A method and apparatus for generating non-gaussian time-domain signals

Abstract

The application discloses a non-Gaussian time-domain signal generation method and device, and belongs to the technical field of vibration simulation. The method comprises the following steps: obtaining a target power spectral density, a target skewness and a target kurtosis; generating Gaussian time-domain signals of each data block according to the target power spectral density; generating reference distribution samples conforming to the target skewness and the target kurtosis according to the Gaussian time-domain signals of each data block; splicing the reference distribution samples of each data block into an initial overall splicing signal as initial input signals of each data block, and respectively iterating the data blocks of the initial overall splicing signal until a preset global convergence criterion is met; and outputting the overall splicing signal meeting the global convergence criterion as a generated non-Gaussian time-domain signal, wherein the non-Gaussian time-domain signal meets target parameters. The application can solve the problems that the existing method is difficult to match the target skewness and kurtosis and has a large amount of calculation.

Description

Technical Field

[0001] This invention belongs to the field of vibration simulation technology, specifically relating to a method and apparatus for generating non-Gaussian time-domain signals. Background Technology

[0002] In vibration durability assessment of engineering structures, it is typically necessary to convert the measured road load spectrum into the power spectral density (PSD) of the shaking table or simulation input. A common method is to calculate the PSD from the measured vibration road spectrum signal and then generate a time-domain random vibration signal using the inverse Fourier transform (IFFT) method. The classical IFFT method can accurately preserve a given PSD, but the generated signal is necessarily a stationary Gaussian process with a constant kurtosis of 3 and a constant skewness of 0. Skewness measures the asymmetry of the probability distribution function about the mean, i.e., the degree of skewness of the distribution tails in the positive and negative directions; the standard normal distribution has a skewness of 0. Kurtosis measures the thickness of the probability distribution tails, i.e., the probability of extreme outliers; the standard normal distribution has a kurtosis of 3.

[0003] However, extensive engineering measurement data shows that the vibration response of vehicles during actual road driving often exhibits significant non-Gaussian characteristics, i.e., kurtosis greater than 3 and skewness possibly not zero. For engineering vehicle power battery systems, which are complex systems involving nonlinear factors such as bolted connections, battery pack stacking contacts, rubber bushings, and battery swapping device gaps, the response characteristics under vibration excitation are highly sensitive to the amplitude distribution of the input signal. Directly using Gaussian distributed time-domain signals for nonlinear dynamic simulations will lead to distortion of the stress-strain response, ultimately causing serious deviations in fatigue life prediction.

[0004] Existing methods for generating non-Gaussian random signals mainly include the zero-memory nonlinear transform (ZMNL) method and the phase optimization method. The ZMNL method first generates a Gaussian signal through linear filtering, and then adjusts its probability density function through a memoryless nonlinear transform. However, the transform process disrupts the signal's power spectrum, requiring repeated iterative corrections and often failing to converge simultaneously. The phase optimization method directly optimizes the phase of the overall signal in the frequency domain to match the target skewness and kurtosis, resulting in high computational cost and poor engineering practicality. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of the prior art and provide a method and apparatus for generating non-Gaussian time-domain signals, solving the problems of existing methods being unable to match target skewness and kurtosis, as well as the large amount of computation.

[0006] To solve the above-mentioned technical problems, the present invention is implemented using the following technical solution:

[0007] In a first aspect, the present invention provides a method for generating a non-Gaussian time-domain signal, comprising: acquiring target parameters for simulation of vibration durability of an engineering structure; the target parameters including target power spectral density, target skewness, and target kurtosis; generating Gaussian time-domain signals for each data block based on the target power spectral density; generating reference distribution samples conforming to the target skewness and target kurtosis based on the Gaussian time-domain signals of each data block; using the reference distribution samples of each data block as the initial input signals of each data block, splicing them into an initial overall spliced ​​signal, and iterating the initial overall spliced ​​signal until it meets a preset global convergence criterion; each iteration includes: performing a global convergence criterion on the overall spliced ​​signal of the current iteration; for the overall spliced ​​signal that does not meet the global convergence criterion, adjusting the amplitude and correcting the spectrum of the input signals of each data block respectively to obtain updated input signals for each data block; splicing the updated input signals of all data blocks into the overall spliced ​​signal for the next iteration; and outputting the overall spliced ​​signal that meets the global convergence criterion as the generated non-Gaussian time-domain signal, wherein the non-Gaussian time-domain signal conforms to the target parameters.

[0008] The aforementioned non-Gaussian time-domain signal generation method, wherein generating Gaussian time-domain signals for each data block based on the target power spectral density includes: determining sampling parameters based on target parameters; constructing a one-sided power spectrum sequence for each data block based on the target power spectral density and sampling parameters; converting the one-sided power spectrum sequence of each data block into a corresponding target amplitude spectrum; generating a random phase for each data block, and constructing a one-sided complex spectrum for each data block based on the random phase and the target amplitude spectrum; and generating a Gaussian time-domain signal for each data block through an inverse real fast Fourier transform based on the one-sided complex spectrum of each data block.

[0009] The aforementioned non-Gaussian time-domain signal generation method further includes statistical error as the target parameter. The step of determining the sampling and transformation parameters based on the target parameter includes: based on the statistical error... Calculate the theoretical number of data blocks , In the formula, The theoretical number of data blocks, This is for floor function; based on the theoretical number of data blocks. The theoretical duration of a single data block is calculated from the total signal duration. , In the formula, The total signal duration; based on the highest frequency component of the signal according to the target power spectral density. Calculate the sampling frequency , Based on the theoretical duration of a single data block and sampling frequency Calculate the number of time-domain sampling points for a single data block , In the formula, For the maximum number of sampling points in a single data block, select less than or equal to The largest even value is used as the number of time-domain sampling points for a single data block. According to the sampling frequency and the number of time-domain sampling points of a single data block Calculating the actual duration of a single data block , Based on the actual duration of a single data block Calculate data block frequency resolution , Based on the total signal duration and the actual duration of a single data block Calculate the actual number of data blocks , In the formula, For floor function; actual number of data blocks The following conditions must be met: .

