Quantile observation likelihood weight updating method for particle filter damage extension prediction

Abstract

The invention discloses a quantile observation likelihood weight updating method for particle filter damage extension prediction. The quantile observation likelihood weight updating method comprises the steps of initializing a particle set and a particle weight in a particle filter damage extension prediction algorithm for a target structure; obtaining a target structure damage size observation value, and constructing a load cycle sequence and a corresponding observation value sequence; obtaining a quantile of damage size observation likelihood probability distribution; fitting is carried out on the quantiles, and parameter values of three-parameter Weibull distribution are obtained; on the basis of particle characterization posterior probability distribution after weight updating, future expansion of structural damage is predicted; and the prediction is repeated until the damage size reaches a threshold, and the structure fails. According to the method, the quantile of the damage observation value is calculated through the dynamic quantile regression, and the quantile is fitted to obtain the quantile observation likelihood probability distribution for updating the particle set weight in the particle filtering damage expansion algorithm, so that the prediction precision and robustness of particle filtering under the influence of complex time-varying factors are improved.

Description

Technical Field

[0001] This invention belongs to the field of fault prediction and health management technology, specifically relating to a method for updating quantile observation likelihood weights in particle filter damage propagation prediction. Background Technology

[0002] Predictive and Health Management (PHM) technology acquires information about mechanical equipment systems online through sensors, and uses this information to diagnose and predict the system's health status in real time. PHM technology has significant theoretical and engineering application value for ensuring system safety and reliability and developing optimal operation and maintenance strategies.

[0003] As the load-bearing platform of mechanical equipment systems, structures primarily exhibit fatigue cracking under alternating service loads. Accurate prediction of structural fatigue damage propagation is crucial for achieving structural health monitoring (PHM). In recent years, with the development of Structural Health Monitoring (SHM) technology, damage propagation prediction methods that integrate online monitoring data of equipment structures have received increasing attention, enabling more accurate predictions. Among existing methods, particle filtering damage propagation prediction, which integrates current damage size observations and prior damage propagation models using Bayesian filtering theory to eliminate the influence of uncertainties on fatigue damage propagation prediction, is considered one of the most promising methods. However, due to the variable service tasks and unsteady, uncertain loads and environmental conditions that equipment structures typically endure during service, the SHM observation data acquired by the structure exhibits a non-Gaussian uncertainty distribution with variance varying over time. Existing particle filter-based damage propagation prediction methods typically assume that the observed noise of the structural SHM (Solution-of-Meaning) model is a zero-mean Gaussian distribution with constant variance. However, when dealing with unsteady-state uncertainties and observed noise during actual structural service, the constant observed noise model cannot describe the true probability distribution. This leads to inaccurate updates of particle weights characterizing the crack state and the posterior probability distribution of the damage propagation model parameters, resulting in reduced accuracy of the estimated crack state and posterior probability distribution of the model parameters. Therefore, constructing an accurate and efficient particle observation likelihood weight update method is a key bottleneck restricting the engineering application of particle filter-based damage propagation prediction methods when dealing with unsteady-state uncertainties and SHM observations during actual structural service. Summary of the Invention

[0004] To address the shortcomings of existing technologies, the present invention aims to provide a method for updating the quantile observation likelihood weights in particle filter damage propagation prediction, thereby solving the problem that monitoring data in fatigue crack propagation prediction is affected by complex time-varying factors. This invention calculates the quantiles of the most recent damage observations through dynamic quantile regression and fits the quantiles to a three-parameter Weibull distribution to obtain a quantile observation likelihood probability distribution. This distribution is then used to update the particle set weights in the particle filter damage propagation algorithm, thereby improving the prediction accuracy and robustness of particle filtering under the influence of complex time-varying factors.

[0005] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0006] The present invention provides a method for updating quantile observation likelihood weights in particle filter damage propagation prediction, comprising the following steps:

[0007] (1) Set the parameters required for dynamic quantile regression in offline state; initialize the particle set and particle weights in the particle filter damage propagation prediction algorithm for the target structure;

[0008] (2) Obtain the observed damage size of the target structure at the current time k during the online service process of the target structure. Constructing a load cyclic sequence and its corresponding observation sequence

[0009] (3) Using a quadratic polynomial to process the load cyclic sequence Corresponding damage size observation sequence Quantile regression was performed to obtain the quantiles of the likelihood probability distribution of the damage size observation at time k;

[0010] (4) The cumulative distribution function of the three-parameter Weibull distribution is used to fit the quantiles obtained in step (3) to obtain the parameter values ​​of the three-parameter Weibull distribution.

[0011] (5) Iterate the particle set at time k-1 using the state equation to obtain the particle set at time k; construct the quantile likelihood probability distribution of damage size observation based on the parameter values ​​of the three-parameter Weibull distribution obtained in step (4), and update the particle filter weights through the quantile likelihood probability distribution; predict the future propagation of structural cracks based on the posterior probability distribution of particle characterization after weight update.

[0012] (6) Take k = k + 1 and repeat steps (2) to (5) until the crack size reaches the threshold and the structure fails.

