A structural probability risk assessment method and system based on SRSMBRA and Copula-MCM

Abstract

The application provides a structure probability risk assessment method and system based on SRSMBRA and Copula-MCM, and the method comprises the following steps: improving the probability matching point of a classical random response surface method, obtaining undetermined coefficients of a Hermite expansion by a random response surface method SRSMBRA based on regression analysis, taking the probability matching point method as a breakthrough point, and constructing a limit state equation of a structure; based on the limit state equation of the structure, constructing a joint probability density function of multi-dimensional random variables of the structure by means of a Copula function and a Vine model, obtaining a failure probability when there is a correlation between the multi-dimensional random variables of the structure based on a structure probability risk assessment method of Copula-MCM; and integrating the structure probability risk assessment of SRSMBRA and Copula-MCM by means of Rosenblatt transformation, obtaining the failure probability by a Copula-SRSMBRA risk assessment method by using a moment method or a Monte Carlo method, and performing efficient and feasible structure probability risk assessment of an engine life-limited part by the above method.

Description

Technical Field

[0001] This invention relates to the field of technology, and in particular to a structural probability risk assessment method and system based on SRSMBRA and Copula-MCM. Background Technology

[0002] With the advancement of science and technology and industrial manufacturing, the performance requirements for engines are becoming increasingly stringent. This has led to increasingly complex engine structures and more complex and harsher service conditions. Even so, the safety level of engines must be guaranteed to be almost 100%. As core components of engines, life-limited parts have always been a focus of attention in terms of safety. China's "Engine Airworthiness Regulations" also require probabilistic risk assessments of engine life-limited parts to ensure that their failure probability remains within an acceptable safe range throughout their entire lifespan. Therefore, probabilistic risk assessment is a crucial and indispensable step in engine airworthiness certification.

[0003] Due to the harsh internal and external environments and complex load conditions experienced by engine life-limiting components, conducting structural probabilistic risk assessments for these components presents numerous challenges. For example, obtaining the structural function of the component is difficult, and the fitted function often exhibits high dimensionality and nonlinearity. Furthermore, some random variables show a degree of correlation. These difficulties directly hinder the development of probabilistic risk assessment methods for life-limiting components. Firstly, they cannot guarantee the accuracy and efficiency of the assessment in certain situations; secondly, they limit the applicability and scope of existing assessment methods.

[0004] Therefore, how to conduct efficient and feasible probabilistic risk assessment of engine life-limiting components has become one of the existing technical problems that urgently need to be solved. Summary of the Invention

[0005] This invention provides a structural probability risk assessment method and system based on SRSMBRA and COPULA-MCM, which is used for efficient and feasible structural probability risk assessment of engine life-limiting components.

[0006] Firstly, a structural probabilistic risk assessment method based on SRSMBRA and COPULA-MCM is provided, including: The probabilistic collocation method of the classical stochastic response surface method is improved by using the stochastic response surface method SRSMBRA based on regression analysis. The probabilistic collocation method is used as the starting point to obtain the undetermined coefficients of the Hermite expansion and construct the limit state equation of the structure. Based on the limit state equation of the structure, a joint probability density function of the multidimensional random variables of the structure is constructed by using the Copula function and the Vine model. Based on the Copula-MCM structural probabilistic risk assessment method, the failure probability when there is a correlation between the multidimensional random variables of the structure is obtained. Structural probabilistic risk assessment integrates SRSMBRA and Copula-MCM through Rosenblatt transformation, and the failure probability is obtained using the step moment method or Monte Carlo method through the Copula-SRSMBRA risk assessment method.

[0007] In one implementation, the steps of the Stochastic Response Surface Method (SRSMBRA) based on regression analysis include: Sort all candidate points in ascending order of their distance from the origin, including the origin. Select points one by one according to the sorting results to form the Hermite coefficient matrix. Check whether the rank of the matrix is ​​equal to the number of rows. If they are equal, continue to select points. If they are not equal, discard the current point and check the next point, until the row rank of the matrix is ​​equal to the number of undetermined coefficients. Select all collocation points that are symmetric about the origin, and combine them to form the final collocation points to establish a stochastic response surface model based on regression analysis; Regression analysis was used to obtain the undetermined coefficients of the Hermite expansion and to construct the limit state equation of the structure.

