Method for simulating downburst wind speed field based on time-varying parameter adaptive wavelet transform

Abstract

The application discloses a method for simulating downburst wind speed field based on time-varying parameter adaptive wavelet transform. The target time scale power spectrum density function of each spatial measuring point and the time scale coherence function of multiple measuring points are set; the adaptive continuous wavelet transform with time-varying parameters is constructed according to the target time scale spectrum and the spatial coherence variation characteristics; further, the complex wavelet coefficients are generated in the adaptive wavelet domain, and the initial wind speed samples are obtained through the adaptive inverse continuous wavelet transform; finally, the closed-loop iterative process of "spectrum amplitude correction-coherent phase synchronization-non-Gaussian quantile mapping" is adopted to obtain the non-stationary non-Gaussian downburst wind speed field samples. The fixed parameter continuous wavelet transform is expanded to the time-varying parameter adaptive continuous wavelet transform, so that the time resolution can be improved near the peak wind speed and local mutation, and the scale resolution can be maintained in the slow change area, thereby providing high-fidelity input wind load for the dynamic reliability analysis of wind-sensitive structures under the action of extreme wind.

Description

Technical Field

[0001] This invention relates to the field of wind resistance analysis of wind engineering structures, and in particular to a method for simulating downburst wind speed fields based on time-varying parameter adaptive wavelet transform. Background Technology

[0002] Downbursts are a typical type of extreme local wind event, characterized by their sudden onset, short duration, localized spatial scale, and rapid intensification of near-surface wind speeds. Compared to conventional atmospheric boundary layer wind fields, downburst wind speed fields typically exhibit more significant non-stationarity and non-Gaussianity; their time-varying average wind speed, fluctuating wind speed intensity, local energy distribution, and spatial coherence structure can all change rapidly over time. For high-rise buildings, long-span bridges, transmission tower systems, wind power structures, and large-span roof structures, high-fidelity simulation of downburst wind loads is a crucial prerequisite for conducting dynamic response analysis, wind-resistant design, and reliability assessment.

[0003] Traditional wind speed field simulation methods are mostly based on the stationary Gaussian assumption, typically using fixed power spectral density functions, empirical coherence functions, and spectral representations to generate wind speed samples. While these methods have some applicability in conventional stationary wind fields, they suffer from significant shortcomings in describing downburst wind speed fields: first, they struggle to simultaneously match time-varying average wind speeds, time-varying fluctuation intensities, and non-Gaussian marginal distributions; second, they fail to describe the characteristics of coherent structures at multiple measurement points as they change over time and scale; and third, fixed basis function or fixed-window time-frequency analysis methods struggle to balance the high temporal resolution near the downburst peak with the frequency resolution of other time periods.

[0004] Continuous wavelet transform (CWT) can provide a time-scale representation of signals, making it suitable for describing local energy variations in non-stationary wind speed signals. Existing simulation methods for non-stationary non-Gaussian vector processes based on CWT can match simulated samples to given marginal distributions, time-scale power spectral density functions, and coherence functions through iterative power and amplitude correction. However, existing methods typically employ wavelet functions with fixed parameters, whose temporal localization window and scale resolution remain constant throughout the simulation period. When wind speed samples contain short-duration strong peaks, local abrupt changes, and rapidly evolving coherent structures, fixed-parameter wavelets are prone to insufficient time-domain resolution near peaks or insufficient scale resolution in flat regions.

[0005] On the other hand, synchronous compression transform can enhance the energy concentration of time-frequency representation and is suitable for instantaneous frequency estimation and component separation of multi-component signals. However, when generating random wind speed field samples, the simulation objective is not to redistribute the energy of a single signal to the instantaneous frequency ridge, but to simultaneously maintain the target time-scale power spectral density function, non-Gaussian edge distribution, and multi-point spatial coherence structure under a large number of samples. Therefore, directly using the synchronously compressed frequency redistribution spectrum as the target for random field simulation may disrupt the original correspondence between the time-scale spectrum and the coherence function, and may not necessarily improve the statistical matching effect of non-Gaussian wind speed fields.

[0006] Therefore, there is an urgent need to propose a new method for simulating downburst wind speed fields that retains the advantage of continuous wavelet transform in directly matching power spectrum and coherence function in the time-scale domain, while also being able to adaptively adjust wavelet window parameters according to the local non-stationary intensity and spatial coherence changes of downbursts, thereby improving the local representation ability near the peak period and the coherence preservation ability at multiple measurement points. Summary of the Invention

[0007] To address the problems of insufficient local time-frequency resolution, difficulty in maintaining spatial time-varying coherence, and difficulty in achieving closed-loop consistent matching between non-Gaussian edge distribution and time-scale spectral structure in existing fixed-parameter continuous wavelet transform wind speed field simulation methods, this invention proposes a downburst wind speed field simulation method based on time-varying parameter adaptive wavelet transform.

[0008] The technical solution adopted in this invention is:

[0009] This embodiment includes the following steps:

[0010] S1. Based on the statistical characteristics of the target downburst wind field, set the time-varying average wind speed, time-varying fluctuating wind speed standard deviation, non-Gaussian edge cumulative distribution function, target time-scale power spectral density function, and target time-scale coherence function between multiple spatial measurement points at each spatial measurement point.

[0011] S2. Based on the time-varying average wind speed, time-varying fluctuating wind speed standard deviation and target time-scale power spectral density function at each spatial measuring point, the local non-stationary intensity of the target downburst wind field at each spatial measuring point is obtained, and then the time-varying window common parameters of the adaptive continuous wavelet transform are determined.

[0012] S3. Determine the amplitude of wavelet coefficients at each spatial measurement point based on the target time-scale power spectral density function and time-varying window common parameters, and obtain the complex wavelet coefficient vector by combining the target time-scale coherence function between multiple spatial measurement points, and then construct the target adaptive wavelet coefficient matrix.

[0013] S4. Generate a set of initial fluctuating wind speed samples by performing adaptive inverse continuous wavelet transform based on the target adaptive wavelet coefficient matrix.

