A reliability evaluation method based on a regularized flow generative model

Abstract

The application provides a reliability evaluation method based on a regularization flow generative model, belongs to the fields of artificial intelligence and reliability evaluation technology, and comprises the following steps: S1, determining a performance function; S2, based on the regularization flow generative model and observation data, performing probability modeling on a multi-dimensional parameter joint distribution to obtain a multi-dimensional parameter joint distribution probability space conversion model; S3, combining the regularization flow generative model with a traditional reliability method to form the reliability evaluation method based on the regularization flow generative model; and S4, based on the multi-dimensional parameter joint distribution probability space conversion model and the performance function, performing iterative reliability calculation through the reliability evaluation method based on the regularization flow generative model to obtain a failure probability. The application can more reasonably consider the nonlinear correlation between random variables, is more accurate and efficient in the reliability problem of a multi-dimensional parameter joint distribution with a nonlinear correlation structure, and has a good application prospect.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of artificial intelligence and reliability evaluation, and in particular to a reliability evaluation method based on a regularized flow generative model. BACKGROUND

[0002] In the field of reliability evaluation, the reliability evaluation method evaluates the reliability of the system under the target condition according to the statistical characteristics, probability distribution of random variables and given function function. Therefore, the reasonable quantification of the uncertainty of random factors is crucial to reliability evaluation. However, the traditional reliability method is generally difficult to reasonably represent the non-linear correlation between random variables for the reliability problem of multi-dimensional parameter joint distribution with non-linear correlation structure. Taking the first-order reliability method (FORM) as an example, this method generally uses a probability transformation method (such as Rackwitz-Fiessler transformation, Nataf transformation) to first convert the multi-dimensional joint distribution from the original probability space to the independent standard normal space, and convert the complex joint distribution reliability problem into a simple independent standard normal space reliability problem, and then perform reliability calculation. However, these probability transformation methods have limitations. For example, Nataf transformation assumes that the correlation structure between variables is Gaussian distribution, so it cannot consider the non-linear correlation between variables, and the result may not be accurate in problems with non-linear correlation. In addition, the calculation of the correlation coefficient in the probability space transformation process of Nataf transformation involves double integration, so in the problem of multi-dimensional joint distribution, the method is difficult to calculate and has low computational efficiency.

[0003] In summary, in the reliability problem of multi-dimensional parameter joint distribution with non-linear correlation structure, the traditional reliability evaluation method has two problems:

[0004] (1) When modeling the joint distribution of random variables with non-linear correlation structure, it is difficult to reasonably represent the non-linear correlation between variables;

[0005] (2) When modeling the joint probability of multi-dimensional parameters, the problem of large calculation difficulty and low computational efficiency is faced. SUMMARY

[0006] The present application provides a reliability evaluation method based on a regularized flow generative model, which can well solve the problem of probability space transformation of multi-dimensional parameter joint distribution with non-linear correlation structure. The method converts the multi-dimensional parameter joint distribution from the original probability space to the independent standard normal space, thereby converting the complex probability distribution reliability problem into a simple probability distribution reliability problem in the independent standard normal space, and the reliability evaluation method formed by combining the traditional reliability method can be easily applied to different problems in the same field.

[0007] To achieve the above object, the application adopts the following technical solutions:

[0008] A reliability evaluation method based on a regularized flow generative model, comprising:

[0009] S1, determining a function function: first, determine the object to be evaluated, extract the key attributes of the object to be evaluated, and construct the function function according to the key attributes;

[0010] S2, based on the regularized flow generative model and the observation data, the probability of the joint distribution of the multi-dimensional parameters is modeled, and the multi-dimensional parameter joint distribution probability space conversion model is obtained: the multi-dimensional parameters are the parameters corresponding to the key attributes of the object to be evaluated; the observation data is obtained by two ways, one is the monitoring data obtained by monitoring the multi-dimensional parameters, and the other is the data generated based on the theoretical distribution of the multi-dimensional parameters; the observation data is used to train the regularized flow generative model, the model parameters are determined by iterative optimization, and the multi-dimensional parameter joint distribution probability space conversion model is constructed based on the model parameters;

[0011] S3, the trained regularized flow generative model is combined with the traditional reliability method to form a reliability evaluation method based on the regularized flow generative model: in the combination process, according to the calculation logic of the selected traditional reliability method, the probability space conversion ability of the multi-dimensional parameter joint distribution probability space conversion model is integrated;

[0012] S4, based on the multi-dimensional parameter joint distribution probability space conversion model and the function function, the iterative reliability calculation is carried out by the reliability evaluation method based on the regularized flow generative model, and the failure probability is obtained.

[0013] In the specification, in step S1, the failure event is defined by the calculation result of the function function: according to the calculation result of the function function, the state of the object to be evaluated is divided, if the function function result is greater than the preset threshold value, the object to be evaluated is in a safe state; if the function function result is equal to the preset threshold value, it is in a limit state; if the function function result is less than the preset threshold value, it is in a failure state, the failure event refers to the event that the function function result is less than the preset threshold value; wherein, the preset threshold value is determined according to the industry standard or design requirement of the object to be evaluated, when the object to be evaluated is a structure, the construction of the function function needs to take the resistance random vector provided by the structure and the action force random vector applied on the structure as the core parameters, to ensure that the function function can reflect the stress balance relationship of the structure.

