Dynamic vibration absorber high-dimensional reliability analysis method and system based on probability box

Abstract

The invention provides a dynamic vibration absorber high-dimensional reliability analysis method and system based on a probability box, and relates to the technical field of dynamic vibration absorber design, the analysis method is used for dynamic vibration absorber reliability analysis of a main steam pipeline, and the analysis method comprises the following steps: S1, obtaining uncertainty variables of a dynamic vibration absorber, modeling the uncertainty variable into a nonparametric probability box variable; s2, performing dimension reduction processing on the high-dimensional uncertainty input variables through a principal component analysis method; s3, adopting an active learning method to train the proxy model, and constructing a mapping relation between the uncertainty variable after dimension reduction and the amplitude response of the mounting points of the multiple dynamic vibration absorbers of the main steam pipeline; and S4, calculating an output response by using the trained agent model in combination with interval Monte Carlo sampling, and analyzing to obtain a corresponding failure probability. According to the invention, the high-dimensional reliability analysis problem can be analyzed and studied when multiple dynamic vibration absorber forms are adopted for arrangement.

Description

Technical Field

[0001] The present invention relates to the technical field of dynamic vibration absorber design, and in particular to a high-dimensional reliability analysis method and system for a dynamic vibration absorber based on a probability box. Background Art

[0002] The main steam pipeline is a key component in large-scale industrial equipment (such as nuclear power plants, thermal power plants, etc.), and its vibration problem directly affects the safety and operating efficiency of the equipment. Dynamic vibration absorbers are widely used in pipeline systems as an effective vibration reduction device. Traditional dynamic vibration absorber designs are mostly based on deterministic parameters, and the influence of parameter uncertainty is not fully considered. However, in actual engineering, due to the uncertainty of factors such as manufacturing, installation, and operating environment, the parameters of dynamic vibration absorbers (such as mass, size, material density, etc.) often fluctuate, which in turn affects their vibration reduction effect. If the influence of uncertainty factors is ignored, it is likely that the vibration reduction effect of the dynamic vibration absorber under actual working conditions will not meet the expected design requirements. Therefore, studying the uncertainty propagation mechanism of dynamic vibration absorbers in pipeline systems and measuring the probability of their normal operation during service are of great significance for the subsequent optimization of the vibration reduction performance of dynamic vibration absorbers.

[0003] However, general reliability analysis mainly uses random variable models to describe the uncertainty of the structure. The random variable model constructs its probabilistic characteristic parameters through sufficient sample data based on the probability method. However, in engineering practice, uncertain parameters with sufficient sample data and limited sample data may exist at the same time. In addition, in practical applications, in order to ensure multi-band vibration reduction and better vibration reduction effects, multiple dynamic vibration absorbers are often arranged on the pipeline. When multiple dynamic vibration absorbers consider their uncertainties at the same time, the original reliability analysis problem is transformed into a high-dimensional reliability analysis problem. In addition, the vibration reduction performance evaluation of dynamic vibration absorbers is usually achieved through finite element simulation analysis. When the traditional Monte Carlo method is used to perform high-dimensional reliability analysis on them, problems such as low computational efficiency and "dimensionality disaster" may be faced.

[0004] In view of this, the inventor of the present application has designed a high-dimensional reliability analysis method for a dynamic vibration absorber based on a probability box, in order to overcome the above technical problems. Summary of the invention

[0005] The technical problem to be solved by the present invention is to overcome the defect that the traditional dynamic vibration absorber design in the prior art is mostly based on deterministic parameters and does not fully consider the influence of parameter uncertainty, and to provide a high-dimensional reliability analysis method and system for dynamic vibration absorbers based on probability boxes.