[0010] The aforementioned non-Gaussian time-domain signal generation method, wherein generating reference distribution samples conforming to the target skewness and kurtosis based on the Gaussian time-domain signals of each data block includes: the Gaussian time-domain signal of each data block is approximately a standard normal distribution; based on the correspondence between the cubic polynomial transformation of the standard normal variable and the first four moments, a four-variable nonlinear equation system is derived; the first four moments represent the mean, variance, skewness, and kurtosis, respectively; the four-variable nonlinear equation system is numerically iterated using Newton's iteration method or a quasi-Newton method to solve the four coefficients of the cubic polynomial transformation; based on the solved cubic polynomial transformation, generating reference distribution samples conforming to the target skewness and kurtosis for each data block includes: generating a random number generator. 1 independent random number that follows a standard normal distribution; The number of time-domain sampling points for a single data block; Substituting each random number into the cubic polynomial transformation for solving, we obtain the corresponding results. A random sample following a Fleishman distribution; for Each random sample is centered and standardized to obtain... There are 1 reference sample, with a length of 1 The reference sample sequence.

[0011] The aforementioned non-Gaussian time-domain signal generation method performs a global convergence determination on the overall spliced ​​signal of the current iteration, including: sequentially splicing the input signals of all data blocks into the overall spliced ​​signal of the current iteration, and calculating the overall skewness and overall kurtosis of the overall spliced ​​signal; comparing the overall skewness and overall kurtosis of the overall spliced ​​signal with the corresponding target skewness and target kurtosis respectively; terminating the iteration when the difference between the overall skewness and the target skewness is less than a preset tolerance and the difference between the overall kurtosis and the target kurtosis is less than a preset tolerance; and performing amplitude adjustment and spectrum correction on the input signals of each data block to obtain updated input signals, and sequentially splicing the updated input signals of each data block into the overall spliced ​​signal of the next iteration.

[0012] The aforementioned non-Gaussian time-domain signal generation method, the total number of sampling points of the overall spliced ​​signal for: , This represents the actual number of data blocks. The number of time-domain sampling points for a single data block; the first The mean of the overall spliced ​​signal in the next iteration for: In the formula, This is an index representing the number of sampling points in the overall spliced ​​signal; For the first Sub-iteration overall splicing signal No. The amplitude of each sampling point;

[0013] No. Sub-iteration overall splicing signal Standard deviation for:

[0014] ,

[0015] No. Sub-iteration overall splicing signal Overall skewness for:

[0016] ,

[0017] No. Sub-iteration overall splicing signal Overall ravine for

[0018] ,

[0019] The first Overall skewness of the next iteration's overall spliced ​​signal and overall ravine Each with the corresponding target skewness and target kurtosis Comparison, when the first The difference between the overall skewness and the target skewness of the next iteration's overall spliced ​​signal Less than the preset tolerance And the difference between the overall kurtosis and the target kurtosis Less than the preset tolerance At that time, that is When the iteration ends, the iteration is terminated.

[0020] The aforementioned non-Gaussian time-domain signal generation method performs amplitude adjustment and spectrum correction on the input signal of each data block to obtain an updated input signal, including: regenerating the reference sample sequence of each data block, and arranging each reference sample in the regenerated reference sample sequence of each data block in ascending order of amplitude, thereby generating the target amplitude sequence of the current iteration of each data block.

[0021] In each data block, each signal point in the input signal of the current iteration is sorted in ascending order of amplitude, and the sorted index of the input signal and its corresponding original time index before sorting are recorded.

[0022] Replace the sorted input signal with the target amplitude sequence of the current iteration for each data block, and map it back to the original time position according to the original time index to generate the amplitude adjustment signal for the current iteration of each data block;

[0023] Perform a real fast Fourier transform on the amplitude adjustment signal of the current iteration for each data block to obtain its complex spectrum data, and extract the phase spectrum of the amplitude adjustment signal of the current iteration for each data block from it;

[0024] The phase spectrum of the amplitude adjustment signal of the current iteration of each data block and the corresponding target amplitude spectrum are used to form a new complex spectrum for each data block; the step of generating the Gaussian time domain signal of each data block according to the target power spectral density includes: generating the target amplitude spectrum of each data block according to the target power spectral density.

[0025] The updated input signal is obtained by taking the inverse Fourier transform of the new complex spectrum of each data block.

[0026] The aforementioned method for generating non-Gaussian time-domain signals, wherein the output of the overall spliced ​​signal that conforms to the global convergence criterion as the generated non-Gaussian time-domain signal includes: splicing all data blocks that satisfy the global convergence criterion in sequence to obtain the non-Gaussian time-domain signal.

[0027] The aforementioned non-Gaussian time-domain signal generation method uses the generated non-Gaussian time-domain signal as the excitation source for random vibration durability simulation.

[0028] Secondly, the present invention provides a non-Gaussian time-domain signal generation method apparatus, comprising: a parameter acquisition module, a target generation module, a reference generation module, an adjustment module, and an output module.

[0029] The parameter acquisition module is used to acquire the target parameters for the vibration durability simulation of engineering structures; the target parameters include target power spectral density, target skewness, and target kurtosis.

[0030] The target generation module is used to generate Gaussian time-domain signals for each data block based on the target power spectral density.

[0031] The reference generation module is used to generate reference distribution samples that conform to the target skewness and target kurtosis based on the Gaussian time-domain signal of each data block.

[0032] The adjustment module is used to iterate over the overall spliced ​​signal composed of reference distribution samples of all data blocks until it meets the preset global convergence criteria. Each iteration includes: for the overall spliced ​​signal that does not meet the preset global convergence criteria, the amplitude of the reference distribution samples of each data block is adjusted and the spectrum is corrected.

[0033] The output module is used to output a spliced ​​signal that meets the global convergence criteria, as a generated non-Gaussian time-domain signal, which conforms to the target parameters.