[0014] In the specification, the key attributes of the object to be evaluated in step S1 specifically include two categories: the first category is the bearing or resistance capacity related attributes possessed by the object to be evaluated, and this category of attributes is denoted as a resistance vector; the second category is the action related attributes applied externally to the object to be evaluated, and this category of attributes is denoted as an action vector; the extraction of key attributes needs to cover the core influencing factors of the reliability evaluation of the object to be evaluated, so as to avoid missing parameters that have a significant impact on the reliability result.

[0015] In the specification, the data generated based on the theoretical distribution simulation of the multi-dimensional parameters in step S2 needs to be determined according to the dimension and distribution complexity of the multi-dimensional parameters: when the dimension of the multi-dimensional parameters is ≤3 and the distribution is a common type, the amount of simulated data is not less than 10,000; when the dimension is >3 or the distribution is a complex nonlinear distribution, the amount of data is not less than 50,000; at the same time, the trained regularization flow generative model needs to be verified: the statistical parameters, the edge distribution histogram, and the joint probability density function of the model generated data and the original observation data are compared to ensure that the distribution feature deviation between the model generated data and the original data is less than a preset deviation threshold.

[0016] In the specification, the multi-dimensional parameter joint distribution probability space conversion model in step S2 includes two types of mapping relationships: the first type is the mapping from the original space to the independent standard normal space, wherein the original space refers to the probability space containing the random variable vector corresponding to the multi-dimensional parameters, and the independent standard normal space refers to the probability space containing the independent standard normal random variable vector; the second type is the mapping from the independent standard normal space to the original space; the specific expressions of the two types of mappings are determined by the parameters of the trained regularization flow generative model, and the two types of mappings are inverse mappings of each other, ensuring the reversibility and accuracy of the probability space conversion.

[0017] In the specification, the traditional reliability method in step S3 includes a first-order reliability method, a second-order reliability method, and a Monte Carlo simulation method; when the selected traditional reliability method is the first-order reliability method, the specific combination of the flow is as follows:

[0018] S3.1 Based on the trained regularization flow generative model, the multi-dimensional parameter joint distribution probability space conversion model is called to obtain the bidirectional conversion logic of the original space and the independent standard normal space;

[0019] S3.2 For the partial derivative of the original space random variable calculated in the iteration process of the first-order reliability method, the difference method is used to solve, and the difference method includes forward difference, backward difference, and central difference;

[0020] S3.3 embeds the conversion logic of S3.1 and the partial derivative solution result of S3.2 into the iteration step of the first-order reliability method algorithm, to form a first-order reliability method evaluation method suitable for nonlinear correlated multi-dimensional parameters.

[0021] In the specification, the implementation details of the difference method in step S3.2 are as follows: the central difference method is preferentially adopted, and the difference step of the central difference method is determined according to the value range of the original space random variable; if there are some random variables whose value range is less than 1, the difference step is fixed at 10 -5 , to ensure the accuracy of the partial derivative calculation.

[0022] In the specification, the specific steps of the iterative reliability calculation in step S4 are as follows:

[0023] S4.1 sets an initial checking point, and the initial checking point takes a zero vector in the independent standard normal space;

[0024] S4.2 calls a multi-dimensional parameter joint distribution probability space conversion model to convert the initial checking point zero vector into original space random variable initial values;

[0025] S4.3 substitutes the original space random variable initial values into the function function, and calculates the sensitivity coefficients of the function function to each random variable in combination with the solved partial derivatives;

[0026] S4.4 calculates the reliability index of the current iteration according to the sensitivity coefficients and the random variable values in the independent standard normal space;

[0027] S4.5 updates the random variable values in the independent standard normal space based on the reliability index of the current iteration and the sensitivity coefficients;

[0028] S4.6 calls the conversion model to convert the random variable values into new original space random variable values, and repeats S4.3-S4.5 with the new original space random variable values and the random variable values to obtain the reliability index after the first iteration.

[0029] In the specification, the termination condition of the iterative reliability calculation in step S4 and the failure probability acquisition method are as follows: the termination condition is that the difference between the reliability indexes of the previous and next iterations is less than a preset error threshold, and the error threshold is determined according to the evaluation accuracy requirement.

[0030] In the specification, when the iteration is terminated, the final reliability index is taken, the failure probability is calculated through the standard normal distribution function, and the original space random variable values corresponding to the final iteration are recorded as the design point of the reliability evaluation.

[0031] In summary, the present application has at least the following beneficial effects:

[0032] The present application makes full use of the powerful ability of the regularized flow generative model to model the joint distribution of complex random variables and the flexibility of the latent variable space of the regularized flow generative model, converts the joint distribution of multi-dimensional parameters from the original probability space to the mutually independent standard normal space, so that the complex probability distribution reliability problem is converted into the simple probability distribution reliability problem in the independent standard normal space. The present application fully utilizes the advantages of the regularized flow generative model in probability transformation, and combines with the traditional reliability method to realize the probability transformation of the multi-dimensional joint distribution with nonlinear correlation structure and the extension of the traditional reliability method. The present application can be easily applied to different problems in the same field. BRIEF DESCRIPTION OF DRAWINGS

[0033] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings needed in the embodiment description will be briefly introduced. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor.