[0006] The present invention solves the above technical problems through the following technical solutions:

[0007] The present invention provides a high-dimensional reliability analysis method for a dynamic vibration absorber based on a probability box, which is characterized in that the analysis method is used for reliability analysis of a dynamic vibration absorber of a main steam pipeline, and the analysis method comprises the following steps: S1, obtaining uncertainty variables of the dynamic vibration absorber, and modeling the uncertainty variables as non-parametric probability box variables; S2, performing dimensionality reduction processing on high-dimensional uncertainty input variables by a principal component analysis method; S3, adopting an active learning method to train an agent model, and constructing a mapping relationship between the uncertainty variables after dimensionality reduction and the amplitude response of the installation points of multiple dynamic vibration absorbers of the main steam pipeline;

[0008] S4. Utilize the trained proxy model combined with interval Monte Carlo sampling to calculate the output response and analyze the corresponding failure probability.

[0009] According to one or more embodiments of the present invention, in step S1, the modeling of the non-parametric probability box variable adopts the following formula: Where x represents the uncertainty variable of the dynamic vibration absorber obtained; and Respectively represent the upper and lower probability distribution boundaries; F X (x) is and All possible CDF curves within the bounding envelope region.

[0010] According to one or more embodiments of the present invention, in step S1, when the amplitude of the installation point of the dynamic vibration absorber of the main steam pipeline exceeds the set threshold amplitude, the dynamic vibration absorber is defined as failed; whether the dynamic vibration absorber fails is determined by the following limit state equation: y = g(X) = δ th -δ FEM (X); where δ FEM (·) represents the amplitude response of the installation point of the dynamic vibration absorber of the main steam pipeline calculated by the finite element method; δ th Indicates setting the threshold amplitude; X = (x1, x2, ... x M ) represents an M-dimensional vector consisting of nonparametric probability box variables.

[0011] According to one or more embodiments of the present invention, step S2 comprises the following steps: 21 , determine the sample space size of the uncertain input variable, and obtain the sample size of the uncertain variable by Monte Carlo sampling according to the sample space size. (1) ,X (2) ,....,X (N) ), and the samples of uncertainty variables are processed by data standardization to obtain S 22, calculate the standardized covariance matrix eigenvalues ​​and corresponding eigenvectors, and determine the sample dimension m after dimensionality reduction and the final dimensionality reduction transformation. The covariance matrix is ​​as follows: Cv i =λ i v i i=1,…,M; where λ i is the eigenvalue; v i is the corresponding eigenvector; t represents the specified cumulative principal component contribution rate, t is between (0,1], and the eigenvalue is λ1≥λ2≥...≥λ M , then the sample dimension m (m<<M) after dimensionality reduction is determined by the following formula: Arrange the corresponding eigenvalues ​​in rows from top to bottom into a matrix, take the first m rows to form the matrix P, and the dimensionality reduction conversion formula is:

[0012] According to one or more embodiments of the present invention, step S3 uses an active learning method to train the Kriging proxy model to construct the uncertainty variable Z after dimension reduction (z1, z2, ... z m ) and the amplitude response of the installation point of the multiple dynamic vibration absorber of the main steam pipeline, the step S3 comprises the following steps:

[0013] S 31 , for the existing training set S t , by measuring each current sample point z t The nonlinear degree F of the neighborhood centered q size, select the next new sample point to appear in the neighborhood with the largest nonlinearity; S 32 , in the candidate sample point set S C The maximum and minimum distance strategy is used to select new sample points, and the candidate sample point set S C It is a group of sample points located in the selected neighborhood obtained by Monte Carlo sampling and distance criterion in the sample space;

[0014] S 33 , use the root mean square error of the Kriging proxy model in the test set as the stopping criterion. When the root mean square error is less than the set value, active learning stops and the construction of the high-precision Kriging proxy model is completed; otherwise, active learning continues to iterate and update the Kriging proxy model.

[0015] According to one or more embodiments of the present invention, step S 31 In the example, the neighborhood contains v points closest to the sample point z t The nearest other sample points, where υ=2m; the nonlinearity is calculated by the active learning function, and the calculation formula is: Among them, G represents the gradient of the current neighborhood; y represents the actual response at the current sample point; y i represents the actual response of other sample points in the current neighborhood; z t represents the closest sample point; z ti Represents the closest sample point z t Other random sample points.

