Fatigue crack growth prediction method and system based on improved particle filtering algorithm

Abstract

The application 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 filtering algorithm. A fatigue crack propagation model constructed according to a stress ratio, material parameters, material fracture toughness, crack closure effect parameters and a stress threshold factor is used to predict the predicted crack length of a sampling particle. When the measured crack length is available, the fitness value of each particle is calculated according to the predicted crack length and the measured crack length, the fitness values are sorted by size, 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, the crack length estimation value is calculated according to the state value of each particle, the prediction is continued when the crack length estimation value does not reach the critical crack length, and the prediction is ended when the crack length estimation value reaches the critical crack length. The application improves the particle diversity and the fatigue crack propagation prediction accuracy.

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:

[0003] 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.

[0004] 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.

[0005] 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.

[0006] 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

[0007] 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 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 of the stress ratio, material parameters, material fracture toughness and 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 particles after resampling.

[0008] In a first aspect, the application provides a fatigue crack propagation prediction method based on an improved particle filtering algorithm, comprising the following steps:

[0009] S1, a 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;

[0010] 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;

[0011] S3, a particle sampling step: sampling n particles from the model parameters to be estimated of 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;

[0012] 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;

[0013] 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;

[0014] 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;

[0015] 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 weight to obtain a new particle set;

[0016] S8. Crack length calculation steps: Calculate the crack length based on the state values ​​of each particle in the particle set to obtain an estimated crack length;

[0017] 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.

[0018] In some embodiments, in step S2, the fatigue crack propagation model is represented as:

[0019]

[0020] 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.

[0021] In some embodiments, the The stress intensity factor amplitude at time t is expressed as:

[0022]

[0023] 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.

[0024] In some embodiments, the The shape factor at time step is expressed as:

[0025]

[0026] wherein, is an intermediate variable, and has no actual meaning, .

[0027] In some embodiments, in step S6, the fitness value of each particle is calculated by using a fitness calculation formula, which is expressed as:

[0028]

[0029] wherein, is the fitness value, is the observation noise variance, is the measured crack length, is the predicted crack length.

[0030] In some embodiments, in step S6, the particles with the fitness value less than a preset fitness threshold are updated in speed and position by using a speed update formula and a position update formula, which are expressed as:

[0031]

[0032]

[0033] wherein, is the j-th particle in the i-th generation in the d-th dimension; is the j-th particle in the i-th generation in the d-th dimension; is the j-th particle in the i-th generation in the d-th dimension; is the j-th particle in the i-th generation in the d-th dimension; is an inertia factor, is the j-th particle in the i-th generation in the d-th dimension; is the j-th particle in the i-th generation in the d-th dimension; is the j-th particle in the i-th generation in the d-th dimension; is a learning factor, and has a value range of [0, 4]; is a random number in [0, 1]; is the j-th particle in the i-th generation in the d-th dimension; is the j-th particle in the i-th generation in the d-th dimension; is the j-th particle in the i-th generation in the d-th dimension; is the j-th particle in the i-th generation in the d-th dimension; is the j-th particle in the i-th generation in the d-th dimension; is the j-th particle in the i-th generation in the d-th dimension; is the j-th particle in the i-th generation in the d-th dimension; is the j-th particle in the i-th generation in the d-th dimension; is the j-th particle in the i-th generation in the d-th dimension; is the j-th particle in the i-th generation in the d-th dimension; is the j-th particle in the i-th generation in the d-th dimension; is the j-th particle in the i-th generation in the d-th dimension; is the j-th particle in the i-th generation in the d-th dimension.

[0034] ​​​In some embodiments, in step S6, the weights of the optimized particles are updated using a weight update formula, which is expressed as:

[0035]

[0036] In the formula, Indicates the first Individual particles The weight of each moment; Indicates the first Individual particles The weight of each moment; Let be the transition probability density function, representing the th Individual particles Time state value Towards Time state value The probability density of state values ​​during transition; For the observation likelihood function, let be the expression for the th... The state value of each particle is Observed at the time The probability density of observing history at any given time; It is the importance probability density function; Indicates from 1 to The history of observation at any given moment.