[0034] Figure 1 The schematic diagram of the reliability evaluation method based on the regularized flow generative model involved in the present application.

[0035] Figure 2a The schematic diagram of the scatter plot of the two-dimensional exponential distribution simulation data involved in the present application.

[0036] Figure 2b The schematic diagram of the three-dimensional statistical histogram of the two-dimensional exponential distribution simulation data involved in the present application.

[0037] Figure 3a The schematic diagram of the marginal statistical histogram of the two-dimensional exponential distribution simulation data involved in the present application.

[0038] Figure 3b The schematic diagram of the marginal statistical histogram of the two-dimensional exponential distribution simulation data involved in the present application.

[0039] Figure 4a The schematic diagram of the scatter plot of the two-dimensional exponential distribution simulation data based on the regularized flow model and simulation data involved in the present application.

[0040] Figure 4b The schematic diagram of the modeling result of the marginal distribution of the two-dimensional exponential distribution simulation data based on the regularized flow model and simulation data involved in the present application.

[0041] Figure 5a ​​A schematic diagram of sample scatter plot and 3D frequency histogram (simulated data) generated based on the trained regularizing flow model.

[0042] Figure 5b A schematic diagram of sample scatter plot and 3D frequency histogram (simulated data) generated based on the trained regularizing flow model.

[0043] Figure 6a A schematic diagram of the result of modeling the joint PDF of two-dimensional exponential distribution by the regularizing flow model.

[0044] Figure 6b A schematic diagram of the theoretical PDF of two-dimensional exponential distribution by the regularizing flow model. DETAILED DESCRIPTION

[0045] In the following, only certain exemplary embodiments are simply described. As those skilled in the art can recognize, the described embodiments can be modified in various different ways without departing from the spirit or scope of the embodiments of the present application. Therefore, the drawings and the description are considered to be exemplary in nature and not restrictive.

[0046] The following disclosure provides many different embodiments, or examples, for implementing different structures of the embodiments of the present application. For the purpose of simplifying the present application, the components and settings of specific examples are described in the following. Of course, they are only examples, and the purpose is not to limit the embodiments of the present application. In addition, the embodiments of the present application can refer to the same reference numerals and / or reference letters in different examples, and such repetition is for the purpose of simplification and clarity, which itself does not indicate the relationship between the various embodiments and / or settings discussed.

[0047] The embodiments of the present application will be described in detail below with reference to the accompanying drawings.

[0048] As shown in Figure 1 , the present embodiment provides a reliability evaluation method based on a regularizing flow generative model, comprising the following steps:

[0049] ​​S1, determining a function function and defining a failure event: first, the object to be evaluated is determined, and the key attributes of the object to be evaluated are extracted, including random variables such as the resistance provided by the object to be evaluated and the force applied to the object to be evaluated; a function function is constructed according to the key attributes, and safety judgment conditions, limit judgment conditions and failure judgment conditions are set according to the industry standards or design requirements of the object to be evaluated, and a failure event is defined by the calculation result of the function function - when the function function result meets the safety judgment condition, the object to be evaluated is in a safe state; when the limit judgment condition is met, it is in a limit state; when the failure judgment condition is met, it is in a failure state;

[0050] S2, based on the regularized flow generative model and the observation data, a joint distribution of multi-dimensional parameters is probabilistically modeled to obtain a multi-dimensional parameter joint distribution probability space conversion model: the multi-dimensional parameters are the parameters corresponding to the key attributes of the object to be evaluated in S1; the observation data is obtained in two ways, one is the monitoring data obtained by actually monitoring the multi-dimensional parameters, and the other is the data generated based on the theoretical distribution of the multi-dimensional parameters (such as 50,000 original data generated for two-dimensional exponential joint distribution multi-dimensional parameter evaluation); the observation data is used to train the regularized flow generative model, and the model parameters are determined by iterative optimization; based on the model parameters, a multi-dimensional parameter joint distribution probability space conversion model is constructed, which includes two types of mapping relationships: the first type is the mapping from the original space to the independent standard normal space, the original space is the space containing the random variable vector corresponding to the multi-dimensional parameters, and the independent standard normal space is the space containing the independent standard normal random variable vector; the second type is the mapping from the independent standard normal space to the original space;

[0051] S3, combining the trained regularized flow generative model with traditional reliability methods to form a reliability evaluation method based on the regularized flow generative model: the traditional reliability methods include first-order reliability method (FORM), second-order reliability method (SORM), Monte Carlo simulation method (MCS), and the above methods are traditional methods commonly used in reliability evaluation field; during the combination, according to the calculation logic of the selected traditional reliability method, the probability space conversion ability of the multi-dimensional parameter joint distribution probability space conversion model in S2 is integrated - for example, when the FORM method is used, the mutual conversion between the original space and the independent standard normal space is realized through the conversion model to adapt to the iterative calculation requirement of the FORM method;

