A rapid simulation method and system for bridge pulsating wind field

Abstract

This application relates to a rapid simulation method and system for a bridge fluctuating wind field. The method involves obtaining the dual-index frequency of each wind speed simulation point at all sampling frequencies and constructing a dual-index frequency matrix. The dual-index frequency matrix is ​​then used to construct a spectral density matrix for the wind speed simulation point at a single sampling frequency. The spectral density matrix of the wind speed simulation point at a single sampling frequency is subjected to Cholesky decomposition to obtain an n×n-dimensional Cholesky decomposition matrix for the single sampling frequency. This process is repeated to obtain Cholesky decomposition matrices for N sampling frequencies. All n×n-dimensional Cholesky decomposition matrices are assembled to obtain an n×n×N-dimensional Cholesky decomposition matrix. Using the harmonic synthesis method and the n×n×N-dimensional Cholesky decomposition matrix, the wind speed time series for all wind speed simulation points in the bridge fluctuating wind field are obtained. This application can improve the efficiency of fluctuating wind field generation.

Description

Technical Field

[0001] The present application relates to the technical field of bridge pulsating wind fields, and in particular to a rapid simulation method and system for bridge pulsating wind fields. Background Art

[0002] To accurately obtain the time history of the buffeting force caused by turbulence, the time history of the fluctuating wind speed on the bridge must first be obtained. Specifically, the time history of the fluctuating wind speed is the basic data for calculating and analyzing the response of bridge structures under crosswind forces. Therefore, its accurate acquisition is crucial for evaluating the safety and stability of bridges. However, in actual operation, due to the limitations of the on-site environment and the constraints of equipment conditions, the fluctuating wind speed time history signals currently obtained through actual measurements are usually very limited. Such limitations include but are not limited to the difficulty of arranging on-site instruments, insufficient measurement time, and interference from natural environmental factors. Therefore, relying solely on field measured data cannot fully meet the requirements for in-depth analysis and design.

[0003] Generally speaking, wind speed simulation can be categorized into two methods: harmonic synthesis and linear filtering. Currently, the harmonic synthesis method is widely used in China to simulate fluctuating wind speeds. This traditional method utilizes spectral decomposition and trigonometric series superposition to simulate random process samples. This method is simple, straightforward, and highly accurate, demonstrating excellent applicability and reliability, particularly for stationary random processes with arbitrary spectral characteristics. However, the simulation process involves Cholesky decomposition of the cross-spectral density matrix, a significant factor affecting the computational efficiency of the harmonic synthesis method. In bridge finite element analysis, due to structural complexity and simulation requirements, a denser wind speed simulation point density indicates more accurate wind speed simulation. This typically requires a large number of simulation points and a long simulation time. Therefore, when applying the harmonic synthesis method, each cosine superposition operation for each dual-index frequency value must undergo a Cholesky decomposition. Since the computational dimensionality of the Cholesky decomposition increases with the number of simulation points, repeating this operation at each time step significantly increases the computational effort, resulting in an extremely large overall computational burden. This phenomenon highlights the significant increase in computational burden of the harmonic synthesis method compared to the linear filtering method when simulating large-scale random processes. Therefore, although the harmonic synthesis method can provide highly accurate simulation results, the computational challenges it faces in practical applications of long-span bridge simulations also require special attention and resolution.

[0004] MATLAB is a mathematical software widely used in scientific computing, data analysis, and visualization. The chol function is a key function in MATLAB, used to calculate the Cholesky decomposition of matrices. However, during use, it was discovered that while the chol function in MATLAB can directly perform Cholesky decomposition on a three-dimensional matrix S(ω), for large wind speed simulation points and sampling frequencies, MATLAB allocates a large amount of computational memory to S(ω), forming a large empty matrix. The decomposition calculations then need to be performed sequentially to fill this empty matrix. This results in wasted memory, and computational efficiency is significantly reduced, especially for matrices with large array dimensions. Summary of the Invention

[0005] The embodiments of the present application provide a method and system for quickly simulating a bridge pulsating wind field to solve the problem of low Cholesky decomposition calculation efficiency in related technologies.

[0006] In a first aspect, a method for rapidly simulating a bridge pulsating wind field is provided, comprising:

[0007] Based on the number of wind speed simulation points n, the number of sampling frequency points N, the frequency increment Δω, and the double-index frequency calculation formula, the double-index frequency corresponding to each wind speed simulation point at N sampling frequency points is obtained, and a double-index frequency matrix with a dimension of n×N is constructed and stored;

[0008] Call the double-index frequency matrix to construct the spectral density matrix of n wind speed simulation points under a single sampling frequency point. The dimension of the spectral density matrix is ​​n×n.

[0009] Perform Cholesky decomposition on the spectral density matrix of n wind speed simulation points at a single sampling frequency point to obtain a Cholesky decomposition matrix with a dimension of n×n at a single sampling frequency point and store it;

[0010] And so on, obtain the corresponding Cholesky decomposition matrix at N sampling frequency points;

[0011] Assemble all Cholesky decomposition matrices of dimension n×n to obtain a Cholesky decomposition matrix of dimension n×n×N;

[0012] Based on the harmonic synthesis method and the Cholesky decomposition matrix with dimension n×n×N, the wind speed time history of all wind speed simulation points in the bridge pulsating wind field is obtained.

