Prediction method for prolonging fatigue crack propagation life based on improved particle filter algorithm

Abstract

The invention discloses a prediction method for prolonging fatigue crack propagation life based on an improved particle filter algorithm. Initial probability distribution p (x0) according to particle filter state The method comprises the following steps: generating a group of particles # imgabs0, predicting the prior probability density of the state at the next moment according to a state evolution equation; updating the weight by # imgabs1 # according to an observed value; re-sampling the existing particle combination by # imgabs2 # to obtain a new particle combination; sampling from the prior probability density distribution # imgabs4 # to obtain particles # imgabs5 #, and calculating the acceptance rate alpha according to the following formula: # imgabs6 #, a random number u is generated in a uniform distribution interval of 1, 1], if # imgabs7 obtains expected estimation # imgabs8 of a current state and takes the number of different types of particles in a particle set as a particle effective number, an effective number threshold value is set, and particles are newly added when the effective number threshold value is lower than the effective number threshold value. The particle diversity is maintained, and the crack prediction precision is improved, so that the residual life of the structure is better evaluated, and formulation of a maintenance interval is guided.

Description

Technical Field

[0001] The invention relates to the technical field of fatigue crack growth prediction, and in particular to a prediction method for improving fatigue crack growth life based on an improved particle filter algorithm. Background Art

[0002] There are four main types of commonly used fatigue crack growth prediction models: (1) physics-based models; (2) data-driven models; (3) knowledge-based models; and (4) hybrid models. It is technically difficult to establish a high-precision physical model, which requires an in-depth and accurate understanding of the physical mechanism. Many models also require a large number of experiments to fit the model parameters, which is time-consuming and costly. Data-driven models avoid the complex physical modeling process, but have high requirements on the quality and quantity of data used to train the model. Insufficient data or large noise will affect the prediction accuracy of the model, and the generalization ability is insufficient. It is difficult to establish a complete knowledge base of knowledge expression and reasoning rules, and as the knowledge base rules continue to expand, the amount of reasoning calculations increases exponentially.

[0003] The hybrid model of data-driven + physical model can improve the physical model by using structural state data, and avoid the defect of low transparency of the data-driven model in the prediction process. The introduction of the physical model reduces the dependence on the quality and quantity of state data, making the prediction process more stable and reliable.

[0004] Dynamic Bayesian Network (DBN) is a commonly used hybrid model. DBN combines graphical model theory with probability theory, uses graph structure to describe the relationship between random variables, and uses this as the basis for decomposing complex high-dimensional probability distributions, simplifies the solution of joint probability distributions of random variables, and enables it to handle a series of uncertain reasoning problems.

[0005] DBN is based on probability theory, which simplifies the reasoning process of probability calculation and makes the reasoning results more convincing. Each node in the network has practical meaning, and compared with common black box models (such as neural networks), it has good understandability and logic. In addition, DBN has low requirements for prior probability, because it can improve the network structure and parameters by continuously accumulating test data and learning in time, and update probability information, so that it can reason under incomplete and uncertain information.

[0006] Among the commonly used DBN reasoning algorithms, the forward and backward algorithms, boundary algorithms and interface algorithms in precise reasoning, and the Boyern-Koller algorithm and factor boundary algorithm in approximate reasoning are only applicable to discrete variables, that is, the state of the variables in the DBN is required to be discontinuous. Kalman filtering, extended Kalman filtering and unscented Kalman filtering are only applicable to continuous variables, while particle filtering (PF) is applicable to both discrete and continuous variables, and also performs well in the case where the variables obey non-Gaussian distribution or have nonlinear relationships. Therefore, the present invention selects PF as the reasoning algorithm of DBN.

[0007] When traditional PF performs DBN inference, multiple resampling processes are required. The final particle set will be composed of a large number of identical particles, which loses particle diversity and leads to a decrease in prediction accuracy. This phenomenon is called particle impoverishment. Summary of the invention

[0008] In view of this, in order to solve the problem of insufficient prediction accuracy caused by the loss of particle diversity when the traditional particle filter (PF) algorithm is applied to fatigue crack growth prediction, an improved resampling method and an adaptive method of adding particles are adopted to maintain particle diversity and improve crack prediction accuracy, so as to better evaluate the remaining life of the structure and guide the formulation of maintenance intervals. The present invention proposes a prediction method for improving fatigue crack growth life based on an improved particle filter algorithm.

