Fatigue crack propagation prediction method and system based on improved particle filter algorithm

Abstract

The invention belongs to the technical field of fatigue crack prediction, and relates to a fatigue crack propagation prediction method and system based on an improved particle filter algorithm, and the method comprises the steps: predicting the predicted crack length of a sampling particle according to a fatigue crack propagation model constructed by a stress ratio, a material parameter, material fracture toughness, a crack closing effect parameter and a stress threshold factor; when the crack length is measured, the fitness value of each particle is calculated according to the predicted crack length and the measured crack length, the fitness values are ranked, small-weight particles are optimized, the weight of the optimized particles is updated, the optimized particles and non-optimized particles are combined to form a temporary particle set, the temporary particle set is re-sampled according to the weight, and the re-sampled temporary particle set is used as an initial particle set; and calculating a crack length estimation value according to the state value of each particle, continuing prediction when the crack length estimation value does not reach the critical crack length, and ending prediction when the crack length estimation value reaches the critical crack length. The particle diversity is improved, and the fatigue crack propagation prediction precision is high.

Description

Technical Field

[0001] This application relates to the field of fault prediction technology, and in particular to a fatigue crack propagation prediction method and system based on an improved particle filter algorithm. Background Technology

[0002] Fatigue cracks are microscopic or macroscopic cracks that gradually initiate and propagate in materials or structures under cyclic loading (repeatedly applied forces or stresses), even if the load does not exceed the material's static strength limit. The initiation and macroscopic propagation of a fatigue crack is a slow, cumulative process that can last for days, years, or even decades, rather than occurring instantaneously. The typical process consists of three stages: Initiation stage: Microscopic defects inside the material ( As Microcracks (typically less than 0.1 mm in size) form at cyclic stress concentration points (such as micropores and grain boundary slip). This stage accounts for 50%-90% of the fatigue life, and the cracks at this stage are easily covered by coatings and oxide layers on the surface of the component, making them difficult to detect using conventional detection methods.

[0003] Stable growth stage: Microcracks grow gradually under cyclic loading (the growth rate is typically...). (mm / cycle), crack length can be observed through ultrasonic, eddy current and other detection technologies, which is the core stage of fatigue life prediction.

[0004] Macroscopically visible stage: At this stage, the cracks are often close to the critical value for unstable fracture (when the crack grows to this critical value, it will rapidly penetrate the component under a single load, causing the component to suddenly fracture), which will pose a great threat to structural safety.

[0005] Fatigue cracking is one of the most common forms of damage in metallic structures, leading to structural degradation and even failure. Accurate prediction of fatigue crack propagation is crucial for ensuring structural safety and developing appropriate maintenance plans. Existing methods for predicting fatigue crack propagation include fracture fatigue analysis, particle filter (PF) algorithms, and prediction methods combining the Paris Crack Growth Model (Paris model). Fracture fatigue analysis (e.g., the Paris model and its improved versions) is suitable for the stable crack propagation stage, but its prediction accuracy is low in other crack propagation stages and when considering various complex factors (e.g., stress ratio and crack closure effect parameters). Prediction methods combining the PF algorithm and the Paris model can improve prediction accuracy, but suffer from particle degradation and depletion problems. Although combining improved algorithms (such as particle optimization algorithms) can mitigate these problems, particle convergence still exists, leading to reduced particle diversity and affecting the accuracy of fatigue crack propagation prediction. Summary of the Invention

[0006] The application provides a fatigue crack propagation prediction method and system based on an improved particle filtering algorithm, considers the influence of stress ratio, material parameters, material fracture toughness, crack closure effect parameters and stress threshold factors under different stress ratios on the fatigue crack propagation rate, takes the crack closure effect parameters as independent model parameters like the material parameters, constructs a fatigue crack propagation model in combination with the stress ratio, the material parameters, the material fracture toughness and the stress threshold factors under different stress ratios, can accurately predict the crack length through the fatigue crack propagation model, improves the fatigue crack propagation prediction precision, and optimizes small weight particles to improve the diversity of the particles after resampling.

[0007] In a first aspect, the application provides a fatigue crack propagation prediction method based on an improved particle filtering algorithm, comprising the following steps: S1, a data acquisition step: acquiring the component width and thickness, the component load range, the component material parameters, the component stress ratio, the component material fracture toughness, the component crack closure effect parameters and the stress threshold factors under different stress ratios; S2, a model construction step: constructing a fatigue crack propagation model according to the stress ratio, the material parameters, the material fracture toughness, the crack closure effect parameters and the stress threshold factors under different stress ratios; S3, a particle sampling step: sampling n particles from the model parameters to be estimated in the fatigue crack propagation model, obtaining the initial state values of the n particles, and forming a particle set with the initial state values of the n particles; the initial weights of the n particles are equal, and are all 1 / n; S4, a crack length prediction step: predicting the crack length of the n particles through the fatigue crack propagation model to obtain the predicted crack length of the n particles; S5, an observation step: observing whether there is a measured crack length, if there is a measured crack length, executing step S6, and if there is no measured crack length, executing step S8; S6, an updating step: calculating the fitness values of the particles according to the predicted crack length of the n particles and the measured crack length, sorting the fitness values of the particles in size, optimizing the particles with a fitness value less than a preset fitness threshold, and updating the weight of the optimized particles; S7, a particle resampling step: combining the optimized particles and the unoptimized particles to form a temporary particle set, resampling the temporary particle set according to the weights to obtain a new particle set; S8, a crack length calculation step: calculating the crack length according to the state values of the particles in the particle set to obtain a crack length estimate value; S9. Judgment Step: Determine whether the estimated crack length has reached the critical crack length. If the estimated crack length has not reached the critical crack length, use the estimated crack length as the predicted crack length for the next moment and return to step S5. If the estimated crack length reaches the critical crack length, end the prediction.

