Structural model updating method

Abstract

The present disclosure provides a structural model updating method, apparatus, electronic device, and storage medium, relating to the fields of statistical simulation and computer science. The structural model updating method comprises: obtaining input variables of the structural model; extracting input variable samples and auxiliary variable samples of the input variables using a statistical simulation method; obtaining posterior samples of the input variables based on the input variable samples using a Bayesian updating method based on structural reliability theory; and updating the structural model based on the posterior samples of the input variables. The present disclosure reduces model uncertainty to a certain extent and improves the accuracy of model-based analysis.

Description

Technical Field

[0001] The present disclosure relates to the fields of statistical simulation and computers, and in particular to a structural model updating method, device, electronic device, and storage medium. Background Art

[0002] In actual engineering problems, in order to reduce costs, simulation structural models are often used instead of actual systems for analysis experiments. Updating the simulation structural model using observation data is called Bayesian updating.

[0003] In related technologies, a common Bayesian updating method is to use the Bayesian updating with structural reliability methods (BUS) to obtain posterior samples of input variables and estimate the posterior distribution based on these posterior samples to update the prior distribution of the input variables and complete the model update.

[0004] However, in actual engineering problems, the lack of data leads to high uncertainty in the input variables. The above scheme cannot directly update the prior distribution of the input variables, and the accuracy of analytical experiments based on structural models also has room for improvement.

[0005] Therefore, there is an urgent need to propose a new Bayesian updating method.

[0006] It should be noted that the information disclosed in the above background technology section is only used to enhance the understanding of the background of the present disclosure, and therefore may include information that does not constitute prior art known to ordinary technicians in the field. Summary of the Invention

[0007] The purpose of the present disclosure is to provide a structural model updating method, device, electronic device and storage medium, which can reduce the uncertainty of the structural model to a certain extent and improve the accuracy of model-based analysis.

[0008] According to one aspect of the present disclosure, a structural model updating method is provided, comprising:

[0009] Obtain input variables for the structural model;

[0010] Constructing auxiliary variables that obey uniform distribution, and extracting input variable samples of the input variables and samples of the auxiliary variables by statistical methods;

[0011] Obtaining a posterior sample of the input variable according to the input variable sample and the auxiliary variable sample by a Bayesian updating method based on structural reliability theory;

[0012] The structural model is updated according to the posterior samples of the input variables.

[0013] In an exemplary embodiment of the present disclosure, the statistical simulation method is a Monte Carlo method, and extracting the input variables and auxiliary variable samples of the input variables by the statistical simulation method includes:

[0014] Obtaining the distribution of the distribution parameters of the input variables;

[0015] Obtaining a plurality of groups of distribution parameter samples of the input variables according to the distribution of the distribution parameters of the input variables;

[0016] The input variables are normalized to make them obey the standard normal distribution, and multiple groups of samples of the input variables obeying the standard normal distribution are obtained.

[0017] Obtaining multiple groups of input variable samples according to the multiple groups of distribution parameter samples of the input variables and the multiple groups of input variable samples that obey the standard normal distribution;

[0018] Draw multiple sets of samples of the auxiliary variables.

[0019] In an exemplary embodiment of the present disclosure, the statistical simulation method is a subset simulation method, and extracting samples of the input variables and auxiliary variable samples by the statistical simulation method includes:

[0020] In a first layer of subset simulation, obtaining the distribution of the distribution parameters of the input variables;

[0021] Obtaining multiple groups of distribution parameter samples of the input variables according to the distribution of the distribution parameters of the input variables;

[0022] Normalizing the input variables to make them obey the standard normal distribution, and obtaining multiple groups of input variable samples obeying the standard normal distribution;

[0023] Obtaining samples of multiple groups of input variables according to the distribution parameter samples of the multiple groups of input variables and the multiple groups of input variable samples that obey the standard normal distribution;

[0024] extracting a plurality of sets of samples of the auxiliary variables;

[0025] The obtained multiple groups of input variable samples and multiple groups of auxiliary variable samples are taken as candidate samples.

[0026] In the second layer and above of the subset simulation, the candidate samples of this layer are determined based on the candidate samples obtained in the previous layer.

[0027] In an exemplary embodiment of the present disclosure, the obtaining of the posterior samples of the input variables by a Bayesian updating method based on structural reliability theory according to the input variable samples and the auxiliary variable samples includes:

[0028] Obtain observation data and construct a likelihood function based on the observation data;

[0029] Inputting the plurality of groups of input variable samples into the structural model, and outputting a plurality of groups of output samples;

[0030] Obtaining multiple sets of likelihood function values ​​according to the multiple sets of output samples and the likelihood function;

[0031] Posterior samples of the input variables are calculated based on the multiple groups of auxiliary variable samples and the multiple groups of likelihood function values.

[0032] In an exemplary embodiment of the present disclosure, obtaining the posterior samples of the input variables by a Bayesian updating method based on structural reliability theory according to the input variable samples and the auxiliary variable samples includes:

[0033] Obtaining observation data and constructing a likelihood function based on the observation data;

[0034] Calculating corresponding inequality limit state function values ​​according to a plurality of input variable samples and auxiliary variable samples;

[0035] Determining a value of a reaction limit according to the value of the inequality limit state function, wherein the reaction limit is a parameter for determining the number of subset simulation layers;

[0036] When the reaction limit is greater than 0, screening out all the input variables and the auxiliary variable samples whose inequality limit state function values ​​are greater than 0 and less than the reaction limit as seeds for generating candidate samples;

[0037] Determine the input variable samples and auxiliary variable samples in the next layer subset based on the obtained candidate sample seeds, and update the value of the reaction limit;

[0038] When the reaction limit is less than 0, all the input variable samples and auxiliary variable samples whose inequality limit state function values ​​are less than 0 are screened out, and posterior samples of the input variables are generated based on these samples.