[0009] In order to achieve the above object, the present invention adopts the following technical solutions:

[0010] The prediction method for improving fatigue crack growth life based on improved particle filter algorithm includes the following steps:

[0011] Step 1: Generate a set of particles according to the initial probability distribution p(x0) of the particle filter state

[0012]

[0013] Step 2: Predict the prior probability density of the state at the next moment based on the state evolution equation

[0014]

[0015] Step 3: Update the weights based on the observed values

[0016] Step 4: Resample the existing particle combination to obtain a new particle combination

[0017] Step 5. From the prior probability density distribution Particles are sampled from

[0018] Step 6. Calculate the acceptance rate α according to the following formula:

[0019] Step 7. Generate a random number u in the uniform distribution interval [0,1] if:

[0020]

[0021] Step 8. Get an estimate of the current state Where E(f(x t ) means taking the average of the predicted values ​​of all particles, that is, finding the expectation, and using the crack length to represent the fatigue life. When the critical crack length is reached, it is considered that the limit life is reached; f(x i ) represents the predicted crack length; where Select the corresponding particles according to step 7.

[0022] Preferably, step 4 and step 5 include:

[0023] stpe45. Take the number of different types of particles in the particle set as the effective number of particles, set the effective number threshold, and add new particles when it is lower than the threshold.

[0024] Preferably, the process of adding new particles is as follows: for observable variables, when generating new particles, random sampling is performed from a normal distribution with the observed data as the mean and the measurement error as the standard deviation to simulate the probability distribution of new particles; new particles of other variables are randomly sampled from the probability distribution obtained by fitting the current particle set.

[0025] Preferably, it also includes:

[0026] step9. Repeat step2 to step8 to obtain observation data multiple times to drive the prediction model update.

[0027] Preferably, it also includes:

[0028] Step 10, M independent particle filters are predicted independently according to step 1 to step 9, and the M particle filter results are fused according to the fusion method to obtain the final estimated value.

[0029] Preferably, the fusion method adopts one of equal-weight fusion, weighted fusion based on effective particle number, or weighted fusion based on mean square error.

[0030] Preferably, the equal-weight fusion is specifically to directly add and average the prediction results of M independent particle filters, and the formula is as follows:

[0031]

[0032] In the formula, a i Represents the prediction result of the i-th PF, i=1,2,…,M,a fu Represents the prediction result after fusion.

[0033] Preferably, the weighted fusion based on the number of effective particles is specifically to determine the weight ratio in the fusion process by calculating the number of effective particles of different particle filters in different time periods. The more effective particles there are, the greater the weight is. The formula is as follows:

[0034]

[0035] Where N ij It represents the number of valid particles after the i-th particle filter has undergone j model state updates. According to the latest particle set, the number of valid particles is counted and the weights of different particle filters are calculated, i = 1, 2, ..., M, and a total of M PFs are weighted averaged.

[0036] Preferably, the weighted fusion based on mean square error is specifically to perform weighted averaging according to the mean square errors of different particle filters after the jth update. The smaller the mean square error, the greater the weight it occupies during fusion. The specific formula is:

[0037]

[0038] In the formula, MSE ij It represents the mean square error between each particle and the observed value at that moment when the i-th particle filter has undergone j model state updates.

[0039] Preferably, the MSE ij The calculation of is as follows:

[0040]

[0041] In the formula, Represents the observed value corresponding to the jth model state update; represents the predicted value of the qth particle in the i-th PF after the jth model state update, q = 1, 2, ..., N PF , each PF has N PF Particles.

[0042] Compared with the prior art, the present invention has the following beneficial effects:

[0043] 1) In the present invention, by improving the resampling method, a particle selective jump process is added compared to the traditional sequential importance resampling algorithm, so that the particles move to the high likelihood area to approximate the true posterior probability density function, maintain particle diversity, and improve the crack prediction accuracy, so as to better evaluate the remaining life of the structure and guide the formulation of maintenance intervals.