[0052] S4, based on the multi-dimensional parameter joint distribution probability space conversion model obtained in S2 and the function function determined in S1, the reliability evaluation method of the regularized flow generating model formed in S3 is iteratively calculated to obtain the failure probability: in the iterative calculation, firstly, an initial checking point is preset, which is usually set as an initial value (such as a zero vector) conforming to the calculation habit; according to the initial checking point, the initial value of the random variable corresponding to the multi-dimensional parameter in the original space is calculated through the conversion model in S2; the initial value of the random variable is substituted into the function function determined in S1 to calculate the function function result, and based on the result and the mathematical characteristics of the function function, the sensitivity coefficient (which reflects the sensitivity of the function function to each random variable) is calculated; according to the sensitivity coefficient, the reliability index is calculated; based on the reliability index, the random variable value in the independent standard normal space is updated; according to the updated random variable value in the independent standard normal space, the updated original space random variable value is calculated through the conversion model in S2, and it is substituted into the function function of S1 again to verify the state; the process of “calculating the function function result→calculating the sensitivity coefficient→calculating the reliability index→updating the random variable value in the independent standard normal space→updating the random variable value in the original space” is repeatedly executed, and when the error of the reliability indexes obtained by the current and previous two calculations is less than a preset error threshold (the error threshold is determined according to the reliability evaluation accuracy requirement of the object to be evaluated), the iteration is terminated, and the failure probability is calculated and output according to the final reliability index and the definition of the failure event in S1.

[0053] In some embodiments, the specific way of “defining the failure event” in step S1 is: dividing the state of the object to be evaluated according to the calculation result of the function function, if the function function result is greater than a preset threshold, the object to be evaluated is in a safe state; if the function function result is equal to the preset threshold, it is in a limit state; if the function function result is less than the preset threshold, it is in a failure state, and the failure event refers to the event that the function function result is less than the preset threshold; wherein the preset threshold is determined according to the industry standard or design requirement of the object to be evaluated, when the object to be evaluated is a structure, the construction of the function function needs to take the resistance random vector provided by the structure and the action force random vector applied on the structure as the core parameters, to ensure that the function function can reflect the stress balance relationship of the structure.

[0054] In some embodiments, the “key attributes of the object to be evaluated” in step S1 specifically include two categories: the first category is the bearing or resistance ability related attributes possessed by the object to be evaluated, such as the compressive strength and bending stiffness of the structure, etc., and the random vector composed of such attributes is referred to as the resistance vector; the second category is the action related attributes applied externally to the object to be evaluated, such as the load and impact force borne by the structure, etc., and the random vector composed of such attributes is referred to as the action force vector; the extraction of key attributes needs to cover the core influencing factors of the reliability evaluation of the object to be evaluated, to avoid missing parameters that have a significant impact on the reliability result.

[0055] In some embodiments, the data generated in step S2 based on the theoretical distribution simulation of the multi-dimensional parameters needs to be determined according to the dimension of the multi-dimensional parameters and the complexity of the distribution: when the dimension of the multi-dimensional parameters is less than or equal to 3 and the distribution is a common type (such as an exponential distribution or a normal distribution), the amount of data generated by simulation is not less than 10,000; when the dimension is greater than 3 or the distribution is a complex nonlinear distribution, the amount of data is not less than 50,000. In the document embodiment, 50,000 original data are generated for the two-dimensional exponential joint distribution of the multi-dimensional parameters. At the same time, the trained regularization flow generative model needs to be verified by comparing the statistical parameters (including the first moment, the second moment, and the linear correlation coefficient) of the model-generated data and the original observation data, the edge distribution histogram, and the joint probability density function (PDF) to ensure that the distribution characteristics of the model-generated data and the original data deviate by less than a preset deviation threshold (such as a statistical parameter deviation of less than or equal to 5%).

[0056] In some embodiments, the multi-dimensional parameter joint distribution probability space conversion model in step S2 includes two types of mapping relationships: the first type is the mapping from the original space to the independent standard normal space, where the original space refers to the probability space containing the random variable vector (denoted as X, the dimension of X is consistent with the number of multi-dimensional parameters) corresponding to the multi-dimensional parameters, and the independent standard normal space refers to the probability space containing the independent standard normal random variable vector (denoted as U, the dimension of U is consistent with X). The second type is the mapping from the independent standard normal space to the original space. The specific expressions of the two types of mappings are determined by the parameters (denoted as W) of the trained regularization flow generative model, and the two types of mappings are inverse mappings of each other, ensuring the reversibility and accuracy of the probability space conversion.

[0057] In some embodiments, the traditional reliability method in step S3 includes the first-order reliability method (FORM), the second-order reliability method (SORM), and the Monte Carlo simulation method (MCS). When the selected traditional reliability method is FORM, the specific process is as follows: S3.1 based on the trained regularization flow generative model, the multi-dimensional parameter joint distribution probability space conversion model is called to obtain the bidirectional conversion logic of the original space and the independent standard normal space; S3.2 for the partial derivative (the partial derivative of the function function with respect to the random variable of the original space) that needs to be calculated in the iterative process of FORM, because the regularization flow generative model is an implicit model, the difference method is used to solve it, including forward difference, backward difference, and central difference; S3.3 the conversion logic of S3.1 and the partial derivative solution result of S3.2 are embedded into the iterative step of the FORM algorithm to form a FORM evaluation method suitable for non-linearly correlated multi-dimensional parameters.

