CN116595798A - Coupling function-based digital twin diagnosis and prediction method, equipment and storage medium for fleet maintenance - Google Patents
Coupling function-based digital twin diagnosis and prediction method, equipment and storage medium for fleet maintenance Download PDFInfo
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Abstract
The invention provides a coupling function-based digital twin diagnosis and prediction method, equipment and a storage medium for fleet maintenance. Firstly modeling the dependence of damage states among a plurality of structures in a fleet by using a coupling function to obtain approximate joint probability distribution for fleet collaborative updating, and deploying the approximate joint probability distribution into a particle filter framework based on the updating step of the coupling function, thereby allowing all structures in the fleet to be updated based on the observation of a single structure, further improving the overall prediction precision of the damage of the structures in the fleet and reducing uncertainty in the process. The present invention relates to an electronic device and a storage medium for performing a coupling function based method for handling a fleet-based maintenance digital twin diagnosis and prediction method. The invention can be integrated into the digital twin maintenance of the fleet, and can improve the operation safety of the whole fleet without increasing the cost or effectively reduce the operation and maintenance cost while maintaining the safety requirement.
Description
Technical Field
The invention belongs to the field of structure life prediction and equipment operation maintenance, and particularly relates to a coupling function-based digital twin diagnosis and prediction method, equipment and a storage medium for fleet maintenance.
Background
In aerospace and mechanical structures, cyclic loading causes initiation and propagation of critical component fatigue cracks, leading to structural failure and affecting structural integrity. To address this challenge, a variety of approaches have been followed, ranging from safe life, breakage safety to damage tolerance. Based on these methods, conventional fleet management employs a unified management approach to ensure structural integrity, i.e., each aircraft uses the same inspection and maintenance plan, with little regard to differences between each aircraft.
Since 1970 s, stand-alone tracking (IAT) technology has been widely used. This technique tracks the damage status of each aircraft by taking into account differences in load and service history. This allows for individual inspection and maintenance plans to be formulated for each aircraft, but the method is still deterministic. In 2010, on the basis of single machine tracking, digital twin of an aircraft structure improves structural damage diagnosis and prediction levels by creating a multi-physical, multi-scale and probabilistic virtual simulation model of the system. The model integrates multiple heterogeneous and uncertain information sources from the model and data to support proactive decisions for fleet maintenance.
Particle Filtering (PF) has been widely used for damage diagnosis and prediction for digital twinning of aeronautical and mechanical structures, as it is capable of simulating non-gaussian nonlinear processes involving knowledge and random uncertainties. Particle filtering uses a set of random samples to approximate the probability distribution of states and parameters and models the changes in states and parameters in a dynamic system through a state space model. The minimum variance estimate of the system state can be obtained by the sample mean instead of the integral operation. In particle filtering, crack propagation is predicted in real time by analysis of simple cracks or empirical formulas, or a reduced order model of complex cracks, and an observation model is obtained based on direct inspection of the cracks or using structural health monitoring techniques (such as fiber bragg gratings or lamb waves). The fusion of the prediction model and the observation model can realize the diagnosis and prediction of the structural crack damage firework process.
However, current digital twin methods based on particle filtering focus mainly on diagnosis and prediction at individual level within the fleet, but rarely on the overall links of the fleet. Due to the similarity of tasks and environments in a fleet, there is also a correlation of damage status between various structures, which provides valuable information available. Which is not considered in conventional individual-oriented particle filtering. While particle filtering can be used to model multiple structures directly, this is a high-dimensional problem, requiring large numbers of particles and thus is difficult to apply to practice. In order to effectively consider the correlation between structures within a fleet and to improve overall fleet diagnostic and predictive accuracy, it is desirable to develop an efficient alternative.