[0013] In some embodiments, based on the number of wind speed simulation points n, the number of sampling frequency points N, the frequency increment Δω, and the dual-index frequency calculation formula, obtaining the dual-index frequency corresponding to each wind speed simulation point at the N sampling frequency points specifically includes:

[0014] Sort each wind speed simulation point according to the coordinate order of the bridge nodes, from left to right or from top to bottom;

[0015] Based on the number of wind speed simulation points n, the number of sampling frequency points N, the frequency increment Δω, and the dual-index frequency calculation formula, the dual-index frequency corresponding to the first wind speed simulation point at N sampling frequency points is obtained;

[0016] At the double index frequency corresponding to the N sampling frequency points of the previous wind speed simulation point, the value is increased. To obtain the double-curve corresponding to the current wind speed simulation point at N sampling frequency points

[0017] Citation frequency.

[0018] In some embodiments, performing Cholesky decomposition on the spectral density matrix of n wind speed simulation points at a single sampling frequency point to obtain a Cholesky decomposition matrix of dimension n×n at a single sampling frequency point specifically includes:

[0019] Sort each wind speed simulation point according to the coordinate order of the bridge nodes, from left to right or from top to bottom;

[0020] At a single sampling frequency point, calculate the Cholesky decomposition elements of the cross-spectrum between the j-th wind speed simulation point and the 1st to j-1th wind speed simulation points, as well as the Cholesky decomposition elements of the autospectrum between the j-th wind speed simulation point and the j-th wind speed simulation point, and assign the remaining Cholesky decomposition elements to 0, j = 1, 2, ..., n;

[0021] Combining the Cholesky decomposition element with the Cholesky decomposition matrix of the j-1th wind speed simulation point to obtain the Cholesky decomposition matrix of the jth wind speed simulation point, where the dimension of the Cholesky decomposition matrix is ​​j×n;

[0022] This process is deduced in this way until the Cholesky decomposition matrix of the n-th wind speed simulation point is calculated, and a Cholesky decomposition matrix of dimension n×n at a single sampling frequency point is obtained.

[0023] In a second aspect, a fast decomposition method of a spectral density matrix is ​​provided, which includes:

[0024] Based on the number of wind speed simulation points n, the number of sampling frequency points N, the frequency increment Δω, and the double-index frequency calculation formula, the double-index frequency corresponding to each wind speed simulation point at N sampling frequency points is obtained, and a double-index frequency matrix with a dimension of n×N is constructed and stored;

[0025] Call the double-index frequency matrix to construct the spectral density matrix of n wind speed simulation points under a single sampling frequency point. The dimension of the spectral density matrix is ​​n×n.

[0026] Perform Cholesky decomposition on the spectral density matrix of n wind speed simulation points at a single sampling frequency point to obtain a Cholesky decomposition matrix with a dimension of n×n at a single sampling frequency point and store it;

[0027] And so on, obtain the corresponding Cholesky decomposition matrix at N sampling frequency points;

[0028] All Cholesky decomposition matrices of dimension n×n are assembled to obtain a Cholesky decomposition matrix of dimension n×n×N.

[0029] In some embodiments, based on the number n of wind speed simulation points, the number N of sampling frequency points, the frequency increment Δω, and the dual-index frequency calculation formula, obtaining the dual-index frequency corresponding to each wind speed simulation point at the N sampling frequency points specifically includes:

[0030] Sort each wind speed simulation point according to the coordinate order of the bridge nodes, from left to right or from top to bottom;

[0031] Based on the number of wind speed simulation points n, the number of sampling frequency points N, the frequency increment Δω, and the dual-index frequency calculation formula, the dual-index frequency corresponding to the first wind speed simulation point at N sampling frequency points is obtained;

[0032] At the double index frequency corresponding to the N sampling frequency points of the previous wind speed simulation point, the value is increased. To obtain the double-curve corresponding to the current wind speed simulation point at N sampling frequency points

[0033] Citation frequency.

[0034] In some embodiments, performing Cholesky decomposition on the spectral density matrix of n wind speed simulation points at a single sampling frequency point to obtain a Cholesky decomposition matrix of dimension n×n at a single sampling frequency point specifically includes:

[0035] Sort each wind speed simulation point according to the coordinate order of the bridge nodes, from left to right or from top to bottom;

[0036] At a single sampling frequency point, calculate the Cholesky decomposition elements of the cross-spectrum between the j-th wind speed simulation point and the 1st to j-1th wind speed simulation points, as well as the Cholesky decomposition elements of the autospectrum between the j-th wind speed simulation point and the j-th wind speed simulation point, and assign the remaining Cholesky decomposition elements to 0, j = 1, 2, ..., n;

[0037] Combining the Cholesky decomposition element with the Cholesky decomposition matrix of the j-1th wind speed simulation point to obtain the Cholesky decomposition matrix of the jth wind speed simulation point, where the dimension of the Cholesky decomposition matrix is ​​j×n;

[0038] The Cholesky decomposition matrices of the n wind speed simulation points are combined to obtain a Cholesky decomposition matrix of dimension n×n at a single sampling frequency point.