[0058] In some embodiments, the implementation details of the "difference method" in step S3.2 are as follows: the central difference method is preferred, and the difference step size (denoted as h) of the central difference method is determined according to the range of values ​​of the original spatial random variable, usually set to the standard deviation of the random variable. ~ If some random variables have extremely small ranges (e.g., less than 1), then the difference step size is fixed at 1. To ensure the accuracy of partial derivative calculations, forward or backward differencing is only an option when the central differencing calculation efficiency is too low (e.g., the multidimensional parameter dimension > 10), and it must be verified that the deviation between the differencing result and the central differencing result is ≤ 10%.

[0059] In some embodiments, the specific steps of "iterative reliability calculation" in step S4 are as follows: S4.1 Set initial verification points, the initial verification points are taken as the zero vector in the independent standard normal space (i.e. (The dimension is consistent with U); S4.2 calls the multidimensional parameter joint distribution probability space transformation model to convert the initial verification points. Initial values ​​of random variables converted to the original space S4.3 will Substitute the function determined in step S1 into the partial derivatives obtained in S3, and calculate the sensitivity coefficients of the function to each random variable; S4.4 Calculate the reliability index of the current iteration based on the sensitivity coefficients and the values ​​of the random variables in the independent standard normal space. S4.5 is based on reliability indicators. With sensitivity coefficients, update the values ​​of random variables in independent standard normal spaces. S4.6 calls the transformation model, which will... Transform into new original space random variable values ,by and Repeat steps S4.3 to S4.5 to obtain... .

[0060] In some embodiments, the termination condition and failure probability acquisition method of the "iterative reliability calculation" in step S4 are as follows: the termination condition is the difference in reliability index between two consecutive iterations. (where k is the number of iterations) is less than a preset error threshold, which is determined based on the evaluation accuracy requirements. In typical scenarios, it is set to... High-precision scene setting When the iteration terminates, the final reliability index is taken. The failure probability is calculated using the standard normal distribution function. ,Right now Where Φ(·) is the cumulative distribution function of the standard normal distribution; simultaneously, the values ​​of the original spatial random variables corresponding to the final iteration are recorded. This serves as a design point for reliability assessment.

[0061] In some embodiments, this method is applicable to reliability assessment scenarios of multidimensional parameter joint distributions with nonlinear correlation structures, including but not limited to reliability assessment of two-dimensional exponential joint distributions, multidimensional log-normal joint distributions, and multidimensional Weibull joint distributions. Compared with traditional probability space transformation methods (such as Nataf transform and Rackwitz-Fiessler transform), this method does not require assuming that the correlation structure between multidimensional parameters is Gaussian, and can directly learn nonlinear correlations through regularized flow generative models. It also avoids the double integral calculations involved in traditional transformations. When the multidimensional parameter dimension is >5, the computational efficiency is improved by more than 30% (based on the sampling efficiency of Monte Carlo simulation).

[0062] In some embodiments, in step S1, the functional function and failure event definitions are determined, and a corresponding functional function is constructed according to the specific problem. For example, the functional function can be represented as:

[0063] ;

[0064] in, Let be a random vector representing the resistance provided by the structure; Let be a random vector representing the force applied to the structure; When this time, it indicates that the structure is in a safe state; When this occurs, it indicates that the structure is in a limit state; When this occurs, it indicates that the structure is in a state of failure.

[0065] In some embodiments, step S2 involves probabilistically modeling the joint distribution of multidimensional parameters based on a regularized flow generative model and observed data to obtain a probability space transformation model of the joint distribution of multidimensional parameters. The probabilistic modeling of its joint distribution can be expressed as:

[0066] Mapping from independent standard normal space to the original space: ;

[0067] Mapping from the original space to the independent standard normal space: ;

[0068] in, X Let the vector of random variables in the original space be represented as: , N Number of random variables; U A vector of random variables in an independent standard normal space can be represented as: , N The number of random variables; W represents the model parameters obtained after training the regularized flow model.

[0069] In some embodiments, the trained regularizing flow generative model in step S3 is combined with a traditional reliability method to form a reliability evaluation method based on the regularizing flow generative model. Taking a first-order reliability method (FORM) as an example, the specific construction process is as follows:

[0070] Step S3.1: modeling the multi-dimensional joint distribution of parameters based on the regularizing flow generative model to obtain a conversion model of the multi-dimensional joint distribution from the original space to the standard normal space;

[0071] Step S3.2: involving partial derivative calculation in the FORM iteration process. Since the regularizing flow generative model is an implicit model, a difference method (such as forward difference, backward difference, central difference, etc.) is used for numerical solution. Taking the central difference as an example:

[0072] ;

[0073] wherein, F is a conversion model from the standard normal space to the original space; and h is a difference step length.

[0074] Step S3.3: fusing the trained regularizing flow generative model into the FORM algorithm based on step S3.1 and step S3.2 to form a reliability evaluation method based on the regularizing flow generative model and the FORM.

[0075] In some embodiments, in step S4, based on the multi-dimensional joint distribution probability space conversion model obtained in step S2, the failure probability is obtained by iterative calculation according to the reliability evaluation method formed in step S3. The specific iterative process includes:

[0076] (1): assuming an initial checking point , which can be generally set as ;

[0077] (2): according to , the initial value of is calculated by the regularizing flow model: ;

[0078] (3): calculating the sensitivity coefficient : ;

[0079] (4): calculating the reliability index : ;

[0080] (5): calculating the new value: ;

[0081] (6): according to the new values, calculate new values: ;

[0082] (7) repeat steps (3)-(6) with new values, and stop the iteration process and output the calculation results when the error of the last two times of reliable index calculation results is less than .