[0034] Compared with the prior art, the beneficial effects achieved by the present invention are as follows:

[0035] The non-Gaussian time-domain signal generation method of the present invention first generates Gaussian time-domain signals for each data block using the target power spectral density. Then, it generates reference distribution samples that conform to the target skewness and kurtosis based on the Gaussian time-domain signals of each data block. Next, it performs a global convergence determination on the overall spliced ​​signal composed of each data block to determine whether it conforms to the target skewness and kurtosis. For data blocks of the overall spliced ​​signal that do not conform, it is iterated separately. Finally, it outputs an overall spliced ​​signal that conforms to the global convergence determination. This avoids a large amount of computation in the overall signal iteration and can solve the problems of existing methods that are difficult to match the target skewness and kurtosis and have a large amount of computation.

[0036] Specifically, it includes the following effects:

[0037] 1) Existing technologies, when adjusting signal amplitude distribution, suffer from severe spectral distortion due to time-domain nonlinear transformations, requiring repeated corrections and often failing to converge simultaneously. This invention proposes a sorting mapping strategy that replaces the amplitude value only according to the sorting position, completely preserving the signal's phase-time structure. This operation causes minimal spectral disturbance and is performed alternately with subsequent frequency-domain amplitude recovery, enabling rapid convergence after multiple iterations to simultaneously satisfy the target power spectrum, target skewness, and target kurtosis.

[0038] 2) This paper proposes a hierarchical iterative approach combining independent data block correction with global convergence determination. Traditional methods typically iterate over the entire long signal, destroying the statistical independence of each data block, and the computational cost of long-sequence FFT is high. This invention independently generates reference samples, sorts and maps them, and corrects their spectrum for each data block, maintaining the independence between data blocks. Global convergence determination is used to judge the overall skewness and kurtosis of the spliced ​​signal, ensuring that the overall skewness and kurtosis of the final output signal are consistent with the target. This structure preserves the independence requirement of each frequency point of the random vibration signal while allowing the computation to be decomposed from long-sequence FFT into multiple short-block FFTs, reducing the computational cost.

[0039] 3) This invention organically integrates the precise PSD control capability of the classical IFFT method with the non-Gaussian distribution capability based on sorting mapping, constructing a unified framework. Users only need to input the target power spectral density, target skewness, and kurtosis to output a non-Gaussian time-domain signal that matches the target power spectral density and whose differences from the target skewness and kurtosis are both less than a preset tolerance. This framework is highly flexible, applicable to non-Gaussian time-domain signals with arbitrary target power spectra, and can provide a high-quality excitation source for vibration fatigue simulation of structures containing nonlinear elements, such as battery packs. Attached Figure Description

[0040] Figure 1 This is a flowchart illustrating the non-Gaussian time-domain signal generation method of Embodiment 1 of the present invention;

[0041] Figure 2 This is a schematic diagram of the parameter settings and simulation effect of the simulation experiment of the non-Gaussian time-domain signal generation method in Embodiment 1 of the present invention. Detailed Implementation

[0042] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the embodiments and specific features in the embodiments are detailed descriptions of the technical solution of the present application, rather than limitations thereof. In the absence of conflict, the embodiments and technical features in the embodiments can be combined with each other.

[0043] In this article, the term "and / or" is merely a description of the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A existing alone, A and B existing simultaneously, or B existing alone. Additionally, the character " / " in this article generally indicates that the preceding and following related objects have an "or" relationship.

[0044] Example 1:

[0045] This embodiment introduces a method for generating non-Gaussian time-domain signals, such as... Figure 1 As shown, it includes:

[0046] S1: Obtain target parameters; the target parameters include target power spectral density, target skewness, and target kurtosis;

[0047] S2: Generate Gaussian time-domain signals for each data block based on the target power spectral density;

[0048] S3: Generate reference distribution samples that conform to the target skewness and target kurtosis based on the Gaussian time domain signal of each data block;

[0049] S4: Use the reference distribution samples of each data block as the initial input signal of each data block, concatenate them into an initial overall concatenation signal, and iterate the initial overall concatenation signal until it meets the preset global convergence criterion; each iteration includes: performing a global convergence criterion on the overall concatenation signal of the current iteration; for the overall concatenation signal that does not meet the global convergence criterion, the input signals of each data block are adjusted in amplitude and corrected in spectrum to obtain the updated input signals of each data block; concatenate the updated input signals of all data blocks into the overall concatenation signal of the next iteration;

[0050] S5: Output the overall spliced ​​signal that meets the global convergence criterion, as the generated non-Gaussian time domain signal, which conforms to the target parameters.

[0051] Step S1 includes:

[0052] The system receives target parameters for the vibration durability simulation of the engineering structure from the user. These target parameters include: target one-sided power spectral density and target skewness. Target kurtosis Statistical error And the total signal duration T. The target one-sided power spectral density can be multiple target one-sided power spectral density control points, or it can be a target one-sided power spectral density curve plotted from multiple target one-sided power spectral density control points.

[0053] Step S2 includes: generating Gaussian time-domain signals for each data block based on the classical IFFT method;

[0054] S21: Determine the sampling parameters based on the target parameters:

[0055] Based on the preset statistical error Calculate the theoretical number of data blocks , In the formula, The theoretical number of data blocks, This is for rounding up;

[0056] Based on the theoretical number of data blocks The theoretical duration of a single data block is calculated from the total signal duration. , In the formula, In this embodiment, the total signal duration is... ;

[0057] Based on the highest frequency component of the signal at the target power spectral density Calculate the sampling frequency The sampling frequency needs to satisfy the Nyquist sampling theorem to prevent high-frequency aliasing. In this embodiment, ;

[0058] Based on the theoretical duration of a single data block and sampling frequency Calculate the number of time-domain sampling points for a single data block , In the formula, For the maximum number of sampling points in a single data block, select less than or equal to The largest even value is used as the number of time-domain sampling points for a single data block. ;

[0059] Based on sampling frequency and the number of time-domain sampling points of a single data block Calculating the actual duration of a single data block , ;

[0060] Based on the actual duration of a single data block Calculate data block frequency resolution , ;

[0061] Based on the total signal duration and the actual duration of a single data block Calculate the actual number of data blocks , In the formula, This is for floor function; because , In the formula, This represents the actual statistical error. The actual number of data blocks, therefore the actual number of data blocks The following conditions must be met: .