[0037] In some embodiments, in step S8, the formula for calculating the crack length based on the state values ​​of each particle in the particle set is expressed as follows:

[0038]

[0039] In the formula, This represents the estimated crack length. Indicates the first Individual particles The state value at any given time.

[0040] Secondly, this application provides a fatigue crack propagation prediction system for implementing the fatigue crack propagation prediction method based on the improved particle filter algorithm described in the first aspect of this application, comprising:

[0041] 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 factor under different stress ratios;

[0042] The model building module constructs a fatigue crack propagation model based on stress ratio, material parameters, material fracture toughness, crack closure effect parameters, and stress threshold factor under different stress ratios.

[0043] 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;

[0044] 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.

[0045] The observation module observes whether there is a measured crack length.

[0046] 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.

[0047] The calculation module calculates a crack length from state values of the particles in the particle set to obtain a crack length estimation value.

[0048] 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.

[0049] 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 a stress ratio, material parameters, material fracture toughness, a crack closure effect parameter and a stress threshold factor under different stress ratios on a fatigue crack propagation rate, take the crack closure effect parameter as an independent model parameter like the material parameters, construct a fatigue crack propagation model in combination of the stress ratio, the material parameters, the material fracture toughness and the stress threshold factor under different stress ratios, and accurately predict a crack length through the fatigue crack propagation model to improve fatigue crack propagation prediction accuracy. The fitness values of the particles are divided into large-weight particles and small-weight particles, the small-weight particles are optimized, weights of the optimized particles are updated, the optimized particles are combined with the unoptimized particles to form a temporary particle set, the temporary particle set is resampled according to the weights, and the diversity of the resampled particles is improved.

[0050] The fatigue crack propagation prediction method and system based on the improved particle filtering algorithm provided in the application introduce a stress ratio and material fracture toughness based on a structure design of a Forman model when constructing a fatigue crack propagation model, and then introduce a crack closure effect parameter and a stress threshold factor under different stress ratios by referring to an Elber model and an improved Schütz model. Structural form is used to describe the crack propagation rate near the threshold. The fatigue crack propagation model constructed by the application considers the influence of stress ratio and crack closure effect parameter on the fatigue crack propagation rate, and can accurately describe the crack propagation rate near the threshold.

[0051] The fatigue crack propagation prediction method and system based on the improved particle filtering algorithm provided by the application only optimize small weight particles when updating particle weights, and do not tend all particles to a high likelihood region, which can avoid particle "convergence", improve the diversity of particles after resampling, and improve the calculation efficiency.

[0052] The details of one or more embodiments of the application are presented in the following drawings and description to make other features, objects and advantages of the application more clear and easy to understand. BRIEF DESCRIPTION OF DRAWINGS

[0053] The drawings described herein are used to provide further understanding of the application, and form a part of the application. The illustrative embodiments of the application and their descriptions are used to explain the application, and do not constitute an improper limitation on the application. In the drawings:

[0054] Figure 1 The flowchart of the fatigue crack propagation prediction method based on the improved particle filtering algorithm according to an embodiment of the application is described;

[0055] Figure 2 The flowchart of the fatigue crack propagation prediction method based on the improved particle filtering algorithm according to another embodiment of the application is described;

[0056] Figure 3 The structural block diagram of the fatigue crack propagation prediction system according to an embodiment of the application is described;

[0057] Figure 4 The schematic diagram of the crack propagation process of 2024-T351 aluminum alloy according to an embodiment of the application is described;

[0058] Figure 5 The schematic diagram of the average data of the crack propagation process of 2024-T351 aluminum alloy according to an embodiment of the application is described;

[0059] Figure 6 The fitting result schematic diagram of the fitted average propagation rate according to an embodiment of the application is described;

[0060] Figure 7 The comparison diagram of the crack propagation prediction results of curve A corresponding to different prediction methods is described;

[0061] Figure 8 The prediction particle distribution schematic diagram of curve A using the PF algorithm is described;

