Jacket platform reliability analysis method based on data combination dimensionality reduction and polynomial chaos expansion

Abstract

The invention discloses a jacket platform reliability analysis method based on data combination dimensionality reduction and polynomial chaos expansion, which comprises the following steps of: performing dimensionality reduction on a jacket platform high-dimensional input sample by adopting a combination dimensionality reduction method, determining a transformation matrix, mapping the high-dimensional input sample and a test sample to a low-dimensional space, and determining the reliability of the jacket platform; the method comprises the following steps: preparing for establishing a dimensionality reduction PCE model, establishing a PCE model in a transformed input space, adaptively selecting a polynomial highest order and a regularization parameter by adopting a sparrow search algorithm, reconstructing a jacket platform PCE model according to the adaptively selected optimal parameter, and calculating a failure probability and a reliability index through random sampling and structural reliability analysis. According to the method, high-dimensional sample data of the jacket platform can be mapped to a low-dimensional space, the modeling efficiency is improved, parameters are adaptively selected, the modeling precision is improved, and high-precision and high-efficiency jacket platform structure reliability analysis is realized.

Description

Technical Field

[0001] The present invention belongs to the technical field of reliability analysis of structural engineering and marine engineering, and specifically relates to a reliability analysis method of a jacket platform structure, and in particular to a jacket platform reliability analysis method based on data combination dimension reduction and polynomial chaos expansion. Background Art

[0002] Jacket platforms are one of the most common structures in offshore engineering and are widely used as supporting structures for oil and gas development, wind power installations, and other offshore facilities. As jacket platforms are usually located in complex and changeable marine environments, such as wind, waves, tides, currents, and earthquakes, it is particularly important to ensure the safety and reliability of their structures. However, jacket platforms have complex structures and a design life of several decades. Their failure forms are diverse and may include fatigue failure, corrosion failure, and ultimate bearing capacity failure. Therefore, accurate reliability analysis is essential to ensure the long-term safe operation of jacket platforms.

[0003] Traditional jacket platform reliability analysis methods mainly rely on Monte Carlo Simulation (MCS). However, Monte Carlo simulation requires a large number of finite element analyses (FEA) to obtain reliable statistical results, so the computing time and resource consumption are huge. In addition, in the reliability analysis of jacket platforms, a large amount of sample data such as structural geometric parameters, material properties and environmental load variables are involved. The challenges faced in processing these high-dimensional data include: computational complexity, data redundancy, storage bottlenecks and difficulty in identifying key influencing factors. Therefore, how to effectively reduce the data dimension while retaining the key information that affects reliability has become an important research topic in reliability analysis.

[0004] Data dimensionality reduction techniques, such as principal component analysis (PCA) and factor analysis (FA), can reduce the dimension of data without losing the main information of sample data, thereby reducing the amount of calculation and complexity. This technology is widely used in high-dimensional data processing and pattern recognition. However, traditional dimensionality reduction methods have certain limitations when dealing with complex nonlinear or uncertain sample data, and it is difficult to effectively capture their potential relationships.

[0005] The surrogate model approximates complex numerical simulations by constructing explicit mathematical expressions, which can significantly reduce computing time and resource consumption while maintaining high accuracy. Polynomial Chaos Expansion (PCE), as a surrogate model technology, has strong mathematical expression capabilities and can effectively capture the nonlinear relationship between input variables and their impact on output responses. In addition, the PCE model can handle uncertainty problems without increasing computational complexity, so it is very suitable for reliability analysis of jacket platforms.

[0006] Solving the polynomial coefficients is the key to building the PCE model. The greedy coordinate descent (BGCD) method based on Bregman iteration has been proven to have the advantages of high efficiency and high precision. The relevant literature is: Zhang J, Yue X, Qiu J, Zhuo L, Zhu J. Sparse polynomial chaos expansion based on Bregman-iterative greedy coordinate descent for global sensitivity analysis. Mechanical Systems and Signal Processing 2021; 157: 107727. In the BGCD algorithm, the highest order of PCE and the regularization parameter are determined based on experience. However, the highest order directly determines the fitting accuracy of the PCE model, and different systems will have different orders to adapt; the regularization parameter determines the sparsity of the PCE model. If it is too large or too small, it will lead to low computational efficiency or large model error. Therefore, choosing the appropriate highest order of PCE and regularization parameter is of great significance for the construction of the PCE model.

[0007] In summary, since the reliability analysis of the jacket platform involves a large number of variables such as structural parameters, material properties and environmental loads, when establishing the PCE model, high-dimensional sample data will cause the "curse of dimensionality" problem, resulting in an exponential increase in the computational cost. In addition, the highest order of PCE and regularization parameters in the BGCD algorithm will affect the model accuracy and computational efficiency. The choice based on experience may not necessarily obtain the optimal solution. The adaptiveness of parameters is more conducive to establishing an accurate model. Summary of the invention

[0008] In view of the above technical problems, the present invention provides a jacket platform reliability analysis method based on data combination dimensionality reduction and polynomial chaos expansion (PCE). The present invention maps the high-dimensional sample data of the jacket platform to a low-dimensional space, thereby improving the modeling efficiency, and adaptively selects parameters to improve the modeling accuracy, thereby realizing high-precision and high-efficiency jacket platform structure reliability analysis.

[0009] The present invention achieves the purpose through the following technical solutions.

