CN114547770B - Fatigue crack assessment method and terminal based on heteroscedastic guided wave-Gaussian process - Google Patents
Fatigue crack assessment method and terminal based on heteroscedastic guided wave-Gaussian process Download PDFInfo
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Abstract
本发明公开了一种基于异方差导波‑高斯过程的疲劳裂纹评估方法及终端，步骤如下：对时变条件下获取航空结构的损伤因子随时间分布的异方差特征进行建模；获取当前时刻航空结构的各分位数损伤因子；获取当前时刻航空结构的裂纹评估结果以及90%不确定度区间。本发明的方法能够有效降低多不确定因素对定量化监测影响的分散性，且能对评估结果的不确定性进行量化，提高了航空结构时变损伤评估的准确性。
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
The invention belongs to the field of aviation structure health monitoring, and particularly relates to a fatigue crack assessment method and a terminal based on a heteroscedastic Guided Wave (GW) -Gaussian Process (GP).
Background
In recent years, structural health monitoring (Structural Health Monitoring, SHM) methods are gradually moving from theoretical research to aeronautical engineering applications. In engineering-oriented applications, accurate damage quantification of individual structures remains a challenging task. In the aviation practical application process, the fatigue crack expansion is a complex process and is mainly influenced by structural variables such as material performance, manufacturing and assembling process, load-time history, use environment and the like. These factors tend to couple with each other, complicating the direction and rate of propagation of fatigue cracks. And for long-term stand-alone structural monitoring, structural health monitoring needs to be performed under different environments and operating conditions, such as at different airports, in different seasons, in different flight missions, and in different pilot operating experiences. Thus, uncertainties to stand-alone structures may be complex and different from one another. Furthermore, one obvious feature of these uncertainties is that the distribution varies with time of service, also known as the heteroscedastic phenomenon. The important features of this uncertainty must be taken into account to achieve accurate damage quantification to individual structural crack lengths.
The gaussian process is a bayesian machine learning method that can deal with nonlinear input-output regression problems. The gaussian process not only can improve the accuracy of the evaluation, but also can provide posterior distribution of the evaluation, and can be used as a criterion for quantifying the uncertainty of the evaluation. The underlying gaussian process method is typically to estimate the mean of the output variables from the input variables. This approach works well when uncertainty distribution assumptions, such as symmetry and homodyne, are satisfied. However, when there is a heteroscedastic phenomenon in the data, the mean and median of the uncertainty distribution may be inconsistent. In this case, the central tendency of the distribution is inaccurately represented by the average value. The median is a value separating the upper half and the lower half of the data population or distribution, is not easily affected by the extreme value, and is a better indicator representing the trend in the data set than the mean value. Quantile regression is an effective tool that can give the effect of interpretation variables on the central and non-central location, scale and distribution shape of response variables. The Gaussian process quantile regression method enables the original assumption of symmetry and homodyne to be relaxed, and meanwhile the advantages of the Gaussian process method are maintained. The invention provides the method for evaluating the fatigue crack under the condition of processing the uncertainty of the heteroscedastic variation by applying the quantile regression method of the Gaussian process, thereby effectively improving the accuracy of diagnosis.
Disclosure of Invention
Aiming at the defects of the prior art, the invention aims to provide a fatigue crack assessment method and a terminal based on a heteroscedastic guided wave-Gaussian process, so as to solve the problem of low assessment accuracy caused by the fact that the heteroscedastic characteristic of time-varying factors is not considered when the Gaussian process is utilized to conduct damage diagnosis in the prior art.
In order to achieve the above purpose, the invention adopts the following technical scheme:
The invention relates to a fatigue crack assessment method based on a heteroscedastic guided wave-Gaussian process, which comprises the following steps:
1) Modeling the heteroscedastic characteristics of the damage factor distribution of the aeronautical structure along with time under the time-varying condition;
2) Acquiring damage factors of each quantile of the aviation structure at the current moment;
3) And obtaining a crack evaluation result of the aviation structure at the current moment and a 90% uncertainty interval.
