Reliability analysis method for system functional materials tube of double-layer rvm combined with metamodel

Abstract

The application discloses a kind of double-layer RVM system function material pipe reliability analysis methods combined with meta-model, and the sample point of gradually approaching importance sampling function is obtained according to iterative updating strategy by the thought of constructing adaptive RVM meta-important sampling model, and the initial RVM model and corresponding importance sampling sample point are obtained after iterative convergence, and the initial adaptive RVM model can effectively identify multiple failure domains and multiple maximum probability points, and generate the candidate sample points required by the second layer adaptive RVM based on MCS.The method of the application can effectively improve the calculation efficiency, and has important reference value and guiding significance for the system reliability engineering problem of multiple failure domains and multiple maximum probability points.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of reliability analysis, and particularly relates to a functional material pipe reliability analysis method. BACKGROUND

[0002] In aviation, aerospace, navigation, petroleum and civil engineering, the existence of uncertain factors seriously affects the safety and reliability of equipment and structures, leading to serious accidents. Therefore, the theory of structural reliability analysis has been systematically studied and applied to the engineering field to improve safety production. The traditional reliability analysis theory does not consider multiple failure modes or multiple maximum probability points, so these calculation methods have the defects of inaccurate calculation results or low calculation efficiency. In actual engineering applications, higher accuracy helps to improve safety production, and higher calculation efficiency helps to improve production efficiency, so it is urgent for the engineering field to propose a reliability analysis method with higher calculation accuracy and higher calculation efficiency. More traditional reliability methods such as first-order second-moment method, importance sampling method, truncated importance sampling method, directional sampling method and reliability analysis methods combined with proxy models have been fully developed. However, due to the complexity of system reliability, system reliability analysis requires high computational cost, and the failure probability cannot be converged to the true value, which greatly limits the safety production and production efficiency in the engineering field.

[0003] Reliability analysis can effectively identify the influence of input variable uncertainty on structural failure and destruction, and can effectively guide and optimize. In the reliability of functional material pipes, system reliability analysis is a difficult problem. The structural reliability analysis of single failure mode can only be applied to some explicit examples or relatively simple implicit engineering examples, and cannot consider whether there are multiple failure modes or multiple maximum probability points in a black box. For the reliability analysis calculation of multiple failure modes, AK-MCS has been applied to a certain extent, but the problem is that the above method still has the problem of excessive calculation amount. SUMMARY

[0004] In order to overcome the prior art, the present application provides a double-layer relevant vector machine (RVM) system function material pipe reliability analysis method combined with a meta-model, an adaptive RVM importance sampling model is constructed according to the idea of importance sampling, and sample points gradually approaching the importance sampling function are obtained according to an iterative updating strategy, initial RVM models and corresponding importance sampling sample points are obtained after iteration convergence, the initial adaptive RVM model can effectively identify multiple failure domains and multiple maximum probability points, and candidate sample points required by the second layer adaptive RVM based on MCS are generated. The method can effectively improve the calculation efficiency, and has important reference value and guiding significance for system reliability engineering problems of multiple failure domains and multiple maximum probability points.

[0005] The technical solution adopted by the present application to solve its technical problems comprises the following steps:

[0006] Step 1: constructing an initial model;

[0007] According to the distribution density function f X (x) of the input variable of the axial functionally graded material pipe, initial sample points are extracted, and function function values are calculated to form a training set T;

[0008] Step 2: constructing an initial RVM model of the limit state function g(X) from T

[0009] Step 3: extracting importance sampling samples;

[0010] According to the formula:

[0011]

[0012] The importance sampling density function h * (x) of the initial RVM model is obtained, and current importance sampling samples are extracted through Markov chain fε π(x) represents a probability classification function, and p fε represents an extended failure probability;

[0013] Step 4: updating the sample training set;

[0014] K-means clustering analysis is performed on the importance sampling samples , K centroids are obtained, and the K centroids and their corresponding function function values are added to the training sample set T, and the RVM model is updated from T

[0015] Step 5: judging convergence;

[0016] A correction factor α is calculated by cross-validation methodcorr Leave-one-out estimate

[0017]

[0018] Where m is the RVM model built during the iteration process. The size of the training set T, i.e., the number of training points in the training set and their corresponding function values. This represents the i-th training point in the training set T. This represents the function value corresponding to the i-th training point; Obtained from the true function values ​​of the training points. It represents the probability classification function established by the RVM model constructed after removing the i-th training sample in the training set; This represents the probability classification function established by the RVM model after removing the i-th training sample from the training set;

[0019] like If the number of training samples m is greater than the specified minimum value m0, then the constructed adaptive RVM meta-importance sampling model is determined to be converged, and proceed to step 6; otherwise, return to step 3.

[0020] Step 6: Calculate the extended failure probability P fε ;

[0021] From the initial RVM model and corresponding important sampling samples Based on the probability density function f of the input variables X (x) generates N ε Sample And estimate the extended failure probability. and the coefficient of variation of its corresponding estimate

[0022] Step 7: Based on the initial RVM model In important sampling pool The RVM model is reconstructed and the correction factor estimate is calculated.