[0013] Furthermore, step (1) specifically includes:

[0014] Define the sample size W required for dynamic quantile regression in offline mode and the quantiles τ of the observed likelihood distribution τ∈{τ1,τ2,τ3,...,τ M}, where the subscript M represents the number of quantiles; initialize the particle set and particle weights in the particle filter damage propagation prediction algorithm for the target structure;

[0015] Specifically, setting the sample size required for dynamic quantile regression and the quantiles of the observed likelihood distribution involves the following steps: In the offline state (k=0), based on the damage monitoring frequency and damage propagation rate characteristics of the target structure, the sample size W for dynamic quantile regression is set. This sample size W represents the use of W observed damage sizes for quantile regression. The selection of the sample size W needs to balance the amount of data required for quantile regression and the number of particle filter iterations. The quantiles {τ1,τ2,τ3,...,τ} used to fit the damage monitoring probability distribution are then set. M}, where M is the number of quantiles, and quantiles τ1, τ2, τ3, ..., τ M They belong to the interval (0,1) and are all distinct;

[0016] Specifically, the initialization of the particle set and particle weights in the particle filter damage propagation prediction algorithm involves determining the damage propagation state equation in the target structure based on its geometry and service conditions, as follows:

[0017]

[0018] Among them, a k Let a be the damage size at time k. k-1 Let ω be the damage size at time k-1. k-1 The noise represents the damage propagation at time k-1, where N is the number of load cycles, ΔN is the load cycle step size, and θ is the load propagation noise at time k-1. k-1 Let θ be the parameter vector of the damage propagation model at time k-1. k Let (da / dN) be the parameter vector of the damage propagation model at time k. k Let be the damage propagation rate at time k, which can be calculated using the Paris model and its improved model.

[0019] Set the number of particles N s For particle sets Initialization is performed, where This represents the i-th particle at initial time k=0, with a total of N particles. s One particle; This represents the damage size of the i-th particle, initialized using the threshold for structural non-destructive testing. Let represent the model parameter components of the i-th particle, which are randomly sampled from the initial distribution of the damage propagation model parameters; and let represent the initial weights of the i-th particle. Set as

[0020] Furthermore, step (2) specifically includes:

[0021] Data is collected at fixed intervals, with each collection session lasting d. l A dataset is constructed once for each damage data point, and for each constructed sequence of observations... and the corresponding load cycle sequence Where time k satisfies Observation sequence and load cycle sequence The construction requires comparing the number of data points collected at time k with the sample size W. If the number of data points collected at time k is less than the sample size W, then the observation sequence is constructed. and load cycle sequence These are the observations obtained at times k=1, k=2, and k, respectively; These represent the load cycles for k=1, k=2, and time k, respectively; if the number of data collected at time k is greater than the sample size W, then an observation sequence is constructed. The values ​​are the observations obtained at times k-W+1 and k-W+2, respectively. in These are the load cycles corresponding to times k-W+1 and k-W+2, respectively.

[0022] Furthermore, step (3) specifically includes:

[0023] (31) Obtain the damage size observation sequence from step (2). and load cycle sequence As sample data, construct a data sample set. Where L is the observation sequence Length;

[0024] (32) A quadratic polynomial quantile regression model was used to analyze the sample dataset. The sample data in the model are fitted, and the quadratic polynomial quantile regression model is expressed as follows:

[0025]

[0026] Where τ is the target quantile, τ=[τ1,τ2,τ3,...,τ M ], τ M Q is the Mth target quantile; τ,k (N * ) represents the damage size corresponding to the quantile τ, and N is the damage size. * The number of load cycles, These are the coefficients of the quadratic polynomial quantile regression model;

[0027] The coefficients of the quadratic polynomial quantile regression model are obtained by optimizing the weighted absolute value of the residuals using a quadratic programming algorithm. The calculation formula is as follows:

[0028]

[0029] Where, ρ τ (·) is the quantile loss function, which is defined as follows:

[0030] ρ τ (u)=u·(τ-I(u<0))

[0031] Where I(·) is the indicator function;

[0032] (33) The load cycle number at the current time k Substituting into the quadratic polynomial quantile regression model, we obtain the predicted damage size value for the target quantile τ. as follows:

[0033]

[0034] Output quantile τ=[τ1,τ2,τ3,...,τ M ], corresponding predicted damage size value in Let τ1, τ2, τ3, ..., τ be the k-quantiles at the current time. M The corresponding predicted damage size.

[0035] Furthermore, step (4) specifically includes:

[0036] (41) The cumulative distribution function of the three-parameter Weibull distribution is used to describe the probability distribution of the observed damage size F(a; γ, η, λ) as follows:

[0037]

[0038] Where a is the damage size, γ is the location parameter, η is the shape parameter, and λ is the scale parameter;

[0039] (42) The quantiles τ = [τ1, τ2, τ3, ..., τ3] obtained in step (3) M ] and its corresponding predicted damage size Above, we set optimization constraints for the three-parameter Weibull distribution parameters, λ. k ∈[0.1,100], η k ∈[0.1,10], Set the initial value of parameter γ. init as follows:

[0040]

[0041] The initial value of parameter η is estimated based on the quantile interval, and two quantiles τ are selected. a τ b , representing the sequence τ=[τ1,τ2,τ3,...,τ M Given any two distinct numbers in the array, with indices a = 1, 2, ..., M and b = 1, 2, ..., M, calculate the initial value η. init as follows:

[0042]

[0043] in, τ are quantiles a , τ b Corresponding predicted damage size;

[0044] The initial value of parameter λ init The calculation is as follows:

[0045]

[0046] The cumulative distribution function of the three-parameter Weibull distribution is fitted using a quadratic programming algorithm to obtain the optimized parameter γ. k η k , λ k The fitted function is as follows:

[0047]

[0048] Where, γ k Let η be the position parameter at time k. k Let λ be the shape parameter at time k. k Let k be the scaling parameter at time k. quantile τ i The corresponding predicted damage size.