Disclosure of Invention
The invention provides a method based on a coupling function to process the diagnosis and prediction problems based on the maintenance of digital twin of a fleet. The coupling function models the joint multivariate distribution of the variables by coupling the dependent structures of the one-dimensional edge distributions of the variables. The invention creatively utilizes the coupling function to model the dependence of damage states among a plurality of structures in the fleet, so as to obtain approximate joint probability distribution for collaborative updating of the fleet, and deploys the approximate joint probability distribution into a particle filter based on the updating step of the coupling function, thereby allowing all structures in the fleet to be updated based on the observation of a single structure, and further improving the overall prediction precision of the damage of the structures in the fleet and reducing uncertainty in the process. The invention can be integrated into the digital twin maintenance of the fleet, and can improve the operation safety of the whole fleet without increasing the cost or effectively reduce the operation and maintenance cost while maintaining the safety requirement.
Drawings
FIG. 1 is a schematic diagram of a coupling function based fleet maintenance digital twin diagnostics and prognostics;
FIG. 2 is a flow chart for updating the impairment states of other structures based on a coupling function;
FIG. 3 is a comparison of the results of a coupling function-based approach and a separately updated particle filter approach diagnosis and prediction;
FIG. 4 shows the result of updating the expansion parameters of the method according to the present invention;
fig. 5 shows the result of updating the extension parameters of the conventional particle filtering method.
Detailed Description
FIG. 1 is a schematic diagram of a coupling function-based fleet maintenance digital twin diagnosis and prediction that correlates structural damage states of individual structures 1 and 2 in respective periods of service through a coupling function.
Specifically, the invention provides a coupling function-based method for processing a diagnosis and prediction method based on fleet maintenance digital twin, which comprises the following steps.
Step 1: construction of digital twin model of initial structure
An initial digital twin model needs to be built in an offline phase before digital twin online deployment can be used for structural damage diagnosis and prediction. The structural digital twin model is a multidisciplinary and multilevel probabilistic simulation model, and the models of aerodynamic, structural, fatigue and the like are integrated into a framework of uncertainty analysis, and the uncertainty of model parameters is considered. The prior distribution of the model parameters is determined through early experiments or engineering experience, so that an initial structure digital twin model is obtained, and the model is continuously updated along with check data in the online deployment process, so that the reliability of model prediction is improved.
Step 2: collecting usage data for each structure within a fleet
First, the usage load needs to be acquired on each structure within the fleet as input to the digital twin model. There are two methods of acquisition of the usage load. The first method is to acquire flight data of an aircraft, including speed, attitude angle, attitude angular speed and the like, and obtain the external load of the structure through pneumatic simulation. The second method is to collect information such as strain and the like through arranging sensors on the structure, and obtain the load outside the structure by combining a load inversion algorithm. For the second method, the selection and arrangement of the sensors need to be considered so that as much information as possible is acquired.
Step 3, predicting structural damage evolution based on structural digital twin model
Based on the use load and the structure external load acquired in the step 2, the evolution of the structural fatigue damage can be predicted through the structure digital twin model. The fatigue crack propagation process for each structure is as follows:
for the fatigue crack propagation process, the state of the system is denoted by crack length a. The evolution of crack length can be expressed as:
wherein ,for crack length increment per load cycle, ΔK is the range of Stress Intensity Factors (SIFs), μ is the material parameter that accounts for uncertainty.
Defining an augmented state vector x using a crack length a and an uncertainty material parameter μ k ＝[μ k ,a k ]' the complete state space model can be modeled as:
y k ＝a k +η k (3)
wherein k is a time step, y k Is an observation of crack length, ω μ,k Is the material parameter mu k The noise term in the evolution is referred to as,is the noise of crack propagation process, obeys Gaussian distribution +.>And->η k Is the measurement noise, obeys zero-mean Gaussian distribution, and delta N is the load circulation step length.