[0008] In one implementation, the number of undetermined coefficients is: in, p Let Hermite be the order of the chaotic polynomial. The dimension of the random variable; The corresponding number of selectable points is: .

[0009] In one embodiment, the structural probability risk assessment method of Copula-MCM includes the following steps: The Vine model is used to represent the joint probability density function of random variables as a product of multiple Pair-Copula functions and multiple marginal probability density functions; Generate sample points for random variables based on the statistical parameters of random samples, select the optimal Pair-Copula function for each pair of correlated random variables based on the sample points, and solve for the corresponding Copula parameters. Based on the random variable sample generation method, generate samples for Monte Carlo simulation. N Group of sample points; For each set of sample points, substitute them into the limit state equation and solve accordingly. Calculate the failure probability of the structure.

[0010] In one implementation, based on the limit state equation of the structure, a joint probability density function of the structure's multidimensional random variables is constructed using the Copula function and the Vine model. Based on the Copula-MCM structural probabilistic risk assessment method, the failure probability is obtained when there is correlation among the structure's multidimensional random variables. Specifically, this includes: Based on probability theory and mathematical statistics, for multidimensional random variables X Its multidimensional joint density function is: ; The conditional probability density function is: ; According to Copula-MCM, the failure probability of the structure is: ; in, G ( X )= g ( x 1, x 2,…, x n ) is the limit state function of the structure; for; for; for; For the indicator function, when the function value is in the failure domain When the function value is in the security domain hour, E for The expectation, assuming that it was carried out N The failure probability of the structure is: ; in, This indicates the number of sample points that fall into the failure domain.

[0011] In one implementation, the multidimensional joint density function is transformed into a form where the marginal distribution is multiplied by multiple Pair-Copula functions using Vine-Copula. The specific construction process includes: Based on Pair-Copula theory and Vine theory, the joint probability density function of random variables is decomposed into the form of the product of the Pair-Copula function and the marginal probability density function; Based on existing or generated sample points, select the desired Copula function type from the candidate Copula functions, solve for the corresponding Copula coefficients, and obtain the corresponding joint probability density function.

[0012] In one implementation, the Rosenblatt transform is represented as: in, It is the inverse function of the cumulative distribution function of the standard normal distribution. This is the conditional distribution function.

[0013] In one implementation, the Copula-SRSMBRA risk assessment method includes the following specific steps: The joint probability density function based on the Vine model derivation structure is expressed as a product of multiple Pair-Copula functions and multiple marginal probability density functions; For relevant random variables X Based on the sample points, solve each candidate Copula model and select the optimal Copula model for each pair of random variables. When there are multiple pairs of related random variables, repeat the solution and selection. If only the statistical characteristic parameters and correlation parameters of the random variables are available, generate the sample size based on the statistical characteristic parameters and correlation parameters. The Copula model parameters for each pair of related random variables are calculated using the MCM algorithm. Expand the expression for the random response surface methodology according to the required order; The undetermined coefficients are solved using the probabilistic collocation method, and the collocation points are then transformed. For the obtained limit state equations, the failure probability is solved using the step moment method or the Monte Carlo method.

[0014] Secondly, a structural probabilistic risk assessment system based on SRSMBRA and Copula-MCM is provided, including: The SRSMBRA module is used to improve the probabilistic collocation method of the classical stochastic response surface method. By using the probabilistic collocation method as the starting point, the SRSMBRA stochastic response surface method based on regression analysis obtains the undetermined coefficients of the Hermite expansion and constructs the limit state equation of the structure. The Copula-MCM module is used to construct the joint probability density function of the multidimensional random variables of a structure based on the limit state equation of the structure, using the Copula function and the Vine model. Based on the Copula-MCM structural probabilistic risk assessment method, it obtains the failure probability when there is a correlation between the multidimensional random variables of the structure. The Copula-SRSMBRA module is used to integrate SRSMBRA and Copula-MCM for structural probability risk assessment through Rosenblatt transformation. The failure probability is obtained using the step moment method or Monte Carlo method through the Copula-SRSMBRA risk assessment method.