[0049] Furthermore, step (5) specifically includes:

[0050] The particle set at time k-1 is obtained by iterating through the state equations, as follows:

[0051]

[0052] in, Let be the damage size component of the i-th particle at time k. Let i be the damage size component of the i-th particle at time k-1, where i = 1, 2, ..., N. s N s The number of particles; Let i be the i-th model parameter component at time k. Let be the i-th model parameter component at time k-1; ΔN is the load cycle number from time k-1 to time k, (da / dN)| k Let ω be the damage propagation rate at time k, and multiply it by ΔN to obtain the damage propagation increment at time k; k-1 The damage propagation noise at time k-1;

[0053] Based on the parameter values ​​of the three-parameter Weibull distribution obtained in step (4), the likelihood probability distribution of the damage size observation quantiles is constructed as follows:

[0054]

[0055] Among them, a k Let γ be the damage size at time k. k Let η be the position parameter at time k. k Let λ be the shape parameter at time k. k Let k be the scaling parameter at time k;

[0056] The particle weights are updated using the following formula:

[0057]

[0058] in, Let be the weight of the i-th particle at time k. Let be the weight of the i-th particle at time k-1. Let be the observed likelihood value of the i-th particle;

[0059] After calculating the weights of all particles, the weights of all particles are normalized as follows:

[0060]

[0061] in, Let N be the normalized weight of the i-th particle at time k. s The number of particles;

[0062] Based on the posterior probability distribution of the particle representation after weight update, the future extension of structural damage is predicted as follows:

[0063] The posterior probability density function for calculating the damage size is as follows:

[0064]

[0065] Among them, ak Let k be the damage size. Let be the damage size of the i-th particle at time k, δ(·) be the Dirac function, and p(a k |y 1:k Let y be a series of observations from the beginning to the current time. 1:k ={y1,y2,...,y k Under the condition of}, a k The probability distribution of y 1:k ={y1,y2,...,y k} represents the damage signals collected by the sensor at times 1, 2, ..., k;

[0066] The posterior probability density function for calculating the parameters of the damage propagation model is expressed as:

[0067]

[0068] Where, θ k Let k be the parameter vector of the damage extension model at time k. Let p(θ) be the model parameter component of the i-th particle at time k. k |y 1:k Let y be a series of observations from the beginning to the current time. 1:k ={y1,y2,...,y k Under the condition of}, θ k The probability distribution;

[0069] The formulas for calculating the maximum a posteriori probability estimates of damage size and damage propagation model parameters are as follows:

[0070]

[0071] in, This is the maximum posterior probability estimate of the damage size at time k. The maximum posterior probability estimate of the damage extension model parameters at time k;

[0072] Starting with the posterior estimate of the damage size, the posterior estimate is projected onto future time points to obtain the predicted trajectory of the future damage, as follows:

[0073] a k+p =a k+p-1 +exp(ω k+p-1 (da / dN)| k+p-1 ΔN

[0074] Among them, a k+p Let a be the damage size at time k+p in the future. k+p-1 ω represents the damage size at time k+p-1 in the future. k+p-1For damage propagation noise; calculate the damage propagation rate (da) j / dN)| k+p-1 At that time, the parameters of the damage propagation model are taken as follows:

[0075] The beneficial effects of this invention are:

[0076] This invention calculates the quantiles of the most recent damage observations through dynamic quantile regression, and fits the quantiles to a three-parameter Weibull distribution to obtain the quantile observation likelihood probability distribution, which is used to update the weights of the particle set characterizing damage expansion. This effectively improves the damage prediction accuracy and robustness of particle filtering under the influence of complex time-varying factors. Attached Figure Description

[0077] Figure 1 This is a flowchart of the method of the present invention.

[0078] Figure 2 The diagram shows the structural dimensions and sensor arrangement in the embodiment.

[0079] Figure 3 The image shows the crack propagation trajectory and crack size observations of the target structure in the embodiment.

[0080] Figure 4a The example shows a quantile line plot of the fitted damage observation values.

[0081] Figure 4b The image shows the fitted plot of the cumulative distribution function of the Weibull distribution in the example.

[0082] Figure 4c The graph shows the probability distribution function fitting of the Weibull distribution in the example.

[0083] Figure 5 The diagram shows the damage propagation prediction results in the example when N=41897 load cycles. Detailed Implementation

[0084] To facilitate understanding by those skilled in the art, the present invention will be further described below with reference to embodiments and accompanying drawings. The content mentioned in the embodiments is not intended to limit the present invention.