In crack growth prediction, a state variable x according to the previous time step is required k-1 And state transitions between two adjacent time steps to predict a state vector x k ；
p(x k ∣y 1:k-1 )＝∫p(x k ∣x k-1 )p(x k-1 ∣y 1:k-1 )dx k-1 (4)
The prediction process of equation 4 may use a variety of uncertainty modeling methods to predict. When particle filtering is used, the specific operation is to predict the particle state of time step k according to equation 2 for each particle and then calculate the particle distribution and mean value.
Step 4, checking any structure in the fleet to obtain damage observation data
When a certain structure in the fleet is arranged to be inspected, the current damage state y of the structure is obtained by visual inspection or nondestructive detection means k . The visual inspection results have larger uncertainty, and nondestructive detection means comprise eddy current flaw detection, penetration detection, X-ray imaging and other means. The obtained damage observations will be used to update the damage status and model parameters in the digital twinning of the structure.
Step 5 updating the damage status of the current structure using particle filtering
When observing value y k When available, use y k Updating state variable x k Is a joint probability distribution of (1):
wherein ,p(xk ∣y 1:k-1 ) Is a likelihood function of the observation model, p (y k ∣x k )p(y k ∣y 1:k-1 ) Is a normalization constant.
In many cases, the posterior Probability Density Function (PDF) is often difficult to directly find by an explicit method. When particle filtering is used, the posterior PDF is approximated using the following;
wherein ,Ns Is the number of particles in the particle filter, delta is the dirac function,is the ith particle, +.>Is the importance weight of the i-th particle.
These particles come from an importance densityThe density should be similar to the required posterior PDF and p (x k ∣y 1:k ) Easy to sample. The most common importance density profile is +.>It simplifies the weight update equation given by equation (7).
wherein ,is a likelihood function. The weights are then normalized by equation (8):
the damage state and model parameters of the structural digital twin model can be updated by using the observed values obtained by inspection through the steps.
Particle filtering presence of particlesThe degradation problem is that only a few particles have a larger weight, while the weight of most particles is negligible. Therefore, after the weight update, a resampling step is usually performed to solve the particle degradation problem, and the basic idea is to discard the particles with small weight and copy the particles with large weight. However, the resampling process may lead to particle depletion problems, i.e. particles become identical copies of several particles after several resampling steps. This may lead to a limited possible crack growth path for the filtering, in particular for model parametersThis can significantly affect the filtering and prediction results.
To solve this problem, regularized Particle Filtering (RPF) uses a kernel density method to introduce successive approximations p (x) of posterior PDF k ∣y 1:k ) As shown in equation (9). .
wherein ,Kh (. Cndot.) is composed ofGiven the scaled kernel function, h is the kernel bandwidth, n x Is the dimension of the state vector. After the resampling procedure, the particles are randomly extracted from successive approximations of the posterior PDF. This regularization step serves to increase the diversity of the particles, thereby preventing particle depletion problems.
Step 6 updating the damage status of other structures based on the coupling function
In step 6, the relationship between the damage states of two structures in the fleet is approximated by a coupling function, thereby updating the damage states of the non-inspected structures using the observations of the inspected structures. The particle distribution of the inspected structure and the structure to be updated at the current time step is extracted from the particle filter, respectively. The particle distribution herein includes structural crack size distribution and crack propagation parameter distribution. The flow is shown in fig. 2.
Coupling (Copula) functionC is a multi-component distribution, which is uniformly distributed over the unit interval. For having cumulative edge distribution F 1 ,…,F N The N-dimensional cumulative joint distribution function F (CDF) of (c) can be written as:
F(x 1 ,…,x N )＝C(F 1 (x 1 ),…,F N (x N )) (10)
the coupling function C and the edge distribution of the individual dimensions can thus be used to represent N as a joint distribution.
