Rapid simulation method and system for bridge fluctuating wind field

Abstract

The invention relates to a rapid simulation method and system for a bridge fluctuating wind field, and the method comprises the steps: obtaining double-index frequencies of each wind speed simulation point under all sampling frequency points, and constructing a double-index frequency matrix; calling a double-index frequency matrix, and constructing a spectral density matrix of a wind speed simulation point under a single sampling frequency point; performing Cholesky decomposition on the spectral density matrix of the wind speed simulation point under the single sampling frequency point to obtain a Cholesky decomposition matrix with the dimension of n * n under the single sampling frequency point; and so on, obtaining a Cholesky decomposition matrix under the N sampling frequency points; all the Cholesky decomposition matrixes with the dimensions of n * n are assembled, and a Cholesky decomposition matrix with the dimensions of n * n * N is obtained; based on a harmonic synthesis method and the Cholesky decomposition matrix with the dimension of n * n * N, the wind speed time history with the wind speed simulation points in the bridge fluctuating wind place is obtained. The generation efficiency of the fluctuating wind field can be improved.

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] In order 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 the bridge structure under the action of crosswind force, so its accurate acquisition is crucial for evaluating the safety and stability of the bridge. However, in actual operation, due to the limitations of the site environment and the constraints of equipment conditions, the fluctuating wind speed time history signals currently measured 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, the data measured on site alone cannot fully meet the requirements for in-depth analysis and design.

[0003] In general, wind speed simulation can be divided into two methods: harmonic synthesis method and linear filtering method. At present, most of the domestic methods use the harmonic synthesis method to simulate and generate fluctuating wind speed, that is, the traditional method of using spectral decomposition and trigonometric series superposition to simulate random process samples. This method is simple and clear, with high accuracy. Especially when facing a stationary random process with arbitrary spectral characteristics, the harmonic synthesis method shows its good applicability and reliability. However, the simulation process involves the Cholesky decomposition of the cross-spectral density matrix, which is an important factor affecting the computational efficiency of the harmonic synthesis method. In the finite element analysis of bridges, due to the complexity of the structure and the simulation requirements, the denser the wind speed simulation points of the bridge, the more accurate the wind speed simulation. Usually, a large number of simulation points and a long simulation time are required. At this time, when applying the harmonic synthesis method, each cosine superposition operation of each double-index frequency value must be Cholesky decomposed. Since the computational dimension of the Cholesky decomposition increases with the number of simulation points, this operation is repeated in each time step, which will significantly increase the amount of calculation, resulting in the overall amount of calculation becoming extremely large. This phenomenon highlights the significant increase in the computational burden of the harmonic synthesis method compared to the linear filtering method when dealing with large-scale random process simulations. Therefore, although the harmonic synthesis method can provide high-precision simulation results, the computational challenges it faces in practical applications in long-span bridge simulations also need special attention and resolution.

[0004] MATLAB is a mathematical software that is widely used in scientific computing, data analysis, and visualization. Among them, the chol function is an important function in MATLAB, which is used to calculate the Cholesky decomposition of the matrix. However, it was found during use that although the chol function in MATLAB can directly perform Cholesky decomposition on the three-dimensional matrix S(ω), when the wind speed simulation points and sampling frequency are large, MATLAB will allocate a large computing memory to S(ω), forming a large empty matrix, and then perform decomposition calculations in sequence to fill this empty matrix. This results in a waste of memory, especially for matrices with large array dimensions, the computing efficiency is greatly reduced. 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 the related art.

[0006] In a first aspect, a rapid simulation method for a bridge pulsating wind field is provided, which comprises:

[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, the dual-index frequency corresponding to each wind speed simulation point at the N sampling frequency points is obtained, specifically including:

[0014] Sort each wind speed simulation point according to the coordinate sequence 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 double index frequency calculation formula, the double index frequency corresponding to the first wind speed simulation point under 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 index corresponding to the current wind speed simulation point at N sampling frequency points

[0017] Citation frequency.

[0018] In some embodiments, 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:

[0019] Sort each wind speed simulation point according to the coordinate sequence 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 under 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 under the self-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;

[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, the dimension of the Cholesky decomposition matrix being j×n;

[0022] This process is repeated 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 comprises:

[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 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 the N sampling frequency points is obtained, specifically including:

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

[0031] 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 the first wind speed simulation point under 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 index corresponding to the current wind speed simulation point at N sampling frequency points

[0033] Citation frequency.