[0044] 2) The present invention also provides an adaptive method for adding new particles. The advantage of this method is that it generates new particles that conform to the probability density distribution, increases the number of particles and particle diversity, ensures the number of effective particles, and thus ensures the prediction accuracy.

[0045] 3) The present invention also discloses the simultaneous use of several independent particle filters for prediction, and then combining the results of these particle filters to obtain the final estimated value, which can eliminate the particle non-independence in a single particle filter, and the fusion is equivalent to increasing the particle diversity. In addition, the difference in prediction results of different particle filters mainly comes from the fact that the initial particles are randomly generated; when the probability distribution is updated according to the likelihood function, the retained particles are also random, and the fusion can smooth this randomness to a certain extent and obtain a more robust prediction result. At the same time, multiple independent particle filters can also use parallel computing to improve the computing efficiency of particle filtering and make online real-time computing possible. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 A schematic diagram of the improved idea of ​​the particle filter (PF) algorithm proposed in the present invention;

[0047] Figure 2 A schematic diagram of a dynamic Bayesian network (DBN) model for crack propagation prediction according to the present invention;

[0048] Figure 3 (a) is a schematic diagram of the comparison and verification results of fatigue crack growth of the DBN prediction standard specimen of the present invention and the test data;

[0049] Figure 4 It is a schematic diagram of crack prediction accuracy (average relative error) under different resampling algorithms of the present invention;

[0050] Figure 5 Schematic diagram of crack prediction accuracy (average coefficient of variation) under different resampling algorithms of the present invention;

[0051] Figure 6 A schematic diagram showing a comparison of crack prediction results (average relative error) between residual resampling of the present invention and adding Metropolis Hasting sampling;

[0052] Figure 7A schematic diagram showing the comparison of crack prediction results (average coefficient of variation) between residual resampling of the present invention and adding Metropolis Hasting sampling;

[0053] Figure 8 A schematic diagram of the crack prediction results (average relative error) of the adaptively added particles of the present invention;

[0054] Fig. 9 A schematic diagram of the crack prediction results (average coefficient of variation) of the adaptively added particles of the present invention;

[0055] Fig.10 It is a schematic diagram for comparing crack prediction results of multiple particle filters (PF) fusion in the present invention. DETAILED DESCRIPTION

[0056] The technical solutions in the embodiments of the present invention will be described clearly and completely below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all the embodiments.

[0057] In the description of the present invention, unless otherwise specified, "plurality" means two or more than two; the orientations or positional relationships indicated by the terms "upper", "lower", "left", "right", "inner", "outer", "front end", "rear end", "head", "tail", etc. are based on the orientations or positional relationships shown in the drawings, and are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operate in a specific orientation, and therefore cannot be understood as limiting the present invention. In addition, the terms "first", "second", "third", etc. are only used for descriptive purposes and cannot be understood as indicating or implying relative importance.

[0058] In the description of the present invention, it should be noted that, unless otherwise clearly specified and limited, the terms "connected" and "connection" should be understood in a broad sense, for example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection or an indirect connection through an intermediate medium. For ordinary technicians in this field, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0059] The technical solution adopted by the present invention is as follows:

[0060] Example 1

[0061] Particle filtering (PF), also known as sequential Monte Carlo, approximates the probability distribution by sampling a group of random samples, and then performs statistical calculations on these samples to obtain the minimum variance estimate of the state. These samples are called "particles". As the number of particles increases, the probability density function described by all particles gradually approaches the probability distribution of the true state, and the effect of optimal Bayesian estimation is obtained.

[0062] The mathematical language description of PF is as follows: Assume that the dynamic time-varying system can be described by the following formula:

[0063]

[0064] Among them, f represents the state evolution equation, which describes the process of the state variable X evolving from time t-1 to time t, v t-1 represents process noise; h represents the observation equation, which describes the dependency between the observable variable Z and the latent variable X, n t represents the measurement noise.