[0015] In one implementation, the steps of the Stochastic Response Surface Method (SRSMBRA) based on regression analysis include: Sort all candidate points in ascending order of their distance from the origin, including the origin. Select points one by one according to the sorting results to form the Hermite coefficient matrix. Check whether the rank of the matrix is ​​equal to the number of rows. If they are equal, continue to select points. If they are not equal, discard the current point and check the next point, until the row rank of the matrix is ​​equal to the number of undetermined coefficients. Select all collocation points that are symmetric about the origin, and combine them to form the final collocation points to establish a stochastic response surface model based on regression analysis; Regression analysis was used to obtain the undetermined coefficients of the Hermite expansion and to construct the limit state equation of the structure.

[0016] This invention provides a structural probabilistic risk assessment method and system based on SRSMBRA and Copula-MCM. The method includes: improving the probabilistic collocation method of the classical stochastic response surface methodology by using SRSMBRA based on regression analysis, taking the probabilistic collocation method as the starting point, obtaining the undetermined coefficients of the Hermite expansion, and constructing the limit state equation of the structure; based on the limit state equation of the structure, constructing the joint probability density function of the structure's multidimensional random variables using Copula functions and Vine models, and obtaining the failure probability when there is correlation between the multidimensional random variables of the structure using the Copula-MCM structural probabilistic risk assessment method; integrating SRSMBRA and Copula-MCM structural probabilistic risk assessment through Rosenblatt transformation, and obtaining the failure probability using the step moment method or Monte Carlo method through the Copula-SRSMBRA risk assessment method. Through the above method, an efficient and feasible structural probabilistic risk assessment of engine life-limited components is performed.

[0017] Other features and advantages of the invention will be set forth in the following description, and will be apparent in part from the description, or may be learned by practicing the invention. The objects and other advantages of the invention may be realized and obtained by means of the structures particularly pointed out in the written description, claims, and accompanying drawings. Attached Figure Description

[0018] The accompanying drawings, which are included to provide a further understanding of the invention and form part of this invention, illustrate exemplary embodiments of the invention and are used to explain the invention, but do not constitute an undue limitation of the invention. In the drawings: Figure 1 This is a flowchart of a structural probability risk assessment method based on SRSMBRA and Copula-MCM according to an embodiment of the present invention; Figure 2 This is a block diagram of a risk assessment method according to an embodiment of the present invention; Figure 3 This refers to the probability collocation method based on regression analysis for SRSMBRA according to an embodiment of the present invention. Figure 4 The flowchart shows the solution process for the structural probability risk assessment algorithm based on Copula-MCM according to an embodiment of the present invention. Figure 5 This is a flowchart illustrating the solution process based on the Copula-SRSMBRA algorithm according to an embodiment of the present invention. Detailed Implementation

[0019] To conduct efficient and feasible structural probability risk assessment of engine life-limited components, a structural probability risk assessment method and system based on SRSMBRA and Copula-MCM are provided.

[0020] The preferred embodiments of the present invention will be described below with reference to the accompanying drawings. It should be understood that the preferred embodiments described herein are for illustration and explanation only and are not intended to limit the present invention. Furthermore, the embodiments and features in the embodiments of the present invention can be combined with each other without conflict.

[0021] It should be noted that the terms "first," "second," etc., in the specification, claims, and accompanying drawings of the embodiments of the present invention are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments described herein can be implemented in a sequence other than that illustrated or described herein.

[0022] like Figure 1-2 As shown, the embodiment provides a structural probabilistic risk assessment method based on SRSMBRA and COPULA-MCM, and the specific implementation steps include: S11. Improve the probabilistic collocation method of the classical stochastic response surface method. Using the stochastic response surface method SRSMBRA based on regression analysis, the probabilistic collocation method is used as the starting point to obtain the undetermined coefficients of the Hermite expansion and construct the limit state equation of the structure.

[0023] In specific implementation, such as Figure 3As shown, to address the problem of implicit high-dimensional structural function in the probabilistic risk assessment method for engine life-limited components, this paper proposes a stochastic response surface method (SRSMBRA) based on regression analysis by improving the probabilistic collocation step of the classical stochastic response surface method. Using the probabilistic collocation method as the starting point, the undetermined coefficients of the Hermite expansion are solved, thereby constructing the limit state equation of the structure.