[0010] A jacket platform reliability analysis method based on data combination dimension reduction and polynomial chaos expansion includes the following steps:

[0011] The combined dimensionality reduction method is used to reduce the dimension of the high-dimensional input samples of the catheter platform and determine the transformation matrix W r , high-dimensional input samples and test samples are mapped to low-dimensional space to prepare for the establishment of dimensionality reduction PCE model. The PCE model is established in the transformed input space, and the sparrow search algorithm is used to adaptively select the highest order and regularization parameters. According to the optimal parameters selected adaptively, the PCE model of the jacket platform is reconstructed. Through random sampling, structural reliability analysis is performed to calculate the failure probability and reliability index.

[0012] The above scheme specifically includes the following steps:

[0013] Step S1, prepare training samples X, Y, and test samples Xt, Yt;

[0014] Step S2: Use the combined dimensionality reduction method to map the high-dimensional input samples to the low-dimensional space and calculate the information matrix K i , and perform feature decomposition;

[0015] Step S3: Select the top r of the cumulative information that exceeds the fixed threshold j features, find r = min{r j} is the optimal dimensionality reduction method, and the transformation matrix W is obtained r , calculate the dimension reduction data X r , Xt r , establish the PCE model in the transformed input space;

[0016] Step S4: Randomly select an initial population [p, λ], and use the sparrow search algorithm to adaptively select [p best ,λ best ];

[0017] Step S5, reconstruct the dimension-reduced PCE model, using the [p best ,λ best ]Build a proxy model that takes into account both accuracy and sparsity;

[0018] Step S6: structural reliability analysis, calculating failure probability and reliability index.

[0019] In the above scheme, step S1 prepares training samples X, Y, test samples Xt, Yt, randomly generates input sample points according to the distribution law and coefficient of variation of the jacket platform input variables, and calls finite element analysis software to perform simulation calculation of structural response.

[0020] In the above scheme, step S2 specifically includes the following steps:

[0021] Step S2.1 Calculate the six information matrices K of the combined dimensionality reduction method according to the following formula: j , where j = 1, 2, 3, 4, 5, 6:

[0022]

[0023] X is a high-dimensional input sample;

[0024] T represents matrix transpose;

[0025] κ is a different kernel function, and the kernel function κ is calculated according to the following formula j :

[0026]

[0027] N is the number of input samples;

[0028] x i Input sample for row i;

[0029] For the Row input sample;

[0030]

[0031] σ is the bandwidth;

[0032] q, η and θ are all random parameters, q ≥ 1, η>0, θ<0;

[0033] is the partial gradient of the jth variable;

[0034] Step S2.2: According to the following formula, the six information matrices K j Perform eigendecomposition:

[0035] K j =WΛW T

[0036] W is the eigenvector matrix;

[0037] Λ is a diagonal matrix with descending eigenvalues;

[0038] Step S2.3 selects the maximum principal component whose cumulative information exceeds the threshold k according to the following formula:

[0039]

[0040] r is the new dimension;

[0041] n is the initial data dimension;

[0042] k is the threshold;

[0043] λ is the eigenvalue.

[0044] In the above scheme, the step S3 selects the first r j features, find r = min{r j} is the optimal dimensionality reduction method, and the transformation matrix W is obtained r , calculate the dimension reduction data X r , Xt r , specifically including the following steps:

[0045] Step S3.1: The dimension of the space after dimensionality reduction corresponding to different methods r j Select the best dimensionality reduction method and determine the first r columns as the transformation matrix W according to the eigenvector matrix r , according to the following formula, each information matrix will get a new dimension r, and the dimensionality reduction method with the smallest dimension is selected:

[0046] r = min {r j}

[0047] Step S3.2: According to the following formula, the transformation matrix W is obtained according to the selected feature space dimension and feature vector matrix: r , and map the original input samples and original training samples to a low-dimensional space:

[0048] X r =K×W r

[0049] Xt r =Kt×W r

[0050] X r is the input sample data of r dimension after dimensionality reduction;

[0051] K is the original input sample information matrix;

[0052] Xt r is the r-dimensional training data after dimensionality reduction;

[0053] Kt is the original training sample information matrix.

[0054] In the above scheme, the step S4 adopts the method of randomly selecting the initial population [p, λ] and adopting the sparrow search algorithm to adaptively select [p best ,λ best ], specifically including the following steps:

[0055] Step S4.1 first selects the initial population [p, λ] and calculates the individual fitness value according to the following formula:

[0056]

[0057] FindX = [p, λ]

[0058] stp∈N +

[0059] 1≤p≤20

[0060] 0≤λ≤10 3

[0061] Fit is the fitness value of the optimization target;

[0062] Y is the response value of the training sample;

[0063] Yt is the response value of the test sample;

[0064] X is the set of optimization variables;

[0065] p is the highest order of the polynomial;

[0066] λ is the regularization parameter;

[0067] RMSE(·) is the root mean square error between the predicted value and the actual value, which is calculated by the following formula:

[0068]

[0069] represents the true value;

[0070] a i represents the predicted value;

[0071] N is the total number of training and testing samples;

[0072] Delineate explorers and followers based on fitness values;

[0073] Step S4.2 iteratively updates the position according to the explorer and follower position update strategy;

[0074] Step S4.3: After the preset number of iterations, the fitness value remains unchanged, the highest order of the polynomial and the regularization parameter remain basically unchanged, and the global optimal individual is output:

[0075] X best =[p best ,λ best ].

[0076] In the above scheme, the step S5, reconstructing the dimension reduction PCE model, adopting the BGCD algorithm to solve, the specific steps are as follows:

[0077] Step S5.1 constructs a PCE model according to the following formula:

[0078]

[0079] x is the input variable sample;

[0080] y is the response of the input sample;

[0081] α=(α i , …, α n ) is an n-dimensional index, i = 1, ..., n, and α i ≥0;

[0082] n is the model dimension;

[0083] ψ α is a multivariate orthogonal polynomial basis;

[0084] - α Usually it is selected according to different data distribution types. If the data is uniformly distributed, the Legendre polynomial basis is used. If the data is Gaussian distributed, the Hermite polynomial basis is used.