[0014] S5. Iterate the initial fluctuating wind speed sample according to the target time-scale power spectral density function, the non-Gaussian edge cumulative distribution function, and the target time-scale coherence function between multiple spatial measurement points until the preset iteration termination condition is met to obtain the standardized fluctuating wind speed sample, which is then converted into a non-stationary non-Gaussian downburst wind speed field sample.

[0015] In step S2, the local non-stationary intensity of the target downburst wind field at each spatial measuring point is obtained by the following formula:

[0016]

[0017] in, Indicates local non-stationary intensity. , and These represent the non-negative weight coefficients of the first, second, and third terms, respectively. This indicates taking the partial derivative with respect to time τ. This represents the time-varying average wind speed. This represents the standard deviation of time-varying fluctuating wind speed. and These represent the maximum values ​​of the time-varying average wind speed and the time-varying fluctuating wind speed standard deviation at the current spatial measuring point over the entire time history, respectively. This represents a preset positive number used to prevent the denominator from being zero. This represents the target time-scale power spectral density function.

[0018] The time-varying window common parameters of the adaptive continuous wavelet transform are determined according to the following steps:

[0019] 1) Select the wavelet type of adaptive continuous wavelet transform, and then preset the window parameters, preset interval, reference window parameters, and adjustment coefficients;

[0020] 2) Based on the local non-stationary intensity of the target downburst wind field and the preset window parameters, preset range, reference window parameters, and adjustment coefficients, candidate time-varying window parameters are obtained at each spatial measuring point.

[0021] 3) The candidate time-varying window parameters at each spatial measurement point are fused to obtain the common parameters of the time-varying window for adaptive continuous wavelet transform.

[0022] The candidate time-varying window parameters at each spatial measuring point are obtained by the following steps: the product of the adjustment coefficient and the local non-stationary intensity is multiplied by one to obtain the intensity influence factor. Then, the ratio of the baseline window parameter to the intensity influence factor is projected onto the preset interval of the window parameter to obtain the candidate time-varying window parameter.

[0023] Step S3 specifically involves:

[0024] S3.1. The time-varying normalized coefficients are obtained by processing the common parameters of the time-varying window, and then the amplitude of the wavelet coefficients of each spatial measuring point is calculated by combining the target time-scale power spectral density function of each spatial measuring point.

[0025] S3.2 At each scale and at each time point, construct an amplitude diagonal matrix based on the amplitude of the wavelet coefficients of each spatial measurement point, and construct a target coherence matrix based on the target time-scale coherence function between multiple spatial measurement points;

[0026] S3.3. Perform positive semi-definite correction on the target coherence matrix to obtain a positive semi-definite coherence matrix, and then process the positive semi-definite coherence matrix to obtain the coherence factor matrix;

[0027] S3.4 Multiply the magnitude diagonal matrix, the coherence factor matrix, and the randomly generated complex Gaussian random vector to obtain the complex wavelet coefficient vector, and then construct the target adaptive wavelet coefficient matrix.

[0028] The amplitude of the wavelet coefficients at each spatial measurement point is obtained by processing according to the following formula:

[0029]

[0030] in, Indicates the scale of the j-th spatial measurement point. ,time The amplitude of wavelet coefficients on the wavelet, Representing scale The absolute value, Represents the time-varying normalized coefficients. This represents the target time-scale power spectral density function at the j-th spatial measurement point at scale. ,time The value that can be taken on.

[0031] Step S5 specifically involves:

[0032] S5.1. Perform adaptive continuous wavelet transform on the current pulsating wind speed sample to obtain the current adaptive wavelet coefficients. Correct the amplitude and phase of the current adaptive wavelet coefficients according to the target time-scale power spectral density function and the target time-scale coherence function between multiple spatial measurement points.

[0033] S5.2 Then, adaptive inverse continuous wavelet transform is performed on the corrected adaptive wavelet coefficients, and then non-Gaussian quantile mapping correction is performed according to the non-Gaussian marginal cumulative distribution function to obtain the updated pulsating wind speed sample.

[0034] S5.3 Calculate the edge distribution error, timescale spectrum error and coherence error of the updated fluctuating wind speed sample, and make a judgment: if the edge distribution error, timescale spectrum error and coherence error are all less than the corresponding preset threshold, then stop the iteration and use the updated fluctuating wind speed sample as the standardized fluctuating wind speed sample.

[0035] Otherwise, proceed to step S5.1;

[0036] S5.4. Based on the time-varying average wind speed and the time-varying fluctuating wind speed standard deviation, the standardized fluctuating wind speed samples are converted into downburst wind speed field samples.

[0037] The edge distribution error, time-scale spectrum error, and coherence error are specifically obtained by processing them according to the following formulas:

[0038]

[0039]

[0040]

[0041]

[0042]

[0043] in, , and These represent the edge distribution error, timescale spectrum error, and coherence error, respectively. Indicates the first After the second generation The first measuring point The empirical quantiles of the simulated samples at each time point These represent the target quantiles at the same measurement point and the same time point, representing the non-Gaussian edge distribution of the target. Indicates the first Each measuring point at time The target non-Gaussian marginal cumulative distribution function, Indicates the first After the nth iteration, the empirical marginal cumulative distribution function corresponding to the simulated sample is obtained. Indicates the preset quantile level. Indicates the quantile level number, This indicates a preset first positive number used to prevent the denominator from being zero. and Let j and k represent the j-th spatial measurement point and the k-th spatial measurement point, respectively. , M represents the total number of spatial measurement points. and This represents the discrete-time point sequence number and the discrete-time point sequence number. K represents the total number of scales. N represents the total number of time points. This indicates that the scale power spectral density function at the j-th spatial measurement point after the r-th iteration is at the scale. ,time The value on, This represents the time-scale power spectral density function of the target at the j-th spatial measurement point at scale. ,time The value on, This represents the time-scale coherence function between the j-th and k-th spatial measurement points after the r-th iteration. ,time The value on, This represents the target time-scale coherence function between the j-th spatial measurement point and the k-th spatial measurement point at scale. ,time The value on, This represents a pre-defined second positive number used to prevent the denominator from being zero.

[0044] The non-stationary, non-Gaussian downburst wind speed field samples are used for dynamic response analysis, wind-induced reliability assessment, wind-resistant design, and wind disaster risk assessment of wind-sensitive structures under the action of downbursts.