[0062] Figure 9 Fig. 2 is a schematic diagram of predicted particle distribution of curve A using the PSO-PF algorithm;

[0063] Figure 10 Fig. 3 is a schematic diagram of predicted particle distribution of curve A using the method and system of the present application;

[0064] Figure 11 Fig. 4 is a comparison diagram of crack propagation prediction results of curve B using different prediction methods;

[0065] Figure 12 Fig. 5 is a schematic diagram of predicted particle distribution of curve B using the PF algorithm;

[0066] Figure 13 Fig. 6 is a schematic diagram of predicted particle distribution of curve B using the PSO-PF algorithm;

[0067] Figure 14 Fig. 7 is a schematic diagram of predicted particle distribution of curve B using the method and system of the present application.

[0068] In the figure, 1 is a data acquisition module, 2 is a model construction module, 3 is a sampling module, 4 is a prediction module, 5 is an observation module, 6 is an updating module, 7 is a calculation module, and 8 is a judgment module. DETAILED DESCRIPTION

[0069] 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 do not 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.

[0070] 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.

[0071] Reference to an "embodiment" in this application means that a particular feature, structure, or characteristic described in connection with the embodiment can be included in at least one embodiment of the application. The appearances of the phrase in various places in the specification are not necessarily all referring to the same embodiment, nor are they necessarily mutually exclusive of one another. As used in this application, the term "exemplary" is intended to mean serving as an instance or illustration. The phrase "based on" is intended to mean "based, at least in part, on" unless explicitly stated otherwise.

[0072] 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", "the", and the like, as used in the present application, are not intended to be singular or to limit the number of entities to one unless specifically so defined in the application. The terms "including", "containing", "having", and the like, as used in the present application, are intended to be broad and encompass the presence of zero, one, or more steps, components, elements, members, or the like, whether disclosed or not, of the processes, methods, systems, products, or devices described in the present application. The terms "connected", "coupled", "attached", and the like, as used in the present application, are intended to be broad and shall be given their broadest interpretation, e.g., whether connected by direct or indirect means, whether connected by electrical or mechanical means, or whether connected by the same or different means.

[0073] 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.

[0074] 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:

[0075] 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 factor under different stress ratios.

[0076] wherein, the stress ratio is a core representation parameter of the fatigue load, is a ratio of the minimum stress to the maximum stress in the cyclic load, reflects the "tension and compression characteristics" and "average stress level" of the load. The material fracture toughness is the maximum stress intensity under the plane strain condition, which resists the unstable propagation of the crack; the material fracture toughness is the core representation of the "toughness level" of the material, and the material with high material fracture toughness (such as low carbon steel) has obvious plastic deformation before fracture, and the material with low material fracture toughness (such as quenched high carbon steel, ceramic) is easy to have brittle fracture. The stress threshold factor is the "critical threshold value" of the 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 / revolution).

[0077] S2, model construction step: constructing the fatigue crack propagation model according to the stress ratio, the material parameter, the material fracture toughness, the crack closure effect parameter and the stress threshold factor under different stress ratios.

[0078] Specifically, the fatigue crack propagation model is expressed as:

[0079]

[0080] In the formula, L (t) represents the component crack length at the moment t, f (t) represents the component material parameter at the moment t, C (t) represents the component crack closure effect parameter at the moment t, K (t) represents the stress intensity factor amplitude at the moment t, Kth (R) represents the stress threshold factor under different stress ratios, R represents the stress ratio, Kc represents the component material fracture toughness, Δt represents the interval of iteration, and L (t) represents the component crack length at the moment t, which is measured based on the loading hole center line of the component as the reference surface. In the formula, L (t) represents the component crack length at the moment t, f (t) represents the component material parameter at the moment t, C (t) represents the component crack closure effect parameter at the moment t, K (t) represents the stress intensity factor amplitude at the moment t, Kth (R) represents the stress threshold factor under different stress ratios, R represents the stress ratio, Kc represents the component material fracture toughness, Δt represents the interval of iteration, and L (t) represents the component crack length at the moment t, which is measured based on the loading hole center line of the component as the reference surface.