[0008] In some embodiments, in step S2, the fatigue crack propagation model is represented as:

[0009] In the formula, express The length of the component crack at any given moment. express Component material parameters at any given time. express Parameters of component crack closure effect at time. express The amplitude of the stress intensity factor at time t. This represents the stress threshold factor under different stress ratios. Indicates the stress ratio. Indicates the fracture toughness of the component material. Indicates the interval of iteration. express The length of the component crack at any given time is measured with the center line of the loading hole of the component as the reference plane.

[0010] In some embodiments, the The stress intensity factor amplitude at time t is expressed as:

[0011] In the formula, Indicates the load range of the component. , Indicates the peak load. Indicates the load valley value; Indicates the thickness of the component. Indicates the width of the component; express The shape factor at time.

[0012] In some embodiments, the The shape factor at time step is expressed as:

[0013] In the formula, This represents an intermediate variable with no practical meaning. .

[0014] In some embodiments, in step S6, the fitness value of each particle is calculated using a fitness calculation formula, which is expressed as:

[0015] In the formula, For fitness value, To observe the noise variance, The measured crack length, To predict crack length.

[0016] In some embodiments, in step S6, particles with fitness values ​​less than a preset fitness threshold are updated in terms of velocity and position using velocity update formulas and position update formulas, which are expressed as follows:

[0017]

[0018] In the formula, Indicates the first Individual particles The first generation 3D velocity components; Indicates the inertia factor. Indicates the first Individual particles The first generation 3D velocity components; This represents the learning factor, with a value range of [0,4]. A random number between [0,1]; Indicates the first Individual particles The first generation The optimal solution for each individual; Indicates in The first generation Dimensional global optimal solution; Indicates the first Individual particles The first generation 3D positional components; Indicates the first Individual particles The first generation Dimensional positional components.

[0019] In some embodiments, in step S6, the weights of the optimized particles are updated using a weight update formula, which is expressed as:

[0020] In the formula, Indicates the first a particle at time t; a weight of a particle at time t; a particle at time t; a weight of a particle at time t; a particle at time t; a transition probability density function, representing a state value of a particle at time t; a particle at time t; a state value of a particle at time t a state value of a particle at time t a probability density of a state value of a particle at time t when the particle is transformed; a likelihood function, representing an observation at time t when a state value of a particle is a particle at time t; a state value of a particle at time t an observation at time t when a state value of a particle is a probability density of an observation history at time t; an importance probability density function; representing an observation history from 1 to t. In some embodiments, in step S8, a calculation formula of the crack length is calculated according to the state value of each particle in the particle set, and is represented as:

[0021]

[0022] In the formula, L represents a crack length estimate value, and xi represents a state value of a particle at time t. a state value of a particle at time t

[0023] In a second aspect, the application provides a fatigue crack propagation prediction system for implementing the fatigue crack propagation prediction method based on the improved particle filtering algorithm in the first aspect of the application, and the system comprises: a data acquisition module, configured to acquire a component width and thickness, a component load range, component material parameters, a component stress ratio, a component material fracture toughness, a component crack closure effect parameter, and stress threshold factors under different stress ratios; a model construction module, configured to construct a fatigue crack propagation model according to the stress ratio, the material parameters, the material fracture toughness, the crack closure effect parameter, and the stress threshold factors under different stress ratios; a sampling module, configured to sample n particles from model parameters to be estimated in the fatigue crack propagation model, to obtain initial state values of the n particles, and to form a particle set by using the initial state values of the n particles; and to combine the optimized particles and the unoptimized particles to form a temporary particle set, and to resample the temporary particle set according to weights to obtain a new particle set; a prediction module, configured to predict crack lengths of the n particles by using the fatigue crack propagation model to obtain predicted crack lengths of the n particles; ​​​​an observation module, configured to observe whether the measured crack length is observed; an updating module, configured to calculate the fitness value of each particle according to the predicted crack length and the measured crack length of the n particles, sort the fitness values of the particles in size, optimize the particles with a fitness value less than a preset fitness threshold, and update the weight of the optimized particles; a calculating module, configured to calculate the crack length according to the state value of each particle in the particle set to obtain a crack length estimation value; a judging module, configured to judge whether the crack length estimation value reaches a critical crack length, send the crack length estimation value to the observation module as a predicted crack length at the next time when the crack length estimation value does not reach the critical crack length, and end the prediction when the crack length estimation value reaches the critical crack length.