[0039] In a third aspect, a fast decomposition system for a spectral density matrix is ​​provided, comprising:

[0040] The first module is used to obtain the dual-index frequency corresponding to each wind speed simulation point at N sampling frequency points based on the number of wind speed simulation points n, the number of sampling frequency points N, the frequency increment Δω, and the dual-index frequency calculation formula, construct and store the dual-index frequency matrix with a dimension of n×N;

[0041] The second module is used to: call the double-index frequency matrix to construct the spectral density matrix of n wind speed simulation points at a single sampling frequency point, where the dimension of the spectral density matrix is ​​n×n; perform Cholesky decomposition on the spectral density matrix of n wind speed simulation points at a single sampling frequency point to obtain a Cholesky decomposition matrix with a dimension of n×n at a single sampling frequency point, and store it; and so on, obtain the corresponding Cholesky decomposition matrix at N sampling frequency points;

[0042] The third module is used to assemble all Cholesky decomposition matrices with a dimension of n×n to obtain a Cholesky decomposition matrix with a dimension of n×n×N.

[0043] In a fourth aspect, a rapid simulation system for a bridge pulsating wind field is provided, comprising:

[0044] The first module is used to obtain the dual-index frequency corresponding to each wind speed simulation point at N sampling frequency points based on the number of wind speed simulation points n, the number of sampling frequency points N, the frequency increment Δω, and the dual-index frequency calculation formula, construct and store the dual-index frequency matrix with a dimension of n×N;

[0045] The second module is used to: call the double-index frequency matrix to construct the spectral density matrix of n wind speed simulation points at a single sampling frequency point, where the dimension of the spectral density matrix is ​​n×n; perform Cholesky decomposition on the spectral density matrix of n wind speed simulation points at a single sampling frequency point to obtain a Cholesky decomposition matrix with a dimension of n×n at a single sampling frequency point, and store it; and so on, obtain the corresponding Cholesky decomposition matrix at N sampling frequency points;

[0046] The third module is used to assemble all Cholesky decomposition matrices of dimension n×n to obtain a Cholesky decomposition matrix of dimension n×n×N;

[0047] The fourth module is used to obtain the wind speed time history of all wind speed simulation points in the bridge pulsating wind field based on the harmonic synthesis method and the Cholesky decomposition matrix with a dimension of n×n×N.

[0048] In a fifth aspect, a storage medium is provided, on which a computer program is stored. When the computer program is executed by a processor, it implements any of the above-mentioned methods for rapid simulation of a bridge pulsating wind field or any of the above-mentioned methods for rapid decomposition of a spectral density matrix.

[0049] In a sixth aspect, an electronic device is provided, comprising a memory and a processor, wherein the memory stores a computer program running on the processor, and when the processor executes the computer program, it implements any of the above-described rapid simulation methods of the bridge pulsating wind field or any of the above-described rapid decomposition methods of the spectral density matrix.

[0050] The beneficial effects of the technical solution provided by this application include:

[0051] In this application, the double-index frequency corresponding to each wind speed simulation point under N sampling frequency points is constructed into a double-index frequency matrix of dimension n×N and stored in advance. When constructing the spectral density matrix of n wind speed simulation points subsequently, it can be directly called without repeated calculation. Then, for the N sampling frequency points, the spectral density matrix of n wind speed simulation points under a single sampling frequency point is constructed to reduce the dimension of the original spectral density matrix of dimension n×n×N to N spectral density matrices of n wind speed simulation points under a single sampling frequency point of n×n. Then, the Cholesky decomposition of the spectral density matrix of n wind speed simulation points under a single sampling frequency point is performed. After the decomposition is completed, all the Cholesky decomposition matrices of N dimensions of n×n are assembled to obtain the final Cholesky decomposition matrix of the spectral density matrix of dimension n×n×N. This can save a lot of time, improve the efficiency of Cholesky decomposition calculation, and thus improve the efficiency of generating pulsating wind fields. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the following briefly introduces the drawings required for use in the description of the embodiments. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without any creative work.

[0053] Figure 1 A flow chart of a rapid simulation method for a bridge pulsating wind field provided in an embodiment of the present application;

[0054] Figure 2 Block diagram of the rapid simulation system for bridge pulsating wind fields provided in an embodiment of the present application. DETAILED DESCRIPTION

[0055] To make the purpose, technical solutions, and advantages of the embodiments of this application more clear, the technical solutions in the embodiments of this application will be clearly and completely described below in conjunction with the drawings in the embodiments of this application. Obviously, the described embodiments are part of the embodiments of this application, not all of the embodiments. Based on the embodiments in this application, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of this application.

[0056] See also Figure 1 As shown, the embodiment of the present application provides a rapid simulation method for a bridge pulsating wind field, which includes:

[0057] 101: Based on the number of wind speed simulation points n, the number of sampling frequency points N, the frequency increment Δω, and the dual-index frequency calculation formula, obtain the dual-index frequency corresponding to each wind speed simulation point at the N sampling frequency points, construct a dual-index frequency matrix with a dimension of n×N, and store it.

[0058] 102: Call the dual-index frequency matrix to construct a spectral density matrix of n wind speed simulation points at a single sampling frequency point. The dimension of the spectral density matrix is ​​n×n. Perform Cholesky decomposition on the spectral density matrix of n wind speed simulation points at a single sampling frequency point to obtain a Cholesky decomposition matrix of n×n dimension at a single sampling frequency point and store it. Repeat this process to obtain the corresponding Cholesky decomposition matrix at N sampling frequency points.

[0059] 103: Assemble all Cholesky decomposition matrices of dimension n×n to obtain a Cholesky decomposition matrix of dimension n×n×N.

[0060] 104: Based on the harmonic synthesis method and the Cholesky decomposition matrix with dimension n×n×N, the wind speed time history of all wind speed simulation points in the bridge pulsating wind field is obtained.