[0085] Reference Figure 1 As shown, the present invention provides a method for updating quantile observation likelihood weights in particle filter damage spread prediction, comprising the following steps:

[0086] (1) Set the parameters required for dynamic quantile regression in offline mode; initialize the particle set and particle weights in the particle filter damage propagation prediction algorithm for the target structure; specifically including:

[0087] Define the sample size W required for dynamic quantile regression in offline mode and the quantiles τ of the observed likelihood distribution τ∈{τ1,τ2,τ3,...,τ M}, where the subscript M represents the number of quantiles; initialize the particle set and particle weights in the particle filter damage propagation prediction algorithm for the target structure;

[0088] Specifically, setting the sample size required for dynamic quantile regression and the quantiles of the observed likelihood distribution involves the following steps: In the offline state (k=0), based on the damage monitoring frequency and damage propagation rate characteristics of the target structure, the sample size W for dynamic quantile regression is set. This sample size W represents the use of W observed damage sizes for quantile regression. The selection of the sample size W needs to balance the amount of data required for quantile regression and the number of particle filter iterations. The quantiles {τ1,τ2,τ3,...,τ} used to fit the damage monitoring probability distribution are then set. M}, where M is the number of quantiles, and quantiles τ1, τ2, τ3, ..., τ M They belong to the interval (0,1) and are all distinct;

[0089] Specifically, the initialization of the particle set and particle weights in the particle filter damage propagation prediction algorithm involves determining the damage propagation state equation in the target structure based on its geometry and service conditions, as follows:

[0090]

[0091] Among them, a k Let a be the damage size at time k. k-1 Let ω be the damage size at time k-1. k-1 The noise represents the damage propagation at time k-1, where N is the number of load cycles, ΔN is the load cycle step size, and θ is the load propagation noise at time k-1. k-1 Let θ be the parameter vector of the damage propagation model at time k-1. k Let (da / dN) be the parameter vector of the damage propagation model at time k. k Let be the damage propagation rate at time k, which can be calculated using the Paris model and its improved model.

[0092] Set the number of particles N s For particle sets Initialization is performed, where This represents the i-th particle at initial time k=0, with a total of N particles. s One particle; This represents the damage size of the i-th particle, initialized using the threshold for structural non-destructive testing. Let represent the model parameter components of the i-th particle, which are randomly sampled from the initial distribution of the damage propagation model parameters; and let represent the initial weights of the i-th particle. Set as

[0093] (2) Obtain the observed damage size of the target structure at the current time k during the online service process of the target structure. Constructing a load cyclic sequence and its corresponding observation sequence Specifically, it includes:

[0094] Data is collected at fixed intervals, with each collection session lasting d. l A dataset is constructed once for each damage data point, and for each constructed sequence of observations... and the corresponding load cycle sequence Where time k satisfies Observation sequence and load cycle sequence The construction requires comparing the number of data points collected at time k with the sample size W. If the number of data points collected at time k is less than the sample size W, then the observation sequence is constructed. and load cycle sequence These are the observations obtained at times k=1, k=2, and k, respectively; These represent the load cycles for k=1, k=2, and time k, respectively; if the number of data collected at time k is greater than the sample size W, then an observation sequence is constructed. The values ​​are the observations obtained at times k-W+1 and k-W+2, respectively. These are the load cycles corresponding to times k-W+1 and k-W+2, respectively.

[0095] (3) Using a quadratic polynomial to process the load cyclic sequence Corresponding damage size observation sequence Quantile regression is performed to obtain the quantiles of the likelihood probability distribution of the damage size observation at time k; specifically including:

[0096] (31) Obtain the damage size observation sequence from step (2). and load cycle sequence As sample data, construct a data sample set. Where L is the observation sequence Length;

[0097] (32) A quadratic polynomial quantile regression model was used to analyze the sample dataset. The sample data in the model are fitted, and the quadratic polynomial quantile regression model is expressed as follows:

[0098]

[0099] Where τ is the target quantile, τ=[τ1,τ2,τ3,...,τ M ], τ M Q is the Mth target quantile; τ,k (N * ) represents the damage size corresponding to the quantile τ, and N is the damage size. * The number of load cycles, These are the coefficients of the quadratic polynomial quantile regression model;

[0100] The coefficients of the quadratic polynomial quantile regression model are obtained by optimizing the weighted absolute value of the residuals using a quadratic programming algorithm. The calculation formula is as follows:

[0101]

[0102] Where, ρ τ (·) is the quantile loss function, which is defined as follows:

[0103] ρ τ (u)=u·(τ-I(u<0))

[0104] Where I(·) is the indicator function;

[0105] (33) The load cycle number at the current time k Substituting into the quadratic polynomial quantile regression model, we obtain the predicted damage size value for the target quantile τ. as follows:

[0106]

[0107] Output quantile τ=[τ1,τ2,τ3,...,τ M ], corresponding predicted damage size value in Let τ1, τ2, τ3, ..., τ be the k-quantiles at the current time. M The corresponding predicted damage size.