[0081] In the embodiment of the application, when the fatigue crack propagation model is constructed, 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 using the function form. The fatigue crack propagation model constructed in the application 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 area of the crack.

[0082] ​​​​​​​​​​​​​Specifically, the stress intensity factor amplitude at the time point is represented as:

[0083]

[0084] 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 point.

[0085] Specifically, the stress intensity factor amplitude at the time point is represented as:

[0086]

[0087] represents an intermediate variable without actual meaning, .

[0088] S3, 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 by the initial state values of the n particles , is the initial state value of the i-th particle; the initial weights of the n particles are equal, and are all 1 / n.

[0089] S4, crack length prediction step: predicting the crack lengths of the n particles through the fatigue crack propagation model to obtain predicted crack lengths of the n particles.

[0090] S5, 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.

[0091] S6, updating step: calculating the fitness values of the particles according to the predicted crack lengths of the n particles and the measured crack lengths, 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.

[0092] Specifically, the fitness values of the particles are calculated by a fitness calculation formula, and the fitness calculation formula is represented as:

[0093]

[0094] is the fitness value,​​​​​​ To observe the noise variance, The measured crack length, To predict crack length.

[0095] 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:

[0096]

[0097]

[0098] 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.

[0099] Specifically, the weights of the optimized particles are updated using the weight update formula, which is expressed as follows:

[0100]

[0101] In the formula, Indicates the first Individual particles The weight of each moment; Indicates the first Individual particles The weight of each moment; Let be the transition probability density function, representing the th The state value of the particle at the time The state value of the particle at the time The state value of the particle at the time The state value of the particle at the time The probability density of the state value at the time of transformation; is an observation likelihood function, representing the observation at the time The state value of the particle at the time The observation at the time The probability density of the observation history at the time is an importance probability density function; The observation history from the time 1 to the time The observation history from the time 1 to the time

[0102] In the embodiments of the present application, the fitness values of the calculated particles are sorted according to the size, the particles are divided into two parts according to a preset fitness threshold, i.e., 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 to make the particles close to the real state, and then the particle set is concentrated in a more optimal solution region, thereby improving the prediction accuracy of fatigue crack propagation.

[0103] S7, particle resampling step: merging the optimized particles and the unoptimized particles to form a temporary particle set, resampling the temporary particle set according to the weight values to obtain a new particle set , is the state value of the particle at the time is the state value of the particle at the time is the state value of the particle at the time

[0104] Specifically, before resampling the weight values of the temporary particle set, the weight values of the particles are normalized. It should be noted that if the weight values are not evenly distributed during resampling, the diversity of the particle set may be lost. The weight values of the particles are normalized before resampling in the present application, which can ensure the rationality of resampling and reduce particle depletion.

[0105] S8, 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.

[0106] Specifically, the calculation formula for calculating the crack length according to the state values of the particles in the particle set is represented as:

[0107]

[0108] In the formula, L represents the crack length estimate, represents the state value of the particle at the time represents the state value of the particle at the time represents the state value of the particle at the time represents the state value of the particle at the time

[0109] S9, judging step: judging whether the crack length estimation value reaches the critical crack length, when the crack length estimation value does not reach the critical crack length, taking the crack length estimation value as the predicted crack length at the next time, returning to step S5, when the crack length estimation value reaches the critical crack length, ending the prediction.

[0110] It should be noted that the steps shown in the above flow 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, model construction step: constructing a fatigue crack propagation model according to stress ratio, material parameters, material fracture toughness, crack closure effect parameters and stress threshold factors under different stress ratios; S2, 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, stress threshold factors under different stress ratios; S3, 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, each being 1 / n; S4, 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, observation step: observing whether there is a measured crack length, if there is a measured crack length, executing step S6, if there is no measured crack length, executing step S8; S6, updating step: calculating the fitness value of each particle according to the predicted crack length of the n particles and the measured crack length, sorting the fitness values of each particle in size, optimizing the particles with fitness values less than the preset fitness threshold, and updating the weights of the optimized particles; S7, 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, crack length calculation step: calculating the crack length according to the state values of each particle in the particle set to obtain a crack length estimation value; S9, judging step: judging whether the crack length estimation value reaches the critical crack length, when the crack length estimation value does not reach the critical crack length, taking the crack length estimation value as the predicted crack length at the next time, returning to step S5, when the crack length estimation value reaches the critical crack length, ending the prediction.