[0016] According to one or more embodiments of the present invention, step S 32 In the formula, the maximum and minimum distance strategy is: d = max(min d(z new ,S t )); where min d(z new ,S t ) represents the new sample point z new and existing sample points S t The minimum distance between .

[0017] According to one or more embodiments of the present invention, step S4 comprises the following steps: 41 , Generate n uniformly distributed random numbers u in the interval [0,1] i (i=1,2,...,n),u i Intersect with the upper and lower bounds of the given probability box, and the coordinates of the intersection point generate a random interval set and S 42 , use the dimension reduction transformation formula to obtain the random interval set after dimension reduction Then the system response corresponding to the random interval set is calculated through the trained Kriging surrogate model. The upper and lower bounds of the failure probability of the multiple dynamic vibration absorber system are obtained by analyzing the upper and lower bounds of the response.

[0019] According to one or more embodiments of the present invention, the upper and lower bounds of the failure probability of the multiple dynamic vibration absorber system are expressed as follows: in, is the minimum failure probability, is the maximum failure probability, and I(·) is the failure indicator function, which is specifically defined as follows:

[0020] The present invention also provides a high-dimensional reliability analysis system for dynamic vibration absorbers based on probability boxes, which is characterized in that the analysis system adopts the high-dimensional reliability analysis method for dynamic vibration absorbers based on probability boxes as described above, and the analysis system includes: a data processing module, which is used to obtain the uncertainty variables of the dynamic vibration absorber and model the uncertainty variables as non-parametric probability box variables; and reduce the dimension of the high-dimensional uncertainty input variables through the principal component analysis method; a training module, which uses an active learning method to train the proxy model, and constructs a mapping relationship between the uncertainty variables after dimension reduction and the amplitude response of the installation points of multiple dynamic vibration absorbers of the main steam pipeline; an analysis module, which uses the trained proxy model combined with interval Monte Carlo sampling to calculate the output response, and analyzes the corresponding failure probability.

[0021] The positive and progressive effects of the present invention are:

[0022] The high-dimensional reliability analysis method of dynamic vibration absorber based on probability box of the present invention has at least the following advantages:

[0023] The probability box-based high-dimensional reliability analysis method and system for dynamic vibration absorbers of the present invention can realize the analysis and research of high-dimensional reliability analysis problems when multiple dynamic vibration absorbers are arranged, and can extend the single reliability analysis problem of a single dynamic vibration absorber to the high-dimensional reliability analysis problem of multiple dynamic vibration absorbers. It can also avoid the problems of low computational efficiency and "dimensionality curse" faced when using traditional Monte Carlo methods for high-dimensional reliability analysis in finite element simulation analysis. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] The above and other features, properties and advantages of the present invention will become more apparent through the following description in conjunction with the accompanying drawings and embodiments, in which the same reference numerals always represent the same features, wherein:

[0025] Figure 1 It is a schematic structural diagram of a six-fold cantilever beam dynamic vibration absorber in one embodiment of the high-dimensional reliability analysis method of a dynamic vibration absorber based on a probability box of the present invention.

[0026] Figure 2 It is a schematic diagram of non-parametric probability box variables in one embodiment of the high-dimensional reliability analysis method of a dynamic vibration absorber based on probability box of the present invention.

[0027] Figure 3 It is a flow chart of an embodiment of a high-dimensional reliability analysis method for a dynamic vibration absorber based on a probability box of the present invention. DETAILED DESCRIPTION

[0028] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the specific embodiments of the present invention are described in detail below with reference to the accompanying drawings.