[0108] (4) The quantiles obtained in step (3) are fitted using the cumulative distribution function of the three-parameter Weibull distribution to obtain the parameter values ​​of the three-parameter Weibull distribution; specifically including:

[0109] (41) The cumulative distribution function of the three-parameter Weibull distribution is used to describe the probability distribution of the observed damage size F(a; γ, η, λ) as follows:

[0110]

[0111] Where a is the damage size, γ is the location parameter, η is the shape parameter, and λ is the scale parameter;

[0112] (42) The quantiles τ = [τ1, τ2, τ3, ..., τ3] obtained in step (3) M ] and its corresponding predicted damage size Above, we set optimization constraints for the three-parameter Weibull distribution parameters, λ. k ∈[0.1,100], η k ∈[0.1,10], Set the initial value of parameter γ. init as follows:

[0113]

[0114] The initial value of parameter η is estimated based on the quantile interval, and two quantiles τ are selected. a τ b , representing the sequence τ=[τ1,τ2,τ3,...,τ M Given any two distinct numbers in the array, with indices a = 1, 2, ..., M and b = 1, 2, ..., M, calculate the initial value η. init as follows:

[0115]

[0116] in, τ are quantiles a , τ b Corresponding predicted damage size;

[0117] The initial value of parameter λ init The calculation is as follows:

[0118]

[0119] The cumulative distribution function of the three-parameter Weibull distribution is fitted using a quadratic programming algorithm to obtain the optimized parameter γ. k η k , λ k The fitted function is as follows:

[0120]

[0121] Where, γ k Let η be the position parameter at time k. k Let λ be the shape parameter at time k. k Let k be the scaling parameter at time k. quantile τ i The corresponding predicted damage size.

[0122] (5) Iterate the particle set at time k-1 using the state equation to obtain the particle set at time k; construct the damage size observation quantile likelihood probability distribution based on the parameter values ​​of the three-parameter Weibull distribution obtained in step (4), and update the particle filter weights using the quantile likelihood probability distribution; predict the future expansion of structural damage based on the posterior probability distribution of the particle characterization after weight update; specifically including:

[0123] The particle set at time k-1 is obtained by iterating through the state equations, as follows:

[0124]

[0125] in, Let be the damage size component of the i-th particle at time k. Let i be the damage size component of the i-th particle at time k-1, where i = 1, 2, ..., N. s N s The number of particles; Let i be the i-th model parameter component at time k. Let be the i-th model parameter component at time k-1; ΔN is the load cycle number from time k-1 to time k, (da / dN)| k Let ω be the damage propagation rate at time k, and multiply it by ΔN to obtain the damage propagation increment at time k; k-1 The damage propagation noise at time k-1;

[0126] Based on the parameter values ​​of the three-parameter Weibull distribution obtained in step (4), the likelihood probability distribution of the damage size observation quantiles is constructed as follows:

[0127]

[0128] Among them, a k Let γ be the damage size at time k. k Let η be the position parameter at time k. k Let λ be the shape parameter at time k. k Let k be the scaling parameter at time k;

[0129] The particle weights are updated using the following formula:

[0130]

[0131] in, Let be the weight of the i-th particle at time k. Let be the weight of the i-th particle at time k-1. Let be the observed likelihood value of the i-th particle;

[0132] After calculating the weights of all particles, the weights of all particles are normalized as follows:

[0133]

[0134] in, Let N be the normalized weight of the i-th particle at time k. s The number of particles;

[0135] Based on the posterior probability distribution of the particle representation after weight update, the future extension of structural damage is predicted as follows:

[0136] The posterior probability density function for calculating the damage size is as follows:

[0137]

[0138] Among them, a k Let k be the damage size. Let be the damage size of the i-th particle at time k, δ(·) be the Dirac function, and p(a k |y 1:k Let y be a series of observations from the beginning to the current time. 1:k ={y1,y2,...,y k Under the condition of}, a k The probability distribution of y 1:k ={y1,y2,...,y k} represents the damage signals collected by the sensor at times 1, 2, ..., k;

[0139] The posterior probability density function for calculating the parameters of the damage propagation model is expressed as:

[0140]

[0141] Where, θ k Let k be the parameter vector of the damage extension model at time k. Let p(θ) be the model parameter component of the i-th particle at time k. k |y 1:k Let y be a series of observations from the beginning to the current time. 1:k ={y1,y2,...,y k Under the condition of}, θ k The probability distribution;

[0142] The formulas for calculating the maximum a posteriori probability estimates of damage size and damage propagation model parameters are as follows:

[0143]

[0144] in, This is the maximum posterior probability estimate of the damage size at time k. The maximum posterior probability estimate of the damage extension model parameters at time k;

[0145] Starting with the posterior estimate of the damage size, the posterior estimate is projected onto future time points to obtain the predicted trajectory of the future damage, as follows:

[0146] a k+p =a k+p-1 +exp(ω k+p-1 (da / dN)| k+p-1 ΔN

[0147] Among them, a k+p Let a be the damage size at time k+p in the future. k+p-1 ω represents the damage size at time k+p-1 in the future. k+p-1 For damage propagation noise; calculate the damage propagation rate (da) j / dN)| k+p-1 At that time, the parameters of the damage propagation model are taken as follows:

[0148] (6) Take k = k + 1 and repeat steps (2) to (5) until the damage size reaches the threshold and the structure fails.