[0065] According to the state evolution equation, the prior probability density of the state at time t can be predicted:

[0066]

[0067] Then, according to the observation value and observation equation at the current moment, the prior probability density is corrected to obtain the posterior probability density of the state at time t, that is, the state is updated:

[0068]

[0069] In the formula, p(z t ∣z 1:t-1 )=∫p(z t ∣x t )p(x t ∣z 1:t-1 )dx t , indicating that the calculation of the posterior probability requires high-dimensional integration, but it is very difficult to perform the integration directly. The Monte Carlo method based on random sampling can transform the integration operation into the summation operation of finite sample points.

[0070] Assume that N can be randomly drawn from the posterior probability distribution PF particles (samples), the calculation of the posterior probability can be expressed as:

[0071]

[0072] In the formula, δ is the Dirac function, and the superscript i represents the particle number, ranging from 1 to N. PF .

[0073] If we want to estimate the expectation of the current state, we can express it as:

[0074]

[0075] N PF The state mean of the sampled particles is the expectation of the current state. But the problem is that the posterior probability is unknown and cannot be sampled directly.

[0076] Therefore, considering sampling from a known distribution, through certain mathematical transformations, we can also obtain an estimate of the posterior state. This known distribution is called the importance probability density function. Therefore, when PF was not yet mature, it was also called the Sequential Importance Sampling (SIS) algorithm.

[0077] When estimating the expectation of the state, the particle states are no longer directly added together to obtain the average, but a weighted average is used:

[0078]

[0079] In the formula, Represents the normalized weight of the particle, weight w t The recursion formula can be expressed as:

[0080]

[0081] In the formula, q represents the importance probability density function. The specific derivation process can be found in relevant literature.

[0082] Scholar Gordon pointed out that after many iterations, the variance of the weights will become larger and larger, and there may even be a phenomenon where a certain weight tends to 1 while the other weights tend to 0, resulting in a lot of computing time being wasted on the vast majority of particles with too small weights. This phenomenon is called particle degeneracy.

[0083] One of the effective means to alleviate the degradation phenomenon is to resample the existing particles (resampling), by randomly copying particles with higher weights and removing particles with too low weights, so that the calculation is concentrated as much as possible on particles that have a greater impact on the posterior probability density. Gordon introduced the resampling step into the SIS algorithm, which resulted in the basic PF algorithm - Sequential Importance Resampling (SIR), the implementation process of which is as follows:

[0084] (1) Generate a set of particles (random samples) based on the initial probability distribution of the state p(x0)

[0085]

[0086] (2) Predict the prior probability density of the state at the next moment based on the state evolution equation

[0087]

[0088] (3) Update the weights based on the observed values

[0089] (4) Particle combination Resample to get a new particle combination

[0090] (5) Obtain a posteriori estimate of the state Return to (2) to continue prediction. t ) means taking the average of the predicted values ​​of all particles, that is, finding the expectation, and using the crack length to represent the fatigue life. When the critical crack length is reached, it is considered that the limit life is reached; f(x i ) represents the predicted crack length;

[0091] In order to obtain more accurate crack propagation prediction results, it is necessary to obtain observation data multiple times to drive the prediction model update to ensure that the model can evolve with the real physical structure. However, each update will resample the original particles. Although resampling alleviates the particle degradation problem in the SIS algorithm, as the resampling proceeds, the final particle set will be composed of a large number of identical particles, which loses particle diversity and leads to a decrease in prediction accuracy. This phenomenon is called particle impoverishment. In response to this problem, the improvement ideas of the present invention are mainly divided into two categories: 1) improving the resampling method; 2) adaptively adding new particles to maintain particle diversity.

[0092] Traditional resampling methods mainly include: Multinomial Resampling, Residual Resampling, Systematic Resampling and Stratified Resampling. The first resampling algorithm introduced by Gordon in SIS was polynomial resampling, but it may result in large weights but no sampling, while small weight particles are sampled multiple times;

[0093] Residual resampling is improved on the basis of polynomial resampling, ensuring that all particles with the largest weights are sampled multiple times and reducing the computational complexity of the algorithm;

[0094] Systematic resampling ensures that sampling is carried out from all parts of the particle space, and larger weights can be resampled more frequently;

[0095] Stratified resampling is not as good as systematic resampling in guaranteeing uniform sampling, but it is better than polynomial and residual in ensuring that high weights are sampled more times.