Further, the step 1) specifically includes:
The active guided wave SHM system excites guided wave signals at a certain time interval through a piezoelectric sensor at an excitation end in the service process of the aviation structure, the guided wave signals are received by a piezoelectric sensor at a receiving end through the transmission of the structure, corresponding damage factors y j are obtained through analysis of the guided wave signals at the receiving end, the corresponding time t j of the damage factors is obtained, the number of the obtained damage factors is M by the time t T at the current moment, and sequences { (t j,yj), j=1, 2 are recorded as the M } The subscript o represents online acquisition, and after d l injury factors are newly acquired, namely when M is an integer multiple of d l, the injury factor y is subjected to heteroscedastic modeling along with the service time t to acquire an injury factor-service time curve with tau= 0.95,0.50,0.05 quantilesThe 3 curves all obey a Gaussian process, the mean function and the covariance function of the 3 Gaussian processes are identical in form, and the parameters of the mean function and the covariance function of the 3 Gaussian processes are different;
Suppose a damage factor-length of service curve of τ quantiles (τ= 0.95,0.50,0.05) Obeying a gaussian process, expressed asWherein the method comprises the steps ofRepresenting a gaussian process, θ being a hyper-parameter of the gaussian process, M τ (T) representing a mean function of the gaussian process, k τ(tp,tq) representing a covariance function of the gaussian process, T p and T q representing any two numbers in the sequence T o＝[t1,t2,…,tM]T, subscripts p=1, 2, M, q=1, 2, M, superscript T representing a transpose of the matrix, there being y o＝[y1,y2,…,yM]T subject to a joint gaussian distribution:
In the formula, Representing gaussian distribution, M τ(to) representing an m×1-dimensional column vector obtained by substituting t o＝[t1,t2,…,tM]T into a mean function M τ (t), setting the mean constant to be 0, so M τ(to) as a column vector with all elements being zero, and K τ(to,to) representing an m×m-dimensional covariance matrix obtained by substituting any two numbers in t o＝[t1,t2,…,tM]T into a covariance function K τ(tp,tq), wherein the covariance function is set as a square index covariance function, and the element at the (p, q) position in the covariance matrix K τ(to,to) is t p,tq∈to and is obtained by calculating the square index covariance function, and the square index covariance function is represented by the following formula:
Wherein, theta 1,θ2 is a parameter of covariance function, also called super parameter of Gaussian process model, fractional number [ theta 1,θ2 ] is abbreviated as theta, constructing loss function L τ of Gaussian process fractional regression model, and optimizing to obtain optimal solution, the loss function is from all obtained damage factors y j to function curve to be solved The expression is as follows:
regression curve due to τ fraction Obeying the Gaussian process, solving the parameters corresponding to the minimum of L τ is equivalent to solving the posterior distributionCorresponding gaussian process model hyper-parameters at maximum value of (c):
In the formula, Is thatThe short term of (a) is that a function to be solved is found by an optimizing algorithm so that posterior distribution is obtainedMaximum parameter, thereby obtaining a tau quantile curveGaussian process model of (c)
Further, the step 2) specifically includes:
Substituting the current time t M into the gaussian process model of the 3 quantile curves constructed in the step 1), and then the tau quantile damage factor y τ(tM) and y o corresponding to the current time t M of the aviation structure meet the joint gaussian distribution of the following formula:
In the formula, only y τ(tM) is unknown, and the damage factor value corresponding to the current time t M and the tau quantile of the aviation structure is obtained through a conditional probability formula:
In the formula, Representing mathematical expectation, K τ(tM,to) representing a 1×m-dimensional covariance matrix calculated by substituting the covariance function into t M and t o＝[t1,t2,…,tM]T at the current time, and K τ(to,to) representing an m×m-dimensional covariance matrix calculated by substituting any two numbers in t o＝[t1,t2,…,tM]T into the covariance function.
Further, the step 3) specifically includes:
Substituting the damage factor values of tau=0.95, tau=0.5 and tau=0.05 quantiles of the aviation structure obtained in the step 2) into a fatigue crack evaluation model to obtain a crack length value, wherein the expression is as follows,
Where, τ=0.50,As a result of the evaluation of the crack length of the aviation structure, when τ=0.95,For an upper bound of 90% of the predicted interval for the aeronautical structure crack length assessment result, τ=0.05,Y pr＝[y1,y2,…,yn]T and a pr＝[a1,a2,…,an]T respectively represent damage factors in the prior data set and known crack length data corresponding to the damage factors, n is the total number of data contained in the prior data set, and beta represents parameters of the fatigue crack evaluation model; A1×n-dimensional covariance matrix calculated for the injury factor located in τ quantiles and the prior dataset y pr＝[y1,y2,…,yn]T, K β(ypr,ypr) is an n×n-dimensional covariance matrix calculated for any two of the prior datasets.