[0149] This embodiment takes the monitoring and prediction of the lug structure of an aerospace connector under variable amplitude fatigue load as an example, as detailed below:

[0150] like Figure 2 The example shown includes the monitored structure and the arrangement of the piezoelectric sensors. Figure 2 Two sensors (PZT1 and PZT2) were arranged on the front of the monitored structure. The thickness of the lugs was 5 mm. A 2 mm crack was pre-made at the edge of the lug hole using an EDM machine for crack initiation and crack direction control. PZT1 was used for excitation at both ends of the pre-made crack, and PZT2 was used for sensing. A random fatigue load spectrum based on the modified FALSTAFF standard load spectrum was applied to the specimen. During the fatigue loading process, piezoelectric sensing signals were collected at 10 s intervals, and the excitation signal frequency was 160 kHz.

[0151] Based on the material parameters of the structural material obtained from the literature, the NASGRO model was selected as the crack propagation model. The model parameters are: NASGRO shape parameter p = 0.25, NASGRO shape parameter q = 1, f = 0.342. The fracture toughness of the lug material was taken as... Stress intensity factor amplitude threshold The model parameter vector θ = [C, m], where parameters C and m are the model parameters of the NASGRO model. The initial distribution of model parameter C follows a log-normal distribution, and the initial distribution of model parameter m follows a normal distribution, i.e., log(C... k )| k＝0 and m k | k＝0 It follows a normal distribution, with a mean vector [-26.76, 3.2] and a covariance matrix of . in Let be the variances of log(C) and m, respectively, and ρ = 0.9979 represent the correlation between the two parameters; the standard deviation of the crack propagation noise is σ. ω =0.5; The initial crack length distribution is a Gaussian distribution N(2,0.2) with the mean being the cut length. 2 The cyclic load step size is ΔN = 20; the number of particles is set to N. s =200, initialize particle set in From the initial distribution of crack length N(2,0.1) 2 Obtained by random sampling from ) and m k (i) | k＝0 From the initial distribution of model parameters The data was obtained through random sampling; finally, the weights of each particle were initialized to...

[0152]

[0153] 1) Initialize quantiles;

[0154] We determine that we need to analyze 7 quantile curves with τ = 0.05, τ = 0.15, τ = 0.35, τ = 0.50, τ = 0.65, τ = 0.85, and τ = 0.95; and set the sample size W = 200 required for dynamic quantile regression.

[0155] 2) Construct the observation sequence;

[0156] A total of 750 sets of load cycle sequences of the verification specimens and the damage factors calculated from their corresponding dynamic load signals were obtained, which constitutes the dataset acquired during the online monitoring process. and Each time d is obtained l = 10 damage factor data points, perform one quantile regression, when k = 10, 20, ... 750, perform one quantile regression of crack length based on the dataset, a total of 75 online assessments; for example, in the 35th assessment, corresponding to k = 350, N = 78863 load cycles, load cycle sequence Observation sequence

[0157] 3) Online quantile regression;

[0158] The hyperparameter values ​​corresponding to the minimum values ​​of the loss functions of the seven quantile regression curves are obtained based on the quadratic programming algorithm, thereby constructing seven crack propagation trend curves.

[0159] Substituting the value at a specific quantile of the damage factor distribution at the current moment into the fatigue crack assessment model, the fatigue crack length at the current moment is obtained, such as... Figure 3 As shown, the circle represents the crack length obtained after the online monitoring damage factor is processed by the fatigue crack assessment model, and the black line represents the actual crack length.

[0160] 4) Online fitting and weight calculation;

[0161] Figure 4a The diagram shows seven quantile regression curves of the monitored crack length data over a certain time window, along with the actual crack length. The dot (·) represents the crack length obtained after applying the online monitoring damage factor to the fatigue crack assessment model. The solid black line represents the actual crack length. The other curves represent the fitted quantile curves, which are fitted to the quantiles at the last moment of the time window, minimizing the observed quantile values. Compared with theoretical quantiles The sum of squared errors is used to determine the parameters of the cumulative distribution function; Figure 4b The cumulative probability CDF fitted at that time point. Figure 4c This is the probability density function of the crack length at the current moment. This Weibull distribution is the heteroscedasticity model for calculating the likelihood probability of the damage size observation quantile in particle filtering. Substituting the crack length particle value into the probability density function yields its likelihood probability, thereby completing the particle weight update.

[0162] 5) Online crack propagation prediction;

[0163] Figure 5 The figure shows the predicted fatigue crack propagation results at the 20th evaluation during crack propagation, corresponding to N = 41897 load cycles. The dashed line represents the predicted trajectory propagation of the future crack by projecting all crack length particles to future time points. The maximum a posteriori estimate of the crack length at each time point is represented by the solid black line, which basically coincides with the actual crack length, indicating that the prediction result is accurate.

[0164] This invention has many specific applications. The above description is only a preferred embodiment of this invention. It should be noted that for those skilled in the art, several improvements can be made without departing from the principle of this invention, and these improvements should also be considered within the scope of protection of this invention.