[0096] Currently, there is no unified statement to clearly point out which resampling algorithm is better, so the present invention first compares the prediction accuracy of these methods for the specific problem of concern, and selects the best method for further research.

[0097] In addition, by introducing Metropolis Hasting sampling in the resampling step, it is agreed that the diversity of particles can be improved. In each update iteration, Metropolis Hasting sampling enables particles to be transferred to different locations, weakening the correlation between particles and alleviating the particle depletion phenomenon; at the same time, particles can be transferred to areas closer to the true state probability density function, making the particle distribution more accurate and reasonable. After the PF resampling algorithm, particles are further screened based on the Metropolis Hasting sampling method. The process is as follows:

[0098] (1) Initial definition. This is completely consistent with the SIR algorithm described above, until step (4): resampling the existing particle combination to obtain a new particle combination. In order to distinguish, the resampled particles at time t are recorded as The posterior particle at time t-1 is

[0099] (2) From the probability distribution Particles are sampled from Here Compared with the previous same;

[0100] (3) Calculate the acceptance rate α according to the following formula:

[0101]

[0102] (4) Generate a random number u in the uniform distribution interval [0,1] if:

[0103]

[0104] The SIR steps are continued later. Compared with the traditional SIR algorithm, this method has an additional particle selective jump process, which makes the particles move to the high likelihood area to approach the true posterior probability density function.

[0105] In addition, particle depletion is caused by the loss of particle diversity, and diversity can be improved by dynamically adding new particles to the original particle set. The key to adaptively adding new particles lies in when to add new particles and how to generate new particles.

[0106] In the present invention, the number of different types of particles in the particle set is taken as the effective number of particles, and a threshold of the effective number is set. When the effective number is lower than the threshold, new particles are added. For observable variables, when generating new particles, random sampling is performed in a normal distribution with the observed data as the mean and the measurement error as the standard deviation to simulate the probability distribution of new particles. New particles of other variables are randomly sampled from the probability distribution obtained by fitting the current particle set.

[0107] As attached Figure 1 The first half shows the process of the idea of ​​Example 1: based on four different resampling algorithms, the crack extension is predicted, and the resampling algorithm with the smallest prediction error is selected; then after the resampling algorithm, MetropolisHasting sampling and screening particles are added; at the same time, it is also necessary to judge whether the number of valid particles meets the requirements in the prediction. When it is lower than the effective threshold, new particles are regenerated and added

[0108] The use process and data of Example 1:

[0109] The implementation effect of the present invention is described for a specific problem of fatigue crack growth prediction. The fatigue test data in the literature (Lu Z, Liu Y. Experimental investigation of random loading sequence effect on fatigue crack growth [J]. Materials & Design, 2011, 32 (10): 4773-4785.) is used to construct a specific dynamic Bayesian network (DBN) model to predict the structural crack growth life.

[0110] The material used in the literature is 7075-T6 aluminum alloy. According to the standard test method for measuring fatigue crack growth rate ASTM E647-08, a compact tension (CT) specimen was used to conduct a fatigue crack growth test under a variable amplitude sinusoidal load.

[0111] The DBN model constructed for predicting crack propagation is as follows: Figure 2 The meaning of each variable is shown in Table 1.

[0112] Table 1 Description of variables of each node in DBN

[0113]

[0114] Figure 2Each single DBN in the DBN completely describes the fatigue crack growth process within a time interval, and the lines between different nodes in the DBN describe the causal relationship between variables. According to the test load, specimen size and material properties, the stress magnitude of the key point and the corresponding stress intensity factor amplitude ΔK can be calculated:

[0115]

[0116] According to Walker crack growth formula:

[0117]

[0118] The crack extension Δa under a specific load cycle N can be predicted, and combined with the initial crack length a0, the current crack length a can be determined:

[0119] a=a0+∑Δa (12)

[0120] The above is a forward prediction process. When the current crack detection data a is obtained obs When the model is updated based on the Bayesian theory, the current crack length and model parameters are re-evaluated, which is a reverse update process. The dotted line between two adjacent DBNs represents the evolution of the prediction model and structural state over time, that is, the Walker model parameters C, m and γ and the final crack length a at the previous moment are transferred to the corresponding variables as the initial values ​​of the parameters and the initial crack length at the next moment, and the calculation continues.