Further, the fatigue crack assessment model is established as follows:
Obtaining damage factor y i data in a crack length state a i of n pairs of known structures through fatigue test or simulation data of a batch structure to form a priori data set (a i,yi), i=1, 2, n, recorded as Assume that the mapping relation a=f (y) of the damage factor y and the crack length a satisfies the gaussian processΒ represents parameters of the model, j=1, 2,..n, the mean function is selected to be m β (y) =0, the covariance function k β(yi,yj) is a complex covariance function, which is obtained by adding the square-index covariance function k SE and the noise covariance function k noise, as shown in the following formula,
Where [ β 1,β2,β3 ] is denoted as β, δ ij represents the Kronecker function, i.e. 1 when i=j, 0 when i+.j, and constructing a negative log-marginal likelihood function based on the a priori dataset ypr＝[y1,…,yi,…,yn]T,apr＝a1,…,ai,…,an]T:
Wherein K β(ypr,ypr) is an n multiplied by n dimensional covariance matrix obtained by substituting any two of the prior data sets y pr＝[y1,…,yi,…,yn]T into a composite covariance function, and solving the hyper-parameters corresponding to the minimum value of the negative logarithmic marginal likelihood function L (beta) to obtain a fatigue crack evaluation model.
The invention also provides a fatigue crack assessment terminal, comprising:
one or more processors;
A memory for storing one or more programs;
The one or more programs, when executed by the one or more processors, cause the one or more processors to implement the fatigue crack assessment method.
The present invention also provides a computer-readable storage medium having stored thereon a computer program, characterized in that the program, when executed by a processor, implements the fatigue crack assessment method.
The invention has the beneficial effects that:
According to the method, the long-term slow trend change of the damage factors caused by the damage of the aviation structure and the short-term rapid change of the damage factors caused by the time-varying factors are analyzed, so that the influence of the time-varying factors on damage evaluation can be effectively reduced, and the reliability of subsequent damage evaluation is effectively ensured through the analysis of the upper and lower bounds of uncertainty of the damage factors.
The method effectively reduces the dispersivity of the quantitative monitoring influence by multiple uncertain factors, can quantify the uncertainty of the evaluation result, and improves the accuracy of time-varying damage evaluation of the aviation structure.
Drawings
FIG. 1 is a flow chart of the method of the present invention.
FIG. 2 is a diagram of a monitored structure and piezoelectric sensor arrangement of an embodiment.
Fig. 3a is a schematic diagram of a heteroscedastic model established when 200 observations were obtained.
FIG. 3b is a schematic diagram of the obtained 600 observation data as a built heteroscedastic model.
FIG. 4 is a fatigue crack assessment model established from the mass specimen crack length-damage factor data.
Fig. 5 is a graph of damage evaluation results of test data of a monitored structure.
Detailed Description
The invention will be further described with reference to examples and drawings, to which reference is made, but which are not intended to limit the scope of the invention.
