Mechanical structure reliability analysis method and system based on active learning agent model

Abstract

The invention discloses a mechanical structure reliability analysis method and system based on an active learning agent model, and belongs to the technical field of mechanical structure reliability analysis, and the method comprises the steps: analyzing the working condition and load condition of a mechanical structure to be subjected to reliability analysis, and determining a performance function of the mechanical structure in combination with the safety working requirements of the structure; based on the principle of equal probability conversion, the input variables are converted into a standard normal space, and Monte Carlo reliability analysis samples are generated; in a standard normal space, using a center cross method to generate a 4n initial fitting sample, calculating a function value of the sample, obtaining an initial response matrix, and fitting an initial proxy model; and establishing a distance constraint learning function based on the existing agent model and the fitting sample, and iteratively updating the agent model, the fitting sample, the response value matrix and the failure probability in combination with a prior reliable circular ring sample reduction method until a reliability analysis result with enough precision is obtained, and ending the reliability analysis system.

Description

Technical Field

[0001] The present invention relates to the technical field of mechanical structure reliability analysis, and in particular to a mechanical structure reliability analysis method and system based on an active learning agent model. Background Art

[0002] With the development of the machinery industry and the requirements of energy conservation and emission reduction, machinery is developing in the direction of lightweight, resulting in the full utilization of the mechanical properties of manufacturing materials. Many important mechanical parts, especially equipment in aerospace and other fields, have the mechanical properties of their materials brought to the extreme. However, due to the uneven distribution of material organization of mechanical structures, the randomness of equipment manufacturing and installation errors, and the subjective uncertainty of human operation, the response of mechanical structures during use has great uncertainty, which brings great safety hazards to the use of mechanical equipment. Therefore, at the beginning of the design, it is necessary to conduct reliability analysis of mechanical structures to prevent major safety accidents.

[0003] The function g(x) of a mechanical structure is usually implicit and requires large-scale finite element calculations, so reliability analysis cannot be performed directly. Therefore, many scholars have conducted research on it for many years, and the reliability analysis methods of mechanical structures have developed rapidly, mainly divided into: numerical approximation methods, simulation methods, and proxy model methods. The numerical approximation methods mainly include the first order reliability analysis method (FORM) and the second order reliability analysis method (SORM). Such methods are based on iterative optimization methods and use Taylor expansion to approximate the limit state equation h(x) (g(x) = 0) of reliability analysis, so as to solve the most likely failure point of the mechanical structure and evaluate the reliability of the mechanical structure; such methods need to solve the derivative of the limit state equation of the mechanical structure, but the mechanical structure often uses the finite element method to solve the response during operation, thus limiting the use of numerical approximation methods, and Taylor expansion can only approximate the limit state function locally, reducing the calculation accuracy. The simulation method mainly refers to the Monte Carlo method and the corresponding improved method. This method is based on the law of large numbers. In order to ensure the accuracy and convergence of the calculation results, a large number of sampling and a large number of functional function calculations (large-scale finite element calculations) are required, resulting in very low calculation efficiency or even impossible to complete reliability analysis in actual engineering, especially for modern mechanical structures that need to be calculated using the finite element method and the problem of low failure probability. In response to the above-mentioned problem of extremely low calculation efficiency, many scholars have proposed the proxy model method. Its basic idea is to use a simple function with less calculation amount to replace the limit state equation of the mechanical structure, and then use the Monte Carlo method for reliability analysis. This method can reduce the calculation cost, but at the same time, it can also use numerical simulation methods to ensure the calculation accuracy. Therefore, it has been widely used. Its core is to achieve accurate fitting of the proxy model to the limit state equation in a certain area. However, this method still requires a lot of calculations for each iteration of the Monte Carlo calculation, and fitting the proxy model also requires multiple finite element calculations, resulting in low calculation efficiency and accuracy of reliability analysis of large and complex mechanical structures, or even difficult to achieve. Summary of the invention

[0004] In order to solve the above technical problems, the present invention provides a mechanical structure reliability analysis method based on an active learning agent model, the method comprising:

[0005] Obtaining influencing factors that affect mechanical structure failure, selecting the influencing factors as input variables for reliability analysis, collecting relevant data of the input variables, and obtaining probability distribution characteristics and parameters of the input variables through probability statistical analysis methods;

[0006] Analyze the working conditions and load conditions of the mechanical structure to be analyzed for reliability, determine the failure mode, and determine the functional function and limit state equation of the mechanical structure in combination with the conditions and requirements for safe operation of the structure;

[0007] The probability distribution characteristics and parameters of the input variables are converted using an equal probability conversion method to generate a Monte Carlo reliability analysis sample;

[0008] Generate an initial fitting sample, perform an inverse transformation on the initial fitting sample, calculate the functional value of the sample, obtain an initial response matrix, and obtain an initial proxy model based on the inverse transformation of the initial fitting sample and the initial response matrix;

[0009] Using a priori reliable ring sample reduction method to select candidate samples and perform reliability analysis on the initial fitting samples;

[0010] Use the learning function with origin distance constraint to select test samples from the new fitting samples;

[0011] Calculating the response value of the test sample, updating the fitting sample and the response value variable, and updating the proxy model according to the new fitting sample and the response value variable;

[0012] The reliability of the mechanical structure is analyzed using the updated surrogate model.

[0013] Optionally, the probability distribution characteristics and parameters of the input variables are converted using an equal probability conversion method to generate a Monte Carlo reliability analysis sample, specifically including:

[0014] Based on the probability distribution characteristics and parameters of the input variables, the input variables are transformed into the standard normal space using an equal probability transformation method, and then a Monte Carlo reliability analysis sample in an n-dimensional space is generated according to the number n of the input variables.