[0061] The principles of this application are as follows:

[0062] Taking n wind speed simulation points as variables, its spectral density matrix S(ω) is:

[0063]

[0064] According to Shinozuka's theory, the random process of the j-th wind speed simulation point, that is, the time history of the fluctuating wind speed, can be simulated by the following formula:

[0065]

[0066] Where N is the number of sampling frequency points. Theoretically, N should be N→∞. In practice, a sufficiently large positive integer can ensure the accuracy of the simulation. In order to use FFT technology in the calculation, N is generally an integer multiple of 2. Δω is the frequency increment, and Δω=ω up / N;ω ml is the double index frequency, and the double index calculation formula is (l=1,2,…,N), (m=1,2,…,n);φ ml is a random phase angle uniformly distributed in [0,2π]; ω up is the upper cutoff frequency; H jm (ω ml ) are the elements in the lower triangular matrix H(ω), and H(ω) is the Cholesky decomposition matrix of S(ω).

[0067] S(ω)=H(ω)H * (ω) (3)

[0068]

[0069] Since S(ω) is generally a complex matrix and a symmetric positive definite matrix, H(ω) is usually also a complex matrix, with real diagonal elements and complex off-diagonal elements. * (ω) is the conjugate transposed matrix of H(ω).

[0070] By observing formula (1), we can find that S(ω) is a multidimensional matrix related to n variables, where 11 (ω) to S nn (ω) has a total of n×n elements, ω is a double-index frequency matrix, ω ml is one of the elements in the double index frequency matrix ω. Based on the above double index frequency formula, since l=1,2,…,N, the double index frequency matrix ω is a two-dimensional matrix of n×N. Similarly, from S 11 (ω) to S nn (ω) A total of n×n elements are all n×N two-dimensional matrices, H 11 (ω) to H nn (ω) are all n×N two-dimensional matrices, so S(ω) is a three-dimensional matrix composed of n two-dimensional matrices, and its dimension is n×n×N. Similarly, the dimension of H(ω) is also n×n×N.

[0071] Cholesky decomposition is a factorization technique in linear algebra used to decompose a symmetric positive definite matrix into the product of two matrices.

[0072] The Cholesky decomposition steps can be summarized as follows:

[0073] Let matrix A be a symmetric positive definite matrix, then there exists a real non-singular lower triangular matrix L such that:

[0074] A=LL * (5)

[0075] Among them, L * is the conjugate transposed matrix of L, and L is:

[0076]

[0077] The decomposition steps are:

[0078] For j = 1, 2, ..., n

[0079]

[0080] From the above formula (6), when j = 1, we only need to calculate l 11 , followed by all 0, the resulting matrix is ​​recorded as L1, when j = 2, only l 21 、l 22 , all the following are 0, and L2 can be obtained by superimposing L1. When j=3, it is only necessary to calculate l 31 、l 32 、l 33 , all the latter are 0, and L3 can be obtained by superimposing L2. It can be seen that the calculation of L j When , only the first j elements need to be calculated, and then the previous L j-1 , you can get it without calculating L j When, repeatedly from l 11 Start calculating, and there is no need to calculate all elements after the first j elements, which can save a lot of settlement time.

[0081] Since the Cholesky decomposition can only process two-dimensional arrays, the spectral density matrix S(ω) of n variables is a three-dimensional matrix of n×n×N. Therefore, the Cholesky decomposition of the n×n two-dimensional array must be performed within N sampling frequency points. The sampling frequency point N is related to the time history and has nothing to do with the computational efficiency of the harmonic synthesis method.

[0082] When simulating the time history of the j-th wind speed simulation point, the double index frequency ω of the j-th wind speed simulation point must be obtained first. jlWhen there are too many wind speed simulation points n for a long-span bridge, Cholesky decomposition is required for each cosine superposition of each double-index frequency. This is why the repeated superposition of the harmonic synthesis method in MATLAB results in a large amount of calculation.

[0083] The frequency calculation formula is based on the double index (l=1,2,…,N),(m=1,2,…,n). Find ω ml The value of The influence of the term is, to be more precise, related to m (representing the mth wind speed simulation point). Then the spectral density matrix of formula (1) can be written as:

[0084]

[0085] Among them, ω ml It can be expressed as:

[0086]

[0087] Because ω ml It is only related to m, so when calculating the Cholesky decomposition of the m-th wind speed simulation point, it is only necessary to add the double index frequency of the previous m-1-th wind speed simulation point That is the double index frequency of the mth point. ml ), there is no need to ml ) matrix to perform Cholesky decomposition. Simply superimpose the first m-1 H(ω) to calculate H(ω ml ). Therefore, a lot of settlement time is saved from Cholesky decomposition. Indirectly convert S(ω ml ) to perform dimensionality reduction.

[0088] It can be seen that in this application, the double-index frequency corresponding to each wind speed simulation point under N sampling frequency points is constructed into a double-index frequency matrix of dimension n×N and stored in advance. When constructing the spectral density matrix of n wind speed simulation points subsequently, it can be directly called without repeated calculations. Then, for the N sampling frequency points, the spectral density matrix of n wind speed simulation points under a single sampling frequency point is constructed to reduce the dimension of the original spectral density matrix of dimension n×n×N to N spectral density matrices of n wind speed simulation points under a single sampling frequency point of n×n. Then, the Cholesky decomposition of the spectral density matrix of n wind speed simulation points under a single sampling frequency point is performed. After the decomposition is completed, all the Cholesky decomposition matrices of N dimensions of n×n are assembled to obtain the final Cholesky decomposition matrix of the spectral density matrix of dimension n×n×N. This can save a lot of time, improve the efficiency of the Cholesky decomposition calculation, and thus improve the efficiency of the pulsating wind field generation.