[0039] In an exemplary embodiment of the present disclosure, updating the structural model according to the posterior samples of the input variables includes:

[0040] Obtaining a prior distribution or a family of prior distributions of the input variable;

[0041] Obtaining a posterior distribution of the input variable based on the posterior samples of the input variable;

[0042] The prior distribution or the prior distribution family of the input variables is replaced with the posterior distribution of the input variables to complete the updating of the structural model.

[0043] In an exemplary embodiment of the present disclosure, the structural model is a wing finite element model, and the input variables of the wing finite element model include:

[0044] A first input variable; the first input variable is the cross-sectional area of ​​the wing stringer;

[0045] A second input variable; the second input variable is the concentrated external load of the wing, and the external load is the resultant force on the wing;

[0046] The third input variable is the length of a closed box segment of the wing.

[0047] According to one aspect of the present disclosure, there is provided a structural model updating device, comprising:

[0048] Input variable acquisition module, used to obtain input variables of the structural model;

[0049] An input variable sample extraction module, configured to extract input variable samples of the input variable by using a statistical simulation method;

[0050] a posterior sample calculation module, configured to obtain a posterior sample of the input variable according to the input variable sample by a Bayesian update method based on reliability;

[0051] An updating module is used to update the structural model according to the posterior samples of the input variables.

[0052] According to one aspect of the present disclosure, there is provided an electronic device, including:

[0053] processor; and

[0054] a memory for storing executable instructions of the processor;

[0055] The processor is configured to execute the structural model updating method described in any one of the above embodiments by executing the executable instructions.

[0056] According to one aspect of the present disclosure, a computer-readable storage medium is provided. When instructions in the storage medium are executed by a processor of an electronic device, the electronic device can execute the structural model updating method described in any one of the above embodiments.

[0057] The exemplary embodiments of the present disclosure may have some or all of the following beneficial effects:

[0058] In the structural model updating method provided in the exemplary embodiment of the present disclosure, first, the input variables of the structural model can be obtained; second, the input variable samples and auxiliary variable samples of the input variables are extracted by a statistical simulation method; then, the posterior samples of the input variables are obtained according to the input variable samples by a Bayesian updating method based on structural reliability theory; finally, the structural model is updated according to the posterior samples of the input variables. On the one hand, the input variable samples extracted according to the statistical simulation method (Monte Carlo method, subset simulation method) are used for Bayesian updating by the Bayesian updating method based on structural reliability theory, which can reduce the uncertainty of the structural model to a certain extent; on the other hand, the uncertainty of the structural model is reduced, which can improve the accuracy of experimental analysis based on this structural model. It should be understood that the above general description and the detailed description below are only exemplary and explanatory, and cannot limit the present disclosure. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] The accompanying drawings are incorporated into and constitute a part of the specification, illustrate embodiments consistent with the present disclosure, and together with the specification, are used to explain the principles of the present disclosure. Obviously, the drawings described below are only some embodiments of the present disclosure, and those skilled in the art can derive other drawings based on these drawings without inventive effort.

[0060] Figure 1 A schematic diagram showing a system architecture of a structural model updating method to which the embodiments of the present disclosure can be applied;

[0061] Figure 2 Schematically shows a flow chart of structural model updating according to one embodiment of the present disclosure;

[0062] FIG3( a ) and FIG3 ( b ) schematically illustrate a schematic diagram of a structural model according to an embodiment of the present disclosure;

[0063] Figure 4 Schematically shows a flow chart of structural model updating according to one embodiment of the present disclosure;

[0064] Figure 5 Schematically shows a flow chart of structural model updating according to one embodiment of the present disclosure;

[0065] Figure 6 Schematically shows a flow chart of structural model updating according to one embodiment of the present disclosure;

[0066] Figure 7 Schematically shows a flow chart of structural model updating according to one embodiment of the present disclosure;

[0067] Figure 8Schematically shows a flow chart of structural model updating according to one embodiment of the present disclosure;

[0068] FIG9( a ) and FIG9 ( b ) schematically illustrate a schematic diagram of a posterior sample distribution of a structural model according to an embodiment of the present disclosure;

[0069] Figure 10 The block diagram of a structure model updating device according to an embodiment of the present disclosure is schematically shown.

[0070] Figure 11 A schematic diagram of the structure of a computer system suitable for implementing an electronic device according to an embodiment of the present disclosure is shown. DETAILED DESCRIPTION

[0071] Example embodiments will now be described more fully with reference to the accompanying drawings. However, the example embodiments can be implemented in a variety of forms and should not be construed as prior to the examples set forth herein; rather, these embodiments are provided so that the present disclosure will be more comprehensive and complete and will fully convey the concepts of the example embodiments to those skilled in the art. The described features, structures, or characteristics may be combined in any suitable manner in one or more embodiments. In the following description, many specific details are provided to provide a full understanding of the embodiments of the present disclosure. However, those skilled in the art will appreciate that the technical solutions of the present disclosure may be practiced while omitting one or more of the specific details, or that other methods, components, devices, steps, etc. may be employed. In other cases, well-known technical solutions are not shown or described in detail to avoid obscuring aspects of the present disclosure.