[0029] Embodiments of the present invention will now be described in detail with reference to the accompanying drawings. Reference will now be made in detail to preferred embodiments of the present invention, examples of which are shown in the accompanying drawings. Wherever possible, the same reference numerals will be used in all drawings to represent the same or similar parts. In addition, although the terms used in the present invention are selected from well-known and commonly used terms, some of the terms mentioned in the specification of the present invention may be selected by the applicant at his or her discretion, and their detailed meanings are explained in the relevant parts of the description herein. In addition, it is required to understand the present invention not only by the actual terms used, but also by the meaning implied by each term.

[0030] The present invention provides a high-dimensional reliability analysis method for a dynamic vibration absorber based on a probability box, the analysis method is used for reliability analysis of a dynamic vibration absorber of a main steam pipeline, and the analysis method comprises the following steps:

[0031] Step S1, obtaining uncertainty variables of the dynamic vibration absorber, and modeling the uncertainty variables as non-parametric probability box (P-box) variables;

[0032] Step S2, reducing the dimension of high-dimensional uncertain input variables by principal component analysis method;

[0033] Step S3, using an active learning method to train the proxy model, and constructing a mapping relationship between the uncertainty variables after dimensionality reduction and the amplitude response of the installation point of the multiple dynamic vibration absorbers of the main steam pipeline;

[0034] Step S4: Utilize the trained proxy model in combination with interval Monte Carlo sampling to calculate the output response and analyze and obtain the corresponding failure probability.

[0035] It should be noted that step S2 uses the principal component analysis method to reduce the dimensionality of high-dimensional input variables to reduce the difficulty of subsequent training of the proxy model and improve computing power; the active learning method in step S3 continuously updates and selects appropriate sample points through iteration, which can minimize the number of required samples while ensuring the accuracy of the model.

[0036] The high-dimensional reliability analysis method of a dynamic vibration absorber based on a probability box of the present invention can extend the single reliability analysis problem of a single dynamic vibration absorber to the high-dimensional reliability analysis problem of multiple dynamic vibration absorbers. In addition, the present invention can also avoid the problems of low computational efficiency and "dimensionality curse" faced when using the traditional Monte Carlo method for high-dimensional reliability analysis in finite element simulation analysis.

[0037] According to a preferred embodiment of the high-dimensional reliability analysis method of a dynamic vibration absorber based on a probability box of the present invention, in step S1, the modeling of non-parametric probability box (P-box) variables adopts the following formula:

[0038]

[0039] Where x represents the uncertainty variable of the dynamic vibration absorber obtained; and Respectively represent the upper and lower probability distribution boundaries; F X (x) is and All possible cumulative distribution function (CDF) curves within the bounding envelope region.

[0040] The probability box (P-box) is an uncertainty variable that can describe both random uncertainty and epistemic uncertainty. It defines uncertainty by using the upper and lower cumulative probability distribution function (CDF) curves as boundaries. The probability box (P-box) can be specifically divided into a parametric P-box and a non-parametric P-box. The non-parametric probability box (P-box) used in this embodiment is a non-parametric P-box.

[0041] like Figure 2 , which is a schematic diagram of non-parametric probability box (P-box) variables in one embodiment of the high-dimensional reliability analysis method of a dynamic vibration absorber based on probability box of the present invention. Figure 2 The horizontal axis in the middle is the uncertain variable, and the specific variable is not specified; curve L1 and curve L2 are the boundaries of the CDF curve; the dotted lines are several representative CDF curves within the boundary.

[0042] According to a preferred embodiment of the high-dimensional reliability analysis method of a dynamic vibration absorber based on a probability box of the present invention, in step S1, when the amplitude of the installation point of the dynamic vibration absorber of the main steam pipeline exceeds the set threshold amplitude, the dynamic vibration absorber is defined as failed; whether the dynamic vibration absorber fails is judged by the following limit state equation:

[0043] y=g(X)=δ th -δ feM (X)

[0044] Among them, δ FEM (·) represents the amplitude response of the installation point of the dynamic vibration absorber of the main steam pipeline calculated by the finite element method; δ th Indicates setting the threshold amplitude; X = (x1, x2, ... x M ) represents an M-dimensional vector consisting of nonparametric probability box variables.