[0024] Compared with the prior art, the fatigue crack propagation prediction method and system based on the improved particle filtering algorithm provided in the application consider the influence of the stress ratio, material parameters, material fracture toughness, crack closure effect parameters and stress threshold factors under different stress ratios on the fatigue crack propagation rate, take the crack closure effect parameters as independent model parameters like the material parameters, construct a fatigue crack propagation model in combination of the stress ratio, material parameters, material fracture toughness and stress threshold factors under different stress ratios, and accurately predict the crack length through the fatigue crack propagation model to improve the fatigue crack propagation prediction precision. The fitness values of the particles are divided into large weight particles and small weight particles, the small weight particles are optimized, the weight of the optimized particles is updated, the optimized particles and the unoptimized particles are combined to form a temporary particle set, the temporary particle set is resampled according to the weight, and the diversity of the resampled particles is improved.

[0025] The fatigue crack propagation prediction method and system based on the improved particle filtering algorithm provided in the application introduce the stress ratio and material fracture toughness based on the structural design of the Forman model when constructing the fatigue crack propagation model, and then introduce the stress threshold factor under different stress ratios based on the Elber model and the improved Schütz model. The fatigue crack propagation model constructed in the application considers the influence of the stress ratio and the crack closure effect parameters on the fatigue crack propagation rate and can accurately describe the crack propagation rate problem in the near-threshold region.

[0026] The fatigue crack propagation prediction method and system based on the improved particle filtering algorithm provided in the application only optimize the small weight particles when updating the particle weight, and do not tend all the particles to the high likelihood region, which can avoid the "convergence" of the particles, improve the diversity of the resampled particles, and improve the calculation efficiency.

[0027] The details of one or more embodiments of the application are set forth in the accompanying drawings and the description below. Other features, objects, and advantages of the application will be apparent from the description of the embodiments and from the claims. BRIEF DESCRIPTION OF DRAWINGS

[0028] The accompanying drawings are included to provide a further understanding of the application and are incorporated in and constitute a part of this application, illustrate embodiments of the application and explain it, but are not for limiting the application. In the drawings: Figure 1 Flow chart of the fatigue crack growth prediction method based on the improved particle filter algorithm according to an embodiment of the application; Figure 2 Flow chart of the fatigue crack growth prediction method based on the improved particle filter algorithm according to another embodiment of the application; Figure 3 Structure block diagram of the fatigue crack growth prediction system according to an embodiment of the application; Figure 4 Schematic diagram of the crack growth process of 2024-T351 aluminum alloy according to an embodiment of the application; Figure 5 Schematic diagram of the average data of the crack growth process of 2024-T351 aluminum alloy according to an embodiment of the application; Figure 6 Schematic diagram of the fitting result of the obtained average growth rate according to an embodiment of the application; Figure 7 Comparison diagram of the crack growth prediction results of curve A corresponding to different prediction methods; Figure 8 Schematic diagram of the prediction particle distribution of curve A using the PF algorithm; Figure 9 Schematic diagram of the prediction particle distribution of curve A using the PSO-PF algorithm; Figure 10 Schematic diagram of the prediction particle distribution of curve A using the method and system of the application; Figure 11 Comparison diagram of the crack growth prediction results of curve B corresponding to different prediction methods; Figure 12 Schematic diagram of the prediction particle distribution of curve B using the PF algorithm; Figure 13 Schematic diagram of the prediction particle distribution of curve B using the PSO-PF algorithm; Figure 14 Schematic diagram of the prediction particle distribution of curve B using the method and system of the application.

[0029] In the figure, 1, data acquisition module, 2, model construction module, 3, sampling module, 4, prediction module, 5, observation module, 6, update module, 7, calculation module, 8, judgment module. DETAILED DESCRIPTION

[0030] In order to make the purpose, technical scheme and advantages of the present application more clear, the present application is described and explained below in combination with the drawings and examples. It should be understood that the specific examples described herein are only used to explain the present application, and are not used to limit the present application. Based on the examples provided in the present application, all other examples obtained by those of ordinary skill in the art without making creative efforts fall within the scope of the present application.

[0031] Obviously, the drawings described below are only some examples or embodiments of the present application, and for those of ordinary skill in the art, the present application can be applied to other similar scenarios without making creative efforts based on these drawings. In addition, it can be understood that although the efforts made in this development process can be complex and lengthy, for those of ordinary skill in the art related to the content disclosed in the present application, some design, manufacture or production changes based on the technical content disclosed in the present application are only routine technical means, and should not be understood as insufficient disclosure of the present application.

[0032] In the present application, "embodiment" means that the specific features, structures or characteristics described in combination with the embodiment can be included in at least one embodiment of the present application. The appearance of this phrase in various places in the specification does not necessarily mean the same embodiment, nor is it an independent or alternative embodiment that is not mutually exclusive with other embodiments. It is explicitly and implicitly understood by those of ordinary skill in the art that the embodiments described in the present application can be combined with other embodiments without conflict.