[0024] In one implementation, the stochastic response surface methodology (SRM) is a surrogate model method. Its main difference from the traditional quadratic polynomial response surface methodology is that the traditional quadratic polynomial response surface methodology directly uses the system's random variables as the system's input to obtain the system response, thereby fitting the limit state surface. In contrast, the stochastic response surface methodology represents the system's random variables using a standard normal distribution and uses Hermite chaotic polynomials to represent the system's limit equations. It then uses the probabilistic collocation method to determine the undetermined coefficients in the Hermite chaotic polynomials, thereby establishing the limit state function of the structure.

[0025] The solution to undetermined coefficients is usually closely related to the selection of collocation points. Generally speaking, p The probabilistic collocation of Hermite chaotic polynomials originates from p The root of the +1 order Hermite chaotic polynomial. Let the highest order of the expanded Hermite chaotic polynomial be . p Then the number of undetermined coefficients in the polynomial is: (1) The corresponding number of selectable points is: (2) Since the selection of collocation points directly affects the accuracy of solving for the undetermined coefficients, theoretically, any full-rank collocation point can be used to solve for the undetermined coefficients of Hermite chaotic polynomials, and the more collocation points selected, the higher the accuracy of the solution. However, using too many collocation points to solve for the undetermined coefficients will consume a lot of resources and may even reduce the accuracy of the solution results. Therefore, this patent improves the probabilistic collocation step of the classical stochastic response surface method and proposes a stochastic response surface method based on regression analysis (SRSMBRA) for solving for the undetermined coefficients of Hermite expansions.

[0026] The algorithm generally follows these steps: Step 1: Sort all candidate points in ascending order of their distance from the origin (the origin must be included in the selection of points). Step 2: Select points one by one according to the sorting to form the Hermite coefficient matrix. Check whether the rank of the matrix is ​​equal to the number of rows. If they are equal, continue to select points. If they are not equal, discard the current point and check the next point until the row rank of the matrix is ​​equal to the number of undetermined coefficients. Step 3: Select all collocation points that are symmetric about the origin, and combine them to form the final collocation points, thus establishing a stochastic response surface model based on regression analysis; Step 4: Use regression analysis to solve for the undetermined coefficients of the Hermite expansion, thereby constructing the limit state equation of the structure.

[0027] S12. Based on the limit state equation of the structure, construct the joint probability density function of the multidimensional random variables of the structure with the help of the Copula function and the Vine model, and obtain the failure probability when there is a correlation between the multidimensional random variables of the structure based on the Copula-MCM structural probability risk assessment method.

[0028] In practical implementation, to address the issue of correlation among structural random variables, a joint probability density function of the multidimensional random variables of the structure is constructed using the Copula function and the Vine model. Combined with the Monte Carlo method, a structural probabilistic risk assessment method based on Copula-MCM is proposed to solve the failure probability when there is correlation among the multidimensional random variables of the structure.

[0029] In one implementation, such as Figure 4 As shown, let the limit state function of the structure be... G ( X )= g ( x 1, x 2,…, x n ), where random variable X The joint probability density function is f ( x 1, x 2,…, x n Then, the failure probability of the structure can be expressed as: (3) According to probability theory and mathematical statistics, when random variables are uncorrelated, their joint probability density function can be expressed as: (4) In practical engineering analysis, the correlation of random variables is ubiquitous. Ignoring this correlation will negatively impact the results of probabilistic risk assessment, and its computational accuracy cannot be guaranteed. Research indicates that the Copula function can effectively handle the correlation problem of random variables in structural probabilistic risk assessment. Since the Copula function is generally used to handle two-dimensional problems, this patent proposes a structural probabilistic risk assessment method based on Copula-MCM, combined with the Monte Carlo method, to solve for the failure probability when there is correlation between multidimensional random variables in a structure.

[0030] Based on probability theory and mathematical statistics, for multidimensional random variables X Its multidimensional joint density function has the following expression: (5) The conditional probability density function can be expressed by the following equation: (6) According to Copula-MCM, the failure probability of a structure can be expressed as: (7) in: For the indicator function, when the function value is in the failure domain When the function value is in the security domain hour, E for The expectation, assuming that it was carried out N After the second sampling, the failure probability of the structure can be expressed as: (8) in: This indicates the number of sample points that fall into the failure domain.