[0045] The wind-sensitive structures include high-rise buildings, long-span bridges, power transmission tower systems, wind power structures, and long-span roof structures.

[0046] The beneficial effects of this invention are:

[0047] (1) This invention extends the fixed-parameter continuous wavelet transform to the time-varying-parameter adaptive continuous wavelet transform, enabling the wavelet window to automatically adjust with the local non-stationary intensity of the downburst and the local energy concentration of the time-scale spectrum. This mechanism can improve the temporal resolution near the peak wind speed and local abrupt changes, while maintaining good scale resolution in the region of gradual change.

[0048] (2) This invention does not use the frequency redistribution spectrum after synchronous compression as the simulation target, but directly corrects the amplitude and coherence phase of wavelet coefficients in the original time-scale domain, thereby avoiding the problem that synchronous compression redistribution may destroy the correspondence between the time-scale power spectral density function and the spatial coherence function.

[0049] (3) This invention proposes a multi-measurement point synchronous phase update mechanism under coherence constraints. At each scale and time point, the target coherence matrix drives the generation and iterative correction of the complex wavelet coefficients of multiple measurement points, which can avoid spatial coherence distortion caused by independent phase correction of each measurement point.

[0050] (4) This invention uses a closed-loop iterative process of “spectral amplitude correction - coherent phase synchronization - non-Gaussian quantile mapping” to simultaneously match the non-Gaussian edge distribution, the target time-scale power spectral density function and the spatial multi-point time-varying coherent structure, making it suitable for simulating strong non-stationary and strong non-Gaussian local wind fields such as downbursts.

[0051] In summary, this invention presents a novel technical solution that differs from wind speed field simulation methods based on underlying Gaussian matrix inversion and stochastic adaptive Fourier decomposition. Through time-varying parameter adaptive continuous wavelet domain modeling and joint correction of time-scale spectrum-coherence-edge distribution, it can provide high-fidelity input wind loads for dynamic reliability analysis of high-rise buildings, long-span bridges, transmission tower systems, wind power structures, and long-span roof structures under extreme wind conditions. Attached Figure Description

[0052] Figure 1 This is a schematic diagram of the method flow in this embodiment.

[0053] Figure 2 This is a schematic diagram showing how time-varying window parameters change with the intensity of local non-stationary events. Detailed Implementation

[0054] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0055] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and do not limit the scope of protection of this invention.

[0056] like Figure 1 As shown, the method in this embodiment includes the following steps:

[0057] S1. Based on the statistical characteristics of the target downburst wind field, set the time-varying average wind speed, time-varying fluctuating wind speed standard deviation, non-Gaussian edge cumulative distribution function, target time-scale power spectral density function, and target time-scale coherence function between multiple spatial measurement points at each spatial measurement point.

[0058] The statistical features also include the spatial coordinates of the measuring points, the sampling time interval, and the peak time of the downburst. This embodiment sets the time-varying average wind speed, time-varying fluctuating wind speed standard deviation, non-Gaussian marginal distribution, target time-scale power spectral density function, and spatial multi-point time-scale coherence function for each measuring point based on measured downburst wind speed records, empirical wind field models, or engineering design requirements. For scenarios lacking complete measured data, the target statistics can be constructed from existing downburst average wind speed models, non-stationary fluctuating intensity models, and empirical coherence functions.

[0059] Suppose the target downburst wind speed field contains M spatial measurement points, and the time discrete points are: The scale discrete points are , The wind speed process at the j-th measuring point is represented as:

[0060]

[0061] in, Let J be the total wind speed at the j-th measuring point. The time-varying average wind speed, For time-varying fluctuating wind speed standard deviation, This represents a standardized non-Gaussian fluctuating wind speed process. The target statistic includes the non-Gaussian marginal cumulative distribution function at the j-th measuring point. Target time-scale power spectral density function And the target time-scale coherence function between the j-th measurement point and the k-th measurement point. .

[0062] S2. Based on the time-varying average wind speed, time-varying fluctuating wind speed standard deviation and target time-scale power spectral density function at each spatial measuring point, the local non-stationary intensity of the target downburst wind field at each spatial measuring point is obtained, and then the time-varying window common parameters of the adaptive continuous wavelet transform are determined.

[0063] Based on the local energy concentration, local non-stationary intensity, and time variation characteristics of the target time-scale power spectral density function, the time-varying window parameter σ(τ) of the adaptive continuous wavelet transform is determined, and a time-varying parameter adaptive continuous wavelet transform and its inverse transform suitable for downburst wind speed fields are constructed.

[0064] Construction of the target adaptive wavelet coefficient matrix: Standardized fluctuating wind speed process at the j-th measuring point Perform time-varying parameter adaptive continuous wavelet transform:

[0065]

[0066] As an optional implementation, a locally non-stationary index is defined. It is a combination of the time-varying average wind speed change rate, the time-varying pulsation intensity change rate, and the target time-scale spectrum change rate.

[0067] In this embodiment, the local non-stationary intensity of the target downburst wind field at each spatial measuring point is specifically obtained by processing the following formula:

[0068]

[0069] in, Indicates local non-stationary intensity. , and These represent the non-negative weight coefficients of the first, second, and third terms, respectively. This indicates taking the partial derivative with respect to time τ. This represents the time-varying average wind speed. This represents the standard deviation of time-varying fluctuating wind speed. and These represent the maximum values ​​of the time-varying average wind speed and the time-varying fluctuating wind speed standard deviation at the current spatial measuring point over the entire time history, respectively. This represents a preset positive number used to prevent the denominator from being zero. This represents the target time-scale power spectral density function.

[0070] The time-varying window parameters are: , or ,in Let j represent the time variable and j represent the spatial measurement point number. The time-varying window parameters are determined by one or more of the following: the energy ridge width of the target time-scale power spectral density function, the local spectral energy gradient, the time-varying average wind speed change rate, the time-varying fluctuation intensity change rate, and the spatial coherence function change rate, and are limited to a preset interval. Inside.