[0033] Unless otherwise defined, technical terms and scientific terms used in the present application shall have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains. The terms "a", "an", "one", "this", and similar referents in the context of describing the application are to be construed to be inclusive, rather than exclusive. The terms "including", "containing", "having", and "comprising" and variations thereof in the present application are meant to encompass the presence of steps, processes, systems, products, or devices, as well as their inherent equivalents. The terms "connected", "coupled", and similar referents in the context of this application are to be construed as be inclusive rather than exclusive.

[0034] The fatigue crack propagation prediction method and system based on the improved particle filtering algorithm described in the present application can be used for fatigue crack propagation prediction.

[0035] Referring to Figure 1 The fatigue crack propagation prediction method based on the improved particle filtering algorithm provided by the embodiments of the present application comprises the following steps: S1, data acquisition step: acquiring the component width and thickness, component load range, component material parameters, component stress ratio, component material fracture toughness, component crack closure effect parameters, and stress threshold factors under different stress ratios.

[0036] The stress ratio is a core representation parameter of the fatigue load, and is the ratio of the minimum stress to the maximum stress in the cyclic load, reflecting the "tension-compression characteristics" and "average stress level" of the load. The material fracture toughness is the maximum stress intensity at which the material resists unstable crack propagation under plane strain conditions; the material fracture toughness is a core representation of the "toughness level" of the material, and a material with high material fracture toughness (such as low-carbon steel) has obvious plastic deformation before fracture, and a material with low material fracture toughness (such as quenched high-carbon steel, ceramic) is prone to brittle fracture. The stress threshold factor is a "critical threshold value" of fatigue crack propagation, specifically when the stress intensity factor amplitude generated by the cyclic load is lower than the stress threshold factor, the fatigue crack almost stops expanding (the expansion rate is less than / cycle).

[0037] S2, model construction step: constructing a fatigue crack propagation model according to the stress ratio, material parameters, material fracture toughness, crack closure effect parameters, and stress threshold factors under different stress ratios.

[0038] Specifically, the fatigue crack propagation model is represented as:

[0039] wherein, represents the component crack length at the time, represents the component material parameter at the time, represents the component crack closure effect parameter at the time, represents the stress intensity factor amplitude at the time, represents the stress threshold factor under different stress ratios, represents the stress ratio, represents the component material fracture toughness, represents the interval of iteration, represents the component crack length at the time, measured with the loading hole centerline of the component as the reference surface.

[0040] In the embodiments of the present application, when constructing the fatigue crack propagation model, the stress ratio and the material fracture toughness are introduced based on the structure design of the Forman model; then, the crack closure effect parameter is introduced by referring to the Elber model and the improved Schütz model, and the crack propagation rate near the threshold is described by the crack propagation rate formula. The fatigue crack propagation model constructed in the present application simultaneously considers the influence of the stress ratio and the crack closure effect parameter on the fatigue crack propagation rate, and can accurately describe the crack propagation rate problem in the near-threshold region of the crack propagation.

[0041] Specifically, the stress intensity factor amplitude at the time is expressed as:

[0042] wherein, represents the component load range, , represents the load peak value, represents the load valley value; represents the component thickness, represents the component width; represents the shape factor at the time.

[0043] Specifically, the shape factor at the time is expressed as:

[0044] wherein, represents an intermediate variable, which has no actual meaning, .

[0045] ​​S3. Particle Sampling Step: Sample n particles from the model parameters to be estimated in the fatigue crack propagation model to obtain the initial state values ​​of the n particles, and form a particle set from the initial state values ​​of the n particles. , For the first The initial state values ​​of the n particles are given; the initial weights of the n particles are equal, each being 1 / n.

[0046] S4. Crack length prediction steps: The crack length of n particles is predicted by using the fatigue crack propagation model to obtain the predicted crack length of n particles.

[0047] S5. Observation steps: Observe whether there is a measured crack length. If there is a measured crack length, proceed to step S6. If there is no measured crack length, proceed to step S8.

[0048] S6. Update steps: Calculate the fitness value of each particle based on the predicted crack length and the measured crack length of n particles, sort the fitness values ​​of each particle by size, optimize the particles whose fitness values ​​are less than the preset fitness threshold, and update the weights of the optimized particles.

[0049] Specifically, the fitness value of each particle is calculated using the fitness calculation formula, which is expressed as follows:

[0050] In the formula, For fitness value, To observe the noise variance, The measured crack length, To predict crack length.

[0051] Specifically, the velocity and position of particles with fitness values ​​less than a preset fitness threshold are optimized and updated using velocity and position update formulas, which are expressed as follows:

[0052]

[0053] In the formula, Indicates the first Individual particles The first generation 3D velocity components; Indicates the inertia factor. Indicates the first Individual particles The first generation 3D velocity components; This represents the learning factor, with a value range of [0,4]. a random number between [0, 1]; denotes the th particle in the th generation of the dimensional individual optimal solution; denotes the th global optimal solution in the th generation of the dimensional individual optimal solution; denotes the th particle in the th generation of the dimensional position component; denotes the th particle in the th generation of the dimensional position component.