Step 6.1 measuring similarity of inspected Structure with other Structure in fleet
When the predicted distributions of crack length and crack propagation parameters are comparable, the potential crack distributions of two individuals are likely to be correlated. The similarity between any two structures within a fleet can thus be determined by measuring the similarity of predicted crack length distributions and the distribution of crack propagation parameters between two individuals. Various similarity measurement methods may be used to measure differences between two distributions, such as Maximum Mean Difference (MMD), KL divergence, etc. Taking MMD as an example, the expression of the maximum mean difference is as follows:
wherein ,x1 and x2 Is to measure two distributions of similarity,is a Regenerated Kernel Hilbert Space (RKHS) under a mapping of a kernel function phi, in which space k (x 1 ,x 2 )＝<φ(x 1 ,x 2 )>。/>Is->Mean embedding of the middle distribution p->If and only if p=q.
At each time step of particle filtering, the fatigue crack length and the distribution of material parameters are available, so these parameters can be extracted to calculate the MMD distance.
Step 6.2 modeling the joint distribution of two crack sizes based on Frank coupling function
The Frank coupling function is used to model random variables with no tail correlation and is determined by only one parameter, facilitating the measurement of the correlation of two crack length distributions. The definition is as follows:
wherein ,u1 and u2 Which are cumulative distributions of two structural crack length distributions, respectively. θ is a correlation parameter in the Frank coupling function.
For the coupling function modeling, a cumulative distribution function of two edge distributions is required. However, in particle filtering, the crack length distribution is represented as discrete sample values x 1 and x2 . To solve this problem, a probability distribution fitting method may be selected to fit the probability density function distribution and obtain a cumulative distribution function by integration. Taking a Kernel Density Estimation (KDE) as an example, the form of the kernel density estimation is described as follows:
where K is the kernel (non-negative function), h >0 is the bandwidth, and is a smoothing parameter.
After the analytical representation of the probability density distribution is obtained, the cumulative distribution function value for each sample can be calculated by integration along the x-axis. Still further, with cubic spline interpolation, an inverse of the cumulative distribution function can be determined, where the cumulative distribution value is the input and the output is the corresponding sample value.
The correlation parameter of the coupling function can be derived from the similarity measure given in step 6.1. Due to the uniform distribution characteristics of the cumulative distribution function, random samples of the cumulative distribution function of the joint distribution can be generated by sampling from the coupling function. These samples can then be converted to new samples using the inverse of the cumulative distribution function.
Step 6.3 fitting and storing the correlation between crack Length and parameters
In each digital twin model of the structure, an a priori distribution of crack length and propagation parameters is given at initialization. As the update is continuously checked, the correlation between the crack length and the model parameters gradually increases. This correlation is lost by combining the crack size particles directly with the propagation parameter particles after updating the crack size distribution by the coupling function. Therefore, it is necessary to measure and store the correlation before the update, so that the correlation is restored after the update.
Given that the dimensions of the crack length and propagation parameters may be high, there are a variety of coupling functions that can be used to measure this similarity, with gaussian coupling functions being more convenient because they are easier to construct and fit to multidimensional joint distributions. The gaussian coupling function calculates the correlation between the crack length and the parameter before the coupling update step and recovers the correlation after the coupling update step.
The formula of the gaussian coupling function is as follows:
wherein ,Φ-1 Is the inverse of the normal distribution of the standard, and R is the covariance matrix.
The specific operation is as follows. First, the edge distribution of each parameter is fitted and converted into a cumulative distribution. The cumulative distribution is then converted to a gaussian distribution using a cumulative distribution inverse function of the gaussian distribution. After converting the edge distribution of each parameter to a gaussian distribution, the covariance between each variable can be directly calculated to generate a correlation matrix. Here, the conversion of each edge distribution into a gaussian distribution is only used to fit the correlation matrix of the gaussian coupling function.
Step 6.4 updating the damage status of the unchecked structure based on the approximate joint probability distribution
After the joint distribution of the crack size distribution of the inspected structure and the structure to be updated is obtained through step 6.3, the posterior estimate of the crack length distribution of the unobserved individual can be updated by using the observed value of the inspected structure through the same method as step 5. Firstly, according to the observed value of the checked structure, the weight of each particle in the joint distribution is calculated. The joint posterior distribution of particles is then updated and by a resampling operation. And finally, extracting edge distribution of crack sizes of the structure to be updated from the joint posterior distribution.