[0083] Example: Two-dimensional exponential joint distribution reliability evaluation case

[0084] Step 1, determine the function function and define the failure event, the function function of this case is composed of two random variables subject to two-dimensional exponential distribution:

[0085] The function function is defined as: ;

[0086] X 1 and the joint probability density function PDF of X 2:

[0087] ;

[0088] The probability density graph of the theoretical joint distribution is shown in Figure 6a and Figure 6b .

[0089] Step 2, based on the regularized flow generation formula model and the 50000 original data generated by the theoretical distribution simulation, the two-dimensional exponential distribution is probabilistically modeled, the two-dimensional exponential distribution probability space conversion model is obtained, the scatter diagram and three-dimensional statistical histogram of the original data are shown in Figure 2a and Figure 2b , the edge statistical histogram is shown in Figure 3a and Figure 3b . Train the model to obtain the probability space conversion model:

[0090] The mapping from the independent standard normal space to the original space: ;

[0091] The mapping from the original space to the independent standard normal space: ;

[0092] According to the trained model, the scatter diagram and three-dimensional statistical histogram of the 50000 simulation data obtained by conversion can be obtained, which are shown in Figure 4a and Figure 4b . The modeling results of the edge distribution of the random variable by the regularized flow model are shown in Figure 5a and Figure 5b . The comparison of the statistical parameters of the simulation data and the original data is shown in Table 1:

[0093] Table 1. Comparison of statistical parameters of simulation data and generated data

[0094]

[0095] From Table 1, it can be seen that the regularization flow model can well represent the first moment, second moment and linear correlation information of the original data. At the same time, through the comparison of the theoretical joint distribution PDF and the joint PDF learned by the regularization flow model, it can be seen that the regularization flow model can not only well represent the edge distribution with obvious skewness characteristics, but also well capture the nonlinear correlation between random variables. Figure 4a and Figure 4b 、 Figure 5a and Figure 5b ,

[0096] Step 3, fuse the trained regularization flow model and the first-order reliability method (FORM) to form a reliability evaluation method based on the regularization flow model and FORM, and the specific construction process is as follows:

[0097] Step S3.1: based on the trained regularization flow model, obtain the conversion model of the multi-dimensional joint distribution from the original space to the standard normal space (as shown in step 2);

[0098] Step S3.2: for the implicit regularization flow model, use the central difference method to approximate the partial derivative:

[0099] ;

[0100] Step S3.3: based on steps S3.1 and S3.2, fuse the trained regularization flow model into the FORM algorithm to form a reliability evaluation method based on the regularization flow model and FORM.

[0101] Step 4, based on the multi-dimensional parameter joint distribution probability space conversion model obtained in step S2, the reliability evaluation method formed in step S3 is used for iterative calculation to obtain the failure probability and design point, and the Nataf+FORM method is used to calculate the failure probability and design point. The results of the two reliability calculation methods and the numerical solution are compared, and the comparison results are shown in Table 2:

[0102] Table 2. Comparison of calculation results

[0103]

[0104] It can be seen from Table 2 that the reliability index and failure probability of NF+FORM are 2.762 and 0.00288 respectively, and the reliability index and failure probability of the numerical solution are 2.754 and 0.00295 respectively, and the calculation result of the method is basically consistent with the result of the numerical solution. The reliability index and failure probability of Nataf+FORM are 2.797 and 0.00258 respectively, and it can be seen that the method NF+FORM proposed in the application is closer to the calculation result of the numerical solution compared with the traditional Nataf+FORM method. It can be seen from the above that in the reliability calculation problem involving a multi-dimensional joint distribution with a nonlinear correlation structure, the regularization flow generative model can better perform probability modeling and more reasonably describe the nonlinear correlation between random variables. Therefore, compared with the traditional reliability analysis method, the reliability evaluation method based on the regularization flow generative model has a more reasonable joint distribution modeling process of complex random variables, more accurate reliability calculation, and can be easily applied to different scenarios in the same field, and has good application prospects.

[0105] The above-described embodiments are used to illustrate the present application and are not intended to limit the present application, so the number of examples can be changed or equivalent elements can be replaced, which still belongs to the scope of the present application.

[0106] From the above detailed description, it can be clear to those skilled in the art that the present application can achieve the above-mentioned purposes, and has met the requirements of the Patent Law.

[0107] Although the preferred embodiments of the present application have been described, those skilled in the art can make further changes and modifications to the embodiments once they know the basic inventive concept. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications falling within the scope of the present application. The above description is only the preferred embodiments of the present application and is not intended to limit the present application. It should be noted that any modification, equivalent replacement and improvement made within the spirit and principle of the present application should be included in the protection scope of the present application.

[0108] It should be noted that the above description of the flow is only for example and illustration, and does not limit the scope of the present application. Those skilled in the art can make various modifications and changes to the flow under the guidance of the present application. However, these modifications and changes are still within the scope of the present application.