[0071] That is, according to Calculate candidate wavelet parameters:

[0072]

[0073] in, This indicates that the projection is onto a preset parameter range. As the baseline window parameter, This is the adjustment coefficient. For multi-point wind speed fields, common parameters can be constructed based on the weighted average of candidate parameters at each measuring point, the maximum local non-stationary index, or the robust quantile. This ensures that all measurement points are coherently constrained within the same time-scale grid.

[0074] The time-varying window common parameters of the adaptive continuous wavelet transform are determined according to the following steps:

[0075] 1) Select the wavelet type for adaptive continuous wavelet transform, and then determine the reference window parameters and adjustment coefficients;

[0076] The adaptive continuous wavelet transform employs analytic wavelets, including Morlet wavelets, generalized Morse wavelets, bump wavelets, or other analytic wavelets that meet the admissibility conditions; among them, Morlet-class wavelets can take the following form:

[0077] ;

[0078] μ is the center frequency parameter, and g is the fast decay window function. Control the localization width of the wavelet in the time direction. For downburst wind speed fields, reduce the localization width during periods of sudden wind speed enhancement, rapid changes in local spectral energy, or rapid evolution of coherent structure. To improve temporal localization capabilities; during periods of relatively stable wind speed changes, appropriately increase... To improve scale or frequency resolution.

[0079] 2) Based on the local non-stationary intensity of the target downburst wind field and the preset window parameter range, the baseline window parameter, and the adjustment coefficient, candidate time-varying window parameters at each spatial measuring point are obtained. The candidate time-varying window parameters at each spatial measuring point are obtained by the following steps: the product of the adjustment coefficient and the local non-stationary intensity is multiplied by one to obtain the intensity influence factor. Then, the ratio of the baseline window parameter to the intensity influence factor is projected into the preset window parameter range to obtain the candidate time-varying window parameters.

[0080] 3) The candidate time-varying window parameters at each spatial measurement point are fused to obtain the common parameters of the time-varying window for adaptive continuous wavelet transform.

[0081] That is, when multiple spatial measurement points need to maintain the same time-scale coherence matrix, a common time-varying window parameter is used. A consistent wavelet transform is performed on all measurement points; the common time-varying window parameters are determined by the weighted average, maximum, or robust quantile of the local non-stationary indices of each measurement point, so as to avoid the estimation bias of the coherence function caused by using different window parameters for different measurement points.

[0082] S3. Determine the amplitude of wavelet coefficients at each spatial measurement point based on the target time-scale power spectral density function and time-varying window common parameters, and obtain the complex wavelet coefficient vector by combining the target time-scale coherence function between multiple spatial measurement points, and then construct the target adaptive wavelet coefficient matrix.

[0083] Step S3 specifically involves:

[0084] S3.1 Obtain the time-varying normalized coefficients based on the common parameters of the time-varying window. Then, by combining the time-scale power spectral density function of each spatial measurement point, the amplitude of the wavelet coefficients of each spatial measurement point is calculated.

[0085] Specifically, the time-varying normalized coefficients are obtained by processing the common parameters of the time-varying window. :

[0086]

[0087]

[0088] in, This indicates that the window parameters are set to The expression of the analytic wavelet in the frequency domain. This represents the frequency variable. For discrete implementations, the time-varying normalized coefficients can be approximated by summing the discrete frequencies.

[0089] S3.2 At each scale and at each time point, construct an amplitude diagonal matrix based on the amplitude of the wavelet coefficients of each spatial measurement point, and construct a target coherence matrix based on the target time-scale coherence function between multiple spatial measurement points;

[0090] S3.3. Perform positive semi-definite correction on the target coherence matrix to obtain a positive semi-definite coherence matrix, and then process the positive semi-definite coherence matrix to obtain the coherence factor matrix;

[0091] S3.4 Multiply the magnitude diagonal matrix, coherence factor matrix and randomly generated complex Gaussian random vector to obtain complex wavelet coefficient vector. Traverse all scales and all time points of the complex wavelet coefficient vector to construct the target adaptive wavelet coefficient matrix.

[0092] That is, for each scale and time Construct the target coherence matrix .like If the estimation error or numerical error does not satisfy positive semidefiniteness, eigenvalue truncation or the nearest positive semidefinite projection is performed. Then, Cholesky decomposition or eigenvalue decomposition is performed on the corrected coherence matrix to obtain the coherence factor matrix. The wavelet phase of all measurement points is driven by the same random complex vector to generate a complex wavelet coefficient vector that satisfies the coherence constraint.

[0093] The amplitude of the target adaptive wavelet coefficients is determined based on the target time-scale power spectral density function; for the j-th measurement point, the m-th scale, and the q-th time point, the amplitude of its wavelet coefficients is... With the target time-scale power spectral density function It satisfies the energy consistency relation.

[0094] The amplitude of the wavelet coefficients at each spatial measurement point is obtained by processing according to the following formula:

[0095]

[0096] in, Indicates the scale of the j-th spatial measurement point. ,time The amplitude of wavelet coefficients on the wavelet, Representing scale The absolute value, Represents the time-varying normalized coefficients. This represents the target time-scale power spectral density function at the j-th spatial measurement point at scale. ,time The value of is given by the superscript 1 / 2, which indicates the square root operation.

[0097] S4. Perform adaptive inverse continuous wavelet transform based on the target adaptive wavelet coefficient matrix to generate a set of initial fluctuating wind speed samples that satisfy the target time-scale spectrum approximation constraints.

[0098] An adaptive inverse continuous wavelet transform is used to generate initial wind speed samples. The target adaptive wavelet coefficient matrix obtained in step S3 is substituted into the adaptive inverse continuous wavelet transform to obtain initial standardized fluctuating wind speed samples from multiple measurement points. For analytical wavelets, a discretized inverse transform formula can be used:

[0099]

[0100] in, Logarithmic scale interval, It is the inverse transform normalization constant related to the time-varying wavelet parameters.

[0101] S5. Iterate the initial fluctuating wind speed sample according to the target time-scale power spectral density function, the non-Gaussian edge cumulative distribution function, and the target time-scale coherence function between multiple spatial measurement points until the preset iteration termination condition is met to obtain the standardized fluctuating wind speed sample, which is then converted into a non-stationary non-Gaussian downburst wind speed field sample.