[0062] S22: Based on the target power spectral density and sampling parameters, construct a one-sided power spectrum sequence for each data block: Perform logarithmic / linear coordinate interpolation on the user-output PSD control points to obtain a power spectrum sequence with equal frequency intervals. Equal frequency intervals refer to the difference between adjacent frequency points in the power spectrum sequence being approximately equal to the target frequency interval. The single-sided power spectrum sequence is In the formula, This is the index of the frequency point.

[0063] S23: Convert the single-sided power spectrum sequence of each data block into the corresponding target amplitude spectrum: According to the power conservation theorem of Fourier transform, the single-sided power spectrum of each data block is converted into the corresponding target amplitude spectrum. The formula for calculating the target amplitude spectrum is as follows:

[0064] ,

[0065] ,

[0066] ,

[0067] In the formula, the one-sided power spectrum corresponds to the target amplitude spectrum. Index of frequency points;

[0068] S24: Generate a random phase for each data block, and construct a one-sided complex spectrum for each data block based on the random phase and the target amplitude spectrum:

[0069] For each data block, generate on the interval [0, 2π). An independent, uniformly distributed random phase ;

[0070] Construct the complex spectrum of the positive frequency portion of each data block based on the target amplitude spectrum and the random phase of each data block:

[0071] , ,

[0072] In the formula, It is an index of the data block. ; It is an imaginary number; It is a data block The one-sided complex spectrum.

[0073] S25: Based on the one-sided complex spectrum of each data block, generate the Gaussian time-domain signal of each data block through inverse real fast Fourier transform:

[0074] The length of each data block is... The one-sided complex spectra are input into the inverse real fast Fourier transform (IRFFT). After constructing conjugate symmetric two-sided complex spectra inside the function, the corresponding output length is... Gaussian time-domain signal of a single data block, data block The Gaussian time-domain signal is:

[0075] , ,

[0076] In the formula, The index is the frequency point of the Gaussian time-domain signal of a single data block; the kurtosis of the Gaussian time-domain signal of each data block is about 3 and the skewness is about 0. The Gaussian time-domain signals of all data blocks are spliced ​​together end to end in the order of the data block indexes to obtain the overall spliced ​​signal, which has a kurtosis of about 3 and a skewness of about 0.

[0077] Step S3 includes:

[0078] The Gaussian time-domain signal of each data block generated in step S2 is approximately a standard normal distribution;

[0079] Using standard normal variables cubic polynomial transformation: Each data block generates a reference sample sequence with target skewness and target kurtosis. Specifically, this includes:

[0080] Based on the correspondence between the cubic polynomial transformation of the standard normal variable and the first four moments, a system of four nonlinear equations is derived; the first four moments represent the mean, variance, skewness and kurtosis, respectively.

[0081] Standardization constraints: mean 0, variance 1, based on standard normal moments: Standard normal variable It is an array of length N, where each value represents the instantaneous amplitude at the corresponding moment; in this embodiment, the mean is... The variance is 0. =1;

[0082] mean The calculation formula is: ;

[0083] variance The calculation formula is: ;

[0084] Skewness The calculation formula is: ;

[0085] cliff The calculation formula is: ;

[0086] The system of four nonlinear equations with solution coefficients can be derived:

[0087] ,

[0088] In the formula, For target skewness; Target kurtosis;

[0089] The four-variable nonlinear equation system is numerically iterated using Newton's iteration method or a quasi-Newton method to solve the four coefficients a, b, c, and d of the cubic polynomial transformation;

[0090] Based on the solved cubic polynomial transformation, a reference distribution sample conforming to the target skewness and target kurtosis is generated for each data block, including:

[0091] Generated by a random number generator Independent random numbers that follow a standard normal distribution ;

[0092] Will Substituting each random number into the cubic polynomial transformation for solving, we obtain the corresponding results. The nth random sample follows a Fleishman distribution; random samples The expression is: , For the index of the random sample, A random sample that follows a Fleishman distribution means that the random sample can be generated by a cubic polynomial transformation of a standard normal random variable.

[0093] right Each random sample is centered and standardized to obtain... There are 1 reference sample, with a length of 1 Reference sample sequence, data block Reference sample sequence for: After the centering and standardization steps, the resulting reference sample sequence has a mean of 0 and a variance of 1.

[0094] Data blocks of The mean of a random sample for: ;

[0095] Data blocks of Standard deviation of a random sample for: ,

[0096] For data blocks The A random sample;

[0097] For data blocks The random samples Centralization and standardization are as follows: , For data blocks No. One reference sample;

[0098] Step S3 can match any target skewness and target kurtosis of the data block, and the computational cost is relatively small.

[0099] Step S4 includes:

[0100] S40: Use the reference sample sequence of each data block generated in step S3 as the initial input signal for each data block;

[0101] S41: Concatenate the initial input signals of each data block into an initial overall concatenation signal in sequence, and iterate the initial overall concatenation signal until it meets the preset global convergence judgment.

[0102] A global convergence determination is performed on the overall spliced ​​signal of the current iteration, including:

[0103] S411: Concatenate the input signals of all data blocks in sequence into the overall concatenated signal of the current iteration, and calculate the overall skewness and overall kurtosis of the overall concatenated signal;

[0104] S412: Compare the overall skewness and overall kurtosis of the overall spliced ​​signal with the corresponding target skewness and target kurtosis respectively. When the difference between the overall skewness and the target skewness is less than the preset tolerance and the difference between the overall kurtosis and the target kurtosis is less than the preset tolerance, terminate the iteration.