Claims

1. A method for updating quantile observation likelihood weights in particle filter damage propagation prediction, characterized in that, The steps are as follows: (1) Set the parameters required for dynamic quantile regression in offline state; initialize the particle set and particle weights in the particle filter damage propagation prediction algorithm for the target structure; (2) Obtain the observed damage size of the target structure at the current time k during the online service process of the target structure. Constructing a load cyclic sequence and its corresponding observation sequence (3) Using a quadratic polynomial to process the load cyclic sequence Corresponding damage size observation sequence Quantile regression was performed to obtain the quantiles of the likelihood probability distribution of the damage size observation at time k; (4) The cumulative distribution function of the three-parameter Weibull distribution is used to fit the quantiles obtained in step (3) to obtain the parameter values ​​of the three-parameter Weibull distribution. (5) Iterate the particle set at time k-1 using the state equation to obtain the particle set at time k; construct the quantile likelihood probability distribution of damage size observation based on the parameter values ​​of the three-parameter Weibull distribution obtained in step (4), and update the particle filter weights through the quantile likelihood probability distribution; predict the future propagation of structural cracks based on the posterior probability distribution of particle characterization after weight update. (6) Take k = k + 1 and repeat steps (2) to (5) until the damage size reaches the threshold and the structure fails.

2. The quantile observation likelihood weight update method for particle filter damage propagation prediction according to claim 1, characterized in that, Step (1) specifically includes: Define the sample size W required for dynamic quantile regression in offline mode and the quantiles τ of the observed likelihood distribution τ∈{τ1,τ2,τ3,...,τ M }, where the subscript M represents the number of quantiles; initialize the particle set and particle weights in the particle filter damage propagation prediction algorithm for the target structure; The specific steps for setting the sample size and quantiles of the observed likelihood distribution for dynamic quantile regression are as follows: In the offline state (k=0), based on the characteristics of the target structure's damage monitoring frequency and damage propagation rate, the sample size W for dynamic quantile regression is set. This sample size W represents the W damage size observations used for quantile regression. The selection of the sample size W needs to balance the amount of data required for quantile regression and the number of particle filter iterations. The quantiles {τ1,τ2,τ3,...,τ} used to fit the damage monitoring probability distribution are set. M }, where M is the number of quantiles, and quantiles τ1, τ2, τ3, ..., τ M They belong to the interval (0,1) and are all distinct; The initialization of the particle set and particle weights in the particle filter damage propagation prediction algorithm is specifically as follows: The damage propagation state equation in the target structure is determined based on the geometry and service conditions of the target structure, as follows: Among them, a k Let a be the damage size at time k. k-1 Let ω be the damage size at time k-1. k-1 The noise represents the damage propagation at time k-1, where N is the number of load cycles, ΔN is the load cycle step size, and θ is the load propagation noise at time k-1. k-1 Let θ be the parameter vector of the damage propagation model at time k-1. k Let (da / dN) be the parameter vector of the damage propagation model at time k. k Let be the damage propagation rate at time k, which can be calculated using the Paris model and its improved model. Set the number of particles N s For particle sets Initialization is performed, where This represents the i-th particle at initial time k=0, with a total of N particles. s One particle; This represents the damage size of the i-th particle, initialized using the threshold for structural non-destructive testing. Let represent the model parameter components of the i-th particle, which are randomly sampled from the initial distribution of the damage propagation model parameters; and let represent the initial weights of the i-th particle. Set as 3. The quantile observation likelihood weight update method for particle filter damage propagation prediction according to claim 2, characterized in that, Step (2) specifically includes: Data is collected at fixed intervals, with each collection session lasting d. l A dataset is constructed once for each damage data point, and for each constructed sequence of observations... and the corresponding load cycle sequence At time k, k = c·d l , Observation sequence and load cycle sequence The construction requires comparing the number of data points collected at time k with the sample size W. If the number of data points collected at time k is less than the sample size W, then the observation sequence is constructed. and load cycle sequence These are the observations obtained at times k=1, k=2, and k, respectively; These represent the load cycles for k=1, k=2, and time k, respectively; if the number of data collected at time k is greater than the sample size W, then an observation sequence is constructed. The values ​​are the observations obtained at times k-W+1 and k-W+2, respectively. These are the load cycles corresponding to times k-W+1 and k-W+2, respectively.

4. The quantile observation likelihood weight update method for particle filter damage propagation prediction according to claim 3, characterized in that, Step (3) specifically includes: (31) Obtain the damage size observation sequence from step (2). and load cycle sequence As sample data, construct a data sample set. Where L is the observation sequence Length; (32) A quadratic polynomial quantile regression model was used to analyze the sample dataset. The sample data in the model are fitted, and the quadratic polynomial quantile regression model is expressed as follows: Where τ is the target quantile, τ=[τ1,τ2,τ3,...,τ M ], τ M Q is the Mth target quantile; τ,k (N * ) represents the damage size corresponding to the quantile τ, and N is the damage size. * The number of load cycles, These are the coefficients of the quadratic polynomial quantile regression model; The coefficients of the quadratic polynomial quantile regression model are obtained by optimizing the weighted absolute value of the residuals using a quadratic programming algorithm. The calculation formula is as follows: Where, ρ τ (·) is the quantile loss function, which is defined as follows: ρ τ (u)=u·(τ-I(u<0)) Where I(·) is the indicator function; (33) The load cycle number at the current time k Substituting into the quadratic polynomial quantile regression model, we obtain the predicted damage size value for the target quantile τ. as follows: Output quantile τ=[τ1,τ2,τ3,...,τ M ], corresponding predicted damage size value in Let τ1, τ2, τ3, ..., τ be the k-quantiles at the current time. M The corresponding predicted damage size.

