CN-122020996-A - Mechanical structure mechanical response proxy model generation method and system under multi-source random variable

CN122020996ACN 122020996 ACN122020996 ACN 122020996ACN-122020996-A

Abstract

The invention provides a method and a system for generating a mechanical structure mechanical response proxy model under a multisource random variable, and relates to the technical field of mechanical structure mechanical response analysis, wherein the method comprises the following steps of S1, generating a structure point set of mechanical structure parameters based on moment integration; S2, assembling a moment integral structure point set of mechanical structure parameters, S3, constructing a mechanical structure mechanical response proxy model under the influence of multi-source random variables, and S4, constructing a sparse mechanical structure mechanical response proxy model for mechanical structure mechanical response analysis. The method generates structural points for constructing the mechanical response proxy model through a unified mechanical structural moment integral structural point generation method, utilizes algebraic accuracy of Gaussian integral based on a moment integral structural point MQDP frame to enable the constructed proxy model to accurately restore response quantity statistical moment and support engineering decision, introduces sparse rule construction to cope with high-dimensional problems, and is used for efficient modeling of multi-parameter and high-dimensional practical engineering problems.

Inventors

GUAN XUEFEI
GONG TIANCI

Assignees

中国工程物理研究院研究生院

Dates

Publication Date: 20260512
Application Date: 20260116

Claims (10)

