Fatigue crack assessment method and terminal based on heteroscedastic guided wave-Gaussian process

Abstract

The present invention discloses a fatigue crack assessment method and terminal based on heteroscedastic guided wave-Gaussian process, and the steps are as follows: modeling the heteroscedastic characteristics of the damage factor of the aviation structure under time-varying conditions; obtaining the quantile damage factors of the aviation structure at the current moment; obtaining the crack assessment result of the aviation structure at the current moment and the 90% uncertainty interval. The method of the present invention can effectively reduce the dispersion of the influence of multiple uncertain factors on quantitative monitoring, and can quantify the uncertainty of the assessment result, thereby improving the accuracy of time-varying damage assessment of aviation structures.

Description

Technical Field

[0001] The present invention relates to the field of aviation structure health monitoring, and specifically to a fatigue crack assessment method and terminal based on heteroscedastic guided wave (GW)-Gaussian process (GP). Background Art

[0002] In recent years, structural health monitoring (SHM) methods are gradually shifting from theoretical research to aerospace engineering applications. In the process of engineering application, accurate damage quantification of a single structure remains a challenging task. In the actual aviation application process, the extension of fatigue cracks is a complex process, which is mainly affected by structural variables such as material properties, manufacturing and assembly processes, load-time history, and use environment. These factors are often coupled with each other, making the extension direction and extension rate of fatigue cracks complicated. In addition, for long-term single-aircraft structural monitoring, structural health monitoring needs to be carried out under different environments and operating conditions, such as at different airports, different seasons, different flight missions, and different pilot operating experience. Therefore, the uncertainties to which a single-aircraft structure is subject may be complex and different from each other. In addition, an obvious feature of these uncertainties is that the distribution changes with the service time, which can also be called heteroscedasticity. This important feature of uncertainty must be taken into account to achieve accurate damage quantification of the crack length of a single structure.

[0003] Gaussian process is a Bayesian machine learning method that can handle nonlinear input-output regression problems. Gaussian process can not only improve the accuracy of evaluation, but also provide the posterior distribution of its evaluation, which can be used as a criterion for quantitative evaluation of uncertainty. The basic Gaussian process method usually estimates the mean of the output variable based on the input variable. This method works well when the uncertainty distribution assumptions, such as symmetry and homoscedasticity, are met. However, when there is heteroscedasticity in the data, the mean and median of the uncertainty distribution may be inconsistent. In this case, it is inaccurate to use the mean to represent the central tendency of the distribution. The median is the value that separates the upper half of the data population or distribution from the lower half, and is not easily affected by extreme values. Compared with the mean, it is a better indicator of the central tendency of the data set. Quantile regression is an effective tool that can give the impact of explanatory variables on the central and non-central location, scale, and distribution shape of the response variable. The Gaussian process quantile regression method relaxes the original assumptions of symmetry and homoscedasticity while retaining the advantages of the Gaussian process method. The present invention proposes to apply the Gaussian process quantile regression method to the fatigue crack assessment problem under heteroscedastic uncertainty conditions, which effectively improves the accuracy of diagnosis. Summary of the invention

[0004] In view of the above-mentioned deficiencies in the prior art, the purpose of the present invention is to provide a fatigue crack assessment method and terminal based on heteroscedastic guided wave-Gaussian process, so as to solve the problem of low assessment accuracy caused by not considering the heteroscedastic characteristics of time-varying factors when using Gaussian process for damage diagnosis in the prior art; the method of the present invention can effectively reduce the dispersion of the influence of multiple uncertain factors on quantitative monitoring, and can quantify the uncertainty of the assessment results, thereby improving the accuracy of time-varying damage assessment of aviation structures.

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

[0006] A fatigue crack assessment method based on heteroscedastic guided wave-Gaussian process of the present invention comprises the following steps:

[0007] 1) Modeling the heteroscedastic characteristics of damage factors of aviation structures under time-varying conditions;

[0008] 2) Obtaining the damage factors of each quantile of the aviation structure at the current moment;

[0009] 3) Obtain the crack assessment results of the aviation structure at the current moment and the 90% uncertainty interval.