[0031] Each n The joint probability density function of each element can be decomposed into a product of a Pair-Copula density function based on conditional correlation and several marginal density functions, which is called the Pair-Copula decomposition.

[0032] in, v j Representing vectors v A vector consisting of any subset of its elements. v -j Indicates the removal of elements v j The resulting vector, c x|v Let the two-dimensional Copula density function be represented, where: (9) (10) Typically, multidimensional joint probability density functions have various Pair-Copula decomposition forms. The graphical tool "Vine" can be used to decompose multidimensional joint probability density functions. This patent, based on Vine-Copula, transforms the multidimensional distribution into a form where the marginal distribution is multiplied by multiple Pair-Copula functions. The specific construction process can be summarized as follows: Step 1: Based on Pair-Copula theory and Vine theory, the joint probability density function of the random variable is decomposed into the form of the product of the Pair-Copula function and the marginal probability density function; Step 2: Select the appropriate Copula function type from the candidate Copula functions based on the existing or generated sample points, solve the corresponding Copula coefficients, and then obtain the corresponding joint probability density function.

[0033] The process of solving the Copula-MCM algorithm can be summarized as follows: Step 1: Use the Vine model to express the joint probability density function of the random variable as a product of multiple Pair-Copula functions and multiple marginal probability density functions; Step 2: Generate sample points for random variables based on the statistical parameters of the random samples, select the optimal Pair-Copula function for each pair of correlated random variables based on the sample points, and solve for the corresponding Copula parameters. Step 3: Generate samples for Monte Carlo simulation based on the random variable sample generation method. N Group of sample points; Step 4: For each set of sample points, substitute them into the limit state equation and solve accordingly. Step 5: Calculate the failure probability of the structure.

[0034] S13. Integrate SRSMBRA and Copula-MCM structural probability risk assessment through Rosenblatt transformation, and obtain the failure probability using the step moment method or Monte Carlo method through the Copula-SRSMBRA risk assessment method.

[0035] In practical implementation, the structural probabilistic risk assessment methods based on SRSMBRA and Copula-MCM are integrated by using Rosenblatt transformation, and a comprehensive model for structural probabilistic risk assessment of engine life-limited components based on Copula-SRSMBRA is proposed to solve the problems of low accuracy and poor efficiency in risk assessment.

[0036] In one implementation, such as Figure 5As shown, each assessment method has its own characteristics and applicable conditions. Combining them organically can fully leverage their advantages, thereby effectively conducting probabilistic risk assessments of engine life-limited components. In the Stochastic Response Surface Method (SRSMBRA) based on regression analysis, the probabilistic collocation method is generally chosen to solve for the undetermined coefficients of the Hermite chaotic polynomial. The accuracy of solving for the undetermined coefficients directly affects the accuracy of the probabilistic risk assessment; therefore, the probabilistic collocation method is a crucial step. However, the probabilistic collocation method requires transforming the standard random variables from the standard space to the original space to obtain the true response of the system. But when considering the correlation of random variables, independent transformation is not possible.

[0037] This section addresses the challenges in probabilistic risk assessment of engine life-limited components, such as implicit structural function, high-dimensional nonlinearity, and correlation among random variables. It proposes the Copula-SRSMBRA algorithm, employing the Rosenblatt equal probability transformation method to concatenate the Copula function and the SRSMBRA method for collocation transformation. The Rosenblatt transformation is expressed as follows: (11) in: It is the inverse function of the cumulative distribution function of the standard normal distribution. This is the conditional distribution function.

[0038] The construction of the multidimensional joint probability density function is as follows: Suppose the structure includes three random variables: Their edge density functions are as follows: The marginal distribution functions are as follows: Their pairwise Pearson linear correlation coefficients are as follows: The joint probability distribution function can then be expressed as: (12) Conditional probability density function It can be represented as: (13) The same and They can be represented as follows: (14) (15) To avoid loss of generality, we construct the joint probability density function using equation (12), and then solve it iteratively. Copula parameters .

[0039] According to the information consulted: (16) in: , , They represent The mean, They represent standard deviation for The joint probability density function.