[0109] Having described the basic concepts, it is obvious to those of ordinary skill in the art after reading this disclosure that the above-described disclosure of the application is merely illustrative and not limiting of the application. Numerous modifications, improvements, and / or alterations can be made to the application, which are apparent to those of ordinary skill in the art after reading this disclosure. Such modifications, improvements, and alterations are intended to be within the spirit and scope of the exemplary embodiments of the application.

[0110] Also, certain terminology has been used for the purpose of reference only, and is not intended to be limiting. For example, terms such as "one embodiment," "an embodiment," and / or "some embodiments" mean that a particular feature, structure, or characteristic described in connection with the embodiment is included in at least one embodiment. Thus, the appearances of the phrase "in one embodiment" or "in an embodiment" or "in some embodiments" in various places throughout this specification are not necessarily referring to the same embodiment. Furthermore, the particular features, structures, or characteristics can be combined in any suitable manner on an embodiment or embodiments. It will be appreciated that no element, component, or method step described herein is intended to be "essential" unless explicitly so described.

[0111] Moreover, those skilled in the art will appreciate that aspects of the application can be embodied as a computer program product, which can include one or more computer readable media having computer readable program code embodied thereon. The computer readable program code can be executed by a computer or computer system to perform various functions as described herein. The computer readable program code can be embodied in any suitable computer readable media, including but not limited to memory devices, optical storage devices, and carrier waves. Accordingly, aspects of the application can be embodied in hardware and / or in software (including firmware, resident software, micro-code, etc.) that runs on a processor or computer system, which can both be substantially referred to as "circuitry," "a module" or "a system." As will be understood by those skilled in the art, the functions of the various aspects of the application can be implemented in a wide variety of ways. Accordingly, the phrase "circuitry configured to" or "module configured to" can be understood to encompass a general structure configured to perform the recited function, and also structure specifically designed to perform the recited function.

[0112] Computer program code for carrying out operations of various aspects of the present application can be written in any combination of one or more programming languages, including an object oriented programming language such as Java, Scala, Smalltalk, Eiffel, JADE, Emerald, C++, C#, VB.NET, Python, conventional procedural programming languages, such as the C programming language, Visual Basic, Fortran 2103, Perl, COBOL 2102, PHP, ABAP, dynamic programming languages, such as Python, Ruby and Groovy, or another programming language. The program code can execute entirely on the user's computer, partly on the user's computer, as a stand-alone software package, partly on the user's computer and partly on a remote computer or entirely on the remote computer or server. In the latter scenario, the remote computer can be connected to the user's computer through any form of network, such as a local area network (LAN) or a wide area network (WAN), or the connection can be made to an external computer (for example, through the Internet) or within a cloud computing environment or as a service, such as software as a service (SaaS).

[0113] Furthermore, the order of presentation of the processing elements and sequences, use of nomenclature, or other descriptive terms herein are not intended to limit the scope of the embodiments or the application in any way. Although the above disclosure discusses several exemplary embodiments of the application, it should be apparent that various changes can be made without departing from the scope of the application and the appended claims. For example, although implementations of the various components discussed above can be realized in hardware devices, they can also be realized as pure software solutions, for example, installed on existing servers or mobile devices.

[0114] Similarly, it is to be noticed that the term "comprising", used in the description, is not intended to exclude other elements or steps. Rather, it is used to indicate that the elements and / or steps that follow are included. It will be apparent that aspects, according to the embodiments as described above, can be implemented in any kind of system, of which the examples given above are intended to be purely exemplary and not limiting. Furthermore, it is to be noted that the use of the singular herein, like "a" or "an", means not one but several, possibly infinitely many. The use of the term "one" in the claims herein is therefore not to be interpreted as meaning one and only one but one or more.

Claims

1. A reliability assessment method based on a regularized flow generative model, characterized in that, include: S1. Determine the functional function: First, identify the object to be evaluated, extract the key attributes of the object to be evaluated, and construct the functional function based on the key attributes. S2. Based on the regularized flow generative model and observation data, probabilistic modeling of the joint distribution of multidimensional parameters is performed to obtain a probability space transformation model of the joint distribution of multidimensional parameters: the multidimensional parameters are the parameters corresponding to the key attributes of the object to be evaluated; the observation data is obtained in two ways: one is the monitoring data obtained by actual monitoring of the multidimensional parameters, and the other is the data generated by simulation based on the theoretical distribution of the multidimensional parameters; the regularized flow generative model is trained using the observation data, the model parameters are determined through iterative optimization, and a probability space transformation model of the joint distribution of multidimensional parameters is constructed based on the model parameters; S3. Combine the trained regularized flow generative model with traditional reliability methods to form a reliability evaluation method based on the regularized flow generative model: In the process of combination, according to the calculation logic of the selected traditional reliability method, the probability space transformation capability of the multi-dimensional parameter joint distribution probability space transformation model is incorporated. S4. Based on the multidimensional parameter joint distribution probability space transformation model and function, iterative reliability calculation is performed using a reliability assessment method based on a regularized flow generative model to obtain the failure probability. Step S3 uses traditional reliability methods, including first-order reliability methods, second-order reliability methods, and Monte Carlo simulation methods. When the selected traditional reliability method is a first-order reliability method, the specific process is as follows: S3.1 Based on the trained regularized flow generative model, the multi-dimensional parameter joint distribution probability space transformation model is called to obtain the bidirectional transformation logic between the original space and the independent standard normal space. S3.2 For the partial derivatives of the function with respect to the original spatial random variables that need to be calculated during the iteration of the first-order reliability method, since the regularized flow generative model is an implicit model, the difference method is used to solve it. The difference method includes forward difference, backward difference, and central difference. S3.3 embeds the transformation logic of S3.1 and the partial derivative solution results of S3.2 into the iterative steps of the first-order reliability method algorithm, forming a first-order reliability method evaluation method that adapts to nonlinear related multidimensional parameters; The specific steps of the iterative reliability calculation in step S4 are as follows: S4.1 Set the initial verification point, which is the zero vector in the independent standard normal space; S4.2 calls the multidimensional parameter joint distribution probability space transformation model to convert the initial verification point zero vector into the initial values ​​of random variables in the original space; S4.3 Substitute the initial values ​​of the random variables into the function and, in conjunction with the partial derivatives obtained from the solution, calculate the sensitivity coefficient of the function to each random variable. S4.4 Calculate the reliability index for the current iteration based on the sensitivity coefficient and the values ​​of random variables in the independent standard normal space; S4.5 Based on the reliability index and sensitivity coefficient of the current iteration, update the values ​​of random variables in the independent standard normal space; S4.6 calls the transformation model to convert the random variable values ​​into new original space random variable values. Then, S4.3~S4.5 are repeated with the new original space random variable values ​​and the random variable values ​​to obtain the reliable index after the first iteration.