[0034] In some embodiments, 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:

[0035] Sort each wind speed simulation point according to the coordinate sequence 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 under 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 under the self-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;

[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, the dimension of the Cholesky decomposition matrix being 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 of a spectral density matrix is ​​provided, comprising:

[0040] The first module is used to: 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, obtain the double index frequency corresponding to each wind speed simulation point under N sampling frequency points, construct a double index frequency matrix with a dimension of n×N and store it;

[0041] The second module is used to: call the double-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 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: 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, obtain the double index frequency corresponding to each wind speed simulation point under N sampling frequency points, construct a double index frequency matrix with a dimension of n×N and store it;

[0045] The second module is used to: call the double-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 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 with a dimension of n×n to obtain a Cholesky decomposition matrix with a dimension of 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, the method for rapidly simulating a bridge pulsating wind field as described above or the method for rapidly decomposing a spectral density matrix as described above is implemented.

[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 a bridge pulsating wind field or any of the above-described rapid decomposition methods of a spectral density matrix.

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

[0051] In the present 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 in the future, 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, and then perform Cholesky decomposition of the spectral density matrix of n wind speed simulation points under a single sampling frequency point. After the decomposition is completed, all 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, thereby saving a lot of time, improving the efficiency of Cholesky decomposition calculation, and thus improving the efficiency of pulsating wind field generation. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the drawings required for use in the description of the embodiments will be briefly introduced below. 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 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 A block diagram of a rapid simulation system for a bridge pulsating wind field provided in an embodiment of the present application. DETAILED DESCRIPTION

[0055] In order to make the purpose, technical solution and advantages of the embodiments of the present application clearer, the technical solution in the embodiments of the present application will be clearly and completely described below in conjunction with the drawings in the embodiments of the present application. Obviously, the described embodiments are part of the embodiments of the present application, not all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field without making creative work 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 double-index frequency calculation formula, obtain the double-index frequency corresponding to each wind speed simulation point under N sampling frequency points, construct a double-index frequency matrix with a dimension of n×N and store it.

[0058] 102: Call the double-index frequency matrix to construct a 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.

[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, the 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 ∞. In fact, 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 of 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. 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 an n × N two-dimensional matrix. Similarly, from S 11 (ω) to S nn (ω) A total of n×n elements are 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:

[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 0s, the resulting matrix is ​​recorded as L1. When j = 2, only l 21 , l 22 , all the latter are 0, and L2 can be obtained by superimposing L1. When j=3, we only need 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 , we only need to calculate the first j elements and then add 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 processing object of Cholesky decomposition can only be a two-dimensional array, 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, and 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 amount of repeated superposition calculations in the harmonic synthesis method in MATLAB is large.

[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 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 This is the double index frequency of the mth point. ml ), there is no need to ml ) matrix for Cholesky decomposition. We only need to 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 the present 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 in the future, 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, and then perform Cholesky decomposition of the spectral density matrix of n wind speed simulation points under a single sampling frequency point. After the decomposition is completed, all 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, thereby saving a lot of time, improving the efficiency of Cholesky decomposition calculation, and thus improving the efficiency of 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 sequence of the bridge nodes;

[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 the 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, 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 frequencies corresponding to the subsequent wind speed simulation points at N sampling frequency points are based on the double index frequencies corresponding to the N sampling frequency points of the previous wind speed simulation point. 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, which specifically includes:

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

[0096] 302: Under a single sampling frequency point, calculate the Cholesky decomposition elements under 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 under the self-spectrum 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, 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 according to steps 302-303 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.

[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. At this time, 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 between the third wind speed simulation point and the third wind speed simulation point under the self-spectrum 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 of the bridge pulsating wind field, 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 double-index frequency calculation formula, obtain the double-index frequency corresponding to each wind speed simulation point under the N sampling frequency points, construct a double-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, 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;

[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 each wind speed simulation point from left to right or from top to bottom according to the coordinate sequence of the bridge node;

[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 the 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 the above step 402, 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, which specifically includes:

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

[0111] 602: Under a single sampling frequency point, calculate the Cholesky decomposition elements under 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 under 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, the 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: 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, obtain the double index frequency corresponding to each wind speed simulation point under N sampling frequency points, construct a double index frequency matrix with a dimension of n×N and store it;