[0010] Furthermore, the step 1) specifically includes:

[0011] During the service process of aviation structures, the active guided wave SHM system excites the guided wave signal at a certain time interval through the piezoelectric sensor at the excitation end. The guided wave signal is transmitted through the structure and received by the piezoelectric sensor at the receiving end. The corresponding damage factor y is obtained by analyzing the guided wave signal at the receiving end. j , and the time t corresponding to the damage factor j , up to the current time t T , the number of damage factors obtained is M, and the sequence {(t j ,y j ),j=1,2,…,M} is recorded as Subscript o indicates online acquisition; each new acquisition d l After the damage factor, that is, when M is d l When the damage factor y is an integer multiple, heteroscedastic modeling is performed on the damage factor y with the service time t to obtain the damage factor-service time curve at τ = 0.95, 0.50, and 0.05 quantiles. The three curves all obey Gaussian processes, and the mean functions and covariance functions of the three Gaussian processes are the same, but the parameters of their respective mean functions and covariance functions are different;

[0012] Damage factor-service time curve assuming τ quantile (τ=0.95,0.50,0.05) It obeys the Gaussian process and is expressed as in represents the Gaussian process, θ is the hyperparameter of the Gaussian process, m τ (t) represents the mean function of the Gaussian process, k τ (t p ,t q ) represents the covariance function of the Gaussian process, t p and t q Represents the sequence t o =[t1,t2,…,t M ] T Any two numbers in , subscript p = 1, 2, ..., M, q = 1, 2, ..., M, superscript T represents the transpose of the matrix; there is y o =[y1,y2,…,y M ] T Obey a joint Gaussian distribution:

[0013]

[0014] In the formula, represents Gaussian distribution, m τ (t o ) means to convert t o =[t1,t2,…,t M ] T Substitute the mean function m τ (t) The obtained M×1-dimensional column vector, assuming that the mean is always equal to 0, so m τ (t o ) is a column vector with all elements equal to zero, K τ (t o ,t o ) means to convert t o =[t1,t2,…,t M ] T Substitute any two numbers into the covariance function k τ (t p ,t q ) The M×M dimensional covariance matrix is ​​calculated; the covariance function is set to the square exponential covariance function, and the covariance matrix K τ (t o ,t o ) in the position (p,q) is t p ,t q ∈t o It is calculated through the square exponential covariance function, which is shown as follows:

[0015]

[0016] Where θ1, θ2 are the parameters of the covariance function, also known as the hyperparameters of the Gaussian process model, and the quantile [θ1, θ2] is abbreviated as θ; the loss function L of the Gaussian process quantile regression model is constructed τ , and optimize to get the optimal solution. The loss function is all the damage factors y j To the function curve that needs to be solved The weighted absolute residual sum of is expressed as follows:

[0017]

[0018] Since the regression curve of τ quantile If it obeys the Gaussian process, then solve L τ The parameter corresponding to the minimum value is equivalent to solving the posterior distribution The maximum value of corresponds to the Gaussian process model hyperparameters:

[0019]

[0020] In the formula, for is the abbreviation of the function that needs to be solved; find the posterior distribution through the optimization algorithm The maximum value parameter, thus obtaining the τ quantile curve Gaussian process model

[0021] Furthermore, the step 2) specifically includes:

[0022] Set the current time t M Substitute into the Gaussian process model of the three quantile curves constructed in step 1), then the current moment t of the aviation structure is M The corresponding τ quantile damage factor y τ (t M ) and y o The joint Gaussian distribution satisfies the following formula:

[0023]

[0024] In the formula, only y τ (t M ) is unknown, and the current moment t of the aviation structure is obtained through the conditional probability formula. M , the damage factor value corresponding to the τ quantile is:

[0025]

[0026] In the formula, represents mathematical expectation; K τ (t M ,t o ) represents the current time tM With t o =[t1,t2,…,t M ] T Substitute the 1×M dimensional covariance matrix calculated by the covariance function; K τ (t o ,t o ) means to convert t o =[t1,t2,…,t M ] T Substitute any two numbers in into the covariance function to obtain the M×M dimensional covariance matrix.