[0015] Optionally, the method for generating the initial fitting sample specifically includes:

[0016] In the standard normal space, 4n initial fitting samples are generated using the following formula:

[0017] x inii =[z 1 ,z 2 ,z 3 ...z i ±m...z n ](i=1,2,3...n)

[0018] Among them, x inii is the i-th initial fitting sample, z 1 =0, z 2 =0,z3 =0....z n =0, get the initial sample matrix X ini :

[0019] x ini =[-2E n ; 2E n ; -4E n ; 4E n ]

[0020] Among them, E n is an n-order unit matrix.

[0021] Optionally, obtaining the initial proxy model specifically includes:

[0022] The initial fitting samples are transformed into the function space through inverse transformation, and the functional function value of each sample is calculated respectively to obtain the initial response matrix G ini =[g 1 ,g 2 ,g 3 ……g 4n ], using the initial fitting sample matrix X ini and the initial response matrix G ini Fit the surrogate model to obtain the initial surrogate model h ini (x).

[0023] Optionally, the specific method of selecting candidate samples and performing reliability analysis on the initial fitting samples using the a priori reliable ring sample reduction method includes:

[0024] Compute Monte Carlo reliability analysis sample x MCS Radius:

[0025] r i =||x MCSi || 2 , in order from small to large MCS Rearrange to get sorted sample x RMCS and sequence number η, where x MCSi For x MCS The i-th sample, x RMCS is the sample after sorting the MCS samples;

[0026] According to the sorted sample x RMCS Calculate the function value of the proxy model and record the sequence number η of the first function value that is negative;

[0027] Round down 0.8η to get the integer η ini , for numbers less than η ini The sorted sample x RMCS Discard and use the sequence number greater than ηini The sorted sample x RMCS After reliability analysis, they are selected as candidate samples.

[0028] Optionally, the method of selecting a test sample from the candidate samples using a learning function constrained by the origin distance specifically includes:

[0029] The learning function of the origin distance constraint includes a surface constraint, a distance constraint and a domain constraint;

[0030] The surface constraint requires that the experimental sample is close to the limit state equation, and the surface constraint is implemented using a proxy model:

[0031] S(x N )=h(x N )

[0032] Among them, x N is the new fitting sample to be determined, S(x N ) is the surface constraint function, h(x N ) is the proxy model function, x N is the new fitting sample to be determined;

[0033] The distance constraint requires that the experimental samples maintain a distance. When each new sample is added to the experimental sample, the distance between the fitted samples is maintained by using the minimum distance from the new sample to all existing fitted samples:

[0034]

[0035] Among them, D(x N ) is the distance constraint function, x i is the i-th variable of the existing fitting sample;

[0036] The distance R(x N ) as a domain constraint:

[0037]

[0038] Among them, R(x N ) is the domain constraint function. Based on the three control functions, the origin distance constraint learning function C is defined. OR (x N )for:

[0039]

[0040] Among them, v is the domain constraint coefficient, which is used to adjust the weight of the domain constraint in the learning function.

[0041] The present invention also discloses a mechanical structure reliability analysis system based on an active learning agent model, the system comprising: an image factor processing module, a mechanical structure function determination module, an analysis sample generation module, an initial agent model module, a candidate sample selection module, a test sample selection module, a model update module and a reliability analysis module;

[0042] The image factor processing module is used to obtain the influencing factors that affect the failure of the mechanical structure, select the influencing factors as input variables for reliability analysis, collect relevant data of the input variables, and obtain the probability distribution characteristics and parameters of the input variables through a probability statistical analysis method;

[0043] The mechanical structure function determination module is used to analyze the working conditions and load conditions of the mechanical structure to be subjected to reliability analysis, determine the failure mode, and determine the functional function and limit state equation of the mechanical structure in combination with the conditions and requirements for safe operation of the structure;

[0044] The analysis sample generation module is used to convert the probability distribution characteristics and parameters of the input variables using an equal probability conversion method to generate a Monte Carlo reliability analysis sample;

[0045] The initial proxy model module is used to generate an initial fitting sample, calculate the functional function value of the sample after inverse transformation of the initial fitting sample, obtain an initial response matrix, and obtain an initial proxy model based on the inverse transformation of the initial fitting sample and the initial response matrix;

[0046] The candidate sample selection module is used to select candidate samples and perform reliability analysis on the initial fitting samples using a priori reliable circular ring sample reduction method;

[0047] The test sample selection module is used to select test samples from the new fitting samples using a learning function constrained by the origin distance;

[0048] The model updating module is used to calculate the response value of the test sample, update the fitting sample and the response value variable, and update the proxy model according to the new fitting sample and the response value variable;

[0049] The reliability analysis module is used to analyze the reliability of the mechanical structure using the updated proxy model.

[0050] Optionally, the analysis sample generation module includes a conversion submodule and a sample generation submodule:

[0051] The conversion submodule is used to convert the input variable into a standard normal space using an equal probability conversion method based on the probability distribution characteristics and parameters of the input variable;

[0052] The sample generation submodule is used to generate Monte Carlo reliability analysis samples in n-dimensional space according to the number n of input variables.