[0040] Combining formulas (12), (13), and (16), we can obtain the correlation coefficient. Derivable The expression is as follows: (17) According to the information consulted: (18) Then, through , , The coefficients can be determined by solving the simultaneous equations (17) and (18). .

[0041] Therefore, for all selected collocations, the collocations can be transformed based on this.

[0042] The specific implementation steps of the Copula-SRSMBRA method are as follows: Step 1: Based on the Vine model, derive the joint probability density function of the structure and express it as a product of multiple Pair-Copula functions and multiple marginal probability density functions.

[0043] Step 2: Analyze the relevant random variables X Based on the sample points, solve each candidate Copula model and select the optimal Copula model for each pair of random variables; Step 3: Calculate the Copula model parameters for each pair of related random variables using the MCM algorithm; Step 4: Expand the expression for the random response surface methodology according to an appropriate order; Step 5: Solve for the undetermined coefficients based on the probabilistic collocation method, and transform the collocation points; Step 6: For the obtained limit state equations, use the step moment method or Monte Carlo method to solve for the failure probability.

[0044] Note: In Step 2, this step needs to be repeated when there are multiple pairs of related random variables. If only the statistical characteristic parameters and correlation parameters of the random variables are available, the sample size is generated based on the statistical characteristic parameters and correlation parameters.

[0045] This embodiment provides a structural probabilistic risk assessment method based on SRSMBRA and COPULA-MCM, addressing the problems of implicit high-dimensionality and high nonlinearity of the structural function function of engine life-limiting components. This method can fit the function function across the entire space, effectively ensuring the accuracy of risk assessment. Step 1: Structural probabilistic risk assessment method based on the Stochastic Response Surface Method (SRSMBRA) of regression analysis. Addressing the issues of implicit and high-dimensional structural function functions in probabilistic risk assessment methods for engine life-limiting components, this embodiment proposes a SRSMBRA based on regression analysis by improving the probabilistic collocation step of the classical stochastic response surface method. Using the probabilistic collocation method as a starting point, it solves for the undetermined coefficients of the Hermite expansion, thereby constructing the limit state equation of the structure. Step 2: Structural probabilistic risk assessment method based on the Copula-MCM function. Addressing the problem of correlation among structural random variables, this embodiment constructs a joint probability density function of multidimensional random variables of the structure using the Copula function and the Vine model. Combined with the Monte Carlo method, a structural probabilistic risk assessment method based on Copula-MCM is proposed to solve for the failure probability when there is correlation among the multidimensional random variables of the structure. Step 3: Comprehensive Model for Probabilistic Risk Assessment of Life-Limited Component Structures Based on the Copula-SRSMBRA Algorithm. By integrating the SRSMBRA and Copula-MCM methods using the Rosenblatt transform, a comprehensive model for probabilistic risk assessment of engine life-limited components based on Copula-SRSMBRA is proposed to address the problems of low accuracy and poor efficiency in risk assessment. This invention provides an efficient and feasible method for probabilistic risk assessment of engine life-limited components, with strong operability and high engineering application value.

[0046] The advantages and positive effects of the method of the present invention are as follows: (1) The structural probability risk assessment method based on SRSMBRA proposed in this invention solves the problem of implicit high dimensionality of the function and can fit the function in the entire space, effectively ensuring the accuracy of risk assessment.

[0047] (2) The structural probability risk assessment method based on Copula-MCM proposed in this invention effectively solves the problem of correlation of structural random variables.

[0048] (3) This invention uses Rosenblatt transformation to connect the SRSMBRA and Copula-MCM methods to form a comprehensive model for risk assessment of life-limited components based on the Copula-SRSMBRA algorithm. This model can effectively solve the problems that the functional function of engine life-limited components is difficult to obtain and the fitted functional function has a high degree of high nonlinearity, which makes it impossible to guarantee the accuracy and efficiency of risk assessment.

[0049] Based on the same technical concept, this application also provides a structural probability risk assessment system based on SRSMBRA and Copula-MCM. Since the principle of the system in solving the problem is similar to that of the structural probability risk assessment method based on SRSMBRA and Copula-MCM, the implementation of the system can refer to the implementation of the method, and the repeated parts will not be described again.