[0089] In the above step 101, based on the number of wind speed simulation points n, the number of sampling frequency points N, the frequency increment Δω, and the dual-index frequency calculation formula, the dual-index frequency corresponding to each wind speed simulation point at N sampling frequency points is obtained, specifically including:

[0090] 201: Sort each wind speed simulation point from left to right or from top to bottom according to the coordinate order of the bridge node;

[0091] 202: Based on the number n of wind speed simulation points, the number N of sampling frequency points, the frequency increment Δω, and the dual-index frequency calculation formula, obtain the dual-index frequency corresponding to the first wind speed simulation point at N sampling frequency points;

[0092] 203: At the double index frequencies corresponding to the N sampling frequency points of the previous wind speed simulation point, all increase To obtain the dual index frequency corresponding to the current wind speed simulation point at N sampling frequency points.

[0093] In this application, the double index frequency corresponding to the first wind speed simulation point at N sampling frequency points is directly calculated using the double index frequency calculation formula, and the double index frequency corresponding to the subsequent wind speed simulation points at N sampling frequency points is based on the double index frequency corresponding to the N sampling frequency points of the previous wind speed simulation point, and the double index frequency corresponding to the N sampling frequency points is increased. It can be seen that compared with repeatedly calling the double-index frequency calculation formula for calculation, this method of increasing the difference can also improve calculation efficiency to a certain extent.

[0094] In the above step 101, Cholesky decomposition is performed on the spectral density matrix of n wind speed simulation points at a single sampling frequency point to obtain a Cholesky decomposition matrix with a dimension of n×n at a single sampling frequency point, specifically including:

[0095] 301: Sort each wind speed simulation point from left to right or from top to bottom according to the coordinate order of the bridge node;

[0096] 302: At a single sampling frequency point, calculate the Cholesky decomposition elements of the cross-spectrum between the j-th wind speed simulation point and the 1st to j-1th wind speed simulation points, as well as the Cholesky decomposition elements of the autospectrum between the j-th wind speed simulation point and the j-th wind speed simulation point. Since the Cholesky decomposition matrix is ​​a lower triangular matrix, the remaining Cholesky decomposition elements are directly assigned 0, and j = 1, 2, ..., n;

[0097] 303: combining the Cholesky decomposition element with the Cholesky decomposition matrix of the j-1th wind speed simulation point to obtain the Cholesky decomposition matrix of the jth wind speed simulation point, where the dimension of the Cholesky decomposition matrix is ​​j×n;

[0098] 304: Loop through steps 302-303 until the Cholesky decomposition matrix of the n-th wind speed simulation point is calculated, and obtain a Cholesky decomposition matrix of dimension n×n at a single sampling frequency point.

[0099] For steps 301-304, formula (6) can be combined. For example, as an example, j=3, then the elements of L2 include l 11 、l 21 、l 22 All are known, and now we only need to calculate the Cholesky decomposition element l under the cross spectrum between the third wind speed simulation point and the first to second wind speed simulation points. 31 、l 32 , and the Cholesky decomposition element l under the self-spectrum between the third wind speed simulation point and the third wind speed simulation point 33 , and then l 31 、l 32 、l 33 By superimposing it with L2, we can get L3 with dimension 3×n.

[0100] Similarly, when j = n, we only need to calculate l n1 、l n2 ,…,l nn , and then with L n-1 By superposition, we can get L with dimension n×n n .

[0101] Based on the above-mentioned rapid simulation method for the fluctuating wind field of a bridge, it can be understood that, in fact, the above-mentioned rapid simulation method also discloses a rapid decomposition method of the spectral density matrix, which includes:

[0102] 401: Based on the number of wind speed simulation points n, the number of sampling frequency points N, the frequency increment Δω, and the dual-index frequency calculation formula, obtain the dual-index frequency corresponding to each wind speed simulation point at the N sampling frequency points, construct a dual-index frequency matrix with a dimension of n×N, and store it;

[0103] 402: Call the dual-index frequency matrix to construct a spectral density matrix of n wind speed simulation points at a single sampling frequency point. The dimension of the spectral density matrix is ​​n×n. Perform Cholesky decomposition on the spectral density matrix of n wind speed simulation points at a single sampling frequency point to obtain a Cholesky decomposition matrix of n×n dimension at a single sampling frequency point, and store it. Repeat this process to obtain the corresponding Cholesky decomposition matrix at N sampling frequency points.

[0104] 403: Assemble all Cholesky decomposition matrices of dimension n×n to obtain a Cholesky decomposition matrix of dimension n×n×N.

[0105] In the above step 401, based on the number of wind speed simulation points n, the number of sampling frequency points N, the frequency increment Δω, and the dual-index frequency calculation formula, the dual-index frequency corresponding to each wind speed simulation point at N sampling frequency points is obtained, specifically including:

[0106] 501: Sort the wind speed simulation points from left to right or from top to bottom according to the coordinate order of the bridge nodes;

[0107] 502: Based on the number n of wind speed simulation points, the number N of sampling frequency points, the frequency increment Δω, and the dual-index frequency calculation formula, obtain the dual-index frequency corresponding to the first wind speed simulation point at N sampling frequency points;

[0108] 503: Increase the double index frequency corresponding to the N sampling frequency points of the previous wind speed simulation point. To obtain the dual index frequency corresponding to the current wind speed simulation point at N sampling frequency points.