Referring to fig. 1, the fatigue crack assessment method based on the heteroscedastic guided wave-gaussian process comprises the following steps:
1) Modeling the heteroscedastic characteristics of the damage factor distribution of the aeronautical structure along with time under the time-varying condition;
Wherein, the step 1) specifically includes:
The active guided wave SHM system excites guided wave signals at a certain time interval through a piezoelectric sensor at an excitation end in the service process of the aviation structure, the guided wave signals are received by a piezoelectric sensor at a receiving end through the transmission of the structure, corresponding damage factors y j are obtained through analysis of the guided wave signals at the receiving end, the corresponding time t j of the damage factors is obtained, the number of the obtained damage factors is M by the time t T at the current moment, and sequences { (t j,yj), j=1, 2 are recorded as the M } The subscript o represents online acquisition, and after d l injury factors are newly acquired, namely when M is an integer multiple of d l, the injury factor y is subjected to heteroscedastic modeling along with the service time t to acquire an injury factor-service time curve with tau= 0.95,0.50,0.05 quantilesThe 3 curves all obey a Gaussian process, the mean function and the covariance function of the 3 Gaussian processes are identical in form, and the parameters of the mean function and the covariance function of the 3 Gaussian processes are different;
Suppose a damage factor-length of service curve of τ quantiles (τ= 0.95,0.50,0.05) Obeying a gaussian process, expressed asWherein the method comprises the steps ofRepresenting a gaussian process, θ being a hyper-parameter of the gaussian process, M τ (T) representing a mean function of the gaussian process, k τ(tp,tq) representing a covariance function of the gaussian process, T p and T q representing any two numbers in the sequence T o＝[t1,t2,…,tM]T, subscripts p=1, 2, M, q=1, 2, M, superscript T representing a transpose of the matrix, there being y o＝[y1,y2,…,yM]T subject to a joint gaussian distribution:
In the formula, Representing gaussian distribution, M τ(to) representing an M x 1-dimensional column vector obtained by substituting t o＝[t1,t2,…,tM]T into a mean function M τ (t), setting the mean constant to be 0, so M τ(to) as a column vector with all elements being zero, K τ(to,to) representing an M x M-dimensional covariance matrix obtained by substituting any two numbers in t o＝[t1,t2,…,tM]T into a covariance function K τ(tp,tq), setting the covariance function as a square index covariance function, setting the element at the (p, q) position in the covariance matrix K τ(to,to) as t p,tq∈to, and calculating the square index covariance function as shown in the following formula,
Wherein, theta 1,θ2 is a parameter of covariance function, also called super parameter of Gaussian process model, fractional number [ theta 1,θ2 ] is abbreviated as theta, constructing loss function L τ of Gaussian process fractional regression model, and optimizing to obtain optimal solution, the loss function is from all obtained damage factors y j to function curve to be solvedThe expression is as follows:
regression curve due to τ fraction Obeying the Gaussian process, solving the parameters corresponding to the minimum of L τ is equivalent to solving the posterior distributionCorresponding gaussian process model hyper-parameters at maximum value of (c):
In the formula, Is thatThe short term of (a) is that a function to be solved is found by an optimizing algorithm so that posterior distribution is obtainedMaximum parameter, thereby obtaining a tau quantile curveGaussian process model of (c)
2) Acquiring damage factors of each quantile of the aviation structure at the current moment;
wherein, the step 2) specifically includes:
Substituting the current time t M into the gaussian process model of the 3 quantile curves constructed in the step 1), and then the tau quantile damage factor y τ(tM) and y o corresponding to the current time t M of the aviation structure meet the joint gaussian distribution of the following formula:
In the formula, only y τ(tM) is unknown, and the damage factor value corresponding to the current time t M and the tau quantile of the aviation structure is obtained through a conditional probability formula:
In the formula, Representing mathematical expectation, K τ(tM,to) representing a 1×m-dimensional covariance matrix calculated by substituting the covariance function into t M and t o＝[t1,t2,…,tM]T at the current time, and K τ(to,to) representing an m×m-dimensional covariance matrix calculated by substituting any two numbers in t o＝[t1,t2,…,tM]T into the covariance function.
3) Obtaining a crack evaluation result of the aviation structure at the current moment and a 90% uncertainty interval;
Wherein, the step 3) specifically includes:
Substituting the damage factor values of tau=0.95, tau=0.5 and tau=0.05 quantiles of the aviation structure obtained in the step 2) into a fatigue crack assessment model (the fatigue crack assessment model represents the relation between the damage factor and the crack length), obtaining a crack length value, wherein the expression is as follows,
Where, τ=0.50,As a result of the evaluation of the crack length of the aviation structure, when τ=0.95,For an upper bound of 90% of the predicted interval for the aeronautical structure crack length assessment result, τ=0.05,Y pr＝[y1,y2,…,yn]T and a pr＝[a1,a2,…,an]T respectively represent damage factors in the prior data set and known crack length data corresponding to the damage factors, n is the total number of data contained in the prior data set, and beta represents parameters of the fatigue crack evaluation model; A1×n-dimensional covariance matrix calculated for the injury factor located in τ quantiles and the prior dataset y pr＝[y1,y2,…,yn]T, K β(ypr,ypr) is an n×n-dimensional covariance matrix calculated for any two of the prior datasets.