[0050] The embodiment provides a structural probabilistic risk assessment system based on SRSMBRA and Copula-MCM, including: The SRSMBRA module is used to improve the probabilistic collocation method of the classical stochastic response surface method. By using the probabilistic collocation method as the starting point, the SRSMBRA stochastic response surface method based on regression analysis obtains the undetermined coefficients of the Hermite expansion and constructs the limit state equation of the structure. The Copula-MCM module is used to construct the joint probability density function of the multidimensional random variables of a structure based on the limit state equation of the structure, using the Copula function and the Vine model. Based on the Copula-MCM structural probabilistic risk assessment method, it obtains the failure probability when there is a correlation between the multidimensional random variables of the structure. The Copula-SRSMBRA module is used to integrate SRSMBRA and Copula-MCM for structural probability risk assessment through Rosenblatt transformation. The failure probability is obtained using the step moment method or Monte Carlo method through the Copula-SRSMBRA risk assessment method.

[0051] In one implementation, the steps of the Stochastic Response Surface Method (SRSMBRA) based on regression analysis include: Sort all candidate points in ascending order of their distance from the origin, including the origin. Select points one by one according to the sorting results to form the Hermite coefficient matrix. Check whether the rank of the matrix is ​​equal to the number of rows. If they are equal, continue to select points. If they are not equal, discard the current point and check the next point, until the row rank of the matrix is ​​equal to the number of undetermined coefficients. Select all collocation points that are symmetric about the origin, and combine them to form the final collocation points to establish a stochastic response surface model based on regression analysis; Regression analysis was used to obtain the undetermined coefficients of the Hermite expansion and to construct the limit state equation of the structure.

[0052] For ease of description, the above sections are divided into modules (or units) according to their functional modules and described separately. Of course, in implementing this invention, the functions of each module (or unit) can be implemented in one or more software or hardware components.

[0053] Although preferred embodiments of the invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments as well as all changes and modifications falling within the scope of the invention.

[0054] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims of this invention and their equivalents, this invention also intends to include these modifications and variations.

Claims

1. A structural probabilistic risk assessment method based on SRSMBRA and Copula-MCM, characterized in that, include: The probabilistic collocation method of the classical stochastic response surface method is improved by using the stochastic response surface method SRSMBRA based on regression analysis. The probabilistic collocation method is used as the starting point to obtain the undetermined coefficients of the Hermite expansion and construct the limit state equation of the structure. Based on the limit state equation of the structure, a joint probability density function of the multidimensional random variables of the structure is constructed by using the Copula function and the Vine model. Based on the Copula-MCM structural probabilistic risk assessment method, the failure probability when there is a correlation between the multidimensional random variables of the structure is obtained. Structural probabilistic risk assessment integrates SRSMBRA and Copula-MCM through Rosenblatt transformation, and the failure probability is obtained using the step moment method or Monte Carlo method through the Copula-SRSMBRA risk assessment method.

2. The method according to claim 1, characterized in that, The steps of the Stochastic Response Surface Method (SRSMBRA) based on regression analysis include: Sort all candidate points in ascending order of their distance from the origin, including the origin. Select points one by one according to the sorting results to form the Hermite coefficient matrix. Check whether the rank of the matrix is ​​equal to the number of rows. If they are equal, continue to select points. If they are not equal, discard the current point and check the next point, until the row rank of the matrix is ​​equal to the number of undetermined coefficients. Select all collocation points that are symmetric about the origin, and combine them to form the final collocation points to establish a stochastic response surface model based on regression analysis; Regression analysis was used to obtain the undetermined coefficients of the Hermite expansion and to construct the limit state equation of the structure.

3. The method according to claim 2, characterized in that, The number of undetermined coefficients is: in, p Let Hermite be the order of the chaotic polynomial. The dimension of the random variable; The corresponding number of selectable points is: 。 4. The method according to claim 3, characterized in that, The Copula-MCM structural probability risk assessment method includes the following steps: The Vine model is used to represent the joint probability density function of random variables as a product of multiple Pair-Copula functions and multiple marginal probability density functions; Generate sample points for random variables based on the statistical parameters of random samples, select the optimal Pair-Copula function for each pair of correlated random variables based on the sample points, and solve for the corresponding Copula parameters. Based on the random variable sample generation method, generate samples for Monte Carlo simulation. N Group of sample points; For each set of sample points, substitute them into the limit state equation and solve accordingly. Calculate the failure probability of the structure.