[0054] Specifically, the weight of the optimized particle is updated by a weight update formula, and the weight update formula is represented as:

[0055] In the formula, w (i, t) denotes the weight of the i th particle at the t th moment; w (i, t + 1) denotes the weight of the i th particle at the t + 1 th moment; f (x i, t | x i, t - 1) is a transition probability density function, which represents the probability density of the state value of the i th particle at the t th moment x i, t - 1 transforming into the state value of the i th particle at the t + 1 th moment x i, t ; g (y | x i, t) is an observation likelihood function, which represents the probability density of the observation history at the t + 1 th moment y given that the state value of the i th particle is x i, t ; w (x i, t) is an importance probability density function; y t + 1 represents the observation history from the 1 th to the t + 1 th moment.

[0056] In the embodiments of the present application, the calculated particle fitness values are sorted according to size, the particles are divided into two parts according to a preset fitness threshold, that is, large-weight particles greater than or equal to the preset fitness threshold and small-weight particles less than the preset fitness threshold, the small-weight particles are optimized, the particles are made to approach the real state, and then the particle set is made to concentrate in a more optimal solution region, so that the fatigue crack propagation prediction precision is improved.

[0057] S7, particle resampling step: the optimized particles and the unoptimized particles are combined to form a temporary particle set, and the temporary particle set is resampled according to the weight to obtain a new particle set​​​​​​​​​​​​​​​​​​ , is the state value of the i-th particle at the time t.

[0058] Specifically, before resampling the temporary particle set weight, the weight of each particle is normalized. It should be noted that if the weight distribution is uneven during resampling, it may lead to loss of diversity of the particle set. The present application normalizes the weight of the particle before resampling to ensure the rationality of resampling and reduce the depletion of particles.

[0059] S8, crack length calculation step: calculating the crack length according to the state value of each particle in the particle set to obtain the crack length estimate.

[0060] Specifically, the calculation formula for calculating the crack length according to the state value of each particle in the particle set is represented as:

[0061] In the formula, represents the crack length estimate, represents the state value of the i-th particle at the time t.

[0062] S9, judgment step: judging whether the crack length estimate reaches the critical crack length. When the crack length estimate does not reach the critical crack length, the crack length estimate is taken as the predicted crack length at the next time, and the step S5 is returned. When the crack length estimate reaches the critical crack length, the prediction is ended.

[0063] It should be noted that the steps shown in the above process or the flowchart of the accompanying drawings can be executed in a computer system such as a set of computer executable instructions, and although the logical order is shown in the flowchart, in some cases, the steps shown or described can be executed in an order different from here. For example, see Figure 2 ​​​​, S1, a model construction step: constructing a fatigue crack propagation model according to a stress ratio, material parameters, material fracture toughness, crack closure effect parameters and stress threshold factors under different stress ratios; S2, a data acquisition step: acquiring a component width and thickness, a component load range, component material parameters, component stress ratios, component material fracture toughness, component crack closure effect parameters and stress threshold factors under different stress ratios; S3, a particle sampling step: sampling n particles from model parameters to be estimated in the fatigue crack propagation model, obtaining initial state values of the n particles, and forming a particle set by the initial state values of the n particles; the initial weights of the n particles are equal, and are all 1 / n; S4, a crack length prediction step: predicting crack lengths of the n particles by the fatigue crack propagation model to obtain predicted crack lengths of the n particles; S5, an observation step: observing whether there is a measured crack length, if there is a measured crack length, performing step S6, and if there is no measured crack length, performing step S8; S6, an updating step: calculating fitness values of the particles according to the predicted crack lengths of the n particles and the measured crack length, sorting the fitness values of the particles in size, optimizing the particles with fitness values less than a preset fitness threshold, and updating weights of the optimized particles; S7, a particle resampling step: combining the optimized particles and the unoptimized particles to form a temporary particle set, and resampling the temporary particle set according to the weights to obtain a new particle set; S8, a crack length calculation step: calculating a crack length according to state values of the particles in the particle set to obtain a crack length estimation value; S9, a judgment step: judging whether the crack length estimation value reaches a critical crack length, when the crack length estimation value does not reach the critical crack length, taking the crack length estimation value as a predicted crack length at a next time, and returning to step S5, and when the crack length estimation value reaches the critical crack length, ending the prediction.

[0064] The fatigue crack propagation prediction method based on the improved particle filtering algorithm provided in the embodiments of the application combines the improved particle filtering algorithm (hereinafter referred to as IPSO-PF algorithm) with a fatigue crack propagation model (i.e. Paris model), corrects the distribution of material parameter particles in the fatigue crack propagation model through actual crack measurement values, improves the fatigue crack propagation prediction accuracy, and solves the problems of low prediction accuracy of the traditional Paris model and neglecting the influence of various uncertain factors in the crack propagation process.

[0065] The embodiments further provide a fatigue crack propagation prediction system, which is used to implement the fatigue crack propagation prediction method based on the improved particle filtering algorithm described in the above embodiments.

[0066] As used below, the terms "module", "unit", "sub-unit", etc. can be a combination of software and / or hardware that implements a predetermined function. Although the apparatus described in the following embodiments is preferably implemented in software, implementation in hardware, or a combination of software and hardware, is also possible and contemplated.