Specifically, the fatigue crack assessment model is established as follows:
Obtaining damage factor y i data in a crack length state a i of n pairs of known structures through fatigue test or simulation data of a batch structure to form a priori data set (a i,yi), i=1, 2, n, recorded as Assume that the mapping relation a=f (y) of the damage factor y and the crack length a satisfies the gaussian processΒ represents parameters of the model, j=1, 2,..n, the mean function is selected to be m β (y) =0, the covariance function k β(yi,yj) is a complex covariance function, which is obtained by adding the square-index covariance function k SE and the noise covariance function k noise, as shown in the following formula,
Where [ β 1,β2,β3 ] is denoted as β, δ ij represents the Kronecker function, i.e. 1 when i=j, 0 when i+.j, and constructing a negative log-marginal likelihood function based on the a priori dataset ypr＝[y1,…,yi,…,yn]T,apr＝[a1,…,ai,…,an]T:
Wherein K β(ypr,ypr) is an n multiplied by n dimensional covariance matrix obtained by substituting any two of the prior data sets y pr＝[y1,…,yi,…,yn]T into a composite covariance function, and solving the hyper-parameters corresponding to the minimum value of the negative logarithmic marginal likelihood function L (beta) to obtain a fatigue crack evaluation model.
In this embodiment, the implementation process of the method of the present invention is specifically described by taking the fatigue load borne by the lug structure of the aviation connector as a time-varying environmental factor, and determining the crack growth of the lug structure under the influence of the fatigue load as an example.
The monitored structure and the piezoelectric sensor of the embodiment are respectively shown in fig. 2,2 pieces of sensors (PZT 1 and PZT 2) are arranged on the front surface of the monitored structure in fig. 2, the thickness of the lug is 5mm, 2mm cracks are prefabricated on the edge of a lug hole by an electric spark cutter for cracking and controlling the crack direction, PZT1 at two ends of the prefabricated crack are used for excitation, PZT2 is used for sensing, and the distance between the two pieces of sensors is 140mm. To evaluate crack length, graduation marks spaced 2mm apart were drawn on the tab along the crack propagation direction. A random fatigue load spectrum obtained based on FALSTAFF standard load spectrum modification is applied to the test piece.
(1) Collecting guided wave signals with different crack lengths of a batch of lug structures, and extracting damage sensitive characteristics;
The signal acquisition mode is that when the crack is expanded to a preset crack length, namely, a scale mark, the piezoelectric sensing signal required by the load-holding 5kN acquisition is called static load signal for short, and the frequency of an excitation signal is 160kHz;
The damage sensitive characteristics of static load signals and dynamic load signals are extracted to calculate damage factors, a one-dimensional characteristic sample set is formed, and the damage factors are calculated by combining the damage factors calculated by the static load signals collected under the load of 5kN and the corresponding crack lengths to form a priori data set The data are used for establishing a fatigue crack evaluation model, and the damage factor calculated by the dynamic load signal of one verification test piece and the corresponding cyclic load number form a data setThe monitoring data acquisition device is used for simulating monitoring data acquired in the online monitoring process;
(2) Verifying 750 groups of damage factors calculated by dynamic load signals of test pieces and corresponding cyclic load numbers, and simulating a data set acquired in an online monitoring process Once every d l = 10 injury factor data acquired, heteroscedastic modeling was performed, i.e. based on the dataset when M = 10,20,..750The heteroscedastic modeling was performed once and crack lengths were evaluated 75 times in total.
The damage factor calculated for verifying the dynamic load signal of the test piece and the corresponding cyclic load number thereof need to be analyzed, and the curve of tau=0.95, tau=0.5 and tau=0.05 quantiles is analyzedAll 3 curves obey 0 mean and the covariance function is a gaussian process of square index covariance functionConstructing respective loss functionsRandomly initializing the super-parameter value;
Acquiring hyper-parameter values corresponding to the minimum values of the loss functions of the 3 quantile regression curves based on an optimizing algorithm, thereby constructing 3 quantile curves Gaussian process model of (c);
(3) The data set to be acquired The time t M corresponding to the last damage factor is substituted into the Gaussian process model of 3 quantile regression curvesAnd acquiring a value on a specific quantile of the distribution of the damage factors at the current moment. Fig. 3a and 3b show 3 quantile regression curves of typical two moments over time of the damage factor data, the black solid line is the median, i.e. the 0.50 quantile curve, the black dotted line and the dash-dot line are the 0.95 and 0.05 quantile curves, respectively, which represent the value of 0.50 quantile in the damage factor distribution at the current moment. Fig. 3a is a model of the heteroscedastic variation established when 200 observations are acquired, and fig. 3b is a model of the heteroscedastic variation established when 200 observations are acquired 600.