[0072] The flowcharts and block diagrams in the accompanying drawings illustrate the possible implementation architecture, functions and operations of the systems, methods and computer program products according to various embodiments of the present invention. In this regard, each box in the flowchart or block diagram can represent a module, program segment, or a part of code, and the above-mentioned module, program segment, or a part of code contains one or more executable instructions for implementing the specified logical function. It should also be noted that in some alternative implementations, the functions marked in the box can also occur in an order different from that marked in the accompanying drawings. For example, two boxes represented in succession can actually be executed substantially in parallel, and they can sometimes be executed in the opposite order, depending on the functions involved. It should also be noted that each box in the block diagram or flowchart, and the combination of boxes in the block diagram or flowchart, can be implemented with a dedicated hardware-based system that performs the specified function or operation, or can be implemented with a combination of dedicated hardware and computer instructions.

[0073] The units involved in the embodiments of the present invention may be implemented in software or hardware, and the units described may also be provided in a processor. In some cases, the names of these units do not limit the units themselves.

[0074] Figure 1 A schematic diagram of the system architecture of an exemplary application environment in which a structural model updating method and apparatus according to an embodiment of the present disclosure can be applied is shown.

[0075] like Figure 1 As shown, the system architecture 100 includes a terminal device 101 and a server 102. It should be understood that Figure 1 The number of terminal devices and servers in the figure is merely illustrative. Any number of terminal devices and databases may be provided according to implementation requirements. For example, the terminal device 101 may be one or more electronic devices with a display screen, including but not limited to desktop computers, portable computers, smart phones, and tablet computers; the server 102 may be a single server or a server cluster consisting of multiple servers.

[0076] The structural model updating method provided in the embodiment of the present disclosure may be executed on the server 102 , and accordingly, the structural model updating device is generally disposed in the server 102 .

[0077] For example, in an exemplary embodiment, after the server 102 receives the structural model input variables from the terminal device 101, it can first extract input variable samples of the input variables through a statistical simulation method; secondly, obtain the posterior samples of the input variables through the BUS method based on the input variable samples; finally, update the structural model based on the posterior samples of the input variables. It is easy for those skilled in the art to understand that the above application scenario is only for example and is not limited to this in this exemplary embodiment; for example, the structural model updating method provided in the embodiment of the present disclosure can also be executed on the terminal device, and accordingly, the structural model device can also be set in the terminal device.

[0078] This exemplary embodiment provides a structural model updating method. The structural model updating method can be applied to the above-mentioned server 102. Figure 2 As shown, the structural model updating method may include the following steps:

[0079] Step S210: obtaining input variables of the structural model.

[0080] Step S220: construct auxiliary variables that obey uniform distribution, and extract input variable samples of the input variables and samples of the auxiliary variables through a statistical simulation method.

[0081] Step S230 : obtaining a posterior sample of the input variable according to the input variable sample and the auxiliary variable sample by a Bayesian updating method based on structural reliability theory.

[0082] Step S240: updating the structural model according to the posterior samples of the input variables.

[0083] In the structural model updating method provided in this example embodiment, on the one hand, the input variable samples extracted according to the statistical simulation method (Monte Carlo method, subset simulation method) are used for Bayesian updating based on the Bayesian updating method of structural reliability theory, which can reduce the uncertainty of the structural model to a certain extent; on the other hand, the uncertainty of the structural model is reduced, which can further improve the accuracy of experimental analysis based on this structural model.

[0084] Next, in another embodiment, the above steps are described in more detail.

[0085] In actual engineering problems, using real systems for experimental analysis often involves great technical difficulty and cost. Therefore, technicians usually use simulated structural models instead of real systems for experiments.

[0086] However, the constructed structural model often differs significantly from the real system. These differences may be caused by modeling errors, measurement errors, or parameter uncertainty. To reduce the discrepancy between the structural model and the real system and mitigate uncertainty, the structural model is often updated using observational data. This method of updating the model using observational data is called Bayesian updating.

[0087] A commonly used Bayesian updating method is to use the Markov Chain Monte Carlo method (MCMC) to obtain posterior samples through continuous sampling and state transition, and estimate the posterior distribution based on these posterior samples. However, the MCMC method still has the problems of insufficient computational accuracy and low efficiency. A more common Bayesian updating method is the Bayesian Updating with Structural Reliability Methods (BUS) method based on structural reliability theory. The BUS method introduces an auxiliary variable X P , thus transforming the Bayesian update problem into a reliability analysis problem. The specific process is as follows:

[0088] For a structural system Y = g(X), where X = (X1,…,X n ) is an n-dimensional input random variable, g(·) is the system performance function, and Y is the output variable. A set of output observations s=(s1,…,s m), and further construct the likelihood function corresponding to each observation value based on the error between the output calculated value and the output observed value:

[0089]

[0090] Where i = 1,…,m, ε i =s i -g(x) is the likelihood function constructed based on the i-th observation error, is the probability density function of the likelihood function. Since the observation errors are independent, the above likelihood function can also be written as:

[0091]

[0092] According to the classic Bayesian formula It can be seen that the prior distribution of the input variable f X (x) can be transformed into the posterior distribution f by the following formula X (x|s):

[0093]

[0094] Since the integral in (3) is inconvenient to calculate, the BUS method introduces an auxiliary variable X that obeys uniform distribution. P Convert the likelihood function into the following form:

[0095]

[0096] Where c is a constant and satisfies cL(s|x)≤1, usually At this time, the following inequality limit state function is constructed based on formula (4):

[0097] h(x,x P )=x P -c·L(s|x) (5)

[0098] The receptive domain Ω defined by equation (5) is the region where the posterior sample x is distributed. Ω is defined as:

[0099] Ω={x P ≤c·L(s|x)} (6)

[0100] At this time, the posterior distribution can be expressed as:

[0101]

[0102] Where I is an indicator function, h(x,x P )≤0, I=1, otherwise I=0.