[0102] That is, the initial pulsating wind speed sample is subjected to closed-loop iterative correction, which includes: adaptive wavelet domain spectral amplitude correction, spatial multi-point coherent phase synchronization correction, and non-Gaussian edge distribution quantile mapping correction.

[0103] The iterative correction does not use the frequency redistribution spectrum after synchronous compression transformation as the direct simulation target. Instead, it performs joint correction on the amplitude, coherent phase and non-Gaussian edge distribution of wavelet coefficients in the original time-scale domain of the adaptive continuous wavelet transform in order to maintain the correspondence between the target time-scale power spectral density function and the target time-scale coherence function.

[0104] This method employs spectral coherence-marginal distribution closed-loop iterative correction to address the redundancy issue inherent in continuous wavelet transform. When arbitrarily specified wavelet coefficients undergo inverse transform followed by forward transform, the original coefficients are typically not completely preserved. Therefore, this invention uses a closed-loop iterative correction method to progressively eliminate the non-preservation error of the adaptive inverse wavelet transform.

[0105] Step S5 specifically involves:

[0106] S5.1, Sample the current pulsating wind speed. The current adaptive wavelet coefficients are obtained by performing an adaptive continuous wavelet transform. The amplitude and phase of the current adaptive wavelet coefficients are corrected based on the target time-scale power spectral density function and the target time-scale coherence function between multiple spatial measurement points, respectively.

[0107] Preferably, the current number The next iteration of the fluctuating wind speed sample Perform adaptive continuous wavelet transform to obtain the current adaptive wavelet coefficients. The current time-scale power spectral density function is estimated from the current adaptive wavelet coefficients. Coherence function with the current time scale Amplitude correction factor is constructed based on the ratio between the target time-scale power spectral density function and the current time-scale power spectral density function, and the amplitude of the current adaptive wavelet coefficients is proportionally corrected. A coherent phase synchronization correction factor is constructed based on the difference between the target time-scale coherence function and the current time-scale coherence function, and the phase of the multi-measurement point adaptive wavelet coefficients is synchronously corrected.

[0108] Amplitude correction: The amplitude of the current wavelet coefficients is replaced or proportionally corrected based on the target time-scale power spectral density function, so that the corrected wavelet coefficient amplitude approaches the target value. .

[0109] In steps S3 and S5, the phase correction includes: constructing the target coherence matrix at each scale and time point. The target coherence matrix is ​​modified by positive semidefinite correction or eigenvalue truncation to decompose it into a coherence factor matrix. The coherence factor matrix is ​​then used to synchronously update the random complex phase vector of multiple measurement points so that the generated wavelet coefficients satisfy the target coherence constraint in the time-scale domain.

[0110] S5.2 Then, adaptive inverse continuous wavelet transform is performed on the corrected adaptive wavelet coefficients to obtain time-domain samples. Then, non-Gaussian quantile mapping correction is performed on the time-domain samples according to the non-Gaussian marginal cumulative distribution function to obtain updated pulsating wind speed samples.

[0111] The non-Gaussian quantile mapping correction specifically involves: sorting or performing probability integral transformation on the current sample values ​​at each time point of each measurement point, and then performing quantile replacement based on the inverse function of the target non-Gaussian marginal cumulative distribution function, so that the corrected samples conform to the target non-Gaussian marginal distribution at the corresponding time points. .

[0112] S5.3. Perform adaptive continuous wavelet transform on the updated fluctuating wind speed sample obtained in step S5.2, calculate its corresponding empirical marginal distribution, time-scale power spectral density function, and time-scale coherence function, and calculate the marginal distribution error, time-scale spectral error, and coherence error accordingly; if the marginal distribution error, time-scale spectral error, and coherence error are all less than the corresponding preset thresholds, stop the iteration and use the updated fluctuating wind speed sample as the standardized fluctuating wind speed sample; otherwise, use the updated fluctuating wind speed sample as the current fluctuating wind speed sample for the next iteration and jump to step S5.1;

[0113] S5.4. Based on the time-varying average wind speed and the standard deviation of the time-varying fluctuating wind speed, the standardized fluctuating wind speed samples are converted into downburst wind speed field samples. That is, the target downburst wind speed field samples are output. The converged standardized fluctuating wind speed samples are then... Substitution The final non-stationary, non-Gaussian downburst wind speed field sample was obtained.

[0114] The edge distribution error, time-scale spectrum error, and coherence error are obtained by processing them according to the following formulas:

[0115]

[0116]

[0117]

[0118]

[0119]

[0120] in, , and These represent the edge distribution error, timescale spectrum error, and coherence error, respectively. Indicates the first After the second generation The first measuring point The empirical quantiles of the simulated samples at each time point These represent the target quantiles at the same measurement point and the same time point, representing the non-Gaussian edge distribution of the target. Indicates the first Each measuring point at time The target non-Gaussian marginal cumulative distribution function, Indicates the first After the nth iteration, the empirical marginal cumulative distribution function corresponding to the simulated sample is obtained. Indicates the preset quantile level, for example , Indicates the quantile level number, This indicates a preset first positive number used to prevent the denominator from being zero. and Let j and k represent the j-th spatial measurement point and the k-th spatial measurement point, respectively. , M represents the total number of spatial measurement points. and This represents the discrete-time point sequence number and the discrete-time point sequence number. K represents the total number of scales. N represents the total number of time points. This indicates that the scale power spectral density function at the j-th spatial measurement point after the r-th iteration is at the scale. ,time The value on, This represents the time-scale power spectral density function of the target at the j-th spatial measurement point at scale. ,time The value on, This represents the time-scale coherence function between the j-th and k-th spatial measurement points after the r-th iteration. ,time The value on, This represents the target time-scale coherence function between the j-th spatial measurement point and the k-th spatial measurement point at scale. ,time The value on, This represents a pre-defined second positive number used to prevent the denominator from being zero.

[0121] The non-stationary, non-Gaussian downburst wind speed field samples are used for dynamic response analysis, wind-induced reliability assessment, wind-resistant design, and wind disaster risk assessment of wind-sensitive structures under the action of downbursts.