[0053] Compared with the prior art, the present invention has the following beneficial effects:

[0054] The present invention uses a method based on a proxy model for reliability analysis. Starting from the basic requirements of the proxy model fitting sample, a learning function with origin distance constraint is established. Aiming at the characteristics of the reliability analysis Monte Carlo sample (MCS sample), a priori reliable ring sample reduction method is proposed. The origin distance constraint learning function and the priori reliable ring sample reduction method are combined to finally realize the reliability analysis of the mechanical structure with high precision and high efficiency. It has the following advantages:

[0055] (1) The construction of the origin distance constraint learning function is based on the position characteristics that the fitting samples should have. It can produce more targeted and effective fitting samples, reduce the number of fitting samples used for accurate fitting of the limit state equation, and thus reduce the number of calculations of the functional function (mainly large-scale finite element calculations for complex mechanical structures), greatly improving the computational efficiency of mechanical structure reliability analysis.

[0056] (2) For large and complex mechanical structures, a large number of fitting samples are required, and the number of iterative calculations increases significantly. In the middle and late stages, the computational cost of each iterative proxy model increases rapidly with the increase in fitting samples, which greatly reduces the computational efficiency. Therefore, the a priori reliable ring sample reduction method is used to reduce the number of calculations of each iterative proxy model during reliability analysis, thereby improving the computational efficiency of reliability analysis.

[0057] (3) The radial basis function has the ability to adapt well to the highly nonlinear limit state function of complex mechanical structures. The present invention uses it as a proxy model, which can fully utilize the effective fitting samples generated by the origin distance constraint learning function, give full play to the advantages of the active learning proxy model, and enable the proposed reliability analysis method to fit the limit state function with high precision.

[0058] (4) The proposed reliability analysis method of the learning function with origin distance constraint + prior reliable ring sample reduction method can improve the calculation efficiency of reliability analysis while ensuring the calculation accuracy of reliability analysis, whether in terms of the number of calculations of the limit state equation or in the calculation of reliability analysis and generation of fitting samples. That is, this method has the characteristics of high precision and high efficiency, which enables it to solve the reliability analysis of large and complex mechanical structures. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] In order to more clearly illustrate the technical solution of the present invention, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0060] Figure 1 It is a diagram of the method steps of the present invention;

[0061] Figure 2 A flowchart of the algorithm proposed for the present invention;

[0062] Figure 3 It is a two-dimensional schematic diagram of the a priori reliable ring sample reduction method;

[0063] Figure 4 A two-dimensional schematic diagram of the learning function with origin distance constraint;

[0064] Figure 5 This is a schematic diagram of the truss structure of Example 2. Specific implementation methods

[0066] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0067] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0068] Embodiment 1

[0069] Mechanical structure reliability analysis method based on active learning agent model, such as Figure 1 As shown, specifically including:

[0070] S1. Obtain the influencing factors that affect the failure of the mechanical structure, select the influencing factors as the input variables of the reliability analysis, collect the relevant data of the input variables, and obtain the probability distribution characteristics and parameters of the input variables through the probability statistical analysis method. Analyze various factors that affect the failure of the mechanical structure, including but not limited to the randomness of the mechanical properties of the manufacturing materials, the non-uniformity of manufacturing errors and installation errors, the uncertainty of the working environment and use conditions, etc., select the important influencing factors as the input variables of the reliability analysis, collect the relevant data of each input variable, and determine the probability distribution characteristics and corresponding parameters of each input variable through the probability statistical analysis method.

[0071] S2 analyzes the working conditions and loading conditions of the mechanical structure to be subjected to reliability analysis, determines its main failure mode, and determines the functional function g(x) and limit state equation h(x) (g(x) = 0) of the structure in combination with the conditions and requirements for safe operation of the structure.

[0072] S3. The probability distribution characteristics and parameters of the input variables are converted using the equal probability conversion method to generate Monte Carlo reliability analysis samples: According to the probability distribution characteristics of each input variable in S1 and its corresponding parameters, all input variables are converted into the standard normal space according to the equal probability conversion method, and then according to the number of input variables n, a Monte Carlo reliability analysis sample (MCS sample) in n-dimensional space is generated.

[0073] S4, generate initial fitting samples, inverse transform the initial fitting samples, calculate the functional value of the samples, obtain the initial response matrix, and obtain the initial surrogate model based on the inverse transformation of the initial fitting samples and the initial response matrix: In the standard normal space, use the formula to generate 4n initial fitting samples

[0074] x inii =[z 1 ,z 2 ,z 3 ...z i ±m...z n ](i=1,2,3...n)

[0075] Among them, x inii is the i-th initial fitting sample, z 1 =0, z 2 =0, z 3 =0……z n =0, m takes the values ​​of 2 and 4 respectively. Finally, the initial sample matrix X is obtained. ini :

[0076] X ini =[-2E n ; 2E n ; -4E n ; 4E n ]

[0077] Among them, China E n is an n-order unit matrix. The initial fitting samples are transformed into the function space through the inverse transformation in step 1, and then the functional function value of each sample is calculated to obtain the initial response matrix G ini =[g 1 ,g 2 ,g 3 ……g 4n ]. Using the initial fitting sample X iniand the initial response matrix G ini Fit the proxy model (augmented radial basis function) to obtain the initial proxy model h ini (x).

[0078] S5 uses the a priori reliable ring sample reduction method to select new fitting samples and perform reliability analysis: Calculate the radius of the MCS sample: r i =||x MCSi || 2 , and x is calculated according to r from small to large MCS Sort and get sorted sample x RMCS (MCS sample) and sequence number η;

[0079] When performing reliability analysis, the sorted samples x are calculated in order RMCS The proxy model function value is η, and the serial number η of the first sample whose function value is negative is recorded. 0.8η is rounded down to get the integer η ini , for numbers less than η ini The sorted sample x RMCS Discard and use the sequence number greater than η ini The sorted sample x RMCS The reliability analysis is performed and the candidate samples are used as the selection of new fitting samples, so that the amount of calculation can be greatly reduced at each iteration of the reliability analysis, and the calculation efficiency of the reliability analysis can be improved. The two-dimensional schematic diagram of this algorithm is shown in Figure 2 shown.