[0023] Will As a candidate sample pool, the U learning function selects and updates sample points from the candidate sample pool and adds them to the training sample set, until the second-layer RVM proxy model converges.

[0024] Step 8: Based on Calculate the correction factor and its corresponding coefficient of variation;

[0025] Modified factor estimate Coefficient of variation Wherein

[0026] Step 9: calculate the failure probability estimate And its coefficient of variation

[0027] The beneficial effects of the present application are as follows:

[0028] The present application aims at the problem of high cost and low efficiency of system reliability failure probability calculation of multiple failure domains and multiple maximum probability points, and proposes a double-layer proxy model combining an adaptive RVM meta-important sampling proxy model and an adaptive RVM model based on MCS. The first-layer adaptive RVM meta-important sampling proxy model generates the required candidate sample points by identifying multiple failure domains or multiple maximum probability points, greatly reduces the calculation time and improves the calculation efficiency. The second-layer adaptive RVM model based on MCS actively learns on the basis of the candidate sample points generated in the first step, accurately identifies the sample points with the largest information quantity near the limit state function according to the learning equation, which improves the accuracy of the reliability failure probability calculation result, reduces the number of calculations, saves the calculation cost and improves the ability to calculate system reliability. BRIEF DESCRIPTION OF DRAWINGS

[0029] Figure 1 The overall technical framework of the present application.

[0030] Figure 2 The present application embodiment simply supports the axial function gradient material pipeline schematic diagram. DETAILED DESCRIPTION

[0031] The present application will be further described below in combination with the drawings and examples.

[0032] In order to improve the low calculation efficiency and poor calculation accuracy of the existing system reliability calculation of multiple failure modes or multiple maximum probability points, the present application combines a modified adaptive RVM meta-model important sampling with a single-layer adaptive RVM model based on MCS, and proposes a new DLRVM method, which further improves the calculation accuracy and calculation efficiency on the single-layer proxy model.

[0033] A double-layer RVM system functional material pipe reliability analysis method combining a meta-model, comprising the following steps:

[0034] Step 1: build an initial model;

[0035] According to the distribution density function f of the axial functional gradient material pipeline input variable X (x) extracts initial sample points and calculates function function values to form a training set T;

[0036] Step 2: Constructing the initial RVM model of g(X) from T

[0037] Step 3: Extracting the importance sampling samples;

[0038] From the formula:

[0039]

[0040] The importance sampling density function of the initial RVM model is obtained , and the current importance sampling samples are extracted by Markov chain

[0041] Step 4: Updating the sample training set;

[0042] The K-means clustering analysis is performed on the importance sampling samples , K centroids are obtained, and the K centroids and their corresponding function function values are added to the training sample set T, and the RVM model is updated from T

[0043] Step 5: Determine convergence;

[0044] The correction factor a is calculated by the cross-validation method corr The leave-one-out estimate value of a is

[0045]

[0046] Where m is the size of the training set T used to construct the RVM model in the iteration process, that is, the training set T contains m training points and their corresponding function function values is obtained from the true function function value of the training point, represents the probability classification function established by the RVM model constructed by removing the i-th training sample in the training set;

[0047] If and the number of training samples m is greater than the specified minimum value m0, it is determined that the adaptive RVM meta-importance sampling model constructed is convergent, and step 6 is entered; otherwise, return to step 3;

[0048] Step 6: Calculate the extended failure probability P fε

[0049] The initial RVM model and the corresponding importance sampling samples According to the distribution density function f X (x) of the input variable, N​ε Sample And estimate the extended failure probability. and the coefficient of variation of its corresponding estimate

[0050] Step 7: Based on the initial RVM model In important sampling pool Update and reconstruct the RVM model, and calculate the correction factor.

[0051] Will As a candidate sample pool, the U learning function selects and updates sample points from the candidate sample pool and adds them to the training sample set, until the second-layer RVM proxy model converges.

[0052] Step 8: Based on Calculate the correction factor and its corresponding coefficient of variation;

[0053] The estimated value of the correction factor coefficient of variation in

[0054] Step 9: Calculate the failure probability estimate and its coefficient of variation Specific implementation examples:

[0056] The overall technical framework of this invention is as follows: Figure 1 As shown.

[0057] An adaptive RVM meta-importance sampling model is constructed based on the idea of ​​meta-importance sampling. Sample points that progressively approximate the importance sampling function are obtained according to an iterative update strategy. The first step of the RVM model is obtained after iterative convergence. and corresponding important sampling points Depend on and Monte Carlo samples This allows us to calculate an estimate of the extended failure probability;

[0058] Using the idea of ​​active learning, the RVM model is continuously updated to construct a model that can handle important sampled samples. Indicator function value Make an accurate RVM model In order to efficiently and accurately solve for the estimated value of the correction factor

[0059] The implementation process is illustrated below through specific examples.