5. The quantile observation likelihood weight update method for particle filter damage propagation prediction according to claim 4, characterized in that, Step (4) specifically includes: (41) The cumulative distribution function of the three-parameter Weibull distribution is used to describe the probability distribution of the observed damage size F(a; γ, η, λ) as follows: Where a is the damage size, γ is the location parameter, η is the shape parameter, and λ is the scale parameter; (42) The quantiles τ = [τ1, τ2, τ3, ..., τ3] obtained in step (3) M ] and its corresponding predicted damage size Above, we set optimization constraints for the three-parameter Weibull distribution parameters, λ. k ∈[0.1,100], η k ∈[0.1,10], Set the initial value of parameter γ. init as follows: The initial value of parameter η is estimated based on the quantile interval, and two quantiles τ are selected. a τ b , representing the sequence τ=[τ1,τ2,τ3,...,τ M Given any two distinct numbers in the array, with indices a = 1, 2, ..., M and b = 1, 2, ..., M, calculate the initial value η. init as follows: in, τ are quantiles a , τ b Corresponding predicted damage size; The initial value of parameter λ init The calculation is as follows: The cumulative distribution function of the three-parameter Weibull distribution is fitted using a quadratic programming algorithm to obtain the optimized parameter γ. k η k , λ k The fitted function is as follows: Where, γ k Let η be the position parameter at time k. k Let λ be the shape parameter at time k. k Let k be the scaling parameter at time k. quantile τ i The corresponding predicted damage size.

6. The quantile observation likelihood weight update method for particle filter damage propagation prediction according to claim 5, characterized in that, Step (5) specifically includes: The particle set at time k-1 is obtained by iterating through the state equations, as follows: in, Let be the damage size component of the i-th particle at time k. Let i be the damage size component of the i-th particle at time k-1, where i = 1, 2, ..., N. s N s The number of particles; Let i be the i-th model parameter component at time k. Let be the i-th model parameter component at time k-1; ΔN is the load cycle number from time k-1 to time k, (da / dN)| k Let ω be the damage propagation rate at time k, and multiply it by ΔN to obtain the damage propagation increment at time k; k-1 The damage propagation noise at time k-1; Based on the parameter values ​​of the three-parameter Weibull distribution obtained in step (4), the likelihood probability distribution of the damage size observation quantiles is constructed as follows: Among them, a k Let γ be the damage size at time k. k Let η be the position parameter at time k. k Let λ be the shape parameter at time k. k The scaling parameter at time k; The particle weights are updated using the following formula: in, Let be the weight of the i-th particle at time k. Let be the weight of the i-th particle at time k-1. Let be the observed likelihood value of the i-th particle; After calculating the weights of all particles, the weights of all particles are normalized as follows: in, Let N be the normalized weight of the i-th particle at time k. s The number of particles; Based on the posterior probability distribution of the particle representation after weight update, the future expansion of structural damage is predicted as follows: The posterior probability density function for calculating the damage size is as follows: Among them, a k Let k be the damage size. Let be the damage size of the i-th particle at time k, δ(·) be the Dirac function, and p(a k |y 1:k Let y be a series of observations from the beginning to the current time. 1:k ={y1,y2,...,y k Under the condition of}, a k The probability distribution of y 1:k ={y1,y2,...,y k } represents the damage signals collected by the sensor at times 1, 2, ..., k; The posterior probability density function for calculating the parameters of the damage propagation model is expressed as: Where, θ k Let k be the parameter vector of the damage extension model at time k. Let p(θ) be the model parameter component of the i-th particle at time k. k |y 1:k Let y be a series of observations from the beginning to the current time. 1:k ={y1,y2,...,y k Under the condition of}, θ k The probability distribution; The formulas for calculating the maximum a posteriori probability estimates of damage size and damage propagation model parameters are as follows: in, This is the maximum posterior probability estimate of the damage size at time k. The maximum posterior probability estimate of the damage extension model parameters at time k; Starting with the posterior estimate of the damage size, the posterior estimate is projected onto future time points to obtain the predicted trajectory of the future crack, as follows: to k+p =a k+p-1 +exp(ω k+p-1 )(from / to)| k+p-1 ΔN Among them, a k+p Let a be the damage size at time k+p in the future. k+p-1 ω represents the damage size at time k+p-1 in the future. k+p-1 For damage propagation noise; calculate the damage propagation rate (da) j / dN)| k+p-1 At that time, the parameters of the damage propagation model are taken as follows:

Images