Step 6.5 restoring the correlation between the updated crack Length and the parameters
And (3) recovering the correlation between the crack length and the parameters in the posterior particles of the structure to be updated by using the correlation matrix obtained by calculation in the step 6.3, and ensuring that the correlation is still maintained in the posterior particles.
Step 7, continuing to predict until the structural maintenance or replacement requirement is met
Predicting damage evolution of each structure, making an overhaul plan of each structure, repeating the steps 3 to 6, arranging inspection for each structure, and updating damage states of other structures by using inspection results until the structure meets the structural maintenance or replacement requirement
Examples
In this embodiment, consider a simple infinite plate with hole edge crack propagation. The plate is subjected to a bi-directional uniform positive pressure. The calculation formula of the stress intensity factor change range delta K is as follows:
where Δσ is the stress variation and a is the crack length.
Paris's law was used as a crack propagation model:
wherein ,for crack length increment per load cycle, C and m are material parameters in Paris' law, which are considered uncertainty parameters.
In this embodiment, a simple heuristic method is used to convert the similarity measure obtained by the maximum mean difference into the correlation parameter in the Frank coupling function, as shown in the following formula:
θ＝θ 0 ×(d 0 -(αd a +(1-α)d μ )) (17)
wherein ,da D is the similarity between the crack lengths of the two structures μ For similarity between two structural crack propagation parameters, θ 0 ，d 0 Is the super parameter to be adjusted, alpha is a weighting factor for balancing d a and dμ Is a weight of (2).
In this example, three specimens having different initial cracks and material parameters were considered, and the crack growth histories were different. The actual parameters of the three samples are shown in table 1. The inspection of each sample was performed at different load cycles and generated by random sampling, and the parameter settings for the proposed method and conventional particle filtering are shown in table 2.
Table 1 assumed true parameters for 3 samples
Table 2 parameter settings of the present embodiment
The diagnosis and prediction results are shown in FIG. 3, and the method proposed by the present invention is compared with the conventional particle filtering method. It can be seen that the reduction in structural uncertainty without observation is mainly due to the update based on the coupling function, which also reduces the uncertainty in the whole crack propagation process. It can also be seen from table 3 that the prediction accuracy is improved.
Table 3 prediction error (RMSE) comparison of 3 samples used
The updating of the crack propagation material parameters based on the proposed method and the conventional particle filtering method is shown in fig. 4 and 5, and it can be seen that the result of the proposed method is very consistent with the conventional particle filtering method. The gaussian coupling function effectively captures the correlation between crack length and propagation parameter distribution in crack propagation. Thus, the uncertainty of the crack propagation parameters is significantly reduced when updated by the inspection results of the structure itself.
The coupling functions include, but are not limited to, frank coupling functions, clayton coupling functions, gummel coupling functions, gaussian coupling functions, and the like.
The similarity measures of the distribution include, but are not limited to, maximum mean difference, KL divergence, etc.
Means of structural inspection include, but are not limited to, visual inspection, eddy current inspection, penetration inspection, and the like.
It will be readily appreciated by those skilled in the art that the foregoing description is merely a preferred embodiment of the invention and is not intended to limit the invention, but any modifications, equivalents, improvements or alternatives falling within the spirit and principles of the invention are intended to be included within the scope of the invention.
Claims (11)
1. A coupling function-based digital twin diagnosis and prediction method for fleet maintenance is characterized by comprising the following steps,
step 1, constructing an initial structure digital twin model;
step 2, collecting the use data of each structure in the fleet;
step 3, predicting structural damage evolution based on a structural digital twin model;
step 4, checking any structure in the fleet to obtain damage observation data;
step 5, updating the damage state of the current structure by using particle filtering;
step 6, updating damage states of other structures based on the coupling function;
and 7, continuing to predict until the structural maintenance or replacement requirement is met.