[0085] β α are the unknown coefficients corresponding to the polynomial basis;

[0086] Step S5.2 truncates the complete polynomial chaotic expansion, and the truncated polynomial chaotic expansion is shown in the following formula:

[0087]

[0088] is the defined multivariate indicator set, where p is the p obtained in step S4 best ;

[0089] Step S5.3 uses the BGCD method to calculate the unknown coefficients of the polynomial.

[0090] Furthermore, the step S5.3 uses the BGCD method to calculate the unknown coefficients of the polynomial, specifically:

[0091] The solution of polynomial coefficients is transformed into an optimization problem using l1 norm and l2 norm regularization.

[0092] Solve the l1 norm and l2 norm minimization problem according to the following formula:

[0093]

[0094] y is the exact response value of the input sample;

[0095] β is the polynomial basis coefficient;

[0096] ψ is the multivariate orthogonal polynomial basis vector;

[0097] ||·||1 means 1 norm;

[0098] ||·||2 represents the 2-norm;

[0099] According to the following formula, the inner loop uses the greedy coordinate descent method to iterate according to the coordinate with the largest energy attenuation:

[0100]

[0101] φ j represents the element in the jth column;

[0102] γ j Represents the residual sum of the true value and predicted value of the input sample except the jth column;

[0103] λ best is the optimal regularization parameter;

[0104] At the same time, the outer loop is updated using the Bregman iteration method according to the following formula:

[0105] During the iteration process, if the error meets the accuracy requirement of 1, the greedy coordinate descent iteration is completed:

[0106]

[0107] represents the polynomial basis coefficients of the t-th iteration;

[0108] β t-1 represents the polynomial basis coefficients of the t-1th iteration;

[0109] Tol1 represents the error threshold of accuracy requirement 1;

[0110] If the error does not meet the accuracy requirement 1, the Bregman iteration is used to update the response value:

[0111] y t+1 =y+(y t -ψβ t+1 )

[0112] y t+1 represents the predicted response value of the t+1th iteration;

[0113] y is the exact response value of the input sample;

[0114] y t represents the predicted response value of the tth iteration;

[0115] ψ represents the multivariate orthogonal polynomial basis vector;

[0116] β t+1 represents the polynomial basis coefficients of the t+1th iteration;

[0117] The iteration stops until the following accuracy requirement 2 is met:

[0118]

[0119] ψ represents the multivariate orthogonal polynomial basis vector;

[0120] β t represents the polynomial basis coefficients of the t-th iteration;

[0121] ||·||2 represents the second norm value;

[0122] Tol2 represents the error threshold of accuracy requirement 2;

[0123] In the above solution, the step S6 calculates the failure probability according to the following formula:

[0124] P f =∫ {x：g(x)≤0} f X (x)dx

[0125] P f is the failure probability of the model;

[0126] f X (x) is the joint probability density function of the input variables;

[0127] g(x) is the limit state function.

[0128] Furthermore, the model reliability index in step S6 is calculated by the following formula:

[0129] δ=-Φ -1 (P f )

[0130] δ is the reliability index of the model;

[0131] Φ -1 (·) is an inverse normal cumulative distribution function.

[0132] Compared with the prior art, the present invention has the following beneficial effects:

[0133] The present invention is oriented to the high-dimensional sample data of the jacket platform, combines the combined dimensionality reduction method with the PCE proxy model, adopts the combined dimensionality reduction method to map the high-dimensional sample data to the low-dimensional space, adopts the PCE proxy model to establish the dimensionality reduction model, and balances the relationship between high-dimensional data and accurate modeling; adopts the sparrow search algorithm to adaptively select the highest order of the polynomial and the regularization parameter in the BGCD algorithm, so as to achieve the effect of accurate modeling and ensuring sparsity; calculates the structural reliability and failure probability based on the dimensionality reduction PCE proxy model, realizes the reliability analysis of the jacket platform structure, and improves the modeling accuracy and efficiency of the proxy model. BRIEF DESCRIPTION OF THE DRAWINGS

[0134] Figure 1 It is a schematic flow chart of the method for analyzing the structural reliability of a jacket platform based on data combination dimension reduction and polynomial chaos expansion of the present invention;

[0135] Figure 2 It is a schematic diagram of the process flow of the data combination dimensionality reduction method of the present invention;

[0136] Figure 3 A schematic diagram of the jacket platform load provided by the present invention;

[0137] Figure 4 A schematic diagram of the structure and displacement distribution of the jacket platform provided by the present invention;

[0138] Figure 5 A schematic diagram of individual contribution rates and cumulative contribution rates of the first eight largest principal components of a jacket platform provided in an embodiment of the present invention;

[0139] Figure 6 The invention provides an iterative curve diagram of fitness variation of adaptive selection parameters of a sparrow search algorithm. DETAILED DESCRIPTION

[0140] Embodiments of the present invention are described in detail below, examples of which are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are intended to be used to explain the present invention, and should not be construed as limiting the present invention.