[0067] Figure 3 is a structural block diagram of a fatigue crack propagation prediction system of an embodiment of the present application, as shown in the figure, the system comprises: Figure 3 a data acquisition module 1, configured to acquire member width and thickness, member load range, member material parameters, member stress ratio, member material fracture toughness, member crack closure effect parameters, and stress threshold factors under different stress ratios; a model construction module 2, configured to construct a fatigue crack propagation model according to the stress ratio, the material parameters, the material fracture toughness, the crack closure effect parameters, and the stress threshold factors under different stress ratios; a sampling module 3, configured to sample n particles from model parameters to be estimated of the fatigue crack propagation model, obtain initial state values of the n particles, and form a particle set with the initial state values of the n particles; combine the optimized particles with the unoptimized particles to form a temporary particle set, and resample the temporary particle set according to weights to obtain a new particle set; a prediction module 4, configured to predict crack lengths of the n particles through the fatigue crack propagation model to obtain predicted crack lengths of the n particles; an observation module 5, configured to observe whether there is a measured crack length; an updating module 6, configured to calculate fitness values of the particles according to the predicted crack lengths of the n particles and the measured crack length, sort the fitness values of the particles in size, optimize the particles with fitness values less than a preset fitness threshold, and update weight values of the optimized particles; a calculation module 7, configured to calculate a crack length from state values of the particles in the particle set to obtain a crack length estimation value; a judgment module 8, configured to judge whether the crack length estimation value reaches a critical crack length, send the crack length estimation value as a predicted crack length at a next time to the observation module 5 when the crack length estimation value does not reach the critical crack length, and end the prediction when the crack length estimation value reaches the critical crack length.

[0068] It should be noted that each of the above modules can be a functional module or a program module, and can be implemented by software or hardware. For the modules implemented by hardware, each of the above modules can be located in the same processor; or each of the above modules can also be located in different processors in any combination.

[0069] ​The following verifies the effectiveness and accuracy of the fatigue crack propagation prediction method and system based on the improved particle filtering algorithm of the present application through specific examples.

[0070] Embodiment: 30 sets of public data of 2024-T351 aluminum alloy crack propagation are used for verification, and the crack propagation processes of the 30 sets of 2024-T351 aluminum alloy are as shown in Figure 4 The average value of the 30 sets of crack propagation degradation data curves is taken as the prior information, and the partial crack lengths of the curve A (specimen 1) with the fastest crack propagation and the curve B (specimen 2) with the slowest crack propagation are taken as the actual observation data, and the crack propagation processes in the two extreme cases are predicted.

[0071] Test data description: The standard compact tension specimen is used for the test, the width and thickness of the specimen are 50 mm and 12 mm respectively, and the initial crack length at the beginning of the test is 18 mm. The test uses a constant amplitude load sinusoidal signal for loading, and the maximum load is 4.5 kN and the minimum load is 0.9 kN.

[0072] The average value of the 30 curves is calculated as the prior information set, as shown in Figure 5 .

[0073] The fatigue crack propagation rate is calculated, and the commonly used calculation methods include the secant method and the incremental polynomial method. The fatigue crack propagation rate obtained by the incremental polynomial method is fitted to obtain the relationship curve between the stress intensity factor amplitude , and generally 5 or 7 points are used to obtain the crack propagation rate at the intermediate point. The crack propagation rate curve obtained by using this method is relatively smooth, and the dispersion of the test data is small. The secant method uses two adjacent points to obtain the crack propagation rate at the intermediate position, and the dispersion of the crack propagation rate obtained by using the secant method is large, but it can more truly reflect the change trend of the test results. In order to verify the effectiveness of the method and system of the present application, the crack propagation rate in the near threshold region needs to be fitted, and in the case that the test data points in the near threshold value region are less, the use of the 7-point incremental polynomial method will result in insufficient effective data points. Therefore, the secant method is used in the method and system of the present application to calculate the crack propagation rate at the intermediate point through the data of two adjacent points.

[0074] (1) , wherein represents the crack increment, represents the crack length at the time , represents the crack length at the time ; represents the cycle increment, represents the crack length at the time ​The number of loops at any given time. express The number of loops at any given time; for and The median value, Indicates the number of iterations.

[0075] According to the formula for calculating the stress intensity factor amplitude given in GB / T 6398-2017, the formula for calculating the stress intensity factor amplitude of a standard compact tensile specimen is as follows: (2) In the formula: Indicates the load range of the component. , Indicates the peak load. Indicates the load valley value; Indicates the thickness of the component. Indicates the width of the component; Represents the shape factor.

[0076] For a standard compact tensile specimen, the shape factor is expressed as: (3) In the formula, This represents an intermediate variable with no practical meaning. , The length of the component crack is measured with the center line of the loading hole as the reference plane.

[0077] The stress intensity factor amplitude is calculated using formulas (2) and (3) above. The average propagation rate of 30 cracks is obtained using formula (1). The obtained average propagation rate is fitted using formula (4). The fitting result is as follows: Figure 6 As shown.

[0078] (4) Obtain the Paris model parameters for 2024-T351 aluminum alloy. , To simplify the calculation process, we can use... Alternative And assume Paris model parameters [ , It follows a bivariate normal distribution.