[0027] Furthermore, the step 3) specifically includes:

[0028] Substitute the damage factor values ​​of the aviation structure at τ=0.95, τ=0.5, τ=0.05 quantiles obtained in step 2) into the fatigue crack assessment model to obtain the crack length value, which is expressed as follows:

[0029]

[0030] In the formula, when τ = 0.50, is the evaluation result of the crack length of the aviation structure; when τ=0.95, is the upper limit of the 90% prediction interval of the evaluation results of the crack length of the aviation structure; when τ = 0.05, The lower bound of the 90% prediction interval of the crack length evaluation results of aviation structures; pr =[y1,y2,…,y n ] T and a pr =[a1,a2,…,a n ] T They represent the damage factor and the corresponding known crack length data in the prior data set respectively; n is the total number of data contained in the prior data set; β represents the parameter of the fatigue crack assessment model; is the damage factor at the τ quantile and the prior data set y pr =[y1,y2,…,y n ] T The calculated 1×n dimensional covariance matrix, K β (y pr ,y pr ) is the n×n dimensional covariance matrix obtained by calculating any two of the prior data sets.

[0031] Furthermore, the establishment process of the fatigue crack assessment model is as follows:

[0032] Obtain n pairs of known structural crack length states a through fatigue test or simulation data of batch structures iThe damage factor y i Data composition prior data set {(a i ,y i ),i=1,2,…,n}, denoted as Assume that the mapping relationship between damage factor y and crack length a = f(y) satisfies the Gaussian process β represents the parameters of the model, j = 1, 2, ..., n; the mean function is selected as m β (y) = 0, covariance function k β (y i ,y j ) is the composite covariance function, which is derived from the square exponential covariance function k SE and noise covariance function k noise Add them together, as shown in the following formula:

[0033]

[0034] In the formula, [β1, β2, β3] is recorded as β, δ ij represents the Kronecker function, i.e., i=j takes 1, i≠j takes 0; based on the prior data set y pr =[y1,…,y i ,…,y n ] T ,a pr =a1,…,a i ,…,a n ] T Construct the negative log marginal likelihood function:

[0035]

[0036] In the formula, K β (y pr ,y pr ) is the prior data set y pr =[y1,…,y i ,…,y n ] T Substitute any two of them into the composite covariance function to obtain the n×n dimensional covariance matrix; solve the hyperparameters corresponding to the minimum value of the negative logarithmic marginal likelihood function L(β) to obtain the fatigue crack assessment model.

[0037] The present invention also provides a fatigue crack assessment terminal, comprising:

[0038] one or more processors;

[0039] A memory for storing one or more programs;

[0040] When the one or more programs are executed by the one or more processors, the one or more processors are caused to implement the fatigue crack assessment method.

[0041] The present invention also provides a computer-readable storage medium having a computer program stored thereon, characterized in that the fatigue crack assessment method is implemented when the program is executed by a processor.

[0042] Beneficial effects of the present invention:

[0043] The present invention analyzes the long-term slow trend change of the damage factor caused by aviation structure damage and the short-term rapid change of the damage factor caused by time-varying factors, so that the method can effectively reduce the impact of time-varying factors on damage assessment, and by analyzing the upper and lower bounds of the uncertainty of the damage factor, the reliability of subsequent damage assessment is effectively guaranteed.

[0044] The method of the present invention effectively reduces the dispersion of the influence of multiple uncertain factors on quantitative monitoring, and can quantify the uncertainty of the evaluation results, thereby improving the accuracy of time-varying damage evaluation of aviation structures. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 Flow chart of the method of the present invention.