[0105] When the difference between the overall skewness and the target skewness is not less than the preset tolerance and the difference between the overall kurtosis and / or the target kurtosis is not less than the preset tolerance, the amplitude adjustment and spectrum correction steps S42 to S45 are performed on the input signals of each data block to obtain updated input signals, and the updated input signals of each data block are sequentially spliced ​​into the overall spliced ​​signal for the next iteration.

[0106] Total number of sampling points of the overall spliced ​​signal for: ;

[0107] No. The global convergence determination process for this iteration is as follows:

[0108] ,

[0109] No. The mean of the overall spliced ​​signal in the next iteration for: ,

[0110] In the formula, This is an index representing the number of sampling points in the overall spliced ​​signal; For the first Sub-iteration overall splicing signal No. The amplitude of each sampling point;

[0111] No. Sub-iteration overall splicing signal Standard deviation for:

[0112] ,

[0113] No. Sub-iteration overall splicing signal Overall skewness for:

[0114] ,

[0115] No. Sub-iteration overall splicing signal Overall ravine for

[0116] ,

[0117] The first Overall skewness of the next iteration's overall spliced ​​signal and overall ravine Each with the corresponding target skewness and target kurtosis Comparison, when the first The difference between the overall skewness and the target skewness of the next iteration's overall spliced ​​signal Less than the preset tolerance And the difference between the overall kurtosis and the target kurtosis Less than the preset tolerance At that time, that is When the iteration ends, the iteration is terminated.

[0118] Steps S42 to S45 refer to performing amplitude adjustment and spectrum correction on the input signal of each data block to obtain the updated input signal, specifically including:

[0119] S42: Generate a reference sample sequence independently for each data block and sort and map it.

[0120] Based on step S3, the reference sample sequence for each data block is regenerated and sorted in ascending order of amplitude in the regenerated reference sample sequence for each data block, thereby generating the target amplitude sequence for the current iteration of each data block.

[0121] In each data block, the input signals of the current iteration are sorted in ascending order of amplitude, and the sorted index of the input signals and their corresponding original time index before sorting are recorded.

[0122] Replace the sorted input signal with the target amplitude sequence of the current iteration for each data block, and map it back to the original time position according to the original time index to generate the amplitude adjustment signal for the current iteration of each data block;

[0123] In one specific embodiment, data block The reference sample sequence regenerated in the second iteration The given values ​​are: {0.5, 0.4, 0.6, 0.7}. After sorting, a data block is generated. The target magnitude sequence for the second iteration is: {0.4, 0.5, 0.6, 0.7}; data block The second input signal is: {0.5, 0.2, 0.3, 0.4}, data block. The second input signal is sorted in ascending order of amplitude to obtain {0.2, 0.3, 0.4, 0.5}, and the sorted index of the input signal is [1, 2, 3, 4], corresponding to the original time index [2, 3, 4, 1]. {0.4, 0.5, 0.6, 0.7} replaces {0.2, 0.3, 0.4, 0.5}, and {0.4, 0.5, 0.6, 0.7} is mapped back to its original time position according to the original time index [2, 3, 4, 1] to generate a data block. The second amplitude adjustment signal is: {0.7, 0.4, 0.5, 0.6};

[0124] This mapping strategy ensures that the amplitude probability distribution of the adjusted signal is completely consistent with the regenerated reference sample sequence, while fully preserving the temporal order of the amplitude of the original input signal.

[0125] S43: Extract the phase spectrum:

[0126] For each data block, a real fast Fourier transform (RFFT) is performed on the amplitude adjustment signal of the current iteration to obtain its complex spectrum data. The phase of each frequency point is then extracted to form the phase spectrum of the amplitude adjustment signal of the current iteration for each data block. No. The iteration is at the... The phase at each frequency point is ;

[0127] S44: Frequency Domain Amplitude Recovery

[0128] The phase spectrum of the signal is adjusted using the amplitude of the current iteration for each data block, and the target amplitude spectrum of each data block generated in step S2 based on the target power spectral density, to form a new complex spectrum for each data block. No. The new complex spectrum in the next iteration is , ;

[0129] Specifically, the phase of the DC and Nyquist frequencies is forced to zero to ensure that the time-domain signal is real.

[0130] S45: IRFFT Update Block: The new complex spectrum of each data block is transformed by the inverse Fourier transform to obtain the updated input signal; the input signal updated in the i-th iteration of data block m is:

[0131] , ,

[0132] For all After each data block completes the above update, return to step S41 to perform the global convergence determination for the next iteration.

[0133] Step 5: Output the final non-Gaussian time domain signal

[0134] Will satisfy the global convergence criterion The data blocks are concatenated sequentially to obtain the time-domain signal. As the final generated time-domain random vibration signal The output signal strictly matches the target PSD, and the errors in skewness and kurtosis with the target value are within the preset tolerance range.

[0135] A certain electric vehicle power battery pack assembly requires random vibration durability simulation. The battery pack contains numerous bolted connections, battery pack stacking contacts, rubber bushings, and gaps in the battery swapping device, making it a typical structural system with nonlinear components. Directly using a Gaussian-distributed random vibration signal for excitation will severely underestimate the amplitude impact response of the contact surfaces, leading to significant deviations in the prediction of weld joint and structural fatigue life.

[0136] To verify the non-Gaussian time-domain signal generation method of this invention, simulation experiments one and two were conducted. The parameter settings and simulation results of simulation experiment one are as follows: Figure 2 As shown.

[0137] Simulation Experiment 1: The one-sided power spectral density (PSD) curve of the target vibration environment was obtained by collecting and processing data from a real vehicle on a reinforced rough road. The control points are shown in Table 1, with a frequency range of 5Hz to 200Hz. High-order statistical analysis of the measured road spectrum data yielded a kurtosis of 5.8 and a skewness of approximately 0 for this condition.

[0138] Table 1 Target Power Spectral Density Control Points

[0139] PSD (g² / Hz) 0.04 0.04 0.01 0.005

[0140] The simulation requires generating a time-domain random acceleration signal with a total duration of 3600 seconds as the input excitation for subsequent nonlinear finite element analysis.