[0079] The Paris model is discretized and used as the state equation describing fatigue crack propagation: (5) In the formula: express The length of the component crack at any given time; represents the component crack length at the time instant, measured with respect to the loading hole centerline of the component as the reference surface; represents the interval of iteration; represents the fatigue crack growth model parameter at the time instant; represents the stress intensity factor amplitude at the time instant.

[0080] To realize the prediction of the propagation of the two cracks, three points on curve A and curve B are taken as actual observation data, respectively. The observation data of curve A (specimen 1) are (10000, 19.254), (20000, 21.026) and (30000, 23.259), respectively. The observation data of curve B (specimen 2) are (10000, 18.553), (20000, 19.310) and (30000, 20.264), respectively. The particle number is taken as 1000, the particle swarm optimization algorithm parameters , and the number of iterations is 50. The IPSO-PF algorithm is used to optimize the half particles with smaller weights in the IPSO-PF algorithm. The Paris model, Paris-PF algorithm, Paris-PSO-PF algorithm and the method and system of the present application are used to predict the crack propagation process of curve A and curve B. The crack propagation prediction curve of curve A is shown in Figure 7 , and the corresponding prediction error and prediction particle distribution are shown in Table 1 and Figure 8 to Figure 10 , respectively. The crack propagation prediction curve of curve B is shown in Figure 11 , and the corresponding prediction particle distribution and prediction error are shown in Table 2 and Figure 12 to Figure 14 , respectively.

[0081] Table 1

[0082] Table 2

[0083] ​​From Table 1 and Table 2, it can be seen that the average prediction error of the two curves based on the Paris model is 27.1%; the average prediction error of the two curves based on the Paris-PF algorithm is 9.2%, the average prediction error of the two curves based on the Paris-PSO-PF algorithm is 2.7%; and the average prediction error of the two curves based on the method and system of the present application is 2.6%. The above results show that, compared with directly using the Paris model for crack propagation, the prediction accuracy is greatly improved based on the Paris-PF algorithm, the Paris-PSO-PF algorithm and the method and system of the present application for crack propagation, indicating that the three methods can effectively correct the crack propagation process and greatly improve the accuracy of crack propagation prediction. However, compared with the Paris-PF algorithm, the Paris-PSO-PF algorithm and the method and system of the present application have higher accuracy in correcting crack propagation. However, since the method and system of the present application only need to optimize half of the particles, while the Paris-PSO-PF algorithm needs to optimize all particles, the method and system of the present application save the calculation space.

[0084] From Figure 8 to Figure 10 and Figure 12 to Figure 14 it can be seen that: when predicting crack propagation to the critical crack based on the traditional Paris-PF algorithm, a large number of particles appear in positions deviating from the true value, especially for the prediction of curve A, a large number of particles are predicted to be around 35000 times, while based on the Paris-PSO-PF algorithm and the method and system of the present application, most of the predicted particles are close to the true value and show a normal distribution characteristic, and the particle distribution is more reasonable.

[0085] The main reason for the above results is that the Paris-PF algorithm has a greater probability of retaining and copying large weight particles during resampling, eliminating small weight particles, leading to sample impoverishment. After the particles are updated according to the first observation information, some particles fall into local optimal traps, and these particles have large weights. When resampling is directly performed, the states of these particles are copied a lot, thereby causing a large number of particles falling into local optimal traps to be retained at the end, reducing the particles close to the true value of the model parameters, and finally leading to a large deviation between the prediction result and the true result. The method and system of the present application tend to high likelihood regions, which is equivalent to "diluting" the weights of particles falling into local optimal traps, avoiding a large number of copies of particles falling into local optimal traps during resampling, improving the diversity of particles, and thus the particle distribution is more reasonable, and finally the prediction result of the method and system of the present application is closer to the true result.

[0086] Any combination of the technical features in the above-described embodiments can be made, and for the sake of brevity, not all possible combinations are described, however, as long as there is no conflict, any combination of the technical features should be considered within the scope of the present disclosure.

[0087] The above-described embodiments only express several implementation manners of the present application, and the description is relatively specific and detailed, but it should not be understood as a limitation on the patent scope of the present application. It should be pointed out that, for ordinary skilled persons in the art, several modifications and improvements can be made without departing from the concept of the present application, and these all belong to the protection scope of the present application. Therefore, the patent protection scope of the present application should be subject to the appended claims.