2. The method for digital twin diagnosis and prognosis of fleet maintenance based on coupling functions according to claim 1, wherein step 1 comprises,
and constructing an initial structure digital twin model in an off-line stage, integrating the pneumatic, structural and fatigue models into a framework of uncertainty analysis, and considering the uncertainty of model parameters, wherein the prior distribution of the model parameters is determined through early-stage experiments or engineering experience.
3. A method of coupling function based fleet maintenance digital twin diagnosis and prognosis as defined in claim 1 in which step 2 includes taking the usage load and the off-structure load on each structure within the fleet as inputs to the digital twin model of the structure.
4. The method for digital twin diagnosis and prediction for fleet maintenance based on coupling functions according to claim 1, wherein the implementation of step 3 is as follows,
based on the use load and the structure external load acquired in the step 2, predicting the evolution of the fatigue damage of the structure through a structure digital twin model, wherein the fatigue crack expansion process of each structure is as follows:
for fatigue crack propagation, the state of the system is denoted by crack length a, and the evolution of the crack length is denoted as:
wherein ,for each load cycle crack length increment, Δk is the range of stress intensity factors SIF, μ is the material parameter taking into account uncertainty;
defining an augmented state vector x using a crack length a and an uncertainty material parameter μ k ＝[μ k ,a k ]' the complete state space model is modeled as:
y k ＝a k +η k (3)
wherein k is a time step, y k Is an observation of crack length, ω μ,k Is the material parameter mu k The noise term in the evolution is referred to as,is the noise of crack propagation process, obeys Gaussian distribution +.>And->η k The noise is measured, zero-mean Gaussian distribution is obeyed, and delta N is the load circulation step length;
in crack growth prediction, a state variable x is based on a previous time step k-1 And state transitions between two adjacent time steps to predict a state vector x k ，
p(x k ∣y 1:k-1 )＝∫p(x k ∣x k-1 )p(x k-1 ∣y 1:k-1 )dx k-1 (4)
When particle filtering is used, the particle state of time step k is predicted for each particle according to equation 2, and the particle distribution and mean value are calculated again.
5. The method for digital twin diagnosis and prognosis of fleet maintenance based on coupling functions according to claim 4, wherein step 4 comprises,
when a certain structure in the fleet is inspected, the current damage state y of the structure is obtained by visual inspection or nondestructive detection means k 。
6. The method for digital twin diagnosis and prognosis of fleet maintenance based on coupling functions according to claim 5, wherein the implementation of step 5 is as follows,
when observing value y k When available, use y k Updating state variable x k Is a joint probability distribution of (1):
wherein ,p(xk ∣y 1:k-1 ) Is a likelihood function of the observation model, p (y k ∣x k )p(y k ∣y 1:k-1 ) Is a normalization constant that is set to a predetermined value,
when particle filtering is used, the posterior PDF is approximated using the following,
wherein ,Ns Is the number of particles in the particle filter, delta is the dirac function,is the ith particle, +.>Is the ith grainThe importance weight of the child(s),
these particles come from an importance densityThe density should be similar to the required posterior PDF and p (x k ∣y 1:k ) Easy sampling, and the importance density distribution adopts +.>It simplifies the weight update equation given by equation (7),
wherein ,the weights are then normalized with equation (8) for likelihood functions:
the damage state and model parameters of the structural digital twin model can be updated by using the observed values obtained by inspection through the steps.
7. The method for digital twin diagnosis and prognosis of fleet maintenance based on coupling functions according to claim 6, wherein step 5 further comprises the steps of,
regularized particle filter RPF using kernel density method to introduce successive approximations p (x) of posterior PDF k ∣y 1:k ) As shown in equation (9),
wherein ,Kh (. Cndot.) is composed ofGiven the scaled kernel function, h is the kernel bandwidth, n x Is the dimension of the state vector.