[0141] As attached Figure 1 As shown in the figure, a reliability analysis method for the jacket platform based on data combination dimensionality reduction and polynomial chaos expansion is used to reduce the dimension of the high-dimensional input samples of the jacket platform by using the combination dimensionality reduction method to determine the transformation matrix W r, high-dimensional input samples and test samples are mapped to low-dimensional space, a PCE model is established in the transformed input space, the sparrow search algorithm is used to adaptively select the highest order and regularization parameters, and the PCE model of the jacket platform is reconstructed according to the adaptively selected optimal parameters. Through random sampling, structural reliability analysis is performed to calculate the failure probability and reliability index.

[0142] The method specifically comprises the following steps:

[0143] Step S1: Prepare training samples X, Y, and test samples Xt, Yt:

[0144] Step S2: Use the combined dimensionality reduction method to map the high-dimensional input samples to the low-dimensional space and calculate the information matrix K j , and perform feature decomposition;

[0145] Step S3: Select the top r of the cumulative information that exceeds the fixed threshold j features, find r = min{r j} is the optimal dimensionality reduction method, and the transformation matrix W is obtained r , calculate the dimension reduction data X r , Xt r , establish the PCE model in the transformed input space;

[0146] Step S4: Randomly select an initial population [p, λ], and use the sparrow search algorithm to adaptively select [p best ,λ best ];

[0147] Step S5, reconstruct the dimension-reduced PCE model, using the [p best ,λ best ]Build a proxy model that takes into account both accuracy and sparsity;

[0148] Step S6: structural reliability analysis, calculating failure probability and reliability index.

[0149] The present invention is aimed at high-dimensional data of geometric parameters, material property parameters, environmental load parameters and constraint parameters of the jacket platform structure. By constructing a framework for structural reliability analysis by mapping high-dimensional data to low-dimensional space based on the combined dimensionality reduction method to construct a PCE proxy model, the combined dimensionality reduction and PCE proxy model that can reduce the dimensionality of multiple types of data are combined, the combined dimensionality reduction method is used to map high-dimensional input data to low-dimensional space, and the PCE proxy model is used to establish a dimensionality reduction model to balance the relationship between high-dimensional data and accurate modeling; the sparrow search algorithm is used to adaptively select the highest order of polynomials and regularization parameters in the BGCD algorithm, so as to achieve the effect of accurate modeling and ensuring sparsity; the structural reliability and failure probability are calculated based on the reduced dimensionality PCE proxy model, so as to realize the reliability analysis of the jacket platform structure, thereby feeding back the influence of uncertainty factors on the safety performance of the jacket, which is helpful for the subsequent structural design and optimization of the jacket platform.

[0150] A specific embodiment of the present invention is as follows:

[0151] The step S1 prepares training samples X, Y, test samples Xt, Yt, randomly generates input sample points according to the input variable distribution law and coefficient of variation of the jacket platform shown in Table 1, and calls finite element analysis software to perform simulation calculation of structural response.

[0152] Table 1 Jacket platform distribution type and distribution parameters

[0153]

[0154] As attached Figure 3 As shown in FIG. 1 , the natural load conditions of the jacket platform in the ocean are complex. This embodiment involves 21 free variables. The input variables of the jacket platform include deck beam height (h / m), deck beam width (b / m), deck thickness (t / m), upper column diameter (d1 / m), bottom column diameter (d2 / m), deck main pipe and horizontal strut diameter (d3 / m), diagonal strut diameter (d4 / m), upper column wall thickness (t1 / m), bottom column wall thickness (t2 / m), deck main pipe and horizontal strut wall thickness (t3 / m), diagonal strut wall thickness (t4 / m), elastic modulus (E / Pa), Poisson's ratio (υ), material density (D / kg / m 3 ), wave height (H / m), wave period (T / s), upper seawater velocity (v1 / m / s 2 ), mid-layer seawater flow velocity (v2 / m / s 2 ), bottom water velocity (v3 / m / s 2 ), wave phase angle (W / m / s 2 ), wind speed (V / m / s), seawater density (ρ / kg / m 3 ).

[0155] As attached Figure 4 As shown in Figure 1, the displacement distribution diagram of the jacket platform under the action of the mean value of 21 free variables, among which the maximum displacement position is the upper and lower deck positions.

[0156] The step S2 uses a combined dimensionality reduction method to map the high-dimensional input sample to a low-dimensional space, specifically comprising the following steps:

[0157] Step S2.1 Calculate the six information matrices K of the combined dimensionality reduction method according to the following formula: j , where j = 1, 2, 3, 4, 5, 6:

[0158] The information matrix K1 is established by assuming that the input variables are linearly related:

[0159]

[0160] Information matrix K 2-5 It assumes that the input variables are nonlinear and is established based on different kernel function transformations:

[0161] K j =κ-1 N κ-κ1 N +1 N κ1 N

[0162] The information matrix K6 is established based on the input variable gradient information:

[0163]

[0164] For the convenience of calculation, K6 is generally approximated by the following formula:

[0165]

[0166] therefore,

[0167]

[0168] X is a high-dimensional input sample;

[0169] T represents matrix transpose;

[0170] j represents the information matrix number;

[0171] is the partial gradient of the jth variable;

[0172] 1 N is the N-order identity matrix;

[0173] N is the number of input samples;

[0174] is the bias gradient of the input sample;

[0175] ρ is the probability density function of the input sample;

[0176] represents the summation index;

[0177] κ represents the kernel matrix after different types of kernel function transformations. κ is calculated according to the following formula: j :

[0178]

[0179] Where N is the number of input samples;

[0180] x i Input sample for row i;

[0181] For the Row input sample;

[0182]

[0183] σ is the bandwidth;

[0184] q, η and θ are all random parameters, q ≥ 1, η > 0, θ < 0;

[0185] Step S2.2: According to the following formula, the six information matrices K j Perform eigendecomposition:

[0186] K j =WΛW T

[0187] W is the eigenvector matrix;

[0188] Λ is a diagonal matrix with descending eigenvalues;

[0189] Λ=diag(λ1,λ2,…,λ n ) is the eigenvalue matrix in which the eigenvalues ​​are arranged in descending order;

[0190] Step S2.3 determines the dimensionality reduction strength according to the information retention threshold. According to the following formula, the cumulative information contained in the largest principal component selected exceeds the threshold k:

[0191]

[0192] r is the spatial dimension after dimensionality reduction;

[0193] n is the initial input sample dimension;

[0194] k is the information retention threshold, in this embodiment, k=0.95;

[0195] λ is the eigenvalue;

[0196] like Figure 5 The figure shows the individual contribution rate and cumulative contribution rate of the first 8 largest principal components of the jacket platform. In this embodiment, the jacket platform establishes an information matrix by the K6 method in the combined dimensionality reduction method. The eigenvalue is derived from the characteristic decomposition of the information matrix. The eigenvalue represents the amount of information contained in the original data of each characteristic direction, and the principal component is determined by the ratio of the eigenvalue to the sum of all eigenvalues. The ratio is also called the individual contribution rate. The first 8 largest principal components are the first 8 characteristic directions in descending order of individual contribution rate, and the cumulative contribution rate is the sum of the individual contribution rates arranged in order.

[0197] The step S3 selects the first r where the accumulated information exceeds a fixed threshold j features, find r = min{r j} is the optimal dimensionality reduction method, and the transformation matrix W is obtained r , calculate the dimension reduction data X r , Xt r , specifically including the following steps:

[0198] Step S3.1: The dimension of the space after dimensionality reduction corresponding to different methods r j Select the best dimensionality reduction method and determine the first r columns as the transformation matrix W according to the eigenvector matrix r :

[0199] r = min {r j}Mode,

[0200] Each information matrix will get a new dimension r, and the dimensionality reduction method with the smallest dimension is selected:

[0201] r = min {r j}

[0202] Step S3.2: According to the following formula, the transformation matrix W is obtained according to the selected feature space dimension and feature vector matrix: r , and map the original input samples and original training samples to a low-dimensional space:

[0203] X r =K×W r

[0204] Xt r =Kt×W r

[0205] X r is the input sample data of r dimension after dimensionality reduction;

[0206] K is the original input sample information matrix;

[0207] Xt r is the r-dimensional training data after dimensionality reduction;

[0208] Kt is the original training sample information matrix;

[0209] In this embodiment, K6 is selected for dimensionality reduction, such as Figure 2 The figure shows the combined dimensionality reduction process flow chart: first, according to the selected high-dimensional input parameter matrix X of the jacket, the corresponding maximum displacement response matrix Y is calculated by finite element simulation; then the information matrix K is established in the above different ways; by characteristic decomposition of the information matrix, it is determined that K6, i.e., the gradient information matrix, can be reduced to the lowest dimension of 3 dimensions when the information retention exceeds 95%; the transformation matrix W obtained according to the corresponding eigenvector r , the original input sample of the catheter rack is mapped to the 3D space, thus achieving effective dimensionality reduction in this embodiment.

[0210] In step S4, the initial population [p, λ] is randomly selected, and the sparrow search algorithm is used to adaptively select [p best ,λ best ], specifically including the following steps:

[0211] Step S4.1 first selects the initial population [p, λ]. In this example, 20 individuals are selected as the initial population, and the individual fitness value is calculated according to the following formula:

[0212]

[0213] Fit is the fitness value;

[0214] Y is the response value of the training sample;

[0215] Yt is the response value of the test sample;

[0216] RMSE(·) is the root mean square error between the predicted value and the actual value, which can be calculated as follows:

[0217]

[0218] represents the true value;

[0219] a i represents the predicted value;

[0220] N is the total number of input samples;

[0221] According to the fitness value, the 20% with the smallest fitness value are explorers, and the remaining 80% are followers;

[0222] Step S4.2 iteratively updates the position according to the explorer and follower position update strategy;

[0223] The explorer's location update strategy is:

[0224]

[0225] The follower's position update strategy is:

[0226]

[0227] During the foraging process, some sparrows are responsible for vigilance. The position update strategy of these individuals is:

[0228]

[0229] represents the jth variable in the i-th individual in the previous generation of the optimized variable;

[0230] represents the jth variable in the i-th individual in the next generation of optimized variables;

[0231] α and L are random numbers between 0 and 1;

[0232] iter max is the maximum number of iterations;

[0233] R2 is the warning value, which is a random number between 0 and 1;

[0234] ST is the warning threshold, which is 0.8 in this embodiment;

[0235] Q is a standard normal distribution random number;

[0236] is the individual with the worst global fitness;

[0237] Indicates the individual with the best fitness in the current population;

[0238] A is a 1×2 matrix, each element of which is randomly assigned a value of 1 or -1. + It can be calculated by the following formula:

[0239] A + =A T (AA T )-1

[0240] is the individual with the best global fitness;

[0241] f i is the current individual fitness value;

[0242] f w is the global worst fitness value;

[0243] f g is the global optimal fitness value;

[0244] β is a control factor that follows a standard normal distribution;

[0245] K is a random number between -1 and 1;

[0246] ε is the error factor, which is 10 -50 ;

[0247] Finally, we get the best fitness parameter X best =[p best ,λ best ];

[0248] Step S4.3: After 20 iterations, when the fitness value remains unchanged, the highest order of the polynomial and the regularization parameter remain basically unchanged, the global optimal individual is output:

[0249] [p best ,λ best ] = [7, 96.4344]

[0250] like Figure 6 This is the curve of the fitness value changing during the iteration of the sparrow search algorithm.