[0141] Step S1: Obtain the target parameters;

[0142] like Figure 2 As shown, the user inputs the above four PSD control points and the total signal duration through the software interface. Power spectrum statistical error Target kurtosis Target skewness Set the maximum number of iterations to 30 and the convergence tolerance to... .

[0143] Step S2: Generate the Gaussian time-domain signal for each data block;

[0144] S21: Determine the sampling parameters:

[0145] According to statistical error Calculate the theoretical number of data blocks , ;

[0146] Calculate the theoretical duration of a single data block , ;

[0147] The highest frequency component of the target PSD signal The sampling frequency is 200Hz. ;

[0148] Calculate the number of time-domain sampling points for a single data block , Choose less than or equal to The maximum even value of 32000 is used as the number of time-domain sampling points for a single data block. ;

[0149] Calculating the actual duration of a single data block , ;

[0150] Calculate data block frequency resolution , ;

[0151] Calculate the actual number of data blocks , Actual number of data blocks It can satisfy: .

[0152] S22: Construct a single-sided power spectrum sequence for each data block: For the four PSD control points, use logarithmic coordinate linear interpolation within the frequency range of 5–200 Hz to obtain a sequence with equal intervals of 0.0125 Hz in the 0–200 Hz range. A single-sided power spectrum sequence at each frequency point The PSD values ​​from 0 to 5 Hz are set to zero. The theoretical frequency domain amplitude at each frequency point is calculated using the formula:

[0153] S23: Construct the target amplitude spectrum:

[0154] For internal frequency points The formula for calculating the target amplitude spectrum is:

[0155] For DC ,

[0156] , , ;

[0157] for ,

[0158] ;

[0159] For Nyquist frequency That is, at 200Hz. ,

[0160] ,

[0161] S24: Generate a random phase and construct a one-sided complex spectrum:

[0162] For each data block, 16001 independent, uniformly distributed random phases are generated in the interval [0, 2π). Forced , Based on the target amplitude spectrum and the random phase of each data block, a complex spectrum of the positive frequency portion of each data block is constructed. The one-sided complex spectrum is:

[0163] , ,

[0164] In the formula, It is an index of the data block;

[0165] S25: Generate the time-domain signal of each data block using inverse real fast Fourier transform:

[0166] Each data block's 16001-bit single-sided complex spectrum is input into the Inverse Real Fast Fourier Transform (IRFFT). Internally, the function constructs a conjugate symmetric double-sided complex spectrum, resulting in the output time-domain signal of a single data block with a length of 32000. time domain signal for:

[0167] , ,

[0168] In the formula, The index of the time-domain signal frequency point for a single data block;

[0169] The 45 blocks were spliced ​​together to obtain an initial Gaussian time-domain signal with a length of 1,440,000 points. Its power spectrum is exactly consistent with the target PSD, with a skewness of about 0.02 and a kurtosis of about 3.01.

[0170] Step S3: Generate a reference distribution sample with target skewness and kurtosis;

[0171] Fleishman polynomial transformation is employed. The target skewness is used. Target kurtosis = 5.8 as input, establish a standard normal variable The cubic polynomial transformation.

[0172] Since the target skewness is 0, the second equation of the four-variable nonlinear equation system can be derived as follows: ,and then The four-element nonlinear equation system simplifies to:

[0173] ,

[0174] The solution obtained using Newton's iterative method .

[0175] In the subsequent step S4, each data block will be generated independently. Independent random numbers that follow a standard normal distribution Substitute into Then, the data is centered and standardized to obtain a reference sample sequence for each data block.

[0176] Step S4: Use the reference sample sequences of the 45 data blocks generated in step S3 as the initial input signals for each data block to start the first iteration.

[0177] S41: Global convergence determination:

[0178] The initial input signals of the current 45 data blocks are sequentially concatenated into an initial overall concatenated signal, such as... Figure 2 As shown, the calculated overall skewness of the initial overall spliced ​​signal is -0.0025 and the overall kurtosis is 4.0282. The difference between these values ​​and the target skewness of 0 and the target kurtosis of 5.8 is much greater than the preset tolerance of 0.1. The initial overall spliced ​​signal does not meet the global convergence judgment. Steps S42 to S45 are executed for the input signals of each data block respectively.

[0179] S42: Independently generate and sort the reference sample sequence for data block 1: For data block 1, regenerate 32,000 independent random numbers following a standard normal distribution. After Fleishman multinomial transformation, centering, and standardization, obtain the regenerated reference sample sequence for data block 1. Arrange each reference sample in the reference sample sequence in ascending order of amplitude to generate the target amplitude sequence for the second iteration of data block 1. Sort the input signal of data block 1 in ascending order of amplitude and record the sorted index of the input signal and its corresponding original time index before sorting. Replace the sorted input signal with the target amplitude sequence of data block 1 in the first iteration and map it back to the original time position according to the original time index to generate the amplitude adjustment signal for the first iteration of data block 1. This operation completely replaces the amplitude probability distribution of the signal with the newly generated reference sample sequence, while preserving the temporal position information of the original input signal.

[0180] S43: Extract the phase spectrum: Adjust the signal for the first iteration of data block 1. Perform RFFT to obtain the corresponding complex spectrum, extract the phase of each frequency point, and force the phase at the DC and Nyquist frequencies to zero to form the phase spectrum of the amplitude-adjusted signal of the first iteration of data block 1.

[0181] S44: Frequency Domain Amplitude Recovery: The phase spectrum of the signal adjusted by the amplitude of data block 1 in the first iteration, and the target amplitude spectrum of data block 1 generated in step S2, are used to form a new complex spectrum for data block 1. The new complex spectrum in the first iteration is , .

[0182] S45: IRFFT Update Block: The new complex spectrum of each data block is transformed by the inverse Fourier transform to obtain the updated input signal; the input signal for the first iteration update of data block m is:

[0183] , , .

[0184] Repeat the above operations S42 to S45 for the remaining 44 blocks in sequence, and each data block generates its own updated input signal.