[0111] The fatigue crack propagation prediction method based on the improved particle filtering algorithm provided in the embodiments of the present 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.

[0112] The embodiments also 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.

[0113] As used below, the terms "module", "unit", "sub-unit" and the like can be a combination of software and / or hardware that implements a predetermined function. Although the devices described in the following embodiments are preferably implemented in software, implementation in hardware, or a combination of software and hardware, is also possible and contemplated.

[0114] Figure 3 FIG. 1 is a structural block diagram of a fatigue crack propagation prediction system according to an embodiment of the present application, as shown in the figure, the system comprises: Figure 3

[0115] a data acquisition module 1, configured to acquire the width and thickness of a component, the load range of the component, material parameters of the component, a stress ratio of the component, material fracture toughness of the component, crack closure effect parameters of the component, and stress threshold factors under different stress ratios;

[0116] 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;

[0117] a sampling module 3, configured to sample n particles from model parameters to be estimated in the fatigue crack propagation model, obtain initial state values of the n particles, form a particle set with the initial state values of the n particles, and 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;

[0118] 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;

[0119] an observation module 5, configured to observe whether there is a measured crack length;

[0120] 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 the weight values of the optimized particles.​

[0121] The calculation module 7 calculates a crack length estimation value according to the state value of each particle in the particle set;

[0122] The judgment module 8 is configured to judge whether the crack length estimation value reaches the critical crack length; when the crack length estimation value does not reach the critical crack length, the crack length estimation value is sent to the observation module 5 as the predicted crack length at the next time; when the crack length estimation value reaches the critical crack length, the prediction is ended.

[0123] It should be noted that each of the above modules can be a functional module or a program module, which 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.

[0124] The following specific examples verify the effectiveness and accuracy of the fatigue crack propagation prediction method and system based on the improved particle filtering algorithm.

[0125] Embodiment: 30 sets of public data of 2024-T351 aluminum alloy crack propagation are used for verification, and the crack propagation process of the 30 sets of 2024-T351 aluminum alloy is as follows 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 length 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 process in the two extreme cases is predicted.

[0126] 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, and the maximum load is 4.5 kN and the minimum load is 0.9 kN.

[0127] The average value of the 30 curves is calculated as the prior information set, as shown in Figure 5 .

[0128] The fatigue crack propagation rate is calculated, and the commonly used calculation methods are the secant method and the incremental polynomial method. The fatigue crack propagation rate obtained by the incremental polynomial method The crack propagation rate curve is relatively smooth, and the dispersion of the test data is small. The secant method is used to obtain the crack propagation rate of the intermediate position by using two adjacent points. 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, the crack propagation rate in the near threshold region needs to be fitted, and in the case of less test data points in the near threshold value region, the use of the 7-point increasing polynomial method will lead to insufficient effective data points. Therefore, the method and system use the secant method to calculate the crack propagation rate of the intermediate point through two adjacent points .

[0129] (1)

[0130] wherein, Δa represents the crack increment, Δc represents the crack length at the moment t, Δn represents the cycle increment, ΔN represents the cycle number at the moment t, ΔN represents the cycle number at the moment t, Δn represents the cycle increment, ΔN represents the cycle number at the moment t, ΔN represents the cycle number at the moment t, is the intermediate value of a and c, ΔN represents the cycle number at the moment t, .