[0103] The application premise of the above-mentioned BUS method is that the input variables have a certain prior distribution. When the distribution parameters of the input variables, such as the mean and standard deviation, are uncertain, the prior distribution of the input variables is a series of distribution families, which makes it impossible for technicians to directly use the BUS method to obtain posterior samples.

[0104] In this exemplary embodiment, the simulated statistical sampling method is combined with the BUS method to obtain posterior samples of input variables when the input variable distribution parameters are uncertain. Specifically, Figure 2 As shown, refer to steps S210 to S240.

[0105] In step S210 , input variables of the structural model are obtained.

[0106] In this exemplary embodiment, the structural model is a wing finite element structural model with uncertain input variable distribution parameters. The wing finite element model is mainly composed of a box segment formed by stringers, ribs, wing walls, and skin, wherein the stringers are rod structures with a cross-sectional area of ​​A, and the ribs, wing walls, and skin are plate structures. The length of a closed box segment formed by all the plate structures is L. The cross-section of the wing model is shown in Figure 3(a), and the shape and force of the wing are shown in Figure 3(b), where P is the approximate concentrated external load. In this wing model, the stringer cross-sectional area A, the length of a closed box segment L, and the concentrated external load P on the wing are used as input variables, and the maximum displacement of the wing in the Y direction is the output response. It is understood that the structural model is not limited to the above-mentioned wing finite element model, and can also be a structural model of other aircraft structures or even a structural model in other fields. This embodiment does not specifically limit this.

[0107] In step S220, auxiliary variables that obey uniform distribution are constructed, and input variable samples of the input variables and samples of the auxiliary variables are extracted through a statistical simulation method.

[0108] In this exemplary embodiment, after obtaining the input variables of the structural model, the Monte Carlo (MC) method can be used to extract samples of the input variables. Figure 4 As shown, specifically, referring to steps S410 to S450:

[0109] In step S410, the distribution of the distribution parameters of the input variables is obtained.

[0110] In this exemplary embodiment, due to the uncertainty of the input variable distribution parameters, the distribution of the input variable distribution parameters can be obtained. Specifically, the distribution of the input variable distribution and its distribution parameters are shown in Tables 1 and 2. In Table 1, all input variables obey the normal distribution, the mean has uncertainty, and the standard deviation is a constant. In Table 2, the mean of all input variables obeys the uniform distribution and has a definite upper and lower bound. It is understandable that the input variables can also obey other distributions, such as exponential distribution or Poisson distribution, and the input variable distribution parameter with uncertainty is not necessarily the mean, but can also be the standard deviation or other distribution parameters, which are not specifically limited here.

[0111] Table 1 Distribution of wing model input variables:

[0112] variable distributed mean Standard deviation <![CDATA[A / m 2 ]]> Normal <![CDATA[μ A ]]> <![CDATA[1×10 -5 ]]> P / N Normal <![CDATA[μ P ]]> 200 L / m Normal <![CDATA[μ L ]]> 0.3

[0113] Table 2 Distribution of input variables of wing model distribution parameters:

[0114] variable distributed Nether Standard deviation <![CDATA[μ A ]]> Uniform <![CDATA[0.8×10 -4 ]]> <![CDATA[1.2×10 -4 ]]> <![CDATA[μ P ]]> Uniform 1700 2300 <![CDATA[μ L ]]> Uniform 2.9 3.1

[0115] In step S420, a plurality of groups of input variable distribution parameter samples are obtained according to the distribution of the input variable distribution parameters.

[0116] In this exemplary embodiment, the probability distribution of the mean value of each input variable is and Get N groups of input variable mean samples i=1,…,N.

[0117] In step S430, the input variables are normalized to make them obey the standard normal distribution, and multiple groups of samples of input variables obeying the standard normal distribution are obtained.

[0118] In this exemplary embodiment, due to the uncertainty of the distribution parameters of the input variables, certain transformations are required to meet the application conditions of the BUS method. Specifically, since the input variables of this exemplary embodiment obey the normal distribution, the input variables A, P, and L can be first normalized to U1, U2, and U3 respectively, and N groups of samples of the normalized input variables can be drawn to obtain and i=1,…,N。

[0119] In step S440, multiple groups of input variable samples are obtained according to the multiple groups of distribution parameter samples of the input variables and the multiple groups of input variable samples that obey the standard normal distribution.

[0120] In this exemplary embodiment, the standard normalized input variable samples Converted into input variable samples (a(i) ,p (i) ,l (i) ), taking input variable A as an example, the conversion can be done through the following formula:

[0121]

[0122] Similarly, we can refer to formula (8) to get p (i) and l (i) .

[0123] In step S450 , samples of the auxiliary variables are extracted according to a standard uniform distribution.

[0124] In this exemplary embodiment, the BUS method introduces an auxiliary variable X P , thus transforming the Bayesian update problem into a reliability analysis problem. In this exemplary embodiment, the variable X that obeys the standard uniform distribution is constructed. P As auxiliary variables, and also extract N groups of auxiliary variable samples x P (i) ,i=1,…,N。

[0125] In step S230, a posterior sample of the input variable is obtained according to the input variable sample and the auxiliary variable sample by using a Bayesian updating method based on structural reliability theory.