[0185] After completing one round of updates, the input signals from all updated data blocks are concatenated into the overall concatenated signal for the second iteration, and the overall skewness and overall kurtosis of the overall concatenated signal for the second iteration are calculated. For example... Figure 2As shown, in this embodiment, the overall kurtosis of the second iteration increased to 4.7479; the overall skewness of the seventh iteration was approximately -0.0064, and the overall kurtosis was 5.7021. The difference between the overall skewness and the target skewness of 0 was 0.0064 < 0.1, and the difference between the overall skewness and the target kurtosis of 5.8 was 0.0979 < 0.1, which satisfied global convergence, and the iteration terminated.

[0186] Step S5: Output the final time-domain non-Gaussian random vibration signal;

[0187] The 45 data blocks, after 7 iterations, were sequentially concatenated to obtain the final time-domain signal with a total duration of 3600 seconds and 1,440,000 sampling points. .

[0188] The signal was used as an acceleration excitation input to the finite element model of the power battery pack for transient dynamic analysis. The stress-time history of key weld points was extracted, and fatigue life was predicted using the rainflow counting method and SN curve.

[0189] Simulation Experiment 2: Generation of Non-Gaussian Signals with Non-Zero Bias

[0190] In another application scenario, a body panel suffered a vibration signal with a skewness of 0.4 and a kurtosis of 4.2 due to a unilateral impact from a road. Using the method of this invention, only step one needs to set the target skewness to 0.4 and the target kurtosis to 4.2. In step S3, the Fleishman equations are automatically solved to obtain the non-zero coefficient c, which is approximately 0.065, generating a reference distribution with the corresponding skewness and kurtosis. After approximately 12 independent block iterations, the final output signal has a skewness of 0.39 and a kurtosis of 4.24, while maintaining the same power spectrum accuracy. This signal can be directly used for vibration table reproduction or simulation of the corresponding structure.

[0191] Example 2:

[0192] Based on the same inventive concept as Embodiment 1, this embodiment introduces a non-Gaussian time-domain signal generation method apparatus, including: a parameter acquisition module, a target generation module, a reference generation module, an adjustment module, and an output module.

[0193] The parameter acquisition module is used to acquire target parameters, including target power spectral density, target skewness, and target kurtosis.

[0194] The target generation module is used to generate Gaussian time-domain signals for each data block based on the target power spectral density.

[0195] The reference generation module is used to generate reference distribution samples that conform to the target skewness and target kurtosis based on the Gaussian time-domain signal of each data block.

[0196] The adjustment module is used to take the reference distribution samples of each data block as the initial input signal of each data block, splice them into an initial overall spliced ​​signal, and iterate the initial overall spliced ​​signal until it meets the preset global convergence judgment. Each iteration includes: performing a global convergence judgment on the overall spliced ​​signal of the current iteration; for the overall spliced ​​signal that does not meet the global convergence judgment, adjusting the amplitude and correcting the spectrum of the input signals of each data block to obtain the updated input signals of each data block; and splicing the updated input signals of all data blocks into the overall spliced ​​signal of the next iteration.

[0197] The output module is used to output a spliced ​​signal that meets the global convergence criteria, as a generated non-Gaussian time-domain signal, which conforms to the target parameters.

[0198] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0199] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0200] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0201] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0202] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the technical principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for generating non-Gaussian time-domain signals, characterized in that, include: Obtain the target parameters for the vibration durability simulation of the engineering structure; the target parameters include target power spectral density, target skewness, and target kurtosis. Generate Gaussian time-domain signals for each data block based on the target power spectral density; Generate reference distribution samples that conform to the target skewness and target kurtosis based on the Gaussian time-domain signal of each data block; The reference distribution samples of each data block are used as the initial input signals of each data block, and are spliced ​​together to form an initial overall spliced ​​signal. The initial overall spliced ​​signal is iterated until it meets the preset global convergence criteria. Each iteration includes: performing a global convergence criterion on the overall spliced ​​signal of the current iteration; for the overall spliced ​​signal that does not meet the global convergence criteria, the input signals of each data block are adjusted in amplitude and corrected in spectrum to obtain the updated input signals of each data block; and the updated input signals of all data blocks are spliced ​​together to form the overall spliced ​​signal of the next iteration. The overall spliced ​​signal that meets the global convergence criteria is output as the generated non-Gaussian time-domain signal, which conforms to the target parameters.

2. The non-Gaussian time-domain signal generation method according to claim 1, characterized in that, The process of generating Gaussian time-domain signals for each data block based on the target power spectral density includes: Determine the sampling parameters based on the target parameters; Based on the target power spectral density and sampling parameters, construct a one-sided power spectrum sequence for each data block; The single-sided power spectrum sequence of each data block is converted into the corresponding target amplitude spectrum; Generate a random phase for each data block, and construct a one-sided complex spectrum for each data block based on the random phase and the target amplitude spectrum; Based on the one-sided complex spectrum of each data block, the Gaussian time-domain signal of each data block is generated by inverse real fast Fourier transform.

3. The non-Gaussian time-domain signal generation method according to claim 2, characterized in that, The target parameter also includes statistical error, and the step of determining the sampling parameter based on the target parameter includes: According to statistical error Calculate the theoretical number of data blocks , In the formula, The theoretical number of data blocks, This is for rounding up; Based on the theoretical number of data blocks The theoretical duration of a single data block is calculated from the total signal duration. , In the formula, This is the total duration of the signal; Based on the highest frequency component of the signal at the target power spectral density Calculate the sampling frequency , ; Based on the theoretical duration of a single data block and sampling frequency Calculate the number of time-domain sampling points for a single data block , In the formula, For the maximum number of sampling points in a single data block, select less than or equal to The largest even value is used as the number of time-domain sampling points for a single data block. ; Based on sampling frequency and the number of time-domain sampling points of a single data block Calculating the actual duration of a single data block , ; Based on the actual duration of a single data block Calculate data block frequency resolution , ; Based on the total signal duration and the actual duration of a single data block Calculate the actual number of data blocks , In the formula, For floor rounding; actual number of data blocks The following conditions must be met: .