[0060] Simply supported axially graded material pipes with a constant Poisson's ratio, Young's modulus, and material density varying along the axial direction, such as... Figure 2 As shown in Table 1, this is an implicit resonance reliability analysis problem with 11 input variables. The information for the random variables is shown in Table 1. In this embodiment, the first two resonance failures of the axially functionally graded material (FJT) pipe are considered; therefore, this is a system reliability problem, and the expression for the implicit functional function is:

[0061]

[0062] G = min(g1, g2, g3, g4)

[0063] Where N F1 For the first-order natural frequency, N F2 E represents the second natural frequency of the pipe. These two values ​​are obtained by solving the pipe's governing equations. F1 and E F2 For the external excitation of the pipeline, based on engineering experience, it is usually 145Hz and 400Hz. The governing equation of the pipeline is:

[0064]

[0065] In the governing equations of the pipeline, the material density is determined by the formula ρ(x) = V. l ρ l +V r ρ r The Young's modulus is determined by the formula E(x) = V. l E l +V r E r Changes are being made, among which V r =1-V l The subscripts l and r represent the leftmost and rightmost ends, respectively, and n is the volume fraction.

[0066] Table 1 Distribution information of random variables

[0067]

[0068]

[0069] The Monte Carlo simulation (MCS) is used as a reference value, and the AK-MCS method is used to compare the proposed method to prove the performance and effectiveness of the proposed method. The initial sample point number of the AK-MCS method is 30, and the initial sample point number of the DLRVM is 16. The results show that the estimated results of the method have good calculation accuracy, and only 222 function functions are called. The number of function function calls of the method is much smaller than that of the MCS method, and slightly smaller than that of the AK-MCS method. Because the candidate sample set of the method has only 5000 samples, which is much less than the 10 5 of the AK-MCS, the CPU time of the method for selecting and updating the training samples in the candidate set is much less than that of the AK-MCS method. The calculation amount of the DLRVM model is greatly reduced.

[0070] Table 2 Reliability analysis results of the axial functionally graded material pipe

[0071]

[0072] Based on the idea that the importance sampling is suitable for multiple failure modes and multiple maximum probability points and the idea that the active learning based on MCS can reduce the calculation amount, a new system reliability analysis calculation method is developed, the candidate points are generated by using the adaptive RVM meta-model importance sampling, in order to improve the calculation accuracy and not increase the additional calculation amount, the adaptive RVM model based on MCS is introduced, and the calculation efficiency and accuracy are effectively improved.

Claims

1.A method for reliability analysis of a double-layer RVM system functional material tube by combining a meta-model, characterized in that, Comprising the following steps: Step 1: Constructing an initial model; Distribution density function of input variable of axial functionally graded material pipe Extract initial sample points and calculate implicit function values to form a training set ; The implicit function function: wherein is the first order natural frequency, is the second order natural frequency of the pipe, both values being obtained by solving the governing equations of the pipe, and is the external excitation of the pipe; Input variables include , , , , , , , , , , ; Step 2: from Constructing limit state functions Initial RVM model of Step 3: Draw importance sampling samples; From the formula: （1） obtaining an initial RVM model an importance sampling density function extracting current importance sampling samples by Markov chain ; denotes a probability classification function, denotes an extended failure probability; Step 4: Updating the sample training set; For important sampling samples K-means clustering analysis is performed to obtain K centroids, and the K centroids and their corresponding function function values are added to the training sample set , and by updating the RVM model ; Step 5: Determining convergence; The correction factor is calculated by cross-validation Leave-one-out estimate : （2） in To build the RVM model during the iteration process training set The size, i.e., the number of elements in the training set. The training points and their corresponding function values ​​are: ; Indicates training set The first in One training point, Indicates the first The function value corresponding to each training point; Obtained from the true function values ​​of the training points. , This means removing the first [item] from the training set. The probability classification function established by the RVM model built after training samples; This indicates removing the first [item] from the training set. The probability classification function established by the RVM model built after training samples; If , and the number of training samples is greater than a specified minimum value , then it is determined that the adaptive RVM meta importance sampling model is converged, and step 6 is entered. Otherwise, return to step 3; Step 6: Calculate the extended failure probability ; from the initial RVM model and the corresponding importance sampling samples , according to the distribution density function of the input variables generate a number of samples and estimate the extended failure probability and the coefficient of variation of its corresponding estimate Step 7: Updating the initial RVM model based on the importance sampling sample pool and computing the correction factor estimate ;​ Will As a candidate sample pool, the U learning function selects and updates sample points from the candidate sample pool and adds them to the training sample set, until the second-layer RVM proxy model converges. ; Step 8: Based on Calculate correction factors and their respective coefficients of variation; correction factor estimate coefficient of variation wherein ; Step 9: Calculate the failure probability estimate and its coefficient of variation .

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