[0251] The present invention first maps the high-dimensional sample data of the jacket platform to a low-dimensional space based on a combined dimension reduction method, thereby solving the "dimensionality curse" problem of the PCE model and improving the modeling efficiency. Then, the Sparrow Search Algorithm (SSA) is used to adaptively select the highest order of PCE and the regularization parameter in the BGCD algorithm, thereby improving the modeling accuracy. Finally, a numerical model of the jacket platform is established based on the proposed data combined dimension reduction-polynomial chaos expansion (CDR-PCE) model, and a structural reliability analysis is performed. The adaptive optimization algorithm uses the Sparrow Search Algorithm, but is not limited to this algorithm.

[0252] In step S5, [p best ,λ best ]Reconstruct the PCE model, transform the engineering problem into a numerical function, reconstruct the dimension-reduced PCE model, and use the BGCD algorithm to solve it. The specific steps are as follows:

[0253] Step S5.1 constructs a PCE model according to the following formula:

[0254]

[0255] x is the input variable sample;

[0256] y is the response of the input sample;

[0257] α=(α i , …, α n ) is an n-dimensional index, i = 1, ..., n, and αi ≥0;

[0258] n is the model dimension;

[0259] ψ α is a multivariate orthogonal polynomial basis;

[0260] - α Usually, it is selected according to different data distribution types. If the data is uniformly distributed, the Legendre polynomial basis is used. If the data is Gaussian distributed, the Hermite polynomial basis is used. In this embodiment, the Legendre polynomial basis is used.

[0261] β α are the unknown coefficients corresponding to the polynomial basis;

[0262] The high-order coupling terms in step S5.2 are difficult to calculate and have little effect on the accuracy of the results. Therefore, conventional PCE uses the truncation method to constrain the actual calculation and truncate the complete polynomial chaos expansion. The truncated polynomial chaos expansion is shown in the following formula:

[0263]

[0264] is the defined multivariate indicator set, where p is the p obtained in step S4 best ;

[0265] Step S5.3: The key to this model is to solve the polynomial coefficients. It is transformed into an optimization problem by using l1 norm and l2 norm regularization, and the BGCD method is used to calculate the unknown polynomial coefficients.

[0266] Solve the l1 norm and l2 norm minimization problem according to the following formula:

[0267]

[0268] y is the exact response value of the input sample;

[0269] β is the polynomial basis coefficient;

[0270] ψ is the multivariate orthogonal polynomial basis vector;

[0271] ||·||1 means 1 norm;

[0272] ||·||2 represents the 2-norm;

[0273] The BGCD solution can accurately and efficiently solve the above problems. The greedy coordinate descent method can accelerate the calculation by iterating according to the coordinates with the largest energy attenuation. According to the following formula, the inner loop uses the greedy coordinate descent method to iterate according to the coordinates with the largest energy attenuation:

[0274]

[0275] φ j represents the element in the jth column;

[0276] γ j Represents the residual sum of the true value and predicted value of the input sample except the jth column;

[0277] λ best is the optimal regularization parameter;

[0278] At the same time, the outer loop is updated using the Bregman iteration method according to the following formula:

[0279] y k+1 =y+(y k -ψβ k+1 )

[0280] y k+1 Represents the updated response value;

[0281] y k Indicates the coordinate response value before updating;

[0282] The step S6, structural reliability analysis includes calculating the model failure probability and reliability index, and the failure probability is calculated according to the following formula:

[0283] P f =∫ {x：g(x)≤0} f X (x)dx

[0284] P f is the failure probability of the model;

[0285] fX(x) is the joint probability density function of the input variables;

[0286] g(x) is the limit state function;

[0287] The model reliability index is calculated by the following formula:

[0288] δ=-ΦΦ -1 (Pf)

[0289] δ is the reliability index of the model;

[0290] Φ -1 (·) is an inverse normal cumulative distribution function.

[0291] The present invention conducts structural reliability analysis of the jacket platform based on data combination dimensionality reduction and polynomial chaos expansion (PCE), calls finite element software to obtain the response under specific input samples, maps high-dimensional input samples to low-dimensional space by combined dimensionality reduction method, and realizes adaptive selection of the highest order of polynomials and regularization parameters by sparrow search algorithm, and finally constructs a dimensionality reduction PCE model. For the final jacket platform PCE model, the structural failure probability and reliability index are calculated.

[0292] By taking MCS as the classic benchmark result, the accuracy and superiority of the proposed CDR-PCE method are verified by comparing it with the approximate methods FORM (first-order reliability method), SORM (second-order reliability method), the proxy model method AK-MCS (active learning Kriging-Monte Carlo simulation), SVR (support vector regression), PCE (polynomial chaos expansion) and the dimensionality reduction model method SAS-HPCFE (sparse active subspace-polynomial combination function).

[0293] Table 2 Comparison of jacket platform structure reliability analysis results using different methods

[0294]

[0295] *δ, Pf, N and ε(%) represent reliability index, failure probability, sample size and error.

[0296] As shown in Table 2, the number of MCS evaluations was reduced due to the high failure probability. Taking the MCS with 16,000 samples as the benchmark, the reliability index was 0.7858 and the failure probability was 0.2160. The calculation results of the CDR-PCE method were 0.7851 and 0.2162, respectively, and the calculation error was only 0.0891% compared with the MCS method. The approximate method did not converge, and the calculation errors of the reliability index of AK-MCS, SVR and S-PCE were 16.5691%, 3.8178% and 0.8526%, respectively. The calculation error of the reliability index of the SAS-HPCFE dimensionality reduction model was 1.6416%. In summary, the CDR-PCE method obtained the most accurate reliability index and failure probability results. Comparing the number of samples required for calculation, CDR-PCE only needs 800 samples to obtain excellent results, and the calculation cost is the lowest among all test methods.