[0121] The crack propagation process of DBN pre-test specimens S1-S6 under variable amplitude sinusoidal load is shown in Figure 3 As shown. It can be seen that due to the randomness of the load, the expansion laws between different specimens are very different, but DBN can still accurately predict the different expansion behaviors of each specimen. On the basis of verifying that DBN can effectively predict the crack growth process, the mean relative percentage error (MRPE) and the mean coefficient of variation (MCV) are used to measure the overall prediction effect of DBN. The calculation formula is:

[0122]

[0123] In the formula, a t is the test data at the tth moment, i.e., the crack observation data, is the crack length estimate predicted by DBN at the tth moment, n represents the signal length of the entire prediction result, and std() represents the standard deviation of the prediction result. Considering different permutations and combinations of crack length measurement errors and crack prediction model errors, as shown in Table 2, the influence of the improved particle filter (PF) algorithm proposed in the present invention on the prediction accuracy of DBN is discussed.

[0124] Table 2 Combinations of different measurement errors and model errors

[0125]

[0126] First, we study the pros and cons of several different resampling algorithms and predict the results. Figure 4 and Figure 5 As shown. It can be seen that the prediction accuracy of the four resampling algorithms is not much different. Relatively speaking, the mean relative percentage error MRPE and mean coefficient of variation MCV of residual resampling are smaller, indicating that its prediction error and uncertainty are lower, and its advantages are more obvious than those of the other resampling algorithms. Therefore, the subsequent calculations of the present invention all use residual resampling.

[0127] Based on residual resampling, Metropolis Hasting sampling is introduced to further screen particles. The prediction results are as follows: Figure 6 and Figure 7 As shown in the figure, it can be seen that after adding Metropolis Hasting sampling, the average prediction error is significantly reduced, and the mean prediction error (MRPE) of crack extension can be reduced from 4.5% to 3.8%. This shows that Metropolis Hasting sampling can retain more and better particles through random walks, so that the particle set can be closer to the probability distribution of the actual crack length, thereby improving the prediction accuracy.

[0128] In addition, when the basic particle filter (PF) is used to update the model state, it is simultaneously determined whether new particles need to be added, and the effective particle number threshold is set to N PF / 2,N PF is the number of existing particles. When the particle diversity does not meet the requirements, add N PF / 10 particles, the comparison results of PF prediction considering adaptive additional particles and basic PF prediction are as follows Figure 8 and Fig. 9 As shown in Figure 2, it can be seen that the adaptive addition of particles significantly improves the prediction accuracy by increasing the diversity of particles, and the mean prediction error (MRPE) of crack extension is reduced from 4.5% to 2.4%.

[0129] Example 2

[0130] In addition to the above-mentioned improvements to the PF algorithm itself, the prediction accuracy can also be improved based on multi-model fusion. Several independent PFs are used for prediction at the same time, and the results of these PFs are combined to obtain the final estimate. This can eliminate the non-independence of particles in a single PF, and fusion is equivalent to increasing particle diversity. In addition, the difference in prediction results of different PFs mainly stems from the fact that the initial particles are randomly generated; when the probability distribution is updated according to the likelihood function, the retained particles are also random. Fusion can smooth out this randomness to a certain extent and obtain more robust prediction results. At the same time, multiple independent PFs can also use parallel computing to improve the computing efficiency of PF and make online real-time computing possible. The present invention considers three different fusion methods:

[0131] (1) Equal weight fusion

[0132] For M independent PFs, assuming that their weights are equal, the results of their respective predictions are directly added and averaged:

[0133]

[0134] In the formula, a i Represents the prediction result of the i-th PF, i=1,2,…,M,a fu represents the prediction result after fusion, E(F(Xi)) is the crack length predicted by a single particle filter, and a i The variables representing the prediction results of the i-th PF (single particle filter) are the same, both of which are crack prediction results.