[0109] In step 402, the spectral density matrix of n wind speed simulation points at a single sampling frequency point is subjected to Cholesky decomposition to obtain a Cholesky decomposition matrix of dimension n×n at a single sampling frequency point, specifically including:

[0110] 601: Sort each wind speed simulation point from left to right or from top to bottom according to the coordinate order of the bridge node;

[0111] 602: At a single sampling frequency point, calculate the Cholesky decomposition elements of the cross-spectrum between the j-th wind speed simulation point and the 1st to j-1th wind speed simulation points, and the Cholesky decomposition elements of the auto-spectrum between the j-th wind speed simulation point and the j-th wind speed simulation point, and assign 0 to the remaining Cholesky decomposition elements, j = 1, 2, ..., n;

[0112] 603: combining the Cholesky decomposition element with the Cholesky decomposition matrix of the j-1th wind speed simulation point to obtain the Cholesky decomposition matrix of the jth wind speed simulation point, where the dimension of the Cholesky decomposition matrix is ​​j×n;

[0113] 604: Combine the Cholesky decomposition matrices of the n wind speed simulation points to obtain a Cholesky decomposition matrix of dimension n×n at a single sampling frequency point.

[0114] Corresponding to the above-mentioned fast decomposition method of the spectral density matrix, an embodiment of the present application further provides a fast decomposition system of the spectral density matrix, which includes:

[0115] The first module is used to obtain the dual-index frequency corresponding to each wind speed simulation point at N sampling frequency points based on the number of wind speed simulation points n, the number of sampling frequency points N, the frequency increment Δω, and the dual-index frequency calculation formula, construct and store the dual-index frequency matrix with a dimension of n×N;

[0116] The second module is used to: call the double-index frequency matrix to construct the spectral density matrix of n wind speed simulation points at a single sampling frequency point, where the dimension of the spectral density matrix is ​​n×n; perform Cholesky decomposition on the spectral density matrix of n wind speed simulation points at a single sampling frequency point to obtain a Cholesky decomposition matrix with a dimension of n×n at a single sampling frequency point, and store it; and so on, obtain the corresponding Cholesky decomposition matrix at N sampling frequency points;

[0117] The third module is used to assemble all Cholesky decomposition matrices with a dimension of n×n to obtain a Cholesky decomposition matrix with a dimension of n×n×N.

[0118] See also Figure 2 As shown, corresponding to the above-mentioned rapid simulation method of the bridge pulsating wind field, the embodiment of the present application further provides a rapid simulation system of the bridge pulsating wind field, which includes:

[0119] The first module is used to obtain the dual-index frequency corresponding to each wind speed simulation point at N sampling frequency points based on the number of wind speed simulation points n, the number of sampling frequency points N, the frequency increment Δω, and the dual-index frequency calculation formula, construct and store the dual-index frequency matrix with a dimension of n×N;

[0120] The second module is used to: call the double-index frequency matrix to construct the spectral density matrix of n wind speed simulation points at a single sampling frequency point, where the dimension of the spectral density matrix is ​​n×n; perform Cholesky decomposition on the spectral density matrix of n wind speed simulation points at a single sampling frequency point to obtain a Cholesky decomposition matrix with a dimension of n×n at a single sampling frequency point, and store it; and so on, obtain the corresponding Cholesky decomposition matrix at N sampling frequency points;

[0121] The third module is used to assemble all Cholesky decomposition matrices of dimension n×n to obtain a Cholesky decomposition matrix of dimension n×n×N;

[0122] The fourth module is used to obtain the wind speed time history of all wind speed simulation points in the bridge pulsating wind field based on the harmonic synthesis method and the Cholesky decomposition matrix with a dimension of n×n×N.

[0123] Corresponding to the above-mentioned rapid simulation method of the bridge fluctuating wind field or the rapid decomposition method of the spectral density matrix, the embodiments of the present application also provide a storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the above-mentioned embodiments. It should be noted that the storage medium of the embodiments of the present application can adopt any combination of one or more computer-readable media. The computer-readable medium can be a computer-readable signal medium or a computer-readable storage medium. The computer-readable storage medium can be, for example, but not limited to: an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, device or component, or any combination thereof. More specific examples (a non-exhaustive list) of computer-readable storage media include: an electrical connection with one or more wires, a portable computer disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disk read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the above. In this document, a computer-readable storage medium can be any tangible medium containing or storing a program that can be used by or in conjunction with an instruction execution system, device, or component.

[0124] A computer-readable signal medium may include a data signal propagated in baseband or as part of a carrier wave, which carries computer-readable program code. Such propagated data signals may take various forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination thereof. A computer-readable signal medium may also be any computer-readable medium other than a computer-readable storage medium that can transmit, propagate, or transport a program for use by or in conjunction with an instruction execution system, apparatus, or device.

[0125] Program code embodied on a computer-readable medium may be transmitted using any appropriate medium, including but not limited to wireless, wireline, optical fiber cable, RF, etc., or any suitable combination of the foregoing.