[0122] The wind-sensitive structures include high-rise buildings, long-span bridges, power transmission tower systems, wind power structures, and long-span roof structures.

[0123] Multi-point impact storm wind speed field sample generation

[0124] This embodiment considers the simulation of downburst wind speed fields at M spatial measuring points. A given sampling time interval is specified. Combined with the simulation duration T, a discrete time series is formed. The spatial coordinates of the measuring points, the center location of the downburst, its movement speed, maximum radial wind speed, peak wind speed time, and the spatial distance between the measuring points are determined based on the engineering scenario.

[0125] First, determine the time-varying average wind speed at each measuring point. and the standard deviation of time-varying fluctuating wind speed Non-Gaussian marginal distribution It can be fitted from measured data, or a Weibull distribution, Gamma distribution, Beta distribution, Johnson distribution, or other non-Gaussian distributions suitable for downburst fluctuating wind speeds can be used. Target time-scale power spectral density function. It can be estimated from measured wind speed records through continuous wavelet transform, or it can be constructed from a parameterized non-stationary wind spectrum model.

[0126] Secondly, determine the time-scale coherence function of multi-point targets in space. The coherence function can depend on the distance between the measuring points, time, scale, and the direction of the downburst. For cases where the coherence function is estimated from measured data, the estimation results can be smoothed to reduce local oscillations caused by finite samples. For cases where an empirical model is given, the coherence attenuation law varying with scale and time can be set based on engineering empirical parameters.

[0127] Then, the analytical Morlet wavelet is selected as the mother wavelet, and common time-varying window parameters are constructed based on the local changes in the target time-scale spectrum. Near the peak of the downburst, due to the rapid changes in mean wind speed and fluctuating wind speed intensity, local non-stationary indicators... Increase It is automatically reduced to improve temporal localization near the peak; in the flat region far from the peak, Returning to a larger baseline value helps maintain better scale resolution and numerical stability.

[0128] Next, the amplitudes of the wavelet coefficients are determined based on the target time-scale power spectral density function, and the synchronization phase of the complex wavelet coefficients at multiple measurement points is generated based on the target coherence matrix. Specifically, for each Construct the magnitude diagonal matrix:

[0129] ;

[0130] Construct the target coherence matrix And obtain the semidefinite correction. .make Take a complex Gaussian random vector Then, a complex wavelet coefficient vector can be generated:

[0131]

[0132] Through the above construction, the wavelet coefficients of different measurement points are not generated independently, but synchronously under the constraint of the target coherence matrix, thus achieving a good spatial coherence structure in the initial stage.

[0133] Subsequently, Perform adaptive inverse continuous wavelet transform to obtain initial samples. Because continuous wavelet transform has redundancy, the wavelet coefficients obtained by re-transforming the initial samples may differ from... There are discrepancies. Therefore, we continue with the closed-loop iterative correction.

[0134] In the r-th iteration, first calculate the adaptive continuous wavelet transform of the current sample. and with target amplitude Replacement or scaling Then in each According to Synchronous correction is performed on the phase of the complex coefficients at multiple measurement points; then, an adaptive inverse continuous wavelet transform is performed to obtain temporary time-domain samples; finally, the non-Gaussian edge distribution of the target is considered. Quantile mapping is performed on the samples. This process is repeated until the marginal distribution error, time-scale spectral error, and coherence error all meet the requirements.

[0135] Finally, the convergent, standardized fluctuating wind speed process is converted into actual wind speed:

[0136]

[0137] The resulting wind speed field samples can be directly used as multi-point input wind loads in structural wind vibration response analysis.

[0138] To verify the technical effectiveness of this method, it can be compared with the fixed-parameter CWT method. Both methods use the same target non-Gaussian edge distribution, target time-scale power spectral density function, and target time-scale coherence function. The only difference is that the fixed-parameter method uses the same wavelet window parameter at all times, while this method uses a different parameter based on the local non-stationary intensity of the downburst. Make adaptive adjustments.

[0139] The comparison metrics include: the Kolmogorov-Smirnov distance or quantile error between the target edge distribution and the simulated edge distribution; the relative error between the target time-scale power spectral density function and the simulated time-scale power spectral density function; the relative error between the target time-scale coherence function and the simulated coherence function; and the preservation effect of local wind speed peaks, local energy concentration areas, and multi-point coherence structures near the peak of the downburst.

[0140] like Figure 2As shown, during the flat period far from the peak, the wavelet window parameter increases, and both this method and the fixed parameter method can achieve good overall statistical matching, improving the frequency / scale resolution. During the peak period when wind speed suddenly increases and local energy is highly concentrated, the local non-stationary intensity increases. This method uses a smaller time-varying window parameter, and the wavelet window parameter decreases, improving the temporal localization capability. It can more accurately capture short-term strong energy changes and maintain a more stable time-scale coherent structure among multiple measurement points.

[0141] The proposed stochastic wind field generation framework, which combines "time-varying parameter adaptive CWT + time-scale spectrum / coherent synchronization correction + non-Gaussian edge closed-loop mapping," has the following characteristics:

[0142] (1) Existing simulation methods for nonstationary non-Gaussian vector processes based on continuous wavelet transform mainly focus on matching edge distributions, time-scale power spectral density functions, and coherence functions through iterative power and amplitude correction under fixed wavelet parameters. Based on this, this method addresses the short-term burstiness and spatial time-varying coherence of downburst wind speed fields by introducing a time-varying wavelet parameter selection mechanism driven by both the target time-scale spectrum and coherence changes, thus expanding the fixed wavelet window into an adaptive window.

[0143] Instead of simply using a continuous wavelet transform with fixed parameters, the wavelet window parameters are determined based on the local energy concentration of the target time-scale power spectral density function, the time-varying rate of change of the average wind speed, the time-varying rate of change of the intensity of the fluctuations, and the rate of change of spatial coherence. This parameter selection mechanism enables a stronger temporal localization representation near the downburst peak and a more stable scale-resolved representation in the flat region. Compared with fixed-parameter CWT-IPAC-like methods, this method adds a σ(τ) selection mechanism driven by the local non-stationary intensity of the downburst, the energy concentration of the target temporal spectrum, and spatial coherence variations, and embeds this parameter selection mechanism into the entire simulation iteration process.