[0126] Method Reference Figure 6 As shown, specifically, refer to steps S610 to S650.

[0127] In step S610, observation data is obtained, and a likelihood function is constructed based on the observation data.

[0128] In this exemplary embodiment, the likelihood function is constructed with reference to formula (1). Assuming that the output observation values ​​obtained are 0.17 and 0.16, the following likelihood function can be constructed based on the obtained observation values:

[0129]

[0130] Among them, σ ε =0.01.

[0131] In step S620, the multiple groups of input variable samples are input into the structural model, and multiple groups of output samples are obtained as output.

[0132] In this exemplary embodiment, the N groups of input variable samples (a (i) ,p (i) ,l (i) ) is input into the wing finite element model to obtain N groups of output samples y (i) ,i=1,…,N。

[0133] In step S630, multiple groups of likelihood function values ​​are obtained according to the multiple groups of output samples and the likelihood function.

[0134] In this exemplary embodiment, the N groups of output samples obtained in step S620 are substituted into the likelihood function obtained in step S610 to calculate N groups of likelihood function values. The value of c is calculated according to equation (4), where the value of constant c is the reciprocal of the maximum likelihood function value.

[0135] In step S640, posterior samples of the input variables are calculated based on the multiple groups of auxiliary variable samples and the multiple groups of likelihood function values.

[0136] In this exemplary embodiment, according to equation (6), the N groups of likelihood function values, the value of constant c and the N groups of auxiliary variable samples obtained in step S450 are substituted into the equation, and finally N' groups of posterior samples are obtained. Generally, N' is numerically smaller than N.

[0137] In this exemplary embodiment of the present disclosure, the method of combining the MC method and the BUS method in the above steps to obtain posterior samples is called the MC-BUS method. However, when the Ω acceptance rate is small, the efficiency of sampling using the MC-BUS method will be greatly reduced. Therefore, in another embodiment of the present disclosure, a more efficient sampling method such as the Subset Simulation (SS) method is combined with the BUS method to obtain posterior samples, namely the SS-BUS method. When the SS method is involved, formula (5) needs to be converted into the following form:

[0138]

[0139] Wherein, t = -ln(c).

[0140] like Figure 5 As shown, specifically, refer to steps S510 to S550.

[0141] In step S510, the distribution parameters of the input variables are obtained.

[0142] In this exemplary embodiment, the distribution of input variables and their distribution parameters are shown in Tables 1 and 2. In Table 1, all input variables follow a normal distribution with uncertain means and constant standard deviations. In Table 2, the means of all input variables follow a uniform distribution with definite upper and lower bounds.

[0143] In step S520, mean samples of multiple groups of input variables are obtained according to the distribution parameters of the input variables.

[0144] In this exemplary embodiment, the probability distribution of the mean value of each input variable is and Get N groups of input variable mean samples i=1,…,N K .

[0145] In step S530, the input variables are normalized to make them obey the standard normal distribution, and multiple groups of samples of input variables obeying the standard normal distribution are obtained.

[0146] In this exemplary embodiment, the input variables A, P and L are normalized to U1, U2 and U3 respectively, and N groups of samples of the normalized input variables are extracted to obtain and i=1,…,N K .

[0147] In step S540, multiple groups of input variable samples are obtained as candidate input variable samples based on the multiple groups of input variable distribution parameter samples and the multiple groups of input variable samples that obey the standard normal distribution.

[0148] In step S550 , multiple groups of samples of the auxiliary variables are extracted.

[0149] In this exemplary embodiment, a variable X is constructed that obeys a standard uniform distribution. P As auxiliary variables, and also extract N groups of auxiliary variable samples x P (i) ,i=1,…,N K .

[0150] In step S560, in the second layer and above of the subset simulation, candidate samples of the current layer are determined based on the candidate samples obtained in the previous layer.

[0151] Specifically, according to equation (8) and the samples obtained in steps S520 to S540, the input variable sample (a (i) ,p (i) ,l (i) ,x P (i) ),i=1,…,N K .

[0152] In this exemplary embodiment, after obtaining the input variable samples suitable for the BUS method, the posterior samples of the input variables are further obtained by the BUS method, and 4-layer subsets are set, with the conditional failure probability p of each layer being t is 0.1. Figure 7 As shown, specifically, in a certain layer subset, refer to steps S710 to S760.

[0153] In step S710, the observation data is obtained and a likelihood function is constructed based on the observation data.

[0154] In this exemplary embodiment, the likelihood function is constructed with reference to formula (1). Assuming that the output observation values ​​obtained are 0.17 and 0.16, the following likelihood function can be constructed based on the obtained observation values:

[0155]

[0156] Among them, σ ε =0.01.

[0157] In step S720, inequality limit state function values ​​of a plurality of input variable samples are calculated.

[0158] In this exemplary embodiment, the input variable sample (a) obtained in step S550 is calculated according to formula (9). (i) ,p (i) ,l (i) ,x P (i) ),i=1,…,N K The inequality limit state function value h′(a (i) ,p (i) ,l (i) ,x P (i) ).

[0159] In step S730, the value of the reaction limit is determined according to the value of the inequality limit state function.