[0297] The present invention is aimed at high-dimensional sample data of geometric parameters, material property parameters, environmental load parameters and constraint parameters of the jacket platform structure, combines the combined dimensionality reduction method with the PCE proxy model, adopts the combined dimensionality reduction method to map the high-dimensional sample data to a low-dimensional space, adopts the PCE proxy model to establish a dimensionality reduction model, and balances the relationship between high-dimensional data and accurate modeling; adopts the sparrow search algorithm to adaptively select the highest order of the polynomial and the regularization parameter in the BGCD algorithm, so as to achieve the effect of accurate modeling and ensuring sparsity; calculates the structural reliability and failure probability based on the dimensionality reduction PCE proxy model, and realizes the reliability analysis of the jacket platform structure.

[0298] The present invention randomly samples input variables, calls finite element analysis software for simulation, combines dimensionality reduction methods to reduce the dimensionality of original high-dimensional input data, and uses a sparrow search algorithm to adaptively select the highest order and regularization parameter of polynomial chaos expansion to construct a dimensionality-reduced polynomial chaos expansion proxy model. Based on the polynomial chaos expansion, the failure probability and structural reliability of the catheter rack platform are calculated. The method of the present invention can extract features from high-dimensional data with different distributions, map them to low-dimensional space, accurately and efficiently establish a dimensionality-reduced polynomial chaos expansion proxy model based on the finite element response data and adaptive parameters of the catheter rack platform, and perform structural reliability analysis, which is beneficial to provide guidance and reference for the structural design, operation and maintenance of the catheter rack platform.

[0299] The preferred embodiments of the present invention disclosed above are only used to help explain the present invention. The preferred embodiments do not describe all the details in detail, nor do they limit the specific implementation methods of the invention. This specification selects and specifically describes the embodiments in order to better explain the principles and practical applications of the present invention, so that those skilled in the art can understand and use the present invention well. The present invention is limited only by the claims and their full scope and equivalents.

Claims

1. A jacket platform reliability analysis method based on data combination dimension reduction and polynomial chaos expansion, characterized in that: The steps include: The combined dimensionality reduction method is used to reduce the dimension of the high-dimensional input samples of the catheter platform and determine the transformation matrix W r , high-dimensional input samples and test samples are mapped to low-dimensional space, a PCE model is established in the transformed input space, the sparrow search algorithm is used to adaptively select the highest order of the polynomial and the regularization parameter, and the PCE model of the jacket platform is reconstructed according to the optimal parameters selected adaptively. Through random sampling, structural reliability analysis is performed to calculate the failure probability and reliability index.

2. The method for analyzing the reliability of a jacket platform based on data combination dimension reduction and polynomial chaos expansion according to claim 1 is characterized in that: The specific steps include: Step S1, prepare training samples X, Y, and test samples Xt, Yt; Step S2: Use the combined dimensionality reduction method to map the high-dimensional input samples to the low-dimensional space and calculate the information matrix K j , and perform feature decomposition; Step S3: Select the top r of the cumulative information that exceeds the fixed threshold j features, find r = min{r j } is the optimal dimensionality reduction method, and the transformation matrix W is obtained r , calculate the dimension reduction data X r , Xt r , establish the PCE model in the transformed input space; Step S4: Randomly select the initial population [p,λ], and use the sparrow search algorithm to adaptively select [p best ,λ best ]; Step S5, reconstruct the dimension-reduced PCE model, using the [p best ,λ best ]Build a proxy model that takes into account both accuracy and sparsity; Step S6: structural reliability analysis, calculating failure probability and reliability index.

3. The jacket platform reliability analysis method based on data combination dimension reduction and polynomial chaos expansion according to claim 2 is characterized in that: The step S1 prepares training samples X, Y, and test samples Xt, Yt, and randomly generates input sample points according to the distribution law and coefficient of variation of the input variables of the jacket platform.

4. The jacket platform reliability analysis method based on data combination dimension reduction and polynomial chaos expansion according to claim 2 is characterized in that: The step S2 specifically includes the following steps: Step S2.1 Calculate the six information matrices K of the combined dimensionality reduction method according to the following formula: j , where j = 1, 2, 3, 4, 5, 6: X is a high-dimensional input sample; T represents matrix transpose; κ is a different kernel function, and the kernel function κ is calculated according to the following formula k : N is the number of input samples; x8 is the input sample of the i-th row; For the Row input sample; σ is the bandwidth; q, η and θ are all random parameters, q ≥ 1, η > 0, θ < 0; is the partial gradient of the jth variable; Step S2.2: According to the following formula, the six information matrices K j Perform eigendecomposition: K j =WΛW ％ W is the eigenvector matrix; Λ is a diagonal matrix with descending eigenvalues; Step S2.3 selects the maximum principal component whose cumulative information exceeds the threshold k according to the following formula: r is the new dimension; n is the initial data dimension; k is the threshold; λ is the eigenvalue.