[0046] Figure 2 FIG. 1 is a diagram showing the arrangement of the monitored structure and the piezoelectric sensor of an embodiment.

[0047] Figure 3a Schematic diagram of the heteroskedasticity model established when obtaining 200 observations.

[0048] Figure 3b Schematic diagram of the heteroskedastic model established to obtain 600 observations.

[0049] Figure 4 Fatigue crack assessment model developed for batch specimen crack length-damage factor data.

[0050] Figure 5 Figure 2 is a damage assessment result diagram of the test data of the monitored structure. DETAILED DESCRIPTION

[0051] In order to facilitate the understanding of those skilled in the art, the present invention is further described below in conjunction with embodiments and drawings. The contents mentioned in the implementation modes are not intended to limit the present invention.

[0052] Reference Figure 1 As shown, a fatigue crack assessment method based on heteroscedastic guided wave-Gaussian process of the present invention comprises the following steps:

[0053] 1) Modeling the heteroscedastic characteristics of damage factors of aviation structures under time-varying conditions;

[0054] Wherein, the step 1) specifically includes:

[0055] During the service process of aviation structures, the active guided wave SHM system excites the guided wave signal at a certain time interval through the piezoelectric sensor at the excitation end. The guided wave signal is transmitted through the structure and received by the piezoelectric sensor at the receiving end. The corresponding damage factor y is obtained by analyzing the guided wave signal at the receiving end. j , and the time t corresponding to the damage factor j , up to the current time t T , the number of damage factors obtained is M, and the sequence {(t j ,y j ),j=1,2,…,M} is recorded as Subscript o indicates online acquisition; each new acquisition d l After the damage factor, that is, when M is d l When the damage factor y is an integer multiple, heteroscedastic modeling is performed on the damage factor y with the service time t to obtain the damage factor-service time curve at τ = 0.95, 0.50, and 0.05 quantiles. The three curves all obey Gaussian processes, and the mean functions and covariance functions of the three Gaussian processes are the same, but the parameters of their respective mean functions and covariance functions are different;

[0056] Damage factor-service time curve assuming τ quantile (τ=0.95,0.50,0.05) It obeys the Gaussian process and is expressed as in represents the Gaussian process, θ is the hyperparameter of the Gaussian process, m τ (t) represents the mean function of the Gaussian process, k τ (t p ,t q ) represents the covariance function of the Gaussian process, t p and t q Represents the sequence t o =[t1,t2,…,t M ] T Any two numbers in , subscript p = 1, 2, ..., M, q = 1, 2, ..., M, superscript T represents the transpose of the matrix; there is y o =[y1,y2,…,y M ] T Obey a joint Gaussian distribution:

[0057]

[0058] In the formula, represents Gaussian distribution, mτ (t o ) means to convert t o =[t1,t2,…,t M ] T Substitute the mean function m τ (t) The obtained M×1-dimensional column vector, assuming that the mean is always equal to 0, so m τ (t o ) is a column vector with all elements equal to zero, K τ (t o ,t o ) means to convert t o =[t1,t2,…,t M ] T Substitute any two numbers into the covariance function k τ (t p ,t q ) The M×M dimensional covariance matrix is ​​calculated; the covariance function is set to the square exponential covariance function, and the covariance matrix K τ (t o ,t o ) in the position (p,q) is t p ,t q ∈t o It is calculated through the square exponential covariance function. The square exponential covariance function is shown as follows:

[0059]

[0060] Where θ1, θ2 are the parameters of the covariance function, also known as the hyperparameters of the Gaussian process model, and the quantile [θ1, θ2] is abbreviated as θ; the loss function L of the Gaussian process quantile regression model is constructed τ , and optimize to get the optimal solution. The loss function is all the damage factors y j To the function curve that needs to be solved The weighted absolute residual sum of is expressed as follows:

[0061]

[0062] Since the regression curve of τ quantile If it obeys the Gaussian process, then solve L τ The parameter corresponding to the minimum value is equivalent to solving the posterior distribution The maximum value of corresponds to the Gaussian process model hyperparameters:

[0063]

[0064] In the formula, for is the abbreviation of the function that needs to be solved; find the posterior distribution through the optimization algorithm The maximum value parameter, thus obtaining the τ quantile curve Gaussian process model

[0065] 2) Obtaining the damage factors of each quantile of the aviation structure at the current moment;

[0066] Wherein, the step 2) specifically includes:

[0067] Set the current time t M Substitute into the Gaussian process model of the three quantile curves constructed in step 1), then the current moment t of the aviation structure is M The corresponding τ quantile damage factor y τ (t M ) and y o The joint Gaussian distribution satisfies the following formula:

[0068]

[0069] In the formula, only y τ (t M ) is unknown, and the current moment t of the aviation structure is obtained through the conditional probability formula. M , the damage factor value corresponding to the τ quantile is:

[0070]

[0071] In the formula, represents mathematical expectation; K τ (t M ,t o ) represents the current time t M With t o =[t1,t2,…,t M ] T Substitute the 1×M dimensional covariance matrix calculated by the covariance function; K τ (t o ,t o ) means to convert t o =[t1,t2,…,t M ] T Substitute any two numbers in into the covariance function to obtain the M×M dimensional covariance matrix.

[0072] 3) Obtain the crack assessment results of the aviation structure at the current moment and the 90% uncertainty interval;

[0073] Wherein, the step 3) specifically includes:

[0074] Substitute the damage factor values ​​of the aviation structure at τ = 0.95, τ = 0.5, and τ = 0.05 quantiles obtained in step 2) into the fatigue crack assessment model (the fatigue crack assessment model represents the relationship between the damage factor and the crack length) to obtain the crack length value, which is expressed as follows:

[0075]

[0076] In the formula, when τ = 0.50, is the evaluation result of the crack length of the aviation structure; when τ=0.95, is the upper limit of the 90% prediction interval of the evaluation results of the crack length of the aviation structure; when τ = 0.05, The lower bound of the 90% prediction interval of the crack length evaluation results of aviation structures; pr =[y1,y2,…,y n ] T and a pr =[a1,a2,…,a n ] T They represent the damage factor and the corresponding known crack length data in the prior data set respectively; n is the total number of data contained in the prior data set; β represents the parameter of the fatigue crack assessment model; is the damage factor at the τ quantile and the prior data set y pr =[y1,y2,…,y n ] T The calculated 1×n dimensional covariance matrix, K β (y pr ,y pr ) is the n×n dimensional covariance matrix obtained by calculating any two of the prior data sets.

[0077] Specifically, the establishment process of the fatigue crack assessment model is as follows:

[0078] Obtain n pairs of known structural crack length states a through fatigue test or simulation data of batch structures i The damage factor y i Data composition prior data set {(a i ,y i ),i=1,2,…,n}, denoted as Assume that the mapping relationship between damage factor y and crack length a = f(y) satisfies the Gaussian process β represents the parameters of the model, j = 1, 2, ..., n; the mean function is selected as m β (y) = 0, covariance function k β (y i ,y j ) is the composite covariance function, which is derived from the square exponential covariance function k SEand noise covariance function k noise Add them together, as shown in the following formula:

[0079]

[0080] In the formula, [β1, β2, β3] is recorded as β, δ ij represents the Kronecker function, i.e., i=j takes 1, i≠j takes 0; based on the prior data set y pr =[y1,…,y i ,…,y n ] T ,a pr =[a1,…,a i ,…,a n ] T Construct the negative log marginal likelihood function:

[0081]

[0082] In the formula, K β (y pr ,y pr ) is the prior data set y pr =[y1,…,y i ,…,y n ] T Substitute any two of them into the composite covariance function to obtain the n×n dimensional covariance matrix; solve the hyperparameters corresponding to the minimum value of the negative logarithmic marginal likelihood function L(β) to obtain the fatigue crack assessment model.