[0045] Taking the six-fold cantilever beam dynamic vibration absorber as an example, the uncertain variables that can be considered for input include: the mass of the vibration absorber mass block, the length, width, and height of the base, the length, width, and height of the cantilever beam, and the material density. When all these uncertain variables are considered, the reliability analysis of the six-fold cantilever beam dynamic vibration absorber can be regarded as a high-dimensional reliability analysis problem.

[0046] As shown Figure 1 in the figure, it is a schematic structure of a six - fold cantilever beam dynamic vibration absorber in an embodiment of the high - dimensional reliability analysis method of the dynamic vibration absorber based on the probability box of the present invention.

[0047] According to a preferred embodiment of the high - dimensional reliability analysis method of the dynamic vibration absorber based on the probability box of the present invention, the step S2 includes the following steps:

[0048] Step S 21 , determine the sample space size of the uncertainty input variables, and through Monte Carlo sampling according to the sample space size, obtain the sample χ=(X (1) , X (2) ,...., X (N) ) of the uncertainty variables, and perform data standardization processing on the sample of the uncertainty variables to obtain which is used to eliminate the dimension inconsistency;

[0049] Step S 22 , calculate the eigenvalues and corresponding eigenvectors of the standardized covariance matrix, and determine the reduced - dimension sample dimension m and the final reduced - dimension transformation. The covariance matrix is as follows:

[0050]

[0051] Cv i =λ i v i i = 1,…, M

[0052] where λ i is the eigenvalue; v i is the corresponding eigenvector;

[0053] Let t represent the specified cumulative principal component contribution rate, t is between (0,1]. Assume the eigenvalues are λ1≥λ2≥...≥λ M , then the reduced - dimension sample dimension m (m << M) is determined by the following formula:

[0054]

[0055] Arrange them in a matrix row - by - row according to the size of the corresponding eigenvalues from top to bottom, take the first m rows to form the matrix P, and the reduced - dimension transformation formula is:

[0056] According to a preferred embodiment of the high - dimensional reliability analysis method of the dynamic vibration absorber based on the probability box of the present invention, the step S3 uses the active learning method to train the Kriging surrogate model, and constructs the reduced - dimension uncertainty variables Z=(z1, z2,…z m) and the amplitude response of the installation point of the multiple dynamic vibration absorber of the main steam pipeline, the step S3 comprises the following steps:

[0057] Step S 31 , for the existing training set S t , by measuring each current sample point z t The nonlinear degree F of the neighborhood centered q Size, select the next new sample point that appears in the neighborhood with the largest nonlinearity;

[0058] Step S 32 , in the candidate sample point set S C The maximum and minimum distance strategy is used to select new sample points, and the candidate sample point set S C It is a group of sample points located in the selected neighborhood obtained by Monte Carlo sampling and distance criterion in the sample space;

[0059] Step S 33 , use the root mean square error of the Kriging proxy model in the test set as the stopping criterion. When the root mean square error is less than the set value, active learning stops and the construction of the high-precision Kriging proxy model is completed; otherwise, active learning continues to iterate and update the Kriging proxy model.

[0060] According to a preferred embodiment of the high-dimensional reliability analysis method of a dynamic vibration absorber based on a probability box of the present invention, the step S 31 In the example, the neighborhood contains v points closest to the sample point z t The nearest other sample point, where υ = 2m;

[0061] The degree of nonlinearity is calculated by the active learning function, and the calculation formula is:

[0062]

[0063] Among them, G represents the gradient of the current neighborhood; y represents the actual response at the current sample point; y i represents the actual response of other sample points in the current neighborhood; z t represents the closest sample point; z ti Represents the closest sample point z t Other random sample points.