5. The jacket platform reliability analysis method based on data combination dimension reduction and polynomial chaos expansion according to claim 2 is characterized in that: The step S3 selects the first r where the accumulated information exceeds a fixed threshold j features, find r = min{r j } is the optimal dimensionality reduction method, and the transformation matrix W is obtained r , calculate the dimension reduction data X r , Xt r , specifically including the following steps: Step S3.1: The dimension of the space after dimensionality reduction corresponding to different methods r j Select the best dimensionality reduction method and determine the first r columns as the transformation matrix W according to the eigenvector matrix r , according to the following formula, each information matrix will get a new dimension r, and the dimensionality reduction method with the smallest dimension is selected: r=min{r j } Step S3.2: According to the following formula, the transformation matrix W is obtained according to the selected feature space dimension and feature vector matrix: r , and map the original input samples and original training samples to a low-dimensional space: X r =K×W r Xt r =Kt×W r X r is the input sample data of r dimension after dimensionality reduction; K is the original input sample information matrix; Xt r is the r-dimensional training data after dimensionality reduction; Kt is the original training sample information matrix.

6. The jacket platform reliability analysis method based on data combination dimension reduction and polynomial chaos expansion according to claim 2 is characterized in that: In step S4, the initial population [p,λ] is randomly selected, and the sparrow search algorithm is used to adaptively select [p best ,λ best ], specifically including the following steps: Step S4.1 first selects the initial population [p,λ] and calculates the individual fitness value according to the following formula: FindX=[p,λ] s.t.p∈N _ 1≤p≤20 0≤λ≤10 a Fit is the fitness value of the optimization target; Y is the response value of the training sample; Yt is the response value of the test sample; X is the set of optimization variables; p is the highest order of the polynomial; λ is the regularization parameter; RMSE(·) is the root mean square error between the predicted value and the actual value, which is calculated by the following formula: represents the true value; a8 represents the predicted value; N is the total number of training and testing samples; Delineate explorers and followers based on fitness values; Step S4.2 iteratively updates the position according to the explorer and follower position update strategy; Step S4.3: After the preset number of iterations, the fitness value remains unchanged, the highest order of the polynomial and the regularization parameter remain basically unchanged, and the global optimal individual is output: X best =[p best 4,4λ best ]。 7. The jacket platform reliability analysis method based on data combination dimension reduction and polynomial chaos expansion according to claim 2 is characterized in that: The step S5, reconstructing the dimension reduction PCE model, adopting the BGCD algorithm to solve, the specific steps are as follows: Step S5.1 constructs a PCE model according to the following formula: x is the input variable sample; y is the response of the input sample; α=(α8,…,α S ) is an n-dimensional index, i = 1,...,n, and α8 ≥ 0; n is the model dimension; ψ α is a multivariate orthogonal polynomial basis; ψ α According to different data distribution types, if the data is uniformly distributed, the Legendre polynomial basis is used; if the data is Gaussian distributed, the Hermite polynomial basis is used; β α are the unknown coefficients corresponding to the polynomial basis; Step S5.2 truncates the complete polynomial chaotic expansion, and the truncated polynomial chaotic expansion is shown in the following formula: is the defined multivariate indicator set, where p is the p obtained in step S4 best Step S5.3 uses the BGCD method to calculate the unknown coefficients of the polynomial.

8. The method for analyzing the reliability of a jacket platform based on data combination dimension reduction and polynomial chaos expansion according to claim 7 is characterized in that: The step S5.3 uses the BGCD method to calculate the unknown coefficients of the polynomial, specifically: The solution of polynomial coefficients is transformed into an optimization problem using l3 norm and l2 norm regularization. Solve the l3 norm and l according to the following formula x Norm minimization problem: y is the exact response value of the input sample; β is the polynomial basis coefficient; ψ is the multivariate orthogonal polynomial basis vector; ‖·‖1 indicates the 1-norm; ‖·‖2 represents the 2-norm; According to the following formula, the inner loop uses the greedy coordinate descent method to iterate according to the coordinate with the largest energy attenuation: φ j represents the element in the jth column; γ j Represents the residual sum of the true value and predicted value of the input sample except the jth column; λ best is the optimal regularization parameter; At the same time, the outer loop is updated using the Bregman iteration method according to the following formula: During the iteration process, if the error meets the accuracy requirement of 1, the greedy coordinate descent iteration is completed: represents the polynomial basis coefficients of the t-th iteration; β t；3 represents the polynomial basis coefficients of the t-1th iteration; Tol1 represents the error threshold of accuracy requirement 1; If the error does not meet the accuracy requirement 1, the Bregman iteration is used to update the response value: and t+1 =y+(y t -ψβ t+1 ) y t_1 represents the predicted response value of the t+1th iteration; y is the exact response value of the input sample; y t represents the predicted response value of the tth iteration; ψ represents the multivariate orthogonal polynomial basis vector; β t_1 represents the polynomial basis coefficients of the t+1th iteration; The iteration stops until the following accuracy requirement 2 is met: ψ represents the multivariate orthogonal polynomial basis vector; β t represents the polynomial basis coefficients of the t-th iteration; ∥·∥ x represents the second norm value; Tol2 represents the error threshold of accuracy requirement 2.

9. The jacket platform reliability analysis method based on data combination dimension reduction and polynomial chaos expansion according to claim 2 is characterized in that: The step S6 calculates the failure probability according to the following formula: Pf=∫ {x:g(x)·0} f X (x)dx P f is the failure probability of the model; f X (x) is the joint probability density function of the input variables; g(x) is the limit state function.

10. The jacket platform reliability analysis method based on data combination dimension reduction and polynomial chaos expansion according to claim 9 is characterized in that: The model reliability index in step S6 is calculated by the following formula: d=-Φ -1 (P f ) δ is the reliability index of the model; Φ -1 (·) is an inverse normal cumulative distribution function.

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