[0135] (2) Weighted fusion based on effective particle number

[0136] By calculating the effective particle numbers of different PFs in different time periods, the weight ratio in the fusion process is determined. The more effective particles there are, the greater the weight is:

[0137]

[0138] Where N ij It indicates the number of valid particles after the i-th PF has experienced j model state updates. According to the latest particle set, the number of valid particles is counted and the weights of different PFs are calculated. i=1,2,…,M, and a total of M PFs are weighted averaged. The more valid particles there are, the more types of particles there are, the more evenly and reasonably the particle distribution is, and the greater the probability of more accurate prediction, so it is given a higher weight during fusion. i and a fu The meaning is the same as formula (15).

[0139] (3) Weighted fusion based on mean square error

[0140] For different PFs, the mean square error (MSE) between the predicted value and the actual observed value of each particle can be calculated at each update. The smaller the overall mean square error, the more accurate the prediction is in subsequent predictions. Therefore, the weighted average is performed based on the mean square error of different PFs after the jth update. The smaller the mean square error, the greater the weight in fusion:

[0141]

[0142] In the formula, MSE ij It means that when the i-th PF has undergone j model state updates, the mean square error between each particle and the observed value at that moment is calculated using the following formula:

[0143]

[0144] In the formula, Represents the observed value corresponding to the jth model state update; represents the predicted value of the qth particle in the i-th PF after the jth model state update, q = 1, 2, ..., N PF , each PF has N PF Particles. i and a ifu The meaning is the same as formula (15).

[0145] As attached Figure 1 As shown in the second half, the idea process of Example 2 is: the calculation results of multiple PFs are fused based on three different fusion methods, so as to select the optimal fusion method for the problem of the present invention. The ultimate goal of the improved algorithm is to optimize the PF algorithm with the smallest prediction error.

[0146] The usage process and data of Example 2:

[0147] Two independent PFs (PF1 and PF2) are used for crack growth prediction, and the number of particles in each PF is N. PF Then, the prediction results of the two PFs are fused using the three different fusion methods described above. The results are as follows: Fig.10As shown. It is found that no matter which fusion method is used, the error after fusion is significantly smaller than that of a single PF, and the mean prediction error (MRPE) of crack extension can be reduced from 4.5% to 1.4% at most. This is because the generation and screening of particles are random during the initial sampling and model state update, and the prediction effects of each PF at the same time are different. Fusion of multiple PFs can weaken this randomness and make the prediction results more robust and reliable. From the prediction results, the prediction performance of fusion with mean square error as the weight is the best. From a physical point of view, a PF with a smaller mean square error means that its model is more accurate, and it has a higher probability of approaching the true distribution in subsequent predictions. It should be given a greater weight during fusion.

[0148] Due to the fusion of 2 N PF The PF of the particle is equivalent to using 2N PF particles, so consider a single PF with 2N PF The predictions when there are 10 particles are shown in Figure 7, such as PF3 and PF4. It can be seen that although the prediction accuracy of PF3 and PF4 is higher than that of PF1 and PF2, it is lower than that of the fusion of PF1 and PF2. This shows that the fusion of PF not only increases the number of particles, but also eliminates the particle non-independence and randomness of a single PF, alleviates the particle depletion phenomenon, and makes the prediction results more robust and reliable. In addition, when the number of particles N PF =2000, it is predicted that 1200 crack growth cycles will take a total of 202s; when the number of particles is 2N PF =4000, it takes 776s, which is nearly 4 times the amount of calculation of the former. PF The PF ratio of the particle is calculated as 1 2N PF The time of particle PF is half of that of particle PF, which indicates that fusion also improves computational efficiency. If multi-PF parallel computing is considered, computational efficiency can be further improved, making it possible to use PF-based DBN for online real-time prediction.

[0149] The conclusions of Example 1 and Example 2 show that the improved PF algorithm proposed in the present invention significantly reduces the prediction error of crack extension amount by optimizing resampling, improving resampling, adding new particles, and multi-model fusion compared with the basic PF algorithm, so that the remaining life of the structure can be predicted more accurately, laying the foundation for rationally formulating maintenance plans, ensuring structural safety and reliability, and avoiding unnecessary costs.

[0150] The above are only preferred specific implementation modes of the present invention, but the protection scope of the present invention is not limited thereto. Any technician familiar with the technical field can make equivalent replacements or changes according to the technical solutions and inventive concepts of the present invention within the technical scope disclosed by the present invention, which should be covered by the protection scope of the present invention.