[0080] S6 uses the learning function C proposed in this patent to constrain the origin distance OR (x N ), select appropriate new samples from candidate samples:

[0081] Learning function C with origin distance constraint OR (x N ): The characteristics of effective fitting samples are studied and summarized into three constraints, namely, surface constraint, distance constraint and domain constraint; for the three constraints, surface control function, distance control function and domain control function are established respectively, and the three functions are coordinated to establish the original point distance constrained learning function (Collaboration-original point constrained learning function, COR):

[0082] The surface constraint requires that the test sample is as close to the limit state equation as possible. In each iteration, assuming that the existing proxy model can fit the limit state equation well, the sample on the proxy model can be approximately considered to be on the limit state equation. Therefore, we use the existing proxy model to implement the surface constraint, that is:

[0083] S(xN )=h(x N )

[0084] Among them, S(x N ) is called the surface control function, where x N is the new fitting sample to be determined. According to the definition of the limit state equation, if we want to realize the surface constraint, we need to find x N Make|S(x N )| has a value of zero.

[0085] The distance constraint requires that all test samples should maintain a certain distance to avoid unnecessary repeated sampling and excessive condition number in the local area, which will affect the calculation accuracy of the proxy model parameters. In order to achieve the distance constraint, each new sample is required to maintain a certain distance from all existing test samples when it is added to the test sample. Therefore, the minimum distance from the new sample to all existing fitting samples is used to maintain the distance between the fitting samples:

[0086]

[0087] Among them, D(x N ) is called the distance control function, where x i is the i-th variable of a certain existing fitting sample, by finding x N Let D(x N ) can be maximized to achieve the distance constraint.

[0088] In the standard normal space, the MCS samples are around the origin, so we take the distance R(x N ) as a domain constraint, so that the test samples are generated in the high probability density area. N )for:

[0089]

[0090] Among them, R(x N ) is called the domain control function, which is obtained by finding x N Let R(x N ) can be minimized to achieve the domain constraint.

[0091] The above three control functions constrain and coordinate with each other to jointly complete the constraints on the fitting samples. Here, based on the implementation method of the three control functions, the above three control functions are organically coordinated, and the origin distance constraint learning function C OR (x N ) is defined as:

[0092]

[0093] Where v is the domain constraint coefficient, which is used to adjust the weight of the domain constraint in the learning function.

[0094] Using the learning function, suitable new samples can be selected from the candidate samples defined in S5. The two-dimensional schematic diagram of this learning function is as follows Figure 3 shown.

[0095] S7. Calculate the response value of the test sample, update the fitting sample and the response value variable, and update the proxy model according to the new fitting sample and the response value variable.

[0096] S8. Use the updated proxy model to analyze the reliability of the mechanical structure.

[0097] Embodiment 2

[0098] This embodiment performs reliability analysis on an engineering example, and its specific structure is as follows: Figure 5 As shown, it is a truss structure composed of 15 members (A 1 -A 15 ), which is subjected to three downward forces P 1 , P 2 and P 3 The role of P 2 If the displacement exceeds the specified range, the entire structure will fail.

[0099] From the above description, we can see that the limit state equation is:

[0100] h(x)=y allow -D(x)

[0101] Where y allow is the allowable value of displacement, D(x) is P 2 The actual displacement produced.

[0102] The input variables are the cross-sectional areas of the 15 rods and the three forces P they bear. 1 , P 2 and P 3 , its distribution characteristics and parameters are shown in the following table.

[0103] The distribution characteristics and parameters of random variables are shown in Table 1:

[0104] Table 1

[0105]

[0106] The calculation process of this case is:

[0107] 1. Based on the existing information, transform n = 18 random input variables into the standard normal space, and generate the corresponding Monte Carlo sample MCS sample x in the standard normal space MCS (There are 1 million samples in total).

[0108] 2. Calculate the radius of the MCS sample: r i =||x MCSi || 2 , and x is calculated according to r from small to large MCS Sort and get sorted sample x RMCS (MCS sample) and sequence number η.

[0109] 3. Generate initial fitting sample X ini : In the standard normal space, according to the double cross center method, 72 (4n) initial fitting samples are generated:

[0110] x inii =[z 1 ,z 2 ,z 3 ...z i ±m...z n ](i=1,2,3...n)

[0111] where x inii is the i-th initial fitting sample, z 1 =0, z 2 =0, z 3 =0……z n =0, m takes the values ​​of 2 and 4 respectively. Finally, the initial sample matrix is ​​obtained:

[0112] X ini =[-2E n ; 2E n ; -4E n ; 4E n ]

[0113] Where E n is an n-order unit matrix.

[0114] 4. Transform the initial fitting sample into the function space through the inverse transformation in step 1, and then calculate the functional value of each sample to obtain the initial response matrix G ini =[g 1 ,g 2 ,g 3 ……g 4n ].

[0115] 5. Using the initial fitting sample X ini and the initial response matrix G iniFit the proxy model (augmented radial basis function) to obtain the initial proxy model h ini (x).

[0116] 6. Use the Monte Carlo method for reliability analysis: sort the sample x RMCS Transform into function space and calculate the proxy model h(x) of these samples (initial proxy model h ini Count the number of sample points nf where the initial proxy model function value is negative, and divide nf by the total number of samples (1 million) to get the failure probability p f , and record the first sorted sample x with a negative proxy model function value RMCSη Serial number η.

