data to obtain the posterior probability of each first expression includes: Based on the first measured data, the first measured crack size of the target metal material in the first target cycle is obtained, and based on the first target expression, the first predicted crack size of the target metal material in the first target cycle is obtained. Based on the error between the first predicted crack size and the first measured crack size, the first likelihood function of the first target expression in the first target cycle is obtained; Based on the first likelihood function, a Bayesian update is performed on the prior probability of the first objective expression in the first objective loop to obtain the posterior probability of the first objective expression in the first objective loop.

3. The method according to claim 2, characterized in that, The multiple first expressions of the target failure mechanism model have their own prior probabilities in the first loop, which follow a mean distribution. The multiple first expressions of the target failure mechanism model, in the first target loop, each have their own likelihood functions that follow a normal distribution; For the first target loop and the target failure mechanism model, after performing a Bayesian update on the prior probability of the first target expression in the first target loop based on the first likelihood function to obtain the posterior probability of the first target expression in the first target loop, the method further includes: The posterior probabilities of the multiple first expressions of the target failure mechanism model in the first target loop are subjected to probability normalization.

4. The method according to any one of claims 1-3, characterized in that, After calculating the second expression of each failure mechanism model based on multiple first expressions of each failure mechanism model and the posterior probability of the corresponding first expressions, the method further includes: Obtain third measured data for each of the multiple third fatigue cracks in the target metallic material; wherein the sampling time and / or sampling location of each third fatigue crack is different from that of the first fatigue crack; Based on multiple sets of third measured data, the parameters of the second expression for each failure mechanism model are updated.

5. The method according to claim 1, characterized in that, For the second target loop, the step of performing a Bayesian update on the prior probability of each of the second expressions based on the second measured data to obtain the posterior probability of each of the second expressions includes: Based on the second measured data, the second measured crack size of the target metal material in the second target cycle is obtained, and based on the multiple second expressions, the second predicted crack size of the target metal material in the second target cycle is obtained for each of the second expressions. Based on the error between each of the second predicted crack sizes and the second measured crack size, a second likelihood function for each of the second expressions in the second target loop is obtained; Based on the second likelihood function of each second expression in the second target loop, a Bayesian update is performed on the prior probability of each second expression in the second target loop to obtain the posterior probability of each second expression in the second target loop.

6. The method according to claim 5, characterized in that, The prior probabilities of the multiple second expressions in the first loop follow a mean distribution; the errors of the multiple second expressions in the second target loop follow a normal distribution. After performing a Bayesian update on the prior probability of each second expression in the second target loop based on the second likelihood function of each second expression in the second target loop, the method further includes: The posterior probabilities of the multiple second expressions in the second target loop are normalized.

7. A health assessment method, characterized in that, The method includes: Obtain fourth measured data of the fourth fatigue crack in the target metallic material; wherein, the fourth measured data includes: the initial crack size of the fourth fatigue crack; Based on the fourth measured data and the preset fusion model, at least one of the multiple health assessment indicators of the target metallic material is evaluated; wherein the fusion model is a model constructed by the method of any one of claims 1-6; the multiple health assessment indicators include: fatigue life, reliability and crack size.

8. The method according to claim 7, characterized in that, The evaluation results include: the predicted crack size of the target metallic material in each cycle; After evaluating at least one of the multiple health assessment indicators of the target metallic material based on the fourth measured data and the preset fusion model, the method further includes: Based on the predicted crack size of the target metal material in each cycle and the preset prediction confidence level, a confidence interval is obtained; wherein, the confidence interval includes: the upper confidence crack size and the lower confidence crack size of the target metal material in each cycle.

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