[0116] The second module is used to: call the double-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 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 also provides a rapid simulation system of the bridge pulsating wind field, which includes:

[0119] The first module is used to: 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, obtain the double index frequency corresponding to each wind speed simulation point under N sampling frequency points, construct a double index frequency matrix with a dimension of n×N and store it;

[0120] The second module is used to: call the double-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 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 with a dimension of n×n to obtain a Cholesky decomposition matrix with a dimension of 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 pulsating wind field or the rapid decomposition method of the spectral density matrix, the embodiment of the present application also provides a storage medium, on which a computer program is stored, and the steps of the above-mentioned embodiments are implemented when the computer program is executed by the processor. It should be noted that the storage medium of the embodiment 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 device, or any combination of the above. More specific examples of computer-readable storage media (non-exhaustive list) 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, which can be used by an instruction execution system, device or device or used in combination with it.

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

[0125] The program code embodied on the 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] Computer program code for performing the operation 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 also conventional procedural programming languages-such as "C" language or similar programming languages. The program code can be executed entirely on the user's computer, partially on the user's computer, as an independent software package, partially on the user's computer and partially on a remote computer, or completely on a remote computer or server. In the case of 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., using an Internet service provider to connect through the Internet).

[0127] Corresponding to the above-mentioned fast simulation method of the bridge pulsating wind field or the fast decomposition method of the spectral density matrix, an embodiment of the present application also 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 the present application, it should be noted that the terms "upper", "lower", etc. 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 the present application and simplifying the description, rather than indicating or implying 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 the present 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 it can be an indirect connection through an intermediate medium, or it can be a connection between the two elements. For those of ordinary skill in the art, the specific meanings of the above terms in the present 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 only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such 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 including 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, the elements defined by the sentence "comprise a ..." do not exclude the presence of other identical elements in the process, method, article or device including the elements.

[0130] The above description is only a specific implementation of the present application, so that those skilled in the art can understand or implement the present application. Various modifications to these embodiments will be apparent to those skilled in the art, and the general principles defined herein can be implemented in other embodiments without departing from the spirit or scope of the present application. Therefore, the present application will not be limited to the embodiments shown herein, but will conform to the widest range consistent with the principles and novel features applied for herein.

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 of 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 double index frequency calculation formula, the double 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 sequence 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 double index frequency calculation formula, the double index frequency corresponding to the first wind speed simulation point under 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. 1 Δω, to obtain the double index n corresponding to the current wind speed simulation point at N sampling frequency points Citation frequency.

3. The rapid simulation method of bridge pulsating wind field according to claim 1, characterized in that: 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 with a dimension of n×n at a single sampling frequency point, which specifically includes: Sort each wind speed simulation point according to the coordinate sequence of the bridge nodes, from left to right or from top to bottom; At a single sampling frequency point, calculate the Cholesky decomposition elements under 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 under the self-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; 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, the dimension of the Cholesky decomposition matrix being j×n; This process is repeated 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 a 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 double index frequency calculation formula, the double 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 sequence 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 double index frequency calculation formula, the double index frequency corresponding to the first wind speed simulation point under 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. 1 Δω, to obtain the double index n corresponding to the current wind speed simulation point at N sampling frequency points Citation frequency.

6. The fast decomposition method of spectral density matrix according to claim 4, characterized in that: 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 with a dimension of n×n at a single sampling frequency point, which specifically includes: Sort each wind speed simulation point according to the coordinate sequence of the bridge nodes, from left to right or from top to bottom; At a single sampling frequency point, calculate the Cholesky decomposition elements under 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 under the self-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; 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, the dimension of the Cholesky decomposition matrix being 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 a spectral density matrix, characterized in that: It includes: The first module is used to: 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, obtain the double index frequency corresponding to each wind speed simulation point under N sampling frequency points, construct a double index frequency matrix with a dimension of n×N and store it; The second module is used to: call the double-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 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 in that: It includes: The first module is used to: 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, obtain the double index frequency corresponding to each wind speed simulation point under N sampling frequency points, construct a double index frequency matrix with a dimension of n×N and store it; The second module is used to: call the double-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 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; 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 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.

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 fast simulation method for the bridge pulsating wind field as described in any one of claims 1 to 3 or the fast decomposition method for the spectral density matrix as described in any one of claims 4 to 6 is implemented.

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