1. A method for generating a mechanical structure mechanical response proxy model under a multisource random variable is characterized by comprising the following steps: s1, generating a structural point set of mechanical structural parameters based on moment integration, and generating moment integration structural points corresponding to each mechanical structural parameter to obtain a polynomial proxy model of mechanical structure mechanical response ; S2, acquiring a one-dimensional moment integral structure point set of each mechanical structure parameter in the step S1, and assembling the moment integral structure point sets of the mechanical structure parameters through tensor product operation, wherein the moment integral structure point sets are as follows: Wherein, the The variance covariance matrix is the mechanical structure parameter And the total number of moment integral structure points is Is a moment integral structure point set; the total number of moment integral structure points related to the multidimensional actual situation; a variance covariance matrix of the mechanical structure parameters; a lower triangular decomposition matrix which is a variance covariance matrix; transpose the symbols for the matrix; Is a moment integral structure point; the number of nodes is integrated for the moment corresponding to the mechanical structure parameter; Is a mechanical structural parameter Random input variables of (a); Assigning a symbol to the user; is the total number of mechanical structure parameters; calculating a symbol for tensor product; S3, constructing a mechanical structure mechanical response proxy model under the influence of the multisource random variables, and inputting the moment integral structure point set obtained in the step S2 to obtain moment integral structure points Corresponding mechanical structure mechanical response proxy model response Solving a system of linear equations to obtain a prediction input The polynomial proxy model of the mechanical structure mechanical response is: ; Wherein, the A polynomial proxy model of mechanical structure mechanical response; A polynomial basis set for a mechanical structure mechanical response proxy model; The method comprises the steps of providing a polynomial base coefficient for a proxy model; And S4, constructing a sparse mechanical structure mechanical response proxy model by using the polynomial proxy model of the mechanical structure mechanical response obtained in the step S3, and analyzing the mechanical response of the specific mechanical structure in an actual engineering application scene.
2. The method for generating the mechanical structure mechanical response proxy model under the multisource random variable according to claim 1, wherein the step S1 is specifically as follows: S11, generating moment integral structure points corresponding to each mechanical structure parameter, setting a certain mechanical structure parameter The probability density function of (2) is Calculate its front Moment of origin of order Construction of mechanical structural parameters Hank matrix of (C) Performing a arbor decomposition to obtain Obtaining mechanical structure parameters Is a decomposition matrix of (2) Acquiring mechanical structural parameters Moment integral structure point of (2) And weight Obtaining moment integral structure points of each mechanical structure parameter; s12, generating one-dimensional parameters of each mechanical structure The integral structure point set of the moment and the one-dimensional proxy model are built, and the mechanical structure parameters obtained in the step S11 are obtained Moment integral structure point of (2) Then the mechanical structure parameters Moment integral structure point set A polynomial proxy model for obtaining mechanical structure mechanical response 。
3. The method for generating a mechanical structure mechanical response proxy model under a multi-source random variable according to claim 2, wherein the polynomial proxy model of the mechanical structure mechanical response in step S12 is: ; Wherein, the A polynomial proxy model of mechanical structure mechanical response; polynomial proxy model coefficients for mechanical structure mechanical response; Is a moment integration node.
4. The method for generating a mechanical response proxy model of a mechanical structure under a multi-source random variable as set forth in claim 1, wherein the variance covariance matrix between the mechanical structure parameters in step S2 is The method comprises the following steps: Wherein, the Is the first of variance covariance matrix Line 1 Column elements.
5. The method for generating a mechanical response proxy model under a multi-source random variable as set forth in claim 1, wherein the proxy model polynomial basis coefficients in step S3 The method comprises the following steps: ; Wherein, the Is a moment integral structure point Responding to the corresponding mechanical structure mechanical response proxy model; for all elements in the proxy model polynomial base set at moment integral structure points A response vector at; polynomial basis coefficients are the proxy model.
6. The method for generating the mechanical structure mechanical response proxy model under the multisource random variable according to claim 1, wherein the step S4 is specifically: S41, performing mechanical structure mechanical response polynomial proxy model sparsification, and introducing a sparse rule Smolyak into a standard moment integration method to realize the mechanical structure mechanical response polynomial proxy model sparsification; S42, obtaining total number of moment integral structure points related to multidimensional practical situation of each moment integral structure point number The number of moment-integral structure-based points MQDPs of the sparse version is always greater than that of the sparse version Using least square method to identify fitting coefficients and determining coefficients of each polynomial basis of the proxy model as Model residual vector at time Obtaining the optimal coefficient corresponding to each polynomial basis of the proxy model The mechanical structure mechanical response proxy model based on the moment integral structure point MQDP polynomials of the obtained sparse version 。
7. The method for generating a mechanical structure mechanical response proxy model under a multi-source random variable according to claim 6, wherein the polynomial basis set of the mechanical structure response problem corresponding to the sparse mechanical structure parameter set in step S41 is: ; ; ; Wherein, the An operation to obtain a polynomial term; a number of point vectors for the moment integration structure in each dimension space; Is a mechanical structural parameter Is the first of (2) A random input variable; the method comprises the steps of counting a number of vectors and a polynomial expression under a variable vector for a corresponding moment integral structure; is the first The number of moment integral structure points of the dimensional space.
8. The method of generating a mechanical structure mechanical response proxy model under a multi-source random variable as set forth in claim 6, wherein the sparse version of the mechanical structure mechanical response proxy model based on the moment-integral structure point MQDP polynomial in step S42 The method comprises the following steps: ; ; Wherein, the A mechanical response proxy model for the mechanical structure; and the optimal coefficient corresponding to each polynomial basis of the proxy model is obtained.
9. The method for generating the mechanical structure mechanical response proxy model under the multi-source random variable according to claim 1, which comprises the following steps: S51, generating a structural point set of the step cantilever beam parameters based on moment integration, and generating moment integration structural points corresponding to each step cantilever Liang Canshu to obtain a polynomial proxy model of the step cantilever Liang Jianduan deflection response ; S52, acquiring a one-dimensional moment integral structure point set of each step cantilever Liang Canshu in the step S51, and assembling to acquire the moment integral structure point set of the step cantilever Liang Canshu through tensor product operation S53, constructing a ladder cantilever Liang Jianduan deflection response proxy model under the influence of a multisource random variable, and inputting the moment integral structure point set obtained in the step S52 to obtain moment integral structure points Corresponding mechanical structure mechanical response proxy model response Solving a system of linear equations to obtain a prediction input Polynomial proxy model for deflection response of stepped cantilever Liang Jianduan ; S54, constructing a sparse ladder cantilever Liang Jianduan deflection response proxy model by using the polynomial proxy model of the ladder cantilever Liang Jianduan deflection response obtained in the step S53, wherein the sparse ladder cantilever Liang Jianduan deflection response proxy model is used for mechanical response analysis of the ladder cantilever in an actual engineering application scene; s55, obtaining indexes of deflection response of the step cantilever Liang Jianduan by using a step cantilever Liang Jianduan deflection response proxy model.
10. An automatic generation system of mechanical structure mechanical response agent model for the generation method of mechanical structure mechanical response agent model under the multi-source random variable according to one of claims 1 to 9, which is characterized by comprising a mechanical structure parameter structure point set generation module, a mechanical structure parameter moment integral structure point set assembly module, a mechanical structure mechanical response agent model construction module and a mechanical structure mechanical response analysis module; the mechanical structure parameter structure point set generating module generates corresponding moment integral structure points of each mechanical structure parameter to construct a one-dimensional proxy model; The mechanical structure parameter moment integral structure point set assembling module assembles the one-dimensional moment integral structure point set of each mechanical structure parameter through tensor product operation to obtain the moment integral structure point set of the mechanical structure parameter; The mechanical structure mechanical response proxy model construction module constructs a mechanical structure mechanical response proxy model under the influence of a multi-source random variable according to the proxy model of the single mechanical structure parameter; The mechanical structure mechanical response analysis module obtains a mechanical structure mechanical response proxy model meeting actual engineering requirements by constructing a sparse mechanical structure mechanical response proxy model based on moment integral structure points MQDP, and is used for mechanical structure mechanical response analysis.