[0083] In this embodiment, the fatigue load borne by the ear structure of an aviation connector is taken as a time-varying environmental factor, and the crack extension of the ear structure under the influence of the fatigue load is determined as an example to specifically illustrate the implementation process of the method of the present invention.

[0084] like Figure 2 The following are respectively the arrangement diagrams of the monitored structure and the piezoelectric sensor of this embodiment; Figure 2 Two sensors (PZT1 and PZT2) are arranged on the front of the monitored structure. The thickness of the ear is 5mm. A 2mm crack is prefabricated by an electric spark cutting machine at the edge of the ear hole for crack initiation and crack direction control. PZT1 at both ends of the prefabricated crack is used for excitation, and PZT2 is used for sensing. The spacing between the two sensors is 140mm. In order to evaluate the crack length, scale lines with an interval of 2mm are drawn on the ear along the crack extension direction. A random fatigue load spectrum modified based on the FALSTAFF standard load spectrum is applied to the specimen.

[0085] (1) Collect guided wave signals of different crack lengths of batch ear structures and extract damage-sensitive features;

[0086] The signal acquisition method is as follows: when the crack extends to the set crack length, i.e. the scale line, the required piezoelectric sensing signal is collected at a load of 5kN, referred to as the static load signal, and the excitation signal frequency is 160kHz; during the fatigue loading process, i.e. when the crack extends between the scale lines, the piezoelectric sensing signal is collected, referred to as the dynamic load signal, the collection time interval is 10s, and the excitation signal frequency is 160kHz;

[0087] The damage sensitive features of static load signals and dynamic load signals are extracted to calculate the damage factor, forming a one-dimensional feature sample set. The damage factor is calculated as follows: the damage factor calculated from the static load signal collected under a load of 5kN and the corresponding crack length form a priori data set These data are used to establish a fatigue crack assessment model; the damage factor calculated from the dynamic load signal of one of the verification specimens and its corresponding cyclic load number form a data set Used to simulate the monitoring data obtained during online monitoring;

[0088] (2) The damage factor calculated by the dynamic load signal of the verification specimen and its corresponding cyclic load number total 750 sets, which are used to simulate the data set obtained during the online monitoring process Get each d l = 10 damage factor data, and conduct heteroscedastic modeling, that is, when M = 10, 20, ... 750, based on the data set Heteroskedasticity modeling was performed once and the crack length was evaluated 75 times online.

[0089] The damage factor calculated for the dynamic load signal of the verification specimen and its corresponding cyclic load number need to be analyzed for the quantile curves of τ=0.95, τ=0.5, and τ=0.05 All three curves obey the zero mean, and the covariance function is a Gaussian process with a squared exponential covariance function. Construct their respective loss functions And randomly initialize the hyperparameter values;

[0090] Based on the optimization algorithm, the hyperparameter values ​​corresponding to the minimum values ​​of the loss functions of the three quantile regression curves are obtained, thereby constructing three quantile curves. Gaussian process model of

[0091] (3) The acquired data set The time t corresponding to the last damage factor in M Substitute into the Gaussian process model of the three quantile regression curves Get the value of the damage factor distribution at a specific quantile at the current moment. Figure 3a and Figure 3bShown are three quantile regression curves of damage factor data changing with time at two typical moments. The black solid line is the median, that is, the 0.50 quantile curve, the black dotted line and the dash-dotted line are the 0.95 and 0.05 quantile curves, respectively, and * indicates the value of the 0.50 quantile in the damage factor distribution at the current moment. Figure 3a The heteroscedastic model was established when obtaining 200 observations. Figure 3b A heteroskedasticity model was established to obtain 600 observations.

[0092] (4) Evaluate the fatigue crack length at the current moment;

[0093] Substitute the value of the specific quantile of the damage factor distribution at the current moment into the fatigue crack assessment model to obtain the fatigue crack length at the current moment, where the 0.50 quantile corresponds to the assessment value, and 0.95 and 0.05 correspond to the upper and lower limits of the 90% prediction interval.