[0064] According to a preferred embodiment of the high-dimensional reliability analysis method of a dynamic vibration absorber based on a probability box of the present invention, the step S 32 In the formula, the maximum and minimum distance strategy is:

[0065] d=max(min d(z new ,S t ))

[0066] Among them, min d(z new ,S t ) represents the new sample point z new and existing sample points S t The minimum distance between .

[0067] According to a preferred embodiment of the high-dimensional reliability analysis method of a dynamic vibration absorber based on a probability box of the present invention, the step S4 comprises the following steps:

[0068] Step S 41 , Generate n uniformly distributed random numbers u in the interval [0,1] i (i=1,2,...,n),u i Intersect with the upper and lower bounds of a given probability box (P-box), and the coordinates of the intersection point generate a random interval set and

[0069] Step S 42 , use the dimension reduction transformation formula to obtain the random interval set after dimension reduction Then the system response corresponding to the random interval set is calculated through the trained Kriging surrogate model. By analyzing the upper and lower bounds of the response, the upper and lower bounds of the failure probability of the multiple dynamic vibration absorber system are obtained.

[0070] According to a preferred embodiment of the high-dimensional reliability analysis method of dynamic vibration absorbers based on probability boxes of the present invention, the expressions of the upper and lower bounds of the failure probability of the multiple dynamic vibration absorber system are as follows:

[0071]

[0072] in, is the minimum failure probability, is the maximum failure probability, and I(·) is the failure indicator function, which is specifically defined as follows:

[0073]

[0074] like Figure 3 As shown in FIG. 1 , a schematic diagram of the process of an embodiment of the high-dimensional reliability analysis method of a dynamic vibration absorber based on a probability box of the present invention is shown. i , get a random interval set To obtain the uncertainty variable; then the dimension reduction transformation formula is used to obtain the random interval set after dimension reduction A Kriging proxy model is generated based on the random interval set after dimensionality reduction, and active learning is continuously performed to iteratively update the Kriging proxy model, and the upper and lower bounds of the failure probability of the random interval response output are calculated.

[0075] As described above, the present invention uses the finite element method and non-parametric probability box (P-box) variables to construct a function that can simultaneously describe random uncertainty and cognitive uncertainty, thereby making the six-fold cantilever beam dynamic vibration absorber analysis model more reliable in practical applications. The present invention uses the principal component analysis method to reduce the difficulty of subsequent training of the proxy model and improve the computing power. The active learning method is used to train the Kriging proxy model, and it is continuously iterated and updated to select more appropriate sample points, further improving the reliability of the model.

[0076] The high-dimensional reliability analysis method of the dynamic vibration absorber based on the probability box of the present invention can realize the analysis and research of the high-dimensional reliability analysis problem when multiple dynamic vibration absorbers are arranged. The analysis method of the present invention can extend the single reliability analysis problem of a single dynamic vibration absorber to the high-dimensional reliability analysis problem of multiple dynamic vibration absorbers. In addition, the present invention can also avoid the problems of low computational efficiency and "dimensionality curse" faced when using the traditional Monte Carlo method for high-dimensional reliability analysis in finite element simulation analysis.

[0077] The present invention also provides a high-dimensional reliability analysis system for a dynamic vibration absorber based on a probability box. The analysis system adopts the high-dimensional reliability analysis method for a dynamic vibration absorber based on a probability box as described above. The analysis system comprises:

[0078] The data processing module is used to obtain the uncertainty variables of the dynamic vibration absorber and model the uncertainty variables as non-parametric probability box variables; and to reduce the dimension of the high-dimensional uncertainty input variables through the principal component analysis method;

[0079] The training module uses active learning methods to train the proxy model and construct the mapping relationship between the uncertainty variables after dimension reduction and the amplitude response of the installation points of the multiple dynamic vibration absorbers of the main steam pipeline;

[0080] The analysis module uses the trained proxy model combined with interval Monte Carlo sampling to calculate the output response and analyzes the corresponding failure probability.