Description

Mechanical structure mechanical response proxy model generation method and system under multi-source random variable Technical Field The invention relates to the technical field of mechanical structure mechanical response analysis, in particular to a method and a system for generating a mechanical structure mechanical response proxy model under a multisource random variable. Background With the increasing need for complex system modeling and predictive maintenance, proxy models are becoming increasingly important in the risk and reliability areas. Along with engineering models such as digital twinning and large-scale simulation models, the model uncertainty quantification and analysis from classical to quantum category provide great challenges for calculation requirements. Therefore, how to build the optimal proxy model becomes critical. The existing proxy modeling method still faces the following challenges when solving a realistic complex black-box calculation model, namely firstly, though a structural point generation rule is critical to all subsequent proxy modeling no matter what kind of basic functions are selected, the general generation rule for evaluating the advantages and disadvantages of the structural point set based on reasonable measurement is lacking at present, and secondly, for certain basic functions, such as a GP/Ke-Li-gold model, the construction and simplification of a high-dimensional actual condition proxy model based on the generated structural points can be extremely complex due to the parameter adjustment process depending on specific cases. The current researches around moment methods include, but are not limited to, a moment-based framework assisted by Bayesian inference for reliability assessment of a robot system under uncertain conditions based on a point-mapped point sparse grid integration method for improving moment estimation efficiency in structural reliability analysis, a Bayesian updating method combining dimension reduction integration for efficiently assessing failure probability of a multi-mode system, and the like. These studies focus mainly on moment estimation and reliability inference, while the present application emphasizes deterministic proxy construction, integrating proxy modeling, uncertainty propagation, and sensitivity analysis into a unified framework based on moment-integral structure points (MQDP, moment quadrature design points). In furtherance of the need for technical improvements to address the above challenges, the present application is directed to developing a deterministic, explicit proxy model building method. The certainty refers to the parameter adjustment process without depending on specific cases like a plurality of self-adaptive methods, and the definiteness refers to the whole process having the mechanization and being capable of making a standardized process for any black box calculation model. To achieve the first object, a structure point generation scheme based on a moment integration method is proposed, and it can be proved mathematically that the structure point is optimal in terms of approximation accuracy when a polynomial basis function is employed, whether orthogonal or not. To achieve the second objective, so that a proxy model is always built, the present solution automatically enumerates conventional polynomial terms from the tensor product of the generated structure points and combines these terms with unknown coefficients by linear superposition, solving them as a system of linear equations using the input-response data evaluated at the structure points. The simplification process can be easily realized by eliminating the items with extremely small coefficients. In this context, the main contribution of the present application is not only to use moment integration for numerical computation, but also to construct a proxy model using moment integration rules as deterministic and uniformly distributed structure point generators. The moment integral structure points thus generated form a unified calculation basis, and can simultaneously support agent fitting, statistical moment evaluation and global sensitivity analysis. Compared with the polynomial chaotic expansion method based on Gaussian integration, the integration rule is mainly used for coefficient projection, and the framework regards the moment integration structure point MQDP as a general structure point for proxy modeling. In addition, by combining sparse grid construction techniques, the method can be extended to high-dimensional reality while maintaining a fully deterministic, non-adaptive formal representation. More importantly, the method establishes standardized construction and simplified flow for any general-purpose computable model with limited-dimensional random input and scalar target output, so that the method can be applied to any general-purpose scene which cannot be processed by special tuning. Disclosure of Invention In order to solve the defects of