[0160] In this exemplary embodiment, a series of incremental parameters 0<b1<b2<...<b h , called the reaction limit, h is the number of subset layers of the SS method, and in this embodiment, h=4. In this exemplary embodiment, the multiple inequality limit state function values ​​calculated in step S720 can be arranged in ascending order, and the (1-p t )·N K The value of the inequality limit state function is taken as the value of the layer subset layer response limit b j , j is the current subset layer number.

[0161] In step S740, when the reaction limit is greater than 0, all the input variables and auxiliary variable samples whose inequality limit state function values ​​are greater than 0 and less than the reaction limit are screened out as seeds for generating candidate samples.

[0162] In this exemplary embodiment, N k satisfy h′(a (i) ,p (i) ,l (i) ,x P (i) )≤max(b j,0) is used as the seed for Markov chain sampling.

[0163] In step S750, the input variable samples and auxiliary variable samples of the next subset simulation layer are determined according to the candidate sample seeds, and the value of the reaction limit is updated.

[0164] In this exemplary embodiment, based on the N generated in S740 k The seeds of input variables and auxiliary variable samples are generated by Markov chain K -N k Whenever a new set of input variable samples and auxiliary variable samples is obtained, t in equation (9) needs to be updated to t new =max{t,L(s|a (j,i) ,p (j,i) ,l (j,i) )}(k=1,…,N K ), and b j Updated to b j =b j -t+t new Repeat steps S710 to S740.

[0165] In step S760, when the reaction limit is less than 0, all the input variable samples and auxiliary variable samples whose inequality limit state function values ​​are less than 0 are screened out, and posterior samples of the input variables are generated based on these samples.

[0166] In this exemplary embodiment, when the value of the reaction limit of a certain layer is less than 0, it indicates that this layer is the last layer of the subset simulation. At this time, all the input variable samples and auxiliary variable samples whose values ​​of the inequality limit state function are less than 0 are screened out, and these samples are used to generate the posterior samples of the input variables.

[0167] It can be understood that when using the SS method, the conditional failure probability p can be set t The number of subset layers is adaptively determined. This embodiment uses a four-layer subset without any special limitation. As shown in Table 3, this exemplary embodiment obtains a set of posterior samples using the MC-BUS method and the SS-BUS method. Table 3 shows the posterior means and standard deviations obtained by the two methods.

[0168] Table 3 Mean and standard deviation of posterior samples of wing model:

[0169]

[0170] It can be seen that the same constant c is obtained according to the MC-BUS method and the SS-BUS method, and the same inequality limit state function h′(x,x PWhen using the MC-BUS method, a total of N = 2 × 10 5 Input variable samples, 1562 posterior samples were obtained. For the SS-BUS method, the sampling size of each layer of subsets is 3000, and finally 3000 posterior distribution samples were obtained through 4 layers of subsets. It can also be seen that the SS-BUS method only needs to call the finite element model 1.2×10 4 times, compared to the 2×10 5 times, which can significantly improve computational efficiency.

[0171] After obtaining the posterior samples of the input variables, the structural model can be updated according to the posterior samples, such as Figure 8 As shown, specifically, refer to steps S810 to S830.

[0172] In step S810, the prior distribution or the prior distribution family of the input variable is obtained.

[0173] In this exemplary embodiment, the prior distributions of the input variables are shown in Tables 1 and 2. In Table 1, all input variables follow a normal distribution with uncertain means and constant standard deviations. In Table 2, the means of all input variables follow a uniform distribution with defined upper and lower bounds.

[0174] In step S820, the posterior distribution of the input variable is obtained based on the posterior samples of the input variable.

[0175] In this exemplary embodiment, as shown in Figure 9, Figures 9(a) and 9(b) show the posterior probability density functions obtained from the posterior samples of the wing model input variables estimated by the MC-BUS method and the SS-BUS method, respectively. It can be seen that, on the one hand, the posterior probability density curves of the two methods are relatively close, and the obtained posterior distributions are roughly the same, demonstrating the effectiveness of the two methods; on the other hand, the posterior distributions of all input variables have reduced uncertainty to a certain extent compared to their prior distributions, demonstrating the technical effects of the present disclosure.

[0176] In step S830, the prior distribution or the family of prior distributions of the input variables is replaced with the posterior distribution of the input variables to complete the updating of the structural model.

[0177] In this exemplary embodiment, in the subsequent model work, the posterior distribution of the input variables is used instead of the prior distribution, which reduces the uncertainty of the model, thereby reducing the deviation between the constructed model and the actual structure, and further improving the accuracy of the model-based experimental analysis.

[0178] It should be noted that although the steps of the method of the present disclosure are described in a specific order in the drawings, this does not require or imply that the steps must be performed in this specific order, or that all steps must be performed to achieve the desired results. Additionally or alternatively, some steps may be omitted, multiple steps may be combined into one step, and / or one step may be decomposed into multiple steps.

[0179] Furthermore, in this exemplary embodiment, a structure model updating device is also provided. The structure model updating device can be applied to a server or a terminal device. Figure 10 As shown, the structural model updating device 1000 may include an input variable acquisition module 1010, an input variable sample extraction module 1020, a posterior sample acquisition module 1030, and an updating module 1040. Among them:

[0180] The input variable acquisition module 1010 can be used to obtain the input variables of the structural model; the input variable sample extraction module 1020 can be used to extract input variable samples of the input variables through a statistical simulation method; the posterior sample acquisition module 1030 can be used to obtain the posterior samples of the input variables according to the input variable samples through a reliability-based Bayesian updating method; the updating module 1040 can be used to update the structural model according to the posterior samples of the input variables.