[0131] According to the stress intensity factor amplitude calculation formula given in GB / T 6398-2017, the calculation formula of the stress intensity factor amplitude of the standard compact tension specimen is represented as:

[0132] (2)

[0133] wherein, ΔP represents the component load range, , ΔPmax represents the load peak value, ΔPmin represents the load valley value; ΔB represents the component thickness, ΔW represents the component width; ΔK represents the shape factor.

[0134] For the standard compact tension specimen, the shape factor is represented as:

[0135] (3)

[0136] wherein,​​​ represents the intermediate variable, which has no physical meaning, , is the component crack length measured with the loading hole centerline as the reference surface.

[0137] The stress intensity factor amplitudes were calculated using the above-mentioned formula (2) and formula (3), the average crack growth rates of the 30 cracks were calculated using formula (1), and the average crack growth rates were fitted using formula (4), and the fitting results are shown in Figure 6 .

[0138] (4)

[0139] The Paris model parameters of 2024-T351 aluminum alloy , . To simplify the calculation process, the Paris model parameters may be replaced by , and it is assumed that the Paris model parameters , obey a bivariate normal distribution.

[0140] Discretize the Paris model and use it as a state equation to describe the fatigue crack growth:

[0141] (5)

[0142] In the formula: represents the component crack length at time ; represents the component crack length at time , measured with the loading hole centerline of the component as the reference surface; represents the interval of iteration; represents the fatigue crack growth model parameters at time ; represents the stress intensity factor amplitude at time .

[0143] To realize the expansion prediction of the two cracks, 3 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 =1000, and the particle swarm optimization algorithm parameters , , the number of iterations is 50, and the PSO algorithm is used to optimize the particles with smaller weights in the IPSO-PF algorithm. The Paris model, the Paris-PF algorithm, the Paris-PSO-PF algorithm, and the method and system of the application are used to predict the crack propagation process of curves A and B. The crack propagation prediction curve of curve A is shown in Figure 7 , and the corresponding prediction error and 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 error and particle distribution are shown in Table 2 and Figure 12 to Figure 14 , respectively.

[0144] Table 1

[0145]

[0146] Table 2

[0147]

[0148] 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 application is 2.6%. The above results show that the Paris-PF algorithm, the Paris-PSO-PF algorithm, and the method and system of the application 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 application have higher accuracy in correcting crack propagation. However, since the method and system of the application only need to optimize half of the particles, while the Paris-PSO-PF algorithm needs to optimize all the particles, the method and system of the application save the calculation space.

[0149] From Figure 8 to Figure 10 and Figure 12 to Figure 14 , it can be seen that when the crack propagation is predicted 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 concentrated around 35000 times, while the particles predicted based on the Paris-PSO-PF algorithm and the method and system of the application are mostly in positions close to the true value, showing a normal distribution characteristic, and the particle distribution is more reasonable.

[0150] The main reason for the above results is that the Paris-PF algorithm has a greater probability of retaining and copying large weight particles in the resampling process, eliminating small weight particles, leading to sample depletion. After the particles are updated according to the first observation information, part of the particles fall into the local optimal trap, and these particles have a large weight. When resampling is directly performed, the state of these particles is copied a lot, thereby causing a large number of particles falling into the local optimal trap to be retained at the end, reducing the particles close to the real value of the model parameter, and finally causing a large deviation between the prediction result and the real result. The method and system of the application tend to a high likelihood region, which is equivalent to "diluting" the weight of the particles falling into the local optimal trap, avoiding a large number of copies of the particles falling into the local optimal trap during resampling, improving the diversity of the particles, and thus the particle distribution is more reasonable, and finally the prediction result of the method and system of the application is closer to the real result.

[0151] Each of the technical features of the above-described embodiments can be combined arbitrarily. To make the description concise, each of the technical features in the above-described embodiments is not described in all possible combinations, but it should be considered that any combination of these technical features is within the scope of the present disclosure, as long as the combination does not cause contradiction.

[0152] The above-described embodiments only express several implementation manners of the application, and the description is more specific and detailed, but it should not be understood as a limitation on the scope of the patent. It should be pointed out that, for ordinary skilled persons in the art, some modifications and improvements can be made without departing from the concept of the application, and these are within the protection scope of the application. Therefore, the protection scope of the patent of the application should be subject to the appended claims.