[0144] (2) This method proposes a synchronous correction mechanism for time-scale spectrum and spatial coherence in the adaptive CWT domain: This method constructs the target coherence matrix at each scale and time point, and realizes the synchronous phase update of complex wavelet coefficients at multiple measurement points through positive semidefinite correction and coherence factor decomposition. This method differs from the method of independently correcting wavelet coefficients at each measurement point, and can maintain the spatial coherence structure of the wind speed field at multiple measurement points during the iteration process.

[0145] Meanwhile, this method proposes a non-Gaussian edge distribution and adaptive time-scale spectrum closed-loop consistency matching method: This method places adaptive wavelet domain spectrum amplitude correction, coherent phase synchronization correction and non-Gaussian quantile mapping in the same closed-loop iterative framework, which solves the problem that non-Gaussian quantile mapping may change the time-scale spectrum and spatial coherence structure.

[0146] (3) Existing simulation schemes based on stochastic adaptive Fourier decomposition or complete kernel dictionary usually generate the underlying Gaussian process through sparse expansion, and then obtain non-Gaussian samples through nonlinear transformation. This method no longer uses the inversion of the underlying Gaussian matrix or the sparse expansion of the kernel dictionary as the core step, but directly constructs and corrects the complex wavelet coefficient matrix in the adaptive continuous wavelet domain, forming a different technical path.

[0147] This method forms a different route for simulating stochastic wind speed fields from synchronous compression analysis and AFD sparse expansion: synchronous compression transformation is mainly used for energy redistribution and component separation, while this method retains the original time-scale domain of continuous wavelet as the statistical matching domain of the stochastic field; this method no longer uses EITAM or complete Szegő-SAFD as the main line, but constructs a wind speed field simulation framework of time-varying parameter adaptive CWT-IPAC type.

[0148] Existing adaptive continuous wavelet transform or adaptive synchronous compression transform methods are mainly used for time-frequency energy concentration, instantaneous frequency estimation, and signal separation of non-stationary multi-component signals. This method does not use the synchronously compressed frequency ridge or component separation result as the simulation target. Instead, it embeds the time-varying parameter adaptive continuous wavelet transform into the random wind speed field generation and statistical matching process, aiming to simultaneously match the non-Gaussian marginal distribution, the target time-scale spectrum, and the spatial multi-point coherence function. Compared with traditional adaptive SST-type signal analysis methods, this method does not use the synchronously compressed spectrum as the simulation target, but performs statistical matching of the target TSPSD and coherence in the original time-scale domain. Therefore, the application purpose, technical problems, and output results are all different.

[0149] In practical engineering applications, the statistical characteristics of the target wind speed field can be determined based on extreme wind meteorological data, downburst measurement records, or numerical weather simulation results of the region where the target structure is located. For high-rise buildings or long-span bridges, multiple simulated measuring points can be arranged at key heights or key nodes of the structure; for transmission tower systems, multiple measuring points can be arranged along the conductor direction and the tower height direction; for wind power structures, wind speed input points can be arranged along the impeller swept surface and the tower height direction.

[0150] The non-stationary, non-Gaussian downburst wind speed field samples generated using this method can be directly used as input to finite element structural models or aeroelastic models for time-history dynamic response analysis, wind-induced fatigue analysis, reliability analysis, and extreme response probability assessment. Compared to traditional stationary Gaussian wind speed samples, the samples generated by this method can more reasonably reflect the peak value, duration, local energy concentration, and multi-point coherence characteristics of downburst wind speeds, thereby improving the reliability of structural wind resistance design and risk assessment results.

[0151] The above detailed embodiments illustrate the technical solution and beneficial effects of the present invention. It should be understood that the above description is only the most preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, additions, and equivalent substitutions made within the scope of the principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for simulating downburst wind speed field based on time-varying parameter adaptive wavelet transform, characterized in that, The method includes the following steps: S1. Based on the statistical characteristics of the target downburst wind field, set the time-varying average wind speed, time-varying fluctuating wind speed standard deviation, non-Gaussian edge cumulative distribution function, target time-scale power spectral density function, and target time-scale coherence function between multiple spatial measurement points at each spatial measurement point. S2. Based on the time-varying average wind speed, time-varying fluctuating wind speed standard deviation and target time-scale power spectral density function at each spatial measuring point, the local non-stationary intensity of the target downburst wind field at each spatial measuring point is obtained, and then the time-varying window common parameters of the adaptive continuous wavelet transform are determined. S3. Determine the amplitude of wavelet coefficients at each spatial measurement point based on the target time-scale power spectral density function and time-varying window common parameters, and obtain the complex wavelet coefficient vector by combining the target time-scale coherence function between multiple spatial measurement points, and then construct the target adaptive wavelet coefficient matrix. S4. Generate a set of initial fluctuating wind speed samples by performing adaptive inverse continuous wavelet transform based on the target adaptive wavelet coefficient matrix. S5. Iterate the initial fluctuating wind speed sample according to the target time-scale power spectral density function, the non-Gaussian edge cumulative distribution function, and the target time-scale coherence function between multiple spatial measurement points until the preset iteration termination condition is met to obtain the standardized fluctuating wind speed sample, which is then converted into a non-stationary non-Gaussian downburst wind speed field sample.

2. The method for simulating downburst wind speed field based on time-varying parameter adaptive wavelet transform according to claim 1, characterized in that: In step S2, the local non-stationary intensity of the target downburst wind field at each spatial measuring point is obtained by the following formula: ； in, Indicates local non-stationary intensity. , and These represent the non-negative weight coefficients of the first, second, and third terms, respectively. This indicates taking the partial derivative with respect to time τ. This represents the time-varying average wind speed. This represents the standard deviation of time-varying fluctuating wind speed. and These represent the maximum values ​​of the time-varying average wind speed and the standard deviation of the time-varying fluctuating wind speed at the current spatial measuring point over the entire time history, respectively. This represents a preset positive number used to prevent the denominator from being zero. This represents the target time-scale power spectral density function.