4. The method for generating non-Gaussian time-domain signals according to claim 1, characterized in that, The step of generating reference distribution samples that conform to the target skewness and target kurtosis based on the Gaussian time-domain signal of each data block includes: The Gaussian time-domain signal of each data block is approximately a standard normal distribution. Based on the correspondence between the cubic polynomial transformation of the standard normal variable and the first four moments, a four-variable nonlinear equation system is derived; the first four moments represent the mean, variance, skewness and kurtosis, respectively. The four coefficients of the cubic polynomial transformation are solved by numerical iteration of the four-variable nonlinear equation system using Newton's iteration method or quasi-Newton's method. Based on the solved cubic polynomial transformation, a reference distribution sample conforming to the target skewness and target kurtosis is generated for each data block, including: Generated by a random number generator 1 independent random number that follows a standard normal distribution; The number of time-domain sampling points for a single data block; Will Substituting each random number into the cubic polynomial transformation for solving, we obtain the corresponding results. A random sample that follows a Fleishman distribution; right Each random sample is centered and standardized to obtain... There are 1 reference sample, with a length of 1 The reference sample sequence.

5. The method for generating non-Gaussian time-domain signals according to claim 1, characterized in that, A global convergence determination is performed on the overall spliced ​​signal of the current iteration, including: The input signals of all data blocks are sequentially concatenated into the overall concatenated signal of the current iteration, and the overall skewness and overall kurtosis of the overall concatenated signal are calculated. The overall skewness and overall kurtosis of the overall spliced ​​signal are compared with the corresponding target skewness and target kurtosis, respectively. The iteration is terminated when the difference between the overall skewness and the target skewness is less than the preset tolerance and the difference between the overall kurtosis and the target kurtosis is less than the preset tolerance. When the difference between the overall skewness and the target skewness is not less than the preset tolerance and the difference between the overall kurtosis and the target kurtosis is not less than the preset tolerance, the amplitude adjustment and spectrum correction are performed on the input signals of each data block to obtain the updated input signals, and the updated input signals of each data block are sequentially spliced ​​into the overall spliced ​​signal for the next iteration.

6. The method for generating non-Gaussian time-domain signals according to claim 5, characterized in that, Total number of sampling points of the overall spliced ​​signal for: , This represents the actual number of data blocks. The number of time-domain sampling points for a single data block; No. The mean of the overall spliced ​​signal in the next iteration for: , In the formula, This is an index representing the number of sampling points in the overall spliced ​​signal; For the first Sub-iteration overall splicing signal No. The amplitude of each sampling point; No. Sub-iteration overall splicing signal Standard deviation for: ， No. Sub-iteration overall splicing signal Overall skewness for: ， No. Sub-iteration overall splicing signal Overall ravine for ， The first Overall skewness of the next iteration's overall spliced ​​signal and overall ravine Each with the corresponding target skewness and target kurtosis Comparison, when the first The difference between the overall skewness and the target skewness of the next iteration's overall spliced ​​signal Less than the preset tolerance And the difference between the overall kurtosis and the target kurtosis Less than the preset tolerance At that time, that is When the iteration ends, the iteration is terminated.

7. The method for generating non-Gaussian time-domain signals according to claim 5, characterized in that, The updated input signal is obtained by performing amplitude adjustment and spectrum correction on the input signal of each data block, including: Regenerate the reference sample sequence for each data block, and sort each reference sample in the regenerated reference sample sequence for each data block in ascending order of amplitude, thereby generating the target amplitude sequence for the current iteration of each data block; In each data block, each signal point in the input signal of the current iteration is sorted in ascending order of amplitude, and the sorted index of the input signal and its corresponding original time index before sorting are recorded. Replace the sorted input signal with the target amplitude sequence of the current iteration for each data block, and map it back to the original time position according to the original time index to generate the amplitude adjustment signal for the current iteration of each data block; Perform a real fast Fourier transform on the amplitude adjustment signal of the current iteration for each data block to obtain its complex spectrum data, and extract the phase spectrum of the amplitude adjustment signal of the current iteration for each data block from it; The phase spectrum of the amplitude adjustment signal of the current iteration of each data block and the corresponding target amplitude spectrum are used to form a new complex spectrum for each data block; the step of generating the Gaussian time domain signal of each data block according to the target power spectral density includes: generating the target amplitude spectrum of each data block according to the target power spectral density. The updated input signal is obtained by taking the inverse Fourier transform of the new complex spectrum of each data block.

8. The method for generating non-Gaussian time-domain signals according to claim 1, characterized in that, The output signal that meets the global convergence criterion is used as the generated non-Gaussian time domain signal, which includes: sequentially splicing together all data blocks that meet the global convergence criterion to obtain the non-Gaussian time domain signal.

9. The method for generating non-Gaussian time-domain signals according to claim 1, characterized in that, The generated non-Gaussian time-domain signal serves as the excitation source for random vibration durability simulation.

10. A method and apparatus for generating non-Gaussian time-domain signals, characterized in that, include: Parameter acquisition module, target generation module, reference generation module, adjustment module, and output module The parameter acquisition module is used to acquire the target parameters for the vibration durability simulation of engineering structures; the target parameters include target power spectral density, target skewness, and target kurtosis. The target generation module is used to generate Gaussian time-domain signals for each data block based on the target power spectral density. The reference generation module is used to generate reference distribution samples that conform to the target skewness and target kurtosis based on the Gaussian time-domain signal of each data block. The adjustment module is used to iterate the overall spliced ​​signal composed of reference distribution samples of all data blocks until it meets the preset global convergence judgment. Each iteration includes: for the overall spliced ​​signal that does not meet the preset global convergence criteria, the amplitude adjustment and spectrum correction are performed on the reference distribution samples of each data block; The output module is used to output a spliced ​​signal that meets the global convergence criteria, as a generated non-Gaussian time-domain signal, which conforms to the target parameters.

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