[0126] The computer program code for performing the operations of the present application can be written in one or more programming languages ​​or a combination thereof, including object-oriented programming languages ​​such as Java, Smalltalk, C++, and conventional procedural programming languages ​​such as "C" or similar programming languages. The program code can be executed entirely on the user's computer, partially on the user's computer, as a separate software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In cases involving a remote computer, the remote computer can be connected to the user's computer through any type of network, including a local area network (LAN) or a wide area network (WAN), or can be connected to an external computer (e.g., via the Internet using an Internet service provider).

[0127] Corresponding to the above-mentioned method for rapid simulation of the bridge pulsating wind field or the method for rapid decomposition of the spectral density matrix, an embodiment of the present application further provides an electronic device, including a memory and a processor, wherein the memory stores a computer program running on the processor, and the processor implements the steps of the above-mentioned embodiments when executing the computer program.

[0128] In the description of this application, it should be noted that the terms "upper" and "lower" and the like indicate orientations or positional relationships based on the orientations or positional relationships shown in the accompanying drawings, and are only for the convenience of describing this application and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as a limitation on this application. Unless otherwise clearly specified and limited, the terms "installed", "connected", and "connected" should be understood in a broad sense, for example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection, or an indirect connection through an intermediate medium, or it can be internal communication between two elements. For those of ordinary skill in the art, the specific meanings of the above terms in this application can be understood according to the specific circumstances.

[0129] It should be noted that, in this application, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship or order between these entities or operations. Moreover, the terms "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device comprising a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In the absence of further restrictions, an element defined by the sentence "comprising a ..." does not exclude the presence of other identical elements in the process, method, article or device comprising the element.

[0130] The foregoing is merely a list of specific embodiments of the present application, intended to enable those skilled in the art to understand or implement the present application. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present application. Therefore, the present application is not limited to the embodiments shown herein, but is intended to conform to the broadest scope consistent with the principles and novel features of the present application.

Claims

1. A rapid simulation method for bridge pulsating wind field, characterized in that: It includes: Based on the number of wind speed simulation points n, the number of sampling frequency points N, the frequency increment Δω, and the double-index frequency calculation formula, the double-index frequency corresponding to each wind speed simulation point at N sampling frequency points is obtained, and a double-index frequency matrix with a dimension of n×N is constructed and stored; Call the double-index frequency matrix to construct the spectral density matrix of n wind speed simulation points under a single sampling frequency point. The dimension of the spectral density matrix is ​​n×n. Perform Cholesky decomposition on the spectral density matrix of n wind speed simulation points at a single sampling frequency point to obtain a Cholesky decomposition matrix with a dimension of n×n at a single sampling frequency point and store it; And so on, obtain the corresponding Cholesky decomposition matrix at N sampling frequency points; Assemble all Cholesky decomposition matrices of dimension n×n to obtain a Cholesky decomposition matrix of dimension n×n×N; Based on the harmonic synthesis method and the Cholesky decomposition matrix with dimension n×n×N, the wind speed time history of all wind speed simulation points in the bridge pulsating wind field is obtained.

2. The rapid simulation method for bridge pulsating wind field according to claim 1, characterized in that: Based on the number of wind speed simulation points n, the number of sampling frequency points N, the frequency increment Δω, and the dual-index frequency calculation formula, the dual-index frequency corresponding to each wind speed simulation point at N sampling frequency points is obtained, specifically including: Sort each wind speed simulation point according to the coordinate order of the bridge nodes, from left to right or from top to bottom; Based on the number of wind speed simulation points n, the number of sampling frequency points N, the frequency increment Δω, and the dual-index frequency calculation formula, the dual-index frequency corresponding to the first wind speed simulation point at N sampling frequency points is obtained; At the double index frequency corresponding to the N sampling frequency points of the previous wind speed simulation point, the value is increased. Δω is used to obtain the double index frequency corresponding to the current wind speed simulation point at N sampling frequency points.

3. The rapid simulation method for bridge pulsating wind field according to claim 1, characterized in that: Perform Cholesky decomposition on the spectral density matrix of n wind speed simulation points at a single sampling frequency point to obtain a Cholesky decomposition matrix with a dimension of n×n at a single sampling frequency point, specifically including: Sort each wind speed simulation point according to the coordinate order of the bridge nodes, from left to right or from top to bottom; At a single sampling frequency point, calculate the Cholesky decomposition elements of the cross-spectrum between the j-th wind speed simulation point and the 1st to j-1th wind speed simulation points, as well as the Cholesky decomposition elements of the autospectrum between the j-th wind speed simulation point and the j-th wind speed simulation point, and assign the remaining Cholesky decomposition elements to 0, j = 1, 2, ..., n; Combining the Cholesky decomposition element with the Cholesky decomposition matrix of the j-1th wind speed simulation point to obtain the Cholesky decomposition matrix of the jth wind speed simulation point, where the dimension of the Cholesky decomposition matrix is ​​j×n; This process is deduced in this way until the Cholesky decomposition matrix of the n-th wind speed simulation point is calculated, and a Cholesky decomposition matrix of dimension n×n at a single sampling frequency point is obtained.