8. A method of digital twin diagnosis and prognosis for fleet maintenance based on coupling functions according to claim 1,
in step 6, approximating the relation between the damage states of two structures in the fleet through a coupling function, thereby updating the damage states of the non-inspected structures by using the observed values of the inspected structures, and respectively extracting particle distribution of the inspected structures and the structures to be updated under the current time step from the particle filter, wherein the particle distribution comprises the crack size distribution and the crack propagation parameter distribution of the structures;
the coupling function C is a multi-element distribution, obeys a uniform distribution over unit intervals, for a distribution F with cumulative edges 1 ,…,F N Is written as N-dimensional cumulative joint distribution function F (CDF)
F(x 1 ,…,x N )＝C(F 1 (x 1 ),…,F N (x N )) (10)
Thus, N is represented as a joint distribution using the coupling function C and the edge distribution of the respective dimension; the method specifically comprises the following steps:
step 6.1, measuring the similarity between the checked structure and other structures in the fleet;
the similarity between any two structures in the fleet is determined by measuring the similarity of predicted crack length distribution and the distribution of crack propagation parameters between two individuals, and the difference between the two distributions is measured by using a Maximum Mean Difference (MMD) method, wherein the expression of the maximum mean difference is as follows:
wherein ,x1 and x2 Is to measure two distributions of similarity,is a regenerated kernel hilbert space RKHS under the mapping of the kernel function phi, in which space k (x 1 ,x 2 )＝<φ(x 1 ,x 2 )>，/>Is->Mean embedding of the middle distribution p->Extracting the fatigue crack length and the distribution of the material parameters to calculate the MMD distance at each time step of the particle filtering if and only if p=q;
step 6.2 modeling a joint distribution of two crack sizes based on a Frank coupling function;
the Frank coupling function is used to model random variables with no tail correlation and is determined by only one parameter, facilitating the measurement of the correlation of two crack length distributions, defined as follows:
wherein ,u1 and u2 Respectively, is the cumulative distribution of the crack length distribution of the two structures, and theta is a correlation parameter in the Frank coupling function;
step 6.3, fitting and storing the correlation between the crack length and the parameters;
calculating the correlation between the crack length and the parameter before the coupling update step by using a Gaussian coupling function, and recovering the correlation after the coupling update step,
the formula of the gaussian coupling function is as follows:
wherein ,Φ-1 Is the inverse of the normal distribution of the standard, R is the covariance matrix;
step 6.4, updating the damage state of the non-inspected structure based on the approximate joint probability distribution;
after the joint distribution of the crack size distribution of the checked structure and the structure to be updated is obtained through the step 6.3, updating the posterior estimation value of the crack length distribution of the unobserved individual by using the observed value of the checked structure through the same method as the step 5;
step 6.5, recovering the correlation between the updated crack length and the parameter;
and (3) recovering the correlation between the crack length and the parameters in the posterior particles of the structure to be updated by using the correlation matrix obtained by calculation in the step 6.3, and ensuring that the correlation is still maintained in the posterior particles.
9. The method for digital twin diagnosis and prognosis of fleet maintenance based on coupling functions according to claim 1, characterized in that step 7 comprises,
predicting the damage evolution of each structure, making a maintenance plan of each structure, repeating the steps 3 to 6, arranging and checking each structure, and updating the damage states of other structures by using the checking result until the structure meets the structural maintenance or replacement requirement.
10. An electronic device, comprising: a processor; a memory; and a program, wherein the program is stored in the memory and configured to be executed by a processor, the program comprising instructions for performing the method of any of claims 1-9.
11. A computer-readable storage medium having stored thereon a computer program, characterized by: the computer program being adapted to be executed by a processor by a method according to any of claims 1-9.
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