Claims

1. A method for improving the prediction of fatigue crack growth life based on an improved particle filter algorithm, characterized in that: The following steps are involved: Step 1: Generate a set of particles according to the initial probability distribution p(x0) of the particle filter state Step 2: Predict the prior probability density of the state at the next moment based on the state evolution equation Step 3: Update the weights based on the observed values Step 4: Resample the existing particle combination to obtain a new particle combination Step 5. From the prior probability density distribution Particles are sampled from Step 6. Calculate the acceptance rate α according to the following formula: Step 7. Generate a random number u in the uniform distribution interval [0,1] if: Step 8. Get an estimate of the current state Where E(f(x t ) means taking the average of the predicted values ​​of all particles, that is, finding the expectation, and using the crack length to represent the fatigue life. When the critical crack length is reached, it is considered that the limit life is reached; f(x i ) represents the predicted crack length; where x t (j) Select the corresponding particles according to step 7.

2. The method for predicting fatigue crack growth life based on improved particle filter algorithm according to claim 1, characterized in that: In step 4 and step 5, adaptively adding particles is also included, specifically: stpe45. Take the number of different types of particles in the particle set as the effective number of particles, set the effective number threshold, and add new particles when it is lower than the threshold.

3. The prediction method for improving fatigue crack growth life based on improved particle filter algorithm according to claim 2, characterized in that: The process of adding new particles is as follows: for observable variables, when generating new particles, random sampling is performed from a normal distribution with the observed data as the mean and the measurement error as the standard deviation to simulate the probability distribution of new particles; new particles of other variables are randomly sampled from the probability distribution obtained by fitting the current particle set.

4. The prediction method for improving fatigue crack growth life based on improved particle filter algorithm according to claim 1, characterized in that: step9. Repeat step2 to step8 to obtain observation data multiple times to drive the prediction model update.

5. The prediction method for improving fatigue crack growth life based on improved particle filter algorithm according to claim 4 is characterized in that: Also includes: Step 10, M independent particle filters are predicted independently according to step 1 to step 9, and the M particle filter results are fused according to the fusion method to obtain the final estimated value.

6. The prediction method for improving fatigue crack growth life based on improved particle filter algorithm according to claim 5, characterized in that: The fusion method adopts one of equal-weight fusion, weighted fusion based on effective particle number, or weighted fusion based on mean square error.

7. The prediction method for improving fatigue crack growth life based on improved particle filter algorithm according to claim 6, characterized in that: The equal-weight fusion is specifically to directly add and average the prediction results of M independent particle filters, and the formula is as follows: In the formula, a i Represents the prediction result of the i-th PF, i=1,2,…,M,a fu Represents the prediction result after fusion.

8. The prediction method for improving fatigue crack growth life based on improved particle filter algorithm according to claim 6, characterized in that: The weighted fusion based on the effective particle number is specifically to determine the weight ratio in the fusion process by calculating the effective particle number of different particle filters in different time periods. The more effective particles there are, the greater the weight is. The formula is as follows: Where N ij It represents the number of valid particles after the i-th particle filter has undergone j model state updates. According to the latest particle set, the number of valid particles is counted and the weights of different particle filters are calculated, i = 1, 2, ..., M, and a total of M PFs are weighted averaged.

9. The prediction method for improving fatigue crack growth life based on improved particle filter algorithm according to claim 6, characterized in that: The weighted fusion based on mean square error is specifically to perform weighted averaging based on the mean square errors of different particle filters after the jth update. The smaller the mean square error, the greater the weight in fusion. The specific formula is: In the formula, MSE ij It represents the mean square error between each particle and the observed value at that moment when the i-th particle filter has undergone j model state updates.

10. The prediction method for improving fatigue crack growth life based on improved particle filter algorithm according to claim 6, characterized in that: The MSE ij The calculation of is as follows: In the formula, Represents the observed value corresponding to the jth model state update; represents the predicted value of the qth particle in the i-th PF after the jth model state update, q = 1, 2, ..., N PF , each PF has N PF Particles.

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