[0094] The fatigue crack assessment model The mapping relationship between crack length and damage factor is established, that is, the damage factor is substituted into the model to obtain the crack length value. The damage factor calculated from the static load signal collected under a load of 5kN and the corresponding crack length constitute a priori data set These data are used to establish a fatigue crack assessment model; the optimal parameters of the model are β1 = 20.028, β2 = 0.385, β3 = 1.016, and the constructed fatigue crack assessment model is as follows Figure 4 shown.

[0095] Evaluation results such as Figure 5 As shown in the figure, the evaluation result is close to the actual crack length, which effectively reduces the impact of the volatility of the damage factor caused by time variation on damage diagnosis and improves the accuracy of diagnosis.

[0096] The present invention has many specific application paths. The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements can be made without departing from the principle of the present invention. These improvements should also be regarded as the protection scope of the present invention.

Claims

1. A fatigue crack assessment method based on heteroscedastic guided wave-Gaussian process, characterized in that: Here are the steps: 1) Modeling the heteroscedastic characteristics of damage factors of aviation structures under time-varying conditions; 2) Obtaining the damage factors of each quantile of the aviation structure at the current moment; 3) Obtain the crack assessment results of the aviation structure at the current moment and the 90% uncertainty interval; The step 1) specifically includes: During the service process of aviation structures, the active guided wave SHM system excites the guided wave signal at a certain time interval through the piezoelectric sensor at the excitation end. The guided wave signal is transmitted through the structure and received by the piezoelectric sensor at the receiving end. The corresponding damage factor y is obtained by analyzing the guided wave signal at the receiving end. j , and the time t corresponding to the damage factor j , up to the current time t T , the number of damage factors obtained is M, and the sequence {(t j ,y j ),j=1,2,…,M} is recorded as Subscript o indicates online acquisition; each new acquisition d l After the damage factor, that is, when M is d l When the damage factor y is an integer multiple, heteroscedastic modeling is performed on the damage factor y with the service time t to obtain the damage factor-service time curve at τ = 0.95, 0.50, and 0.05 quantiles. The three curves all obey Gaussian processes, and the mean functions and covariance functions of the three Gaussian processes are the same, but the parameters of their respective mean functions and covariance functions are different; Damage factor-service time curve assuming τ quantile It obeys the Gaussian process and is expressed as in represents the Gaussian process, θ is the hyperparameter of the Gaussian process, m τ (t) represents the mean function of the Gaussian process, k τ (t p ,t q ) represents the covariance function of the Gaussian process, t p and t q Represents the sequence t o =[t1,t2,…,t M ] T Any two numbers in , subscript p = 1, 2, ..., M, q = 1, 2, ..., M, superscript T represents the transpose of the matrix; there is y o =[y1,y2,…,y M ] T Obey a joint Gaussian distribution: In the formula, represents Gaussian distribution, m τ (t o ) means to convert t o =[t1,t2,…,t M ] T Substitute the mean function m τ (t) The obtained M×1-dimensional column vector, assuming that the mean is always equal to 0, so m τ (t o ) is a column vector with all elements equal to zero, K τ (t o ,t o ) means to convert t o =[t1,t2,…,t M ] T Substitute any two numbers into the covariance function k τ (t p ,t q ) The M×M dimensional covariance matrix is ​​calculated; the covariance function is set to the square exponential covariance function, and the covariance matrix K τ (t o ,t o ) in the position (p,q) is t p ,t q ∈t o It is calculated through the square exponential covariance function, which is shown as follows: Where θ1, θ2 are the parameters of the covariance function, also known as the hyperparameters of the Gaussian process model, and the quantile [θ1, θ2] is abbreviated as θ; the loss function L of the Gaussian process quantile regression model is constructed τ , and optimize to get the optimal solution. The loss function is all the damage factors y j To the function curve that needs to be solved The weighted absolute residual sum of is expressed as follows: Since the regression curve of τ quantile If it obeys the Gaussian process, then solve L τ The parameter corresponding to the minimum value is equivalent to solving the posterior distribution The maximum value of corresponds to the Gaussian process model hyperparameters: In the formula, for is the abbreviation of the function that needs to be solved; find the posterior distribution through the optimization algorithm The maximum value parameter, thus obtaining the τ quantile curve Gaussian process model The step 2) specifically includes: Set the current time t M Substitute into the Gaussian process model of the three quantile curves constructed in step 1), then the current moment t of the aviation structure is M The corresponding τ quantile damage factor y τ (t M ) and y o The joint Gaussian distribution satisfies the following formula: In the formula, only y τ (t M ) is unknown, and the current moment t of the aviation structure is obtained through the conditional probability formula. M , the damage factor value corresponding to the τ quantile is: In the formula, represents mathematical expectation; K τ (t M ,t o ) represents the current time t M With t o =[t1,t2,…,t M ] T Substitute the 1×M dimensional covariance matrix calculated by the covariance function; K τ (t o ,t o ) means to convert t o =[t1,t2,…,t M ] T Substitute any two numbers into the covariance function to obtain the M×M dimensional covariance matrix; The step 3) specifically includes: Substitute the damage factor values ​​of the aviation structure at τ = 0.95, τ = 0.5, and τ = 0.05 quantiles obtained in step 2) into the fatigue crack assessment model to obtain the crack length value, which is expressed as follows: In the formula, when τ = 0.50, is the evaluation result of the crack length of the aviation structure; when τ=0.95, is the upper limit of the 90% prediction interval of the evaluation results of the crack length of the aviation structure; when τ = 0.05, The lower bound of the 90% prediction interval of the crack length evaluation results of aviation structures; pr =[y1,y2,…,y n ] T and a pr =[a1,a2,…,a n ] T They represent the damage factor and the corresponding known crack length data in the prior data set respectively; n is the total number of data contained in the prior data set; β represents the parameter of the fatigue crack assessment model; is the damage factor at the τ quantile and the prior data set y pr =[y1,y2,…,y n ] T The calculated 1×n dimensional covariance matrix, K β (y pr ,y pr ) is the n×n dimensional covariance matrix obtained by calculating any two of the prior data sets.