[0117] 7. After the initial fitting is completed, the iterative process of increasing the fitting samples and the fitting accuracy begins. For the kth iteration:

[0118] 7.1 Establishing a learning function and using the existing proxy model h k-1 (x) and existing samples X k-1 , establish the learning function C of the origin distance constraint OR (x N ):

[0119]

[0120] Where x N is the new fitting sample to be determined.

[0121] 7.2 Determine whether the number of iterations satisfies k>4n.

[0122] 8. Iteratively increase the fitting samples and fitting accuracy stage:

[0123] 8.1 does not meet the condition of step 7.2, that is, k≤4n, use the sorted sample x RMCS As candidate samples, use the learning function C constrained by the learning function origin distance OR (x N ) From the candidate sample x RMCS Select new fitting sample x from N . Then add it to the fitted sample X k-1 (The first iteration is the initial fitting sample x ini ), update the fitting sample to obtain the new fitting sample X k :X k =[-2E n ; 2E n ; -4E n ; 4E n ;x 1 ;x 2 ;......;xk-1 ;x N ]

[0124] Calculate the function value of the new fitting sample to obtain g(x N ), update the matrix G k-1 (The first iteration is matrix G) to get the new matrix G k =[G k-1 g(x N )].

[0125] Using the initial fitting sample X k and the matrix G k Fit the surrogate model (augmented radial basis function) to obtain the surrogate model h k (x). Based on the agent model h k (x) and sorted sample x RMCS , use the method in step 6 to perform reliability analysis and record the first sorted sample x with a negative function value RMCSη Serial number η.

[0126] Determine whether the algorithm meets the iterative stopping conditions. If so, stop the algorithm, obtain the final failure probability, and complete the reliability analysis. Otherwise, proceed to step 7.

[0127] 8.2 satisfies the condition of step 7.2, that is, k>4n, and 0.8η is rounded down to get the integer η ini , using the sequence number η ini The sorted sample x after RMCSηini As candidate samples, use the learning function C constrained by the learning function origin distance OR (x N ) From the candidate sample x RMCSηini Select new fitting sample x from N , and then add it to the fitted sample X k-1 (The first iteration is the initial fitting sample x ini ), update the fitting sample to obtain the new fitting sample X k :X k =[-2E n ; 2E n ; -4E n ; 4E n ;x 1 ;x 2 ;......;x k-1 ;x k ]

[0128] Calculate the function value of the new fitting sample to obtain g(x N ), update the matrix G k-1 (The first iteration is matrix G) to get the new matrix G k =[Gk-1 g(x N )].

[0129] Using the initial fitting sample X k and the matrix G k Fit the surrogate model (augmented radial basis function) to obtain the surrogate model h k (x). Based on the agent model h k (x) and sorted sample x RMCS , use the method in step 6 to perform reliability analysis and record the first sorted sample x with a negative function value RMCSη Serial number η.

[0130] Determine whether the algorithm meets the iteration stop condition, if it does, stop the algorithm, get the final failure probability and complete the reliability analysis, otherwise continue to step 7.

[0131] 9. In order to further illustrate the advantages of the present invention, several similar typical reliability analysis methods are listed here for comparison, and the calculation results are shown in the table. It can be seen from Table 2 that the a priori reliable ring sample reduction method has no effect on the reliability calculation results and calculation efficiency, but the a priori reliable ring sample reduction method can reduce 41.167% of the calculation amount in the middle and late iterations, thereby improving the calculation efficiency of the reliability analysis; it can be seen from the calculation results that within the limited maximum number of iterations (due to the limitation of computing power, the maximum number of iterations is set to 200 here), the method proposed by the present invention can use fewer fitting samples to obtain accurate reliability calculation results, and other methods have obtained calculation results with large errors. This is because other methods cannot obtain algorithm convergence within the limited maximum number of iterations, and the final computer process of all reliability analysis methods proves that the reliability analysis method proposed by the present invention has the characteristics of high precision and high efficiency.

[0132] Table 2

[0133] method <![CDATA[Failure probability P f > <![CDATA[N call ]]> err(％) λ(%) MCS <![CDATA[3.89×10 -4 ]]> <![CDATA[1×10 6 ]]> — — ARBF+COR <![CDATA[3.89×10 -4 ]]> 148 0 41.167 AK+EFF <![CDATA[5.13×10 -4 ]]> 272 31.877 41.167 AK+U <![CDATA[2.63×10 -4 ]]> 272 32.391 41.167 AK+H <![CDATA[4.14×10 -4 ]]> 272 64.267 41.167 AK+REIF <![CDATA[5.04×10 -4 ]]> 272 29.563 41.167 AK+REIF2 <![CDATA[1.64×10 -4 ]]> 272 57.841 41.167

[0134] Embodiment 3

[0135] A mechanical structure reliability analysis system based on an active learning agent model, the system comprising: an image factor processing module, a mechanical structure function determination module, an analysis sample generation module, an initial agent model module, a candidate sample selection module, a test sample selection module, a model update module and a reliability analysis module;

[0136] The image factor processing module is used to obtain the influencing factors that affect the failure of the mechanical structure, select the influencing factors as input variables for reliability analysis, collect relevant data of the input variables, and obtain the probability distribution characteristics and parameters of the input variables through probability statistical analysis methods.

[0137] The mechanical structure function determination module is used to analyze the working conditions and load conditions of the mechanical structure to be subjected to reliability analysis, determine the failure mode, and determine the functional function g(x) and the limit state equation h(x) (g(x)=0) of the mechanical structure in combination with the conditions and requirements for safe operation of the structure.

