Random load spectrum iteration method based on nonlinear correction of transmission function

Abstract

The application discloses a random load spectrum iteration method based on transfer function nonlinear correction, which comprises target load spectrum processing and statistical quantity analysis, initial transfer function identification, transfer function nonlinear correction iteration, multi-dimension error calculation and integration.

Description

Technical Field

[0001] This invention relates to the field of random oscillation testing technology, and in particular to a random load spectrum iterative method based on transfer function nonlinear correction. Background Technology

[0002] Random vibration testing is being used more and more in vibration testing. Compared with traditional sinusoidal vibration testing, random vibration testing has greater advantages. It can simulate various actual vibration conditions, such as the stress on road vehicles, aircraft, and rail vehicles, as well as the stress on various components. It can use a vibration test bench to reproduce the load state of the test specimen in actual operation, so that the stress state of the specimen in the test is consistent with the actual working state, thus making the durability assessment of the specimen more accurate.

[0003] Due to the nonlinearity of the test system, the reproduction of the random load spectrum in random vibration tests requires an iterative process. Traditional iterative methods assume the nonlinear test system is a linear time-invariant system, excite the