3. The method for simulating downburst wind speed field based on time-varying parameter adaptive wavelet transform according to claim 1, characterized in that: The time-varying window common parameters of the adaptive continuous wavelet transform are determined according to the following steps: 1) Select the wavelet type of adaptive continuous wavelet transform, and then preset the window parameters, preset interval, reference window parameters, and adjustment coefficients; 2) Based on the local non-stationary intensity of the target downburst wind field and the preset window parameters, preset range, reference window parameters, and adjustment coefficients, candidate time-varying window parameters are obtained at each spatial measuring point. 3) The candidate time-varying window parameters at each spatial measurement point are fused to obtain the common parameters of the time-varying window for adaptive continuous wavelet transform.

4. The method for simulating downburst wind speed field based on time-varying parameter adaptive wavelet transform according to claim 3, characterized in that: The candidate time-varying window parameters at each spatial measuring point are obtained by the following steps: the product of the adjustment coefficient and the local non-stationary intensity is multiplied by one to obtain the intensity influence factor. Then, the ratio of the baseline window parameter to the intensity influence factor is projected onto the preset interval of the window parameter to obtain the candidate time-varying window parameter.

5. The method for simulating downburst wind speed field based on time-varying parameter adaptive wavelet transform according to claim 1, characterized in that: Step S3 specifically involves: S3.

1. The time-varying normalized coefficients are obtained by processing the common parameters of the time-varying window, and then the amplitude of the wavelet coefficients of each spatial measuring point is calculated by combining the target time-scale power spectral density function of each spatial measuring point. S3.2 At each scale and at each time point, construct an amplitude diagonal matrix based on the amplitude of the wavelet coefficients of each spatial measurement point, and construct a target coherence matrix based on the target time-scale coherence function between multiple spatial measurement points; S3.

3. Perform positive semi-definite correction on the target coherence matrix to obtain a positive semi-definite coherence matrix, and then process the positive semi-definite coherence matrix to obtain the coherence factor matrix; S3.4 Multiply the magnitude diagonal matrix, the coherence factor matrix, and the randomly generated complex Gaussian random vector to obtain the complex wavelet coefficient vector, and then construct the target adaptive wavelet coefficient matrix.

6. The method for simulating downburst wind speed field based on time-varying parameter adaptive wavelet transform according to claim 1, characterized in that: The amplitude of the wavelet coefficients at each spatial measurement point is obtained by processing according to the following formula: ； in, Indicates the scale of the j-th spatial measurement point. ,time The amplitude of wavelet coefficients on the wavelet, Representing scale The absolute value, Represents the time-varying normalized coefficients. This represents the target time-scale power spectral density function at the j-th spatial measurement point at scale. ,time The value that can be taken on.

7. The method for simulating downburst wind speed field based on time-varying parameter adaptive wavelet transform according to claim 1, characterized in that: Step S5 specifically involves: S5.

1. Perform adaptive continuous wavelet transform on the current pulsating wind speed sample to obtain the current adaptive wavelet coefficients. Correct the amplitude and phase of the current adaptive wavelet coefficients according to the target time-scale power spectral density function and the target time-scale coherence function between multiple spatial measurement points. S5.2 Then, adaptive inverse continuous wavelet transform is performed on the corrected adaptive wavelet coefficients, and then non-Gaussian quantile mapping correction is performed according to the non-Gaussian marginal cumulative distribution function to obtain the updated pulsating wind speed sample. S5.3 Calculate the edge distribution error, timescale spectrum error and coherence error of the updated fluctuating wind speed sample, and make a judgment: if the edge distribution error, timescale spectrum error and coherence error are all less than the corresponding preset threshold, then stop the iteration and use the updated fluctuating wind speed sample as the standardized fluctuating wind speed sample. Otherwise, proceed to step S5.1; S5.

4. Based on the time-varying average wind speed and the time-varying fluctuating wind speed standard deviation, the standardized fluctuating wind speed samples are converted into downburst wind speed field samples.

8. The method for simulating downburst wind speed field based on time-varying parameter adaptive wavelet transform according to claim 7, characterized in that: The edge distribution error, time-scale spectrum error, and coherence error are specifically obtained by processing them according to the following formulas: ； ； ； ； ； in, , and These represent the edge distribution error, timescale spectrum error, and coherence error, respectively. Indicates the first After the second generation The first measuring point The empirical quantiles of the simulated samples at each time point These represent the target quantiles at the same measurement point and the same time point, representing the non-Gaussian edge distribution of the target. Indicates the first Each measuring point at time The target non-Gaussian marginal cumulative distribution function, Indicates the first After the nth iteration, the empirical marginal cumulative distribution function corresponding to the simulated sample is obtained. Indicates the preset quantile level. Indicates the quantile level number, This indicates a preset first positive number used to prevent the denominator from being zero. and Let j and k represent the j-th spatial measurement point and the k-th spatial measurement point, respectively. , M represents the total number of spatial measurement points. and This represents the discrete-time point sequence number and the discrete-time point sequence number. K represents the total number of scales. N represents the total number of time points. This indicates that the scale power spectral density function at the j-th spatial measurement point after the r-th iteration is at the scale. ,time The value on, This represents the time-scale power spectral density function of the target at the j-th spatial measurement point at scale. ,time The value on, This represents the time-scale coherence function between the j-th and k-th spatial measurement points after the r-th iteration. ,time The value on, This represents the target time-scale coherence function between the j-th spatial measurement point and the k-th spatial measurement point at scale. ,time The value on, This represents a pre-defined second positive number used to prevent the denominator from being zero.

9. The method for simulating downburst wind speed field based on time-varying parameter adaptive wavelet transform according to claim 1, characterized in that: The non-stationary, non-Gaussian downburst wind speed field samples are used for dynamic response analysis, wind-induced reliability assessment, wind-resistant design, and wind disaster risk assessment of wind-sensitive structures under the action of downbursts.

10. The method for simulating downburst wind speed field based on time-varying parameter adaptive wavelet transform according to claim 9, characterized in that: The wind-sensitive structures include high-rise buildings, long-span bridges, power transmission tower systems, wind power structures, and long-span roof structures.

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