[0138] According to the stress, constraint, geometric size and safety requirements of the mechanical structure for which reliability analysis is required, the key input variables, failure locations, failure modes and safety factors of the mechanical structure are studied, the probability distribution characteristics and parameters of the key input variables are determined, and the functional function g(x) and the limit state equation h(x) (g(x)=0) of the research object are established. 1 ,x 2 ,x 3 ……x n ) are n key random input variables that affect the failure of the mechanical structure.

[0139] The analysis sample generation module is used to transform the probability distribution characteristics and parameters of the input variables using an equal probability transformation method to generate Monte Carlo reliability analysis samples; the analysis sample generation module includes a transformation submodule and a sample generation submodule:

[0140] The conversion submodule is used to convert the input variables into a standard normal space using an equal probability conversion method based on the probability distribution characteristics and parameters of the input variables;

[0141] The sample generation submodule is used to generate Monte Carlo reliability analysis samples in n-dimensional space according to the number of input variables n.

[0142] According to each input variable (x 1 ,x 2 ,x 3 ……x n )'s probability distribution characteristics and related parameters are converted into the corresponding normal distribution using the equal probability conversion method, and then converted into the standard normal space, and the Monte Carlo method is used to generate the reliability analysis sample MCS sample x MCS . Calculate the radius of the MCS sample: r i =||x MCSi || 2 , and then calculate x according to r from small to large MCS Sort and get sorted sample x RMCS and sequence number η.

[0143] The initial proxy model module is used to generate an initial fitting sample using a double cross center method, calculate the functional function value of the sample after inverse transformation of the initial fitting sample, obtain an initial response matrix, and obtain an initial proxy model based on the inverse transformation of the initial fitting sample and the initial response matrix;

[0144] The method of generating the initial fitting sample specifically includes:

[0145] In the standard normal space, 4n initial fitting samples are generated using the following formula:

[0146] x inii =[z 1 ,z 2 ,z 3 ...z i ±m...z n ](i=1,2,3...n)

[0147] Among them, x inii is the i-th initial fitting sample, z 1 =0, z 2 =0,z 3 =0....z n =0, m takes the values ​​of 2 and 4 respectively, and the initial sample matrix X is obtained ini :

[0148] x ini =[-2E n ; 2E n ; -4E n ; 4E n ]

[0149] Among them, E n is an n-order unit matrix.

[0150] The initial proxy model is obtained by:

[0151] The initial fitting samples are transformed into the function space through inverse transformation, and the functional function value of each sample is calculated respectively to obtain the initial response matrix G ini =[g 1 ,g 2 ,g 3 ……g 4n ], using the initial fitting sample matrix X ini and the initial response matrix G ini Fit the proxy model (augmented radial basis function) to obtain the initial proxy model h ini (x).

[0152] The candidate sample selection module is used to select candidate samples and conduct reliability analysis on the initial fitting samples using a priori reliable circular ring sample reduction method;

[0153] Compute the radius of a Monte Carlo reliability analysis sample:

[0154] r i =||x MCSi || 2 , in order from small to large MCS Rearrange to get sorted sample x RMCS and sequence number η; when performing reliability analysis, the sorted samples x RMCS Calculate the function value of the proxy model and record the first sequence number η whose function value is negative; round down 0.8η to get the integer η ini , for numbers less than η ini The sorted sample x RMCS Discard and use the sequence number greater than η ini The sorted sample x RMCS After reliability analysis, the samples are used as candidate samples. Therefore, the amount of calculation can be greatly reduced in each iteration of reliability analysis, and the calculation efficiency of reliability analysis can be improved. The two-dimensional schematic diagram of this algorithm is shown in Figure 2 shown.

[0155] The test sample selection module is used to select test samples from the new fitting samples using the learning function constrained by the origin distance. The learning function C OR (x N ): The characteristics of effective fitting samples are studied and summarized into three constraints, namely, face constraint, distance constraint and domain constraint; for the three constraints, face control function, distance control function and domain control function are established respectively, and the three functions are coordinated to establish the origin distance constrained learning function (Collaboration-original point constrained learning function, COR).

[0156] The surface constraint requires the test sample to be as close to the limit state equation as possible. In each iteration, assuming that the existing proxy model can fit the limit state equation well, the sample on the proxy model can be approximately considered to be on the limit state equation. Use the existing proxy model to implement the surface constraint, that is, the surface control function:

[0157] S(x N )=h(x N )

[0158] Among them, x N is the new fitting sample to be determined; from the definition of the limit state equation, if we want to realize the surface constraint, we need to find x N Make|S(x N)| is zero. The distance constraint requires that all test samples maintain a certain distance to avoid unnecessary repeated sampling and excessive condition number in the local area, which affects the calculation accuracy of the proxy model parameters. In order to realize the distance constraint, each new sample is required to maintain a certain distance from all existing test samples when it is added to the test sample. Therefore, the minimum distance from the new sample to all existing fitting samples is used to maintain the distance between the fitting samples. The distance control function is:

[0159]

[0160] Among them, x i is the i-th variable of the existing fitting sample; by finding x N Let D(x N ) can be maximized to achieve the distance constraint; in the standard normal space, the MCS samples are around the origin, so the distance R(x N ) as a domain constraint, so that the test samples are generated in the high probability density area, that is, the domain control function:

[0161]

[0162] The above three control functions constrain and coordinate with each other to jointly complete the constraints on the fitting samples. Here, based on the implementation methods of the three control functions, the above three control functions are organically coordinated to define the origin distance constraint learning function C OR (x N )for:

[0163]

[0164] Among them, v is the domain constraint coefficient, which is used to adjust the weight of the domain constraint in the learning function. Using the learning function, suitable new samples can be selected from the defined candidate samples. The two-dimensional schematic diagram of this learning function is as follows Figure 4 shown.