[0181] Figure 11 A schematic diagram of the structure of a computer system suitable for implementing an electronic device according to an embodiment of the present disclosure is shown.

[0182] It should be noted that Figure 11 The computer system 1100 of the electronic device shown is only an example and should not limit the functions and scope of use of the embodiments of the present disclosure.

[0183] like Figure 11 As shown, the computer system 1100 includes a central processing unit (CPU) 1101, which can perform various appropriate actions and processes according to the program stored in the read-only memory (ROM) 1102 or the program loaded from the storage unit 1108 to the random access memory (RAM) 1103. Various programs and data required for system operation are also stored in the RAM 1103. The CPU 1101, ROM 1102, and RAM 1103 are connected to each other via a bus 1104. An input / output (I / O) interface 1105 is also connected to the bus 1104.

[0184] The following components are connected to the I / O interface 1105: an input section 1106 including a keyboard, a mouse, and the like; an output section 1107 including devices such as a cathode ray tube (CRT), a liquid crystal display (LCD), and a speaker; a storage section 1108 including a hard disk; and a communication section 1109 including a network interface card such as a LAN card or a modem. The communication section 1109 performs communication processing via a network such as the Internet. A drive 1110 is also connected to the I / O interface 1105 as needed. Removable media 1111, such as a magnetic disk, an optical disk, a magneto-optical disk, or a semiconductor memory, is installed in the drive 1110 as needed, so that computer programs read therefrom can be installed into the storage section 1108 as needed.

[0185] In particular, according to an embodiment of the present disclosure, the process described below with reference to the flowchart can be implemented as a computer software program. For example, an embodiment of the present disclosure includes a computer program product, which includes a computer program carried on a computer-readable medium, and the computer program includes program code for executing the method shown in the flowchart. In such an embodiment, the computer program can be downloaded and installed from a network via the communication section 1109, and / or installed from a removable medium 1111. When the computer program is executed by the central processing unit (CPU) 1101, the various functions defined in the method and apparatus of the present application are performed.

[0186] In an exemplary embodiment of the present disclosure, a computer-readable storage medium is also provided, on which a program product capable of implementing the above-mentioned method of this specification is stored. In some possible implementations, various aspects of the present disclosure can also be implemented in the form of a program product, which includes program code. When the program product is run on a terminal, the program code is used to enable the terminal device to execute the various exemplary implementations and steps according to the present disclosure described in the above-mentioned "Exemplary Method" section of this specification.

[0187] According to embodiments of the present disclosure, a program product for implementing the above-described method can be implemented in a portable compact disc read-only memory (CD-ROM) and include program code, which can be executed on a terminal device, such as a personal computer. However, the program product of the present disclosure is not limited thereto; the readable storage medium can be any tangible medium containing or storing a program, which can be used by or in conjunction with an instruction execution system, apparatus, or device.

[0188] The program product can adopt any combination of one or more readable media. The readable medium can be a readable signal medium or a readable storage medium. The readable medium can be, for example, but not limited to, a system, device or component of electricity, magnetism, light, electromagnetic, infrared, or semiconductor, or any of the above combinations. More specific examples (non-exhaustive list) of readable storage media include: an electrical connection with one or more wires, a portable disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disk read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the above.

[0189] A computer-readable signal medium may include a data signal propagated in baseband or as part of a carrier wave, which carries readable program code. Such propagated data signals may take a variety of forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination thereof. A readable signal medium may also be any readable medium other than a readable storage medium that can transmit, propagate, or transfer a program for use by or in conjunction with an instruction execution system, apparatus, or device.

[0190] The program code embodied on the readable medium may be transmitted via any appropriate medium, including but not limited to wireless, optical fiber, cable, RF, or any suitable combination thereof.

[0191] Furthermore, the figures above are merely illustrative of the processes included in the methods according to exemplary embodiments of the present disclosure and are not intended to be limiting. It is readily understood that the processes illustrated in the figures above do not indicate or limit the temporal order of these processes. Furthermore, it is readily understood that these processes may be executed synchronously or asynchronously, for example, in multiple modules.

[0192] Other embodiments of the present disclosure will readily occur to those skilled in the art after considering the specification and practicing the invention disclosed herein. This application is intended to cover any variations, uses, or adaptations of the present disclosure that follow the general principles of the present disclosure and include common knowledge or customary techniques in the art not disclosed herein. The description and examples are to be considered as exemplary only, with the true scope and spirit of the present disclosure being indicated by the claims.

Claims

1. A structural model updating method, characterized in that: include: Obtain input variables of a structural model; wherein the structural model is a wing finite element model, and the input variables of the wing finite element model include: a first input variable: the first input variable is the cross-sectional area of ​​the wing stringers; a second input variable: the second input variable is the concentrated external load of the wing, and the concentrated external load of the wing is the resultant force acting on the wing; a third input variable: the third input variable is the length of a closed box segment of the wing; Constructing auxiliary variables that obey uniform distribution, and extracting input variable samples of the input variables and samples of the auxiliary variables by statistical methods; Obtaining a posterior sample of the input variable according to the input variable sample and the auxiliary variable sample by a Bayesian updating method based on structural reliability theory; updating the structural model according to the posterior samples of the input variables; The statistical method is a subset simulation method, and extracting samples of the input variables and samples of the auxiliary variables by the statistical simulation method includes: In a first layer of subset simulation, obtaining the distribution of the distribution parameters of the input variables; Obtaining multiple groups of distribution parameter samples of the input variables according to the distribution of the distribution parameters of the input variables; Normalizing the input variables to make them obey the standard normal distribution, and obtaining multiple groups of input variable samples obeying the standard normal distribution; Obtaining samples of multiple groups of input variables according to the distribution parameter samples of the multiple groups of input variables and the multiple groups of input variable samples that obey the standard normal distribution; extracting a plurality of sets of samples of the auxiliary variables; The obtained multiple groups of input variable samples and multiple groups of auxiliary variable samples are taken as candidate samples; In the second layer and above of the subset simulation, the candidate samples of this layer are determined based on the candidate samples obtained in the previous layer.