Claims

1. A method for predicting fatigue crack growth based on an improved particle filter algorithm, characterized by, The method comprises the following steps: S1, a data acquisition step: acquiring component width and thickness, component load range, component material parameters, component stress ratio, component material fracture toughness, component crack closure effect parameters, and stress threshold factors under different stress ratios; S2, a model construction step: constructing a fatigue crack propagation model according to the stress ratio, material parameters, material fracture toughness, crack closure effect parameters, and stress threshold factors under different stress ratios; S3, a particle sampling step: sampling n particles from the model parameters to be estimated in the fatigue crack propagation model, obtaining initial state values of the n particles, and forming a particle set from the initial state values of the n particles; the initial weights of the n particles are equal, and each is 1 / n; S4, a crack length prediction step: predicting the crack length of the n particles through the fatigue crack propagation model to obtain predicted crack lengths of the n particles; S5, an observation step: observing whether there is a measured crack length, if there is a measured crack length, executing step S6, and if there is no measured crack length, executing step S8; S6, an updating step: calculating the fitness values of the particles according to the predicted crack lengths of the n particles and the measured crack length, sorting the fitness values of the particles in size, optimizing the particles with fitness values less than a preset fitness threshold, and updating the weights of the optimized particles; S7, a particle resampling step: combining the optimized particles and the unoptimized particles to form a temporary particle set, and resampling the temporary particle set according to the weights to obtain a new particle set; S8, a crack length calculation step: calculating the crack length according to the state values of the particles in the particle set to obtain a crack length estimate value; S9, a judgment step: judging whether the crack length estimate value reaches a critical crack length, when the crack length estimate value does not reach the critical crack length, taking the crack length estimate value as a predicted crack length at the next moment and returning to step S5, and when the crack length estimate value reaches the critical crack length, ending the prediction.

2. The method of claim 1, wherein the method is characterized by: In step S2, the fatigue crack propagation model is represented as: wherein denotes the component crack length at the time instant, denotes the component material parameter at the time instant, denotes the component crack closure effect parameter at the time instant, denotes the stress intensity factor amplitude at the time instant, denotes the stress threshold factor at different stress ratios, denotes the stress ratio, denotes the component material fracture toughness, denotes the interval of iteration, denotes the component crack length at the time instant, measured with respect to the loading hole centerline of the component.

3. The method of claim 2, wherein the method is characterized by: The The stress intensity factor amplitude at the time instant is represented as: wherein denotes the component load range, , denotes the load peak, denotes the load valley; denotes the component thickness, denotes the component width; denotes the shape factor at the instant of time.

4. The method of claim 3, wherein the method is characterized by, The The shape factor at the moment is expressed as: In the formula, denotes an intermediate variable, which has no actual meaning, .

5. The method of claim 1, wherein the method is characterized by: In step S6, the fitness values of the particles are calculated by using a fitness calculation formula, and the fitness calculation formula is represented as: wherein is a fitness value, is an observation noise variance, is a measured crack length, is a predicted crack length.

6. The method of claim 1, wherein the method is characterized by: In step S6, the particles with fitness values less than a preset fitness threshold are optimized and updated in speed and position by using a speed updating formula and a position updating formula, and the speed updating formula and the position updating formula are represented as: In the formula, Indicates the first Individual particles The first generation 3D velocity components; Indicates the inertia factor. Indicates the first Individual particles The first generation 3D velocity components; This represents the learning factor, with a value range of [0,4]. A random number between [0,1]; Indicates the first Individual particles The first generation The optimal solution for each individual; Indicates in The first generation Dimensional global optimal solution; Indicates the first Individual particles The first generation 3D positional components; Indicates the first Individual particles The first generation Dimensional positional components.

7. The method of claim 1, wherein the method is characterized by: In step S6, the weights of the optimized particles are updated by using a weight updating formula, and the weight updating formula is represented as: where denotes the weight of the th particle at time ; denotes the weight of the th particle at time ; is the transition probability density function, which denotes the probability density of the state value of the th particle at time ; to the state value of the th particle at time ; is the observation likelihood function, which denotes the probability density of the observation at time given the state value of the th particle is ; is the importance probability density function; denotes the observation history from time 1 to time .

8. The method of claim 1, wherein the method is characterized by: In step S8, a calculation formula for calculating the crack length according to the state values of the particles in the particle set is represented as: In the formula, This represents the estimated crack length. Indicates the first Individual particles The state value at any given time.

9. A fatigue crack growth prediction system for implementing the method of fatigue crack growth prediction based on the improved particle filter algorithm according to any one of claims 1 to 8, characterized in that, The method comprises the following steps: The data acquisition module is used to acquire component width and thickness, component load range, component material parameters, component stress ratio, component material fracture toughness, component crack closure effect parameters, and stress threshold factors under different stress ratios; The model construction module is used to construct a fatigue crack propagation model according to the stress ratio, material parameters, material fracture toughness, crack closure effect parameters, and stress threshold factors under different stress ratios; The sampling module samples n particles from model parameters to be estimated of the fatigue crack propagation model, obtains initial state values of the n particles, and forms a particle set with the initial state values of the n particles; the optimized particles are combined with the unoptimized particles to form a temporary particle set, and the temporary particle set is resampled according to weights to obtain a new particle set; The prediction module predicts crack lengths of the n particles through the fatigue crack propagation model to obtain predicted crack lengths of the n particles; The observation module observes whether there is a measured crack length; The updating module calculates fitness values of the particles according to the predicted crack lengths of the n particles and the measured crack length, sorts the fitness values of the particles in size, optimizes the particles with fitness values less than a preset fitness threshold, and updates weights of the optimized particles; The calculation module calculates a crack length estimation value from state values of the particles in the particle set; The judgment module is configured to judge whether the crack length estimation value reaches a critical crack length, send the crack length estimation value to the observation module as a predicted crack length at a next time when the crack length estimation value does not reach the critical crack length, and end the prediction when the crack length estimation value reaches the critical crack length.

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