[0165] The model updating module is used to calculate the response value of the test sample, update the fitting sample and the response value variable, and update the proxy model according to the new fitting sample and the response value variable;

[0166] The reliability analysis module is used to analyze the reliability of the mechanical structure using the updated proxy model. It determines whether the algorithm meets the iteration stop condition. If it does, the calculation is stopped. If it does not, the learning function with the origin distance constraint is added and iterated again to obtain the reliability analysis result of the mechanical structure.

[0167] After the initial fitting is completed, the iterative increase of fitting samples and fitting accuracy begins. For the kth iteration:

[0168] Establish a learning function and use the existing agent model h k-1 (x) and existing samples X k-1 , establish the learning function C of the origin distance constraint OR (x N ):

[0169]

[0170] Where x N is the new fitting sample to be determined, and the coefficient v is 0.2.

[0171] Determine whether the number of iterations satisfies k>4n.

[0172] Iteratively increase the fitting samples and fitting accuracy stage:

[0173] When k≤4n, use the sorted sample x RMCS As candidate samples, use the learning function C constrained by the learning function origin distance OR (x N ) From the candidate sample x RMCS Select new fitting sample x from N . Then add it to the fitted sample X k-1 (The first iteration is the initial fitting sample x ini ), update the fitting sample to obtain the new fitting sample X k :

[0174] X k =[-2E n ; 2E n ; -4E n ; 4E n ;x 1 ;x 2 ;......;x k-1 ;x N ]

[0175] Calculate the function value of the new fitting sample to obtain g(x N ), update the matrix G k-1 (The first iteration is matrix G) to get the new matrix G k =[G k-1 g(x N )].

[0176] Using the initial fitting sample X k and the matrix G k Fit the surrogate model (augmented radial basis function) to obtain the surrogate model h k (x). Based on the agent model h k (x) and sorted sample x RMCS Perform reliability analysis and record the first sorted sample x with a negative function valueRMCSη Serial number η.

[0177] Determine whether the algorithm meets the iterative stopping conditions. If so, stop the algorithm, obtain the final failure probability, and complete the reliability analysis. Otherwise, proceed to step 8.

[0178] To satisfy the condition k>4n, 0.8η is rounded down to get the integer η ini , using the sequence number η ini The sorted sample x after RMCSηini As candidate samples, use the learning function C constrained by the learning function origin distance OR (x N ) From the candidate sample x RMCSηini Select new fitting sample x from N , and then add it to the fitted sample X k-1 (The first iteration is the initial fitting sample x ini ), update the fitting sample to obtain the new fitting sample X k :

[0179] X k =[-2E n ; 2E n ; -4E n ; 4E n ;x 1 ;x 2 ;......;x k-1 ;x k ]

[0180] Calculate the function value of the new fitting sample to obtain g(x N ), update the matrix G k-1 (The first iteration is to get the new matrix G for matrix G k =[G k-1 g(x N )].

[0181] Using the initial fitting sample X k and the matrix G k Fit the surrogate model (augmented radial basis function) to obtain the surrogate model h k (x). Based on the agent model h k (x) and sorted sample x RMCS Perform reliability analysis and record the first sorted sample x with a negative function value RMCSη Serial number η.

[0182] Determine whether the algorithm meets the iterative stopping conditions, if so, stop the algorithm, get the final failure probability, and complete the reliability analysis, otherwise continue to the previous step.

[0183] The iteration stopping condition of this algorithm is:

[0184]

[0185] Where m is max(n,5), and n is the number of random input variables. E , then the stopping condition is met, otherwise it is not met. In order to ensure a certain accuracy, let P E =10 -4 , p fi is the failure probability of the i-th iteration.

[0186] The above shows and describes the main features and advantages of the present invention. It is obvious to those skilled in the art that the present invention is not limited to the details of the above exemplary embodiments, and that the present invention can be implemented in other specific forms without departing from the spirit or essential features of the present invention. Therefore, no matter from which point of view, the embodiments should be regarded as exemplary and non-restrictive. The scope of the present invention is defined by the appended claims rather than the above description, and it is intended that all changes that fall within the meaning and scope of the equivalent elements of the claims are included in the present invention.

[0187] The embodiments described above are only descriptions of the preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Without departing from the design spirit of the present invention, various modifications and improvements made to the technical solutions of the present invention by ordinary technicians in this field should all fall within the protection scope determined by the claims of the present invention.

Claims

1. A mechanical structure reliability analysis method based on an active learning agent model, characterized in that: The method comprises: Obtaining influencing factors that affect mechanical structure failure, selecting the influencing factors as input variables for reliability analysis, collecting relevant data of the input variables, and obtaining probability distribution characteristics and parameters of the input variables through probability statistical analysis methods; Analyze the working conditions and load conditions of the mechanical structure to be analyzed for reliability, determine the failure mode, and determine the functional function and limit state equation of the mechanical structure in combination with the conditions and requirements for safe operation of the structure; The probability distribution characteristics and parameters of the input variables are converted using an equal probability conversion method to generate a Monte Carlo reliability analysis sample; Generate an initial fitting sample, perform an inverse transformation on the initial fitting sample, calculate the functional value of the sample, obtain an initial response matrix, and obtain an initial proxy model based on the inverse transformation of the initial fitting sample and the initial response matrix; Using a priori reliable ring sample reduction method to select candidate samples and perform reliability analysis on the initial fitting samples; Use the learning function with origin distance constraint to select test samples from the new fitting samples; Calculating the response value of the test sample, updating the fitting sample and the response value variable, and updating the proxy model according to the new fitting sample and the response value variable; The reliability of the mechanical structure is analyzed using the updated surrogate model.