4. A fast decomposition method for spectral density matrix, characterized in that: It includes: Based on the number of wind speed simulation points n, the number of sampling frequency points N, the frequency increment Δω, and the double-index frequency calculation formula, the double-index frequency corresponding to each wind speed simulation point at N sampling frequency points is obtained, and a double-index frequency matrix with a dimension of n×N is constructed and stored; Call the double-index frequency matrix to construct the spectral density matrix of n wind speed simulation points under a single sampling frequency point. The dimension of the spectral density matrix is ​​n×n. Perform Cholesky decomposition on the spectral density matrix of n wind speed simulation points at a single sampling frequency point to obtain a Cholesky decomposition matrix with a dimension of n×n at a single sampling frequency point and store it; And so on, obtain the corresponding Cholesky decomposition matrix at N sampling frequency points; All Cholesky decomposition matrices of dimension n×n are assembled to obtain a Cholesky decomposition matrix of dimension n×n×N.

5. The fast decomposition method of spectral density matrix according to claim 4, characterized in that: Based on the number of wind speed simulation points n, the number of sampling frequency points N, the frequency increment Δω, and the dual-index frequency calculation formula, the dual-index frequency corresponding to each wind speed simulation point at N sampling frequency points is obtained, specifically including: Sort each wind speed simulation point according to the coordinate order of the bridge nodes, from left to right or from top to bottom; Based on the number of wind speed simulation points n, the number of sampling frequency points N, the frequency increment Δω, and the dual-index frequency calculation formula, the dual-index frequency corresponding to the first wind speed simulation point at N sampling frequency points is obtained; At the double index frequency corresponding to the N sampling frequency points of the previous wind speed simulation point, the value is increased. Δω is used to obtain the double index frequency corresponding to the current wind speed simulation point at N sampling frequency points.

6. The fast decomposition method of spectral density matrix according to claim 4, characterized in that: Perform Cholesky decomposition on the spectral density matrix of n wind speed simulation points at a single sampling frequency point to obtain a Cholesky decomposition matrix with a dimension of n×n at a single sampling frequency point, specifically including: Sort each wind speed simulation point according to the coordinate order of the bridge nodes, from left to right or from top to bottom; At a single sampling frequency point, calculate the Cholesky decomposition elements of the cross-spectrum between the j-th wind speed simulation point and the 1st to j-1th wind speed simulation points, as well as the Cholesky decomposition elements of the autospectrum between the j-th wind speed simulation point and the j-th wind speed simulation point, and assign the remaining Cholesky decomposition elements to 0, j = 1, 2, ..., n; Combining the Cholesky decomposition element with the Cholesky decomposition matrix of the j-1th wind speed simulation point to obtain the Cholesky decomposition matrix of the jth wind speed simulation point, where the dimension of the Cholesky decomposition matrix is ​​j×n; The Cholesky decomposition matrices of the n wind speed simulation points are combined to obtain a Cholesky decomposition matrix of dimension n×n at a single sampling frequency point.

7. A fast decomposition system for spectral density matrix, characterized in that: It includes: The first module is used to obtain the dual-index frequency corresponding to each wind speed simulation point at N sampling frequency points based on the number of wind speed simulation points n, the number of sampling frequency points N, the frequency increment Δω, and the dual-index frequency calculation formula, construct and store the dual-index frequency matrix with a dimension of n×N; The second module is used to: call the double-index frequency matrix to construct the spectral density matrix of n wind speed simulation points at a single sampling frequency point, where the dimension of the spectral density matrix is ​​n×n; perform Cholesky decomposition on the spectral density matrix of n wind speed simulation points at a single sampling frequency point to obtain a Cholesky decomposition matrix with a dimension of n×n at a single sampling frequency point, and store it; and so on, obtain the corresponding Cholesky decomposition matrix at N sampling frequency points; The third module is used to assemble all Cholesky decomposition matrices with a dimension of n×n to obtain a Cholesky decomposition matrix with a dimension of n×n×N.

8. A rapid simulation system for bridge pulsating wind field, characterized by: It includes: The first module is used to obtain the dual-index frequency corresponding to each wind speed simulation point at N sampling frequency points based on the number of wind speed simulation points n, the number of sampling frequency points N, the frequency increment Δω, and the dual-index frequency calculation formula, construct and store the dual-index frequency matrix with a dimension of n×N; The second module is used to: call the double-index frequency matrix to construct the spectral density matrix of n wind speed simulation points at a single sampling frequency point, where the dimension of the spectral density matrix is ​​n×n; perform Cholesky decomposition on the spectral density matrix of n wind speed simulation points at a single sampling frequency point to obtain a Cholesky decomposition matrix with a dimension of n×n at a single sampling frequency point, and store it; and so on, obtain the corresponding Cholesky decomposition matrix at N sampling frequency points; The third module is used to assemble all Cholesky decomposition matrices of dimension n×n to obtain a Cholesky decomposition matrix of dimension n×n×N; The fourth module is used to obtain the wind speed time history of all wind speed simulation points in the bridge pulsating wind field based on the harmonic synthesis method and the Cholesky decomposition matrix with a dimension of n×n×N.

9. A storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the method for rapidly simulating a bridge pulsating wind field according to any one of claims 1 to 3 or the method for rapidly decomposing a spectral density matrix according to any one of claims 4 to 6 is implemented.

10. An electronic device comprising a memory and a processor, wherein the memory stores a computer program running on the processor, wherein: When the processor executes the computer program, the method for rapidly simulating a bridge pulsating wind field as claimed in any one of claims 1 to 3 or the method for rapidly decomposing a spectral density matrix as claimed in any one of claims 4 to 6 is implemented.

Images