2. The reliability assessment method based on a regularized flow generative model according to claim 1, characterized in that, In step S1, failure events are defined by the calculation results of the function: the state of the object to be evaluated is divided according to the calculation results of the function. If the result of the function is greater than the preset threshold, the object to be evaluated is in a safe state. If the result of the function is equal to the preset threshold, then it is in a limit state; If the result of the function is less than the preset threshold, it is in a failure state. The failure event refers to the event where the result of the function is less than the preset threshold. The preset threshold is determined according to the industry standards or design requirements of the object to be evaluated. When the object to be evaluated is a structure, the construction of the function needs to use the random vector of resistance provided by the structure and the random vector of force applied to the structure as core parameters to ensure that the function can reflect the force balance relationship of the structure.

3. The reliability assessment method based on a regularized flow generative model according to claim 1 or 2, characterized in that, In step S1, the key attributes of the object to be evaluated specifically include two categories: the first category is the load-bearing or resistance-related attributes of the object itself, and the random vector formed by these attributes is denoted as the resistance vector; the second category is the attributes related to the external forces applied to the object, and the random vector formed by these attributes is denoted as the force vector. The extraction of key attributes needs to cover the core influencing factors of the reliability assessment of the object to be evaluated, and avoid omitting parameters that have a significant impact on the reliability results.

4. The reliability assessment method based on a regularized flow generative model according to claim 1, characterized in that, In step S2, the amount of data generated based on the theoretical distribution of multidimensional parameters needs to be determined according to the dimension and distribution complexity of the multidimensional parameters: when the dimension of the multidimensional parameters is ≤3 and the distribution is of a common type, the amount of data generated by simulation should not be less than 10,000; when the dimension is >3 or the distribution is a complex nonlinear distribution, the amount of data should not be less than 50,000. At the same time, the trained regularized flow generative model needs to be validated: compare the statistical parameters, marginal distribution histograms, and joint probability density functions of the model-generated data and the original observation data to ensure that the distribution characteristics deviation between the model-generated data and the original data is less than a preset deviation threshold.

5. The reliability assessment method based on a regularized flow generative model according to claim 1 or 4, characterized in that, In step S2, the multidimensional parameter joint distribution probability space transformation model includes two types of mapping relationships: the first type is the mapping from the original space to the independent standard normal space, where the original space refers to the probability space containing the random variable vectors corresponding to the multidimensional parameters, and the independent standard normal space refers to the probability space containing mutually independent standard normal random variable vectors; the second type is the mapping from the independent standard normal space to the original space. The specific expressions of the two types of mappings are determined by the parameters of the trained regularized flow generative model, and the two types of mappings are inverse mappings to each other, ensuring the reversibility and accuracy of the probability space transformation.

6. The reliability assessment method based on a regularized flow generative model according to claim 1, characterized in that, The implementation details of the difference method in step S3.2 are as follows: the central difference method is preferred, and the difference step size of the central difference method is determined according to the range of values ​​of the original spatial random variables; if some random variables have values ​​less than 1, the difference step size is fixed at 10. -5 This ensures the accuracy of partial derivative calculations.

7. The reliability assessment method based on a regularized flow generative model according to claim 1, characterized in that, The termination condition and failure probability acquisition method for the iterative reliability calculation in step S4 are as follows: The termination condition is that the difference between the reliability indicators of two consecutive iterations is less than the preset error threshold, and the error threshold is determined according to the evaluation accuracy requirements.

8. The reliability assessment method based on a regularized flow generative model according to claim 7, characterized in that, When the iteration terminates, the final reliability index is taken, and the failure probability is calculated using the standard normal distribution function. At the same time, the original spatial random variable value corresponding to the final iteration is recorded as the design point for reliability assessment.

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