2. The mechanical structure reliability analysis method based on active learning agent model according to claim 1 is characterized in that: The probability distribution characteristics and parameters of the input variables are converted using an equal probability conversion method to generate a Monte Carlo reliability analysis sample, specifically including: Based on the probability distribution characteristics and parameters of the input variables, the input variables are transformed into the standard normal space using an equal probability transformation method, and then a Monte Carlo reliability analysis sample in an n-dimensional space is generated according to the number n of the input variables.

3. The mechanical structure reliability analysis method based on active learning agent model according to claim 1 is characterized in that: The method of generating the initial fitting sample specifically includes: In the standard normal space, 4n initial fitting samples are generated using the following formula: x inii =[z1,z2,z3...z i ±m...z n ](i=1,2,3...n) Among them, x inii is the i-th initial fitting sample, z1=0, z2=0, z3=0....z n =0, get the initial sample matrix X ini : x ini \[-2E n ;2E n ;-4E n ;4E n ] Among them, E n is an n-order unit matrix.

4. The mechanical structure reliability analysis method based on active learning agent model according to claim 1 is characterized in that: The initial proxy model is obtained by: The initial fitting samples are transformed into the function space through inverse transformation, and the functional function value of each sample is calculated respectively to obtain the initial response matrix G ini =[g1,g2,g3……g 4n ], using the initial fitting sample matrix X ini and the initial response matrix G ini Fit the surrogate model to obtain the initial surrogate model h ini (x).

5. The mechanical structure reliability analysis method based on active learning agent model according to claim 1 is characterized in that: The specific method of selecting candidate samples and performing reliability analysis on the initial fitting samples using the a priori reliable ring sample reduction method includes: Compute Monte Carlo reliability analysis sample x MCS Radius: r i =||x MCSi ||2, in order from small to large MCS Rearrange to get sorted sample x RMCS and sequence number η, where x MCSi For x MCS The i-th sample, x RMCS is the sample after sorting the MCS samples; According to the sorted sample x RMCS Calculate the function value of the proxy model and record the sequence number η of the first function value that is negative; Round down 0.8η to get the integer η ini , for numbers less than η ini The sorted sample x RMCS Discard and use sequence numbers greater than η ini The sorted sample x RMCS After reliability analysis, they are selected as candidate samples.

6. The mechanical structure reliability analysis method based on active learning agent model according to claim 1 is characterized in that: The method of selecting a test sample from the candidate samples using a learning function constrained by the origin distance specifically includes: The learning function of the origin distance constraint includes a surface constraint, a distance constraint and a domain constraint; The surface constraint requires that the experimental sample is close to the limit state equation, and the surface constraint is implemented using a proxy model: S(x N )=h(x N ) Among them, x N is the new fitting sample to be determined, S(x N ) is the surface constraint function, h(x N ) is the proxy model function, x N is the new fitting sample to be determined; The distance constraint requires that the experimental samples maintain a distance. When each new sample is added to the experimental sample, the distance between the fitted samples is maintained by using the minimum distance from the new sample to all existing fitted samples: Among them, D(x N ) is the distance constraint function, x i is the i-th variable of the existing fitting sample; The distance R(x N ) as a domain constraint: Among them, R(x N ) is the domain constraint function. Based on the three control functions, the origin distance constraint learning function C is defined. OR (x N )for: Among them, v is the domain constraint coefficient, which is used to adjust the weight of the domain constraint in the learning function.

7. A mechanical structure reliability analysis system based on an active learning agent model, the system being used to implement the mechanical structure reliability analysis method according to any one of claims 1 to 6, characterized in that: The system includes: an image factor processing module, a mechanical structure function determination module, an analysis sample generation module, an initial proxy model module, a candidate sample selection module, a test sample selection module, a model update module and a reliability analysis module; The image factor processing module is used to obtain the influencing factors that affect the failure of the mechanical structure, select the influencing factors as input variables for reliability analysis, collect relevant data of the input variables, and obtain the probability distribution characteristics and parameters of the input variables through a probability statistical analysis method; The mechanical structure function determination module is used to analyze the working conditions and load conditions of the mechanical structure to be subjected to reliability analysis, determine the failure mode, and determine the functional function and limit state equation of the mechanical structure in combination with the conditions and requirements for safe operation of the structure; The analysis sample generation module is used to convert the probability distribution characteristics and parameters of the input variables using an equal probability conversion method to generate a Monte Carlo reliability analysis sample; The initial proxy model module is used to generate an initial fitting sample, calculate the functional function value of the sample after inverse transformation of the initial fitting sample, obtain an initial response matrix, and obtain an initial proxy model based on the inverse transformation of the initial fitting sample and the initial response matrix; The candidate sample selection module is used to select candidate samples and perform reliability analysis on the initial fitting samples using a priori reliable circular ring sample reduction method; The test sample selection module is used to select test samples from the new fitting samples using a learning function constrained by the origin distance; The model updating module is used to calculate the response value of the test sample, update the fitting sample and the response value variable, and update the proxy model according to the new fitting sample and the response value variable; The reliability analysis module is used to analyze the reliability of the mechanical structure using the updated proxy model.

8. The mechanical structure reliability analysis system based on active learning agent model according to claim 7 is characterized in that: The analysis sample generation module includes a conversion submodule and a sample generation submodule: The conversion submodule is used to convert the input variable into a standard normal space using an equal probability conversion method based on the probability distribution characteristics and parameters of the input variable; The sample generation submodule is used to generate Monte Carlo reliability analysis samples in n-dimensional space according to the number n of input variables.

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