Claims

1. A fatigue crack propagation prediction method based on an improved particle filter algorithm, characterized in that, Includes the following steps: S1. Data acquisition steps: 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 factor under different stress ratios; S2. Model construction steps: Construct a fatigue crack propagation model based on stress ratio, material parameters, material fracture toughness, crack closure effect parameters, and stress threshold factor under different stress ratios. 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; the initial weights of the n particles are equal, all being 1 / n; 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. 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. 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. S7. Particle resampling step: Merge the optimized particles with the unoptimized particles to form a temporary particle set, and resample the temporary particle set according to the weights to obtain a new particle set. S8. Crack length calculation steps: Calculate the crack length based on the state values ​​of each particle in the particle set to obtain an estimated crack length; 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.

2. The fatigue crack propagation prediction method based on the improved particle filter algorithm according to claim 1, characterized in that, In step S2, the fatigue crack propagation model is represented as follows: 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 . 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.

3. The fatigue crack propagation prediction method based on the improved particle filter algorithm according to claim 2, characterized in that, The The stress intensity factor amplitude at time t is expressed as: 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.

4. The fatigue crack propagation prediction method based on the improved particle filter algorithm according to claim 3, characterized in that, The The shape factor at time step is expressed as: In the formula, This represents an intermediate variable with no practical meaning. .

5. The fatigue crack propagation prediction method based on the improved particle filter algorithm according to claim 1, characterized in that, In step S6, the fitness value of each particle is calculated using the fitness calculation formula, which is expressed as follows: In the formula, For fitness value, To observe the noise variance, The measured crack length, To predict crack length.

6. The fatigue crack propagation prediction method based on the improved particle filter algorithm according to claim 1, characterized in that, 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. The velocity update formulas and position update formulas are expressed as follows: 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 fatigue crack propagation prediction method based on the improved particle filter algorithm according to claim 1, characterized in that, In step S6, the weights of the optimized particles are updated using the weight update formula, which is expressed as: In the formula, Indicates the first Individual particles The weight of each moment; Indicates the first Individual particles The weight of each moment; Let be the transition probability density function, representing the th Individual particles Time state value Towards Time state value The probability density of state values ​​during transition; For the observation likelihood function, let be the expression for the th... The state value of each particle is Observed at the time The probability density of observing history at any given time; It is the importance probability density function; Indicates from 1 to The history of observation at any given moment.

8. The fatigue crack propagation prediction method based on the improved particle filter algorithm according to claim 1, characterized in that, In step S8, the formula for calculating the crack length based on the state values ​​of each particle in the particle set is expressed as follows: 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 propagation prediction system, used to implement the fatigue crack propagation prediction method based on the improved particle filter algorithm as described in any one of claims 1 to 8, characterized in that, include: 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 factor under different stress ratios; The model building module constructs a fatigue crack propagation model based on stress ratio, material parameters, material fracture toughness, crack closure effect parameters, and stress threshold factor under different stress ratios. The sampling module samples 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 forms a particle set from the initial state values ​​of the n particles; the optimized particles are merged with the unoptimized particles to form a temporary particle set, and the temporary particle set is resampled according to the weights to obtain a new particle set; The prediction module uses a fatigue crack propagation model to predict the crack length of n particles, thus obtaining the predicted crack length of n particles. The observation module checks whether the crack length can be measured. The update module calculates the fitness value of each particle based on the predicted crack length and the measured crack length of n particles, sorts the fitness values ​​of each particle by size, optimizes the particles whose fitness values ​​are less than the preset fitness threshold, and updates the weights of the optimized particles. The calculation module calculates the crack length estimate based on the state values ​​of each particle in the particle set. The judgment module is configured to: determine whether the estimated crack length has reached the critical crack length; if the estimated crack length has not reached the critical crack length, send the estimated crack length as the predicted crack length for the next moment to the observation module; and end the prediction when the estimated crack length reaches the critical crack length.

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