2. The fatigue crack assessment method based on heteroscedastic guided wave-Gaussian process according to claim 1 is characterized in that: The establishment process of the fatigue crack assessment model is as follows: Obtain n pairs of known structural crack length states a through fatigue test or simulation data of batch structures i The damage factor y i Data composition prior data set {(a i ,y i ),i=1,2,…,n}, denoted as Assume that the mapping relationship between damage factor y and crack length a = f(y) satisfies the Gaussian process β represents the parameters of the model, j = 1, 2, ..., n; the mean function is selected as m β (y) = 0, covariance function k β (y i ,y j ) is the composite covariance function, which is derived from the square exponential covariance function k SE and noise covariance function k noise Add them together, as shown below: In the formula, [β1, β2, β3] is recorded as β, δ ij represents the Kronecker function, i.e., it takes 1 when i=j and takes 0 when i≠j; based on the prior data set y pr =[y1,…,y i ,…,y n ] T ,a pr =[a1,…,a i ,…,a n ] T Construct the negative log marginal likelihood function: In the formula, K β (y pr ,y pr ) is the prior data set y pr =[y1,…,y i ,…,y n ] T Substitute any two of them into the composite covariance function to obtain the n×n dimensional covariance matrix; solve the hyperparameters corresponding to the minimum value of the negative logarithmic marginal likelihood function L(β) to obtain the fatigue crack assessment model.

3. A fatigue crack assessment terminal, characterized in that: include: one or more processors; A memory for storing one or more programs; When the one or more programs are executed by the one or more processors, the one or more processors are enabled to implement the method according to any one of claims 1 to 2.

4. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the program is executed by a processor, the method according to any one of claims 1 to 2 is implemented.

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