[0081] The high-dimensional reliability analysis system of a dynamic vibration absorber based on a probability box of the present invention has the advantages of the high-dimensional reliability analysis method of a dynamic vibration absorber based on a probability box of the present invention, and can extend the single reliability analysis problem of a single dynamic vibration absorber to the high-dimensional reliability analysis problem of multiple dynamic vibration absorbers, and can avoid the problems of low computational efficiency and "dimensionality curse" faced when using traditional Monte Carlo methods for high-dimensional reliability analysis in finite element simulation analysis.

[0082] Although the specific embodiments of the present invention are described above, it should be understood by those skilled in the art that these are only examples, and the protection scope of the present invention is defined by the appended claims. Those skilled in the art may make various changes or modifications to these embodiments without departing from the principles and essence of the present invention, but these changes and modifications all fall within the protection scope of the present invention.

Claims

1. A high-dimensional reliability analysis method for dynamic vibration absorbers based on probability boxes, characterized in that: The analysis method is used for reliability analysis of a dynamic vibration absorber of a main steam pipeline, and the analysis method comprises the following steps: S1. Obtain the uncertainty variables of the dynamic vibration absorber and model the uncertainty variables as non-parametric probability box variables; S2. Reduce the dimension of high-dimensional uncertain input variables through principal component analysis; S3, using active learning method to train the proxy model, and construct the mapping relationship between the uncertainty variables after dimension reduction and the amplitude response of the installation points of the multiple dynamic vibration absorbers of the main steam pipeline; S4. Utilize the trained proxy model combined with interval Monte Carlo sampling to calculate the output response and analyze the corresponding failure probability.

2. The high-dimensional reliability analysis method of dynamic vibration absorber based on probability box according to claim 1 is characterized in that: In step S1, the modeling of the non-parametric probability box variable adopts the following formula: Where x represents the uncertainty variable of the dynamic vibration absorber obtained; and F X (x) represent the upper and lower probability distribution boundaries respectively; F X (x) is and F X (x) All possible cumulative distribution function curves within the boundary envelope region.

3. The high-dimensional reliability analysis method of dynamic vibration absorber based on probability box according to claim 1 is characterized in that: In step S1, when the amplitude of the installation point of the dynamic vibration absorber of the main steam pipeline exceeds the set threshold amplitude, the dynamic vibration absorber is defined as failed; whether the dynamic vibration absorber fails is determined by the following limit state equation: y=g(X)=δ th -d FEM (X) Among them, δ FEM (·) represents the amplitude response of the installation point of the dynamic vibration absorber of the main steam pipeline calculated by the finite element method; δ th Indicates setting the threshold amplitude; X = (x1, x2, ... x M ) represents an M-dimensional vector consisting of nonparametric probability box variables.

4. The high-dimensional reliability analysis method of dynamic vibration absorber based on probability box according to claim 1 is characterized in that: The step S2 comprises the following steps: S 21 , determine the sample space size of the uncertain input variable, and obtain the sample size of the uncertain variable by Monte Carlo sampling according to the sample space size. (1) ,X (2) ,....,X (N) ), and the samples of uncertainty variables are processed by data standardization to obtain S 22 , calculate the standardized covariance matrix eigenvalues ​​and corresponding eigenvectors, and determine the sample dimension m after dimensionality reduction and the final dimensionality reduction transformation. The covariance matrix is ​​as follows: Cv i =λ i v i i=1,…,M Among them, λ i is the eigenvalue; v i is the corresponding eigenvector; Let \(t\) represent the cumulative principal component contribution rate that can be specified, where \(t\in(0,1]\). Assume the eigenvalues are \(\lambda_1\geq\lambda_2\geq\cdots\geq\lambda\) M , then the dimension \(m\) (\(m\ll M\)) of the sample after dimensionality reduction is determined by the following formula: Arrange the corresponding eigenvalues ​​in rows from top to bottom into a matrix, take the first m rows to form the matrix P, and the dimensionality reduction conversion formula is:

5. The high-dimensional reliability analysis method for dynamic vibration absorbers based on probability box according to claim 1 is characterized in that: The step S3 uses an active learning method to train the Kriging proxy model to construct the uncertainty variable Z after dimensionality reduction (z1, z2, ... z m ) and the amplitude response of the installation point of the multiple dynamic vibration absorber of the main steam pipeline, the step S3 comprises the following steps: S 31 , for the existing training set S t , by measuring each current sample point z t The nonlinear degree F of the neighborhood centered q Size, select the next new sample point that appears in the neighborhood with the largest nonlinearity; S 32 , in the candidate sample point set S C The maximum and minimum distance strategy is used to select new sample points, and the candidate sample point set S C It is a group of sample points located in the selected neighborhood obtained by Monte Carlo sampling and distance criterion in the sample space; S 33 , use the root mean square error of the Kriging proxy model in the test set as the stopping criterion. When the root mean square error is less than the set value, active learning stops and the construction of the high-precision Kriging proxy model is completed; otherwise, active learning continues to iterate and update the Kriging proxy model.

6. The high-dimensional reliability analysis method for dynamic vibration absorbers based on probability box according to claim 5 is characterized in that: The step S 31 The neighborhood contains v points closest to the sample point z t The nearest other sample point, where υ = 2m; The degree of nonlinearity is calculated by the active learning function, and the calculation formula is: Among them, G represents the gradient of the current neighborhood; y represents the actual response at the current sample point; y i represents the actual response of other sample points in the current neighborhood; z t represents the closest sample point; z ti Represents the closest sample point z t Other random sample points.

7. The high-dimensional reliability analysis method for dynamic vibration absorbers based on probability box according to claim 5 is characterized in that: The step S 32 In the formula, the maximum and minimum distance strategy is: d=max(min d(z new ,S t )) Among them, min d(z new ,S t ) represents the new sample point z new and existing sample points S t The minimum distance between .

8. The high-dimensional reliability analysis method for dynamic vibration absorbers based on probability box according to claim 1 is characterized in that: The step S4 comprises the following steps: S 41 , Generate n uniformly distributed random numbers u in the interval [0,1] i (i=1,2,...,n),u i Intersect with the upper and lower bounds of the given probability box, and the coordinates of the intersection point generate a random interval set and S 42 , use the dimension reduction transformation formula to obtain the random interval set after dimension reduction Then the system response corresponding to the random interval set is calculated through the trained Kriging surrogate model. The upper and lower bounds of the failure probability of the multiple dynamic vibration absorber system are obtained by analyzing the upper and lower bounds of the response.

9. The high-dimensional reliability analysis method for dynamic vibration absorbers based on probability box according to claim 8, characterized in that: The expressions of the upper and lower bounds of the failure probability of the multiple dynamic vibration absorber system are as follows: in, is the minimum failure probability, is the maximum failure probability, and I(·) is the failure indicator function, which is specifically defined as follows:

10. A high-dimensional reliability analysis system for dynamic vibration absorbers based on probability boxes, characterized in that: The analysis system adopts the high-dimensional reliability analysis method of the dynamic vibration absorber based on the probability box according to any one of claims 1 to 9, and the analysis system comprises: The data processing module is used to obtain the uncertainty variables of the dynamic vibration absorber and model the uncertainty variables as non-parametric probability box variables; and to reduce the dimension of the high-dimensional uncertainty input variables through the principal component analysis method; The training module uses active learning methods to train the proxy model and construct the mapping relationship between the uncertainty variables after dimension reduction and the amplitude response of the installation points of the multiple dynamic vibration absorbers of the main steam pipeline; The analysis module uses the trained proxy model combined with interval Monte Carlo sampling to calculate the output response and analyzes the corresponding failure probability.

Images