5. The method according to claim 4, characterized in that, Based on the limit state equation of the structure, a joint probability density function of the structure's multidimensional random variables is constructed using the Copula function and the Vine model. A structural probabilistic risk assessment method based on Copula-MCM is used to obtain the failure probability when there is correlation among the structure's multidimensional random variables, specifically including: Based on probability theory and mathematical statistics, for multidimensional random variables X Its multidimensional joint density function is: ； The conditional probability density function is: ； According to Copula-MCM, the failure probability of the structure is: ； in, G ( X )= g ( x 1, x 2,…, x n ) is the limit state function of the structure; for; for; for; For the indicator function, when the function value is in the failure domain When the function value is in the security domain hour, E for The expectation, assuming that it was carried out N The failure probability of the structure is: ； in, This indicates the number of sample points that fall into the failure domain.

6. The method according to claim 5, characterized in that, The multidimensional joint density function is transformed into a form where the marginal distribution is multiplied by multiple Pair-Copula functions using Vine-Copula. The specific construction process includes: Based on Pair-Copula theory and Vine theory, the joint probability density function of random variables is decomposed into the form of the product of the Pair-Copula function and the marginal probability density function; Based on existing or generated sample points, select the desired Copula function type from the candidate Copula functions, solve for the corresponding Copula coefficients, and obtain the corresponding joint probability density function.

7. The method according to claim 6, characterized in that, The Rosenblatt transform is represented as follows: in, It is the inverse function of the cumulative distribution function of the standard normal distribution. This is the conditional distribution function.

8. The method according to claim 7, characterized in that, The specific steps of the Copula-SRSMBRA risk assessment method include: The joint probability density function based on the Vine model derivation structure is expressed as a product of multiple Pair-Copula functions and multiple marginal probability density functions; For relevant random variables X Based on the sample points, solve each candidate Copula model and select the optimal Copula model for each pair of random variables. When there are multiple pairs of related random variables, repeat the solution and selection. If only the statistical characteristic parameters and correlation parameters of the random variables are available, generate the sample size based on the statistical characteristic parameters and correlation parameters. The Copula model parameters for each pair of related random variables are calculated using the MCM algorithm. Expand the expression for the random response surface methodology according to the required order; The undetermined coefficients are solved using the probabilistic collocation method, and the collocation points are then transformed. For the obtained limit state equations, the failure probability is solved using the step moment method or the Monte Carlo method.

9. A structural probability risk assessment system based on SRSMBRA and Copula-MCM, characterized in that, include: The SRSMBRA module is used to improve the probabilistic collocation method of the classical stochastic response surface method. By using the probabilistic collocation method as the starting point, the SRSMBRA stochastic response surface method based on regression analysis obtains the undetermined coefficients of the Hermite expansion and constructs the limit state equation of the structure. The Copula-MCM module is used to construct the joint probability density function of the multidimensional random variables of a structure based on the limit state equation of the structure, using the Copula function and the Vine model. Based on the Copula-MCM structural probabilistic risk assessment method, it obtains the failure probability when there is a correlation between the multidimensional random variables of the structure. The Copula-SRSMBRA module is used to integrate SRSMBRA and Copula-MCM for structural probability risk assessment through Rosenblatt transformation. The failure probability is obtained using the step moment method or Monte Carlo method through the Copula-SRSMBRA risk assessment method.

10. The system according to claim 9, characterized in that, The steps of the Stochastic Response Surface Method (SRSMBRA) based on regression analysis include: Sort all candidate points in ascending order of their distance from the origin, including the origin. Select points one by one according to the sorting results to form the Hermite coefficient matrix. Check whether the rank of the matrix is ​​equal to the number of rows. If they are equal, continue to select points. If they are not equal, discard the current point and check the next point, until the row rank of the matrix is ​​equal to the number of undetermined coefficients. Select all collocation points that are symmetric about the origin, and combine them to form the final collocation points to establish a stochastic response surface model based on regression analysis; Regression analysis was used to obtain the undetermined coefficients of the Hermite expansion and to construct the limit state equation of the structure.

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