2. The method according to claim 1, characterized in that The statistical method is the Monte Carlo method, and extracting the input variable samples of the input variables and the samples of the auxiliary variables by the statistical method includes: Obtaining the distribution of the distribution parameters of the input variables; Obtaining a plurality of groups of distribution parameter samples of the input variables according to the distribution of the distribution parameters of the input variables; Normalizing the input variables to make them obey the standard normal distribution, and obtaining multiple groups of samples of the input variables obeying the standard normal distribution; Obtaining multiple groups of input variable samples according to the multiple groups of distribution parameter samples of the input variables and the multiple groups of input variable samples that obey the standard normal distribution; Draw multiple sets of samples of the auxiliary variables.

3. The structural model updating method according to claim 2, characterized in that: The step of obtaining the posterior samples of the input variables by a Bayesian updating method based on structural reliability theory according to the input variable samples and the auxiliary variable samples includes: Obtain observation data and construct a likelihood function based on the observation data; Inputting the plurality of groups of input variable samples into the structural model, and outputting a plurality of groups of output samples; Obtaining multiple sets of likelihood function values ​​according to the multiple sets of output samples and the likelihood function; Posterior samples of the input variables are calculated based on the multiple groups of auxiliary variable samples and the multiple groups of likelihood function values.

4. The structural model updating method according to claim 1, characterized in that: The step of obtaining the posterior samples of the input variables by a Bayesian updating method based on structural reliability theory according to the input variable samples and the auxiliary variable samples includes: Obtaining observation data and constructing a likelihood function based on the observation data; Calculating corresponding inequality limit state function values ​​according to a plurality of input variable samples and auxiliary variable samples; Determining a value of a reaction limit according to the value of the inequality limit state function, wherein the reaction limit is a parameter for determining the number of subset simulation layers; When the reaction limit is greater than 0, screening out all the input variables and the auxiliary variable samples whose inequality limit state function values ​​are greater than 0 and less than the reaction limit as seeds for generating candidate samples; Determine the input variable samples and auxiliary variable samples in the next layer subset according to the candidate sample seeds, and update the value of the reaction limit; When the reaction limit is less than 0, all the input variable samples and auxiliary variable samples whose inequality limit state function values ​​are less than 0 are screened out, and posterior samples of the input variables are generated according to the input variable samples and the auxiliary variable samples.

5. The structural model updating method according to claim 1, characterized in that: The updating of the structural model according to the posterior samples of the input variables includes: Obtaining a prior distribution or a family of prior distributions of the input variable; Obtaining a posterior distribution of the input variable according to the posterior samples of the input variable; The prior distribution or the prior distribution family of the input variables is replaced with the posterior distribution of the input variables to complete the updating of the structural model.

6. A structural model updating device, characterized in that: include: An input variable acquisition module is used to acquire input variables of a structural model; wherein the structural model is a wing finite element model, and the input variables of the wing finite element model include: a first input variable: the first input variable is the cross-sectional area of ​​the wing stringers; a second input variable: the second input variable is the concentrated external load of the wing, and the concentrated external load of the wing is the resultant force acting on the wing; a third input variable: the third input variable is the length of a closed box segment of the wing; An input variable extraction module, configured to construct auxiliary variables that obey a uniform distribution, and extract input variable samples of the input variable and samples of the auxiliary variables by using a statistical method; a posterior sample calculation module, configured to obtain a posterior sample of the input variable according to the input variable sample and the auxiliary variable sample by a Bayesian updating method based on structural reliability theory; An updating module, configured to update the structural model according to the posterior samples of the input variables; Wherein, the statistical method is a subset simulation method, and the sampling of the input variables and the auxiliary variable samples by the statistical simulation method includes: in the first layer of subset simulation, obtaining the distribution of the distribution parameters of the input variables; obtaining multiple groups of distribution parameter samples of the input variables based on the distribution of the distribution parameters of the input variables; normalizing the input variables to make them obey the standard normal distribution, and obtaining multiple groups of input variable samples obeying the standard normal distribution; obtaining multiple groups of input variable samples based on the multiple groups of distribution parameter samples of input variables and the multiple groups of input variable samples obeying the standard normal distribution; extracting multiple groups of samples of the auxiliary variables; using the obtained multiple groups of input variable samples and multiple groups of auxiliary variable samples as candidate samples; in the second layer and above of the subset simulation, determining the candidate samples of this layer based on the candidate samples obtained in the previous layer.

7. An electronic device, characterized in that: include: processor; as well as a memory for storing executable instructions of the processor; The processor is configured to execute the structural model updating method according to any one of claims 1 to 5 by executing the executable instructions.

8. A non-transitory computer-readable storage medium, characterized in that When the instructions in the storage medium are executed by a processor of an electronic device, the electronic device is enabled to execute the structural model updating method according to any one of claims 1 to 5.

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