(4) Evaluating the length of the fatigue crack at the current moment;
substituting the value of the specific index of the damage factor distribution obtained at the current moment into a fatigue crack evaluation model to obtain the fatigue crack length at the current moment, wherein 0.50 index corresponds to an evaluation value, and 0.95 and 0.05 correspond to the upper and lower boundaries of a 90% prediction interval.
Wherein fatigue crack assessment modelThe mapping relation between the crack length and the damage factor is established, namely the damage factor is substituted into the model to obtain the crack length value. The damage factor calculated by the static load signal collected under the load-keeping condition of 5kN and the corresponding crack length form a priori data setThese data were used to build a fatigue crack assessment model with optimal parameters β 1＝20.028,β2＝0.385,β3 =1.016, as shown in fig. 4.
The evaluation result is shown in fig. 5, and is close to the actual crack length, so that the influence of the fluctuation of the damage factors caused by time variation on damage diagnosis is effectively reduced, and the accuracy of the diagnosis is improved.
The present invention has been described in terms of the preferred embodiments thereof, and it should be understood by those skilled in the art that various modifications can be made without departing from the principles of the invention, and such modifications should also be considered as being within the scope of the invention.
Claims (4)
1. A fatigue crack assessment method based on a heteroscedastic guided wave-Gaussian process is characterized by comprising the following steps:
1) Modeling the heteroscedastic characteristics of the damage factor distribution of the aeronautical structure along with time under the time-varying condition;
2) Acquiring damage factors of each quantile of the aviation structure at the current moment;
3) Obtaining a crack evaluation result of the aviation structure at the current moment and a 90% uncertainty interval;
The step 1) specifically comprises the following steps:
The active guided wave SHM system excites guided wave signals at a certain time interval through a piezoelectric sensor at an excitation end in the service process of the aviation structure, the guided wave signals are received by a piezoelectric sensor at a receiving end through the transmission of the structure, corresponding damage factors y j are obtained through analysis of the guided wave signals at the receiving end, the corresponding time t j of the damage factors is obtained, the number of the obtained damage factors is M by the time t T at the current moment, and sequences { (t j,yj), j=1, 2 are recorded as the M } The subscript o represents online acquisition, and after d l injury factors are newly acquired, namely when M is an integer multiple of d l, the injury factor y is subjected to heteroscedastic modeling along with the service time t to acquire an injury factor-service time curve with tau= 0.95,0.50,0.05 quantilesThe 3 curves all obey a Gaussian process, the mean function and the covariance function of the 3 Gaussian processes are identical in form, and the parameters of the mean function and the covariance function of the 3 Gaussian processes are different;
suppose a tau quantile damage factor-length of service curve Obeying a gaussian process, expressed asWherein the method comprises the steps ofRepresenting a gaussian process, θ being a hyper-parameter of the gaussian process, M τ (T) representing a mean function of the gaussian process, k τ(tp,tq) representing a covariance function of the gaussian process, T p and T q representing any two numbers in the sequence T o＝[t1,t2,…,tM]T, subscripts p=1, 2, M, q=1, 2, M, superscript T representing a transpose of the matrix, there being y o＝[y1,y2,…,yM]T subject to a joint gaussian distribution:
In the formula, Representing gaussian distribution, M τ(to) representing an m×1-dimensional column vector obtained by substituting t o＝[t1,t2,…,tM]T into a mean function M τ (t), setting the mean constant to be 0, so M τ(to) as a column vector with all elements being zero, and K τ(to,to) representing an m×m-dimensional covariance matrix obtained by substituting any two numbers in t o＝[t1,t2,…,tM]T into a covariance function K τ(tp,tq), wherein the covariance function is set as a square index covariance function, and the element at the (p, q) position in the covariance matrix K τ(to,to) is t p,tq∈to and is obtained by calculating the square index covariance function, and the square index covariance function is represented by the following formula:
Wherein, theta 1,θ2 is a parameter of covariance function, also called super parameter of Gaussian process model, fractional number [ theta 1,θ2 ] is abbreviated as theta, constructing loss function L τ of Gaussian process fractional regression model, and optimizing to obtain optimal solution, the loss function is from all obtained damage factors y j to function curve to be solved The expression is as follows:
regression curve due to τ fraction Obeying the Gaussian process, solving the parameters corresponding to the minimum of L τ is equivalent to solving the posterior distributionCorresponding gaussian process model hyper-parameters at maximum value of (c):
In the formula, Is thatThe short term of (a) is that a function to be solved is found by an optimizing algorithm so that posterior distribution is obtainedMaximum parameter, thereby obtaining a tau quantile curveGaussian process model of (c)
The step 2) specifically comprises the following steps:
Substituting the current time t M into the gaussian process model of the 3 quantile curves constructed in the step 1), and then the tau quantile damage factor y τ(tM) and y o corresponding to the current time t M of the aviation structure meet the joint gaussian distribution of the following formula:
In the formula, only y τ(tM) is unknown, and the damage factor value corresponding to the current time t M and the tau quantile of the aviation structure is obtained through a conditional probability formula:
In the formula, K τ(tM,to) represents a 1 XM-dimensional covariance matrix obtained by substituting the covariance function calculation into t M and t o＝[t1,t2,…,tM]T at the current moment, and K τ(to,to) represents an M-dimensional covariance matrix obtained by substituting any two numbers in t o＝[t1,t2,…,tM]T into the covariance function calculation;
The step 3) specifically comprises the following steps:
Substituting the damage factor values of tau=0.95, tau=0.5 and tau=0.05 quantiles of the aviation structure obtained in the step 2) into a fatigue crack evaluation model to obtain a crack length value, wherein the expression is as follows:
where, τ=0.50, As a result of the evaluation of the crack length of the aviation structure, when τ=0.95,For an upper bound of 90% of the predicted interval for the aeronautical structure crack length assessment result, τ=0.05,Y pr＝[y1,y2,…,yn]T and a pr＝[a1,a2,…,an]T respectively represent damage factors in the prior data set and known crack length data corresponding to the damage factors, n is the total number of data contained in the prior data set, and beta represents parameters of the fatigue crack evaluation model; A1×n-dimensional covariance matrix calculated for the injury factor located in τ quantiles and the prior dataset y pr＝[y1,y2,…,yn]T, K β(ypr,ypr) is an n×n-dimensional covariance matrix calculated for any two of the prior datasets.
2. The fatigue crack assessment method based on the heteroscedastic guided-wave gaussian process according to claim 1, characterized in that the fatigue crack assessment model is established as follows:
Obtaining damage factor y i data in a crack length state a i of n pairs of known structures through fatigue test or simulation data of a batch structure to form a priori data set (a i,yi), i=1, 2, n, recorded as Assume that the mapping relation a=f (y) of the damage factor y and the crack length a satisfies the gaussian processΒ represents parameters of the model, j=1, 2,..n, the mean function is selected to be m β (y) =0, and the covariance function k β(yi,yj) is a complex covariance function, and the complex covariance function is obtained by adding a square index covariance function k SE and a noise covariance function k noise, as shown in the following formula:
where [ β 1,β2,β3 ] is denoted as β, δ ij represents the Kronecker function, i.e. 1 when i=j, 0 when i+.j, and constructing a negative log-marginal likelihood function based on the a priori dataset ypr＝[y1,…,yi,…,yn]T,apr＝[a1,…,ai,…,an]T:
Wherein K β(ypr,ypr) is an n multiplied by n dimensional covariance matrix obtained by substituting any two of the prior data sets y pr＝[y1,…,yi,…,yn]T into a composite covariance function, and solving the hyper-parameters corresponding to the minimum value of the negative logarithmic marginal likelihood function L (beta) to obtain a fatigue crack evaluation model.
3. A fatigue crack assessment terminal, comprising:
one or more processors;
A memory for storing one or more programs;
the one or more programs, when executed by the one or more processors, cause the one or more processors to implement the method of any of claims 1-2.
4. A computer readable storage medium, on which a computer program is stored, characterized in that the program, when being executed by a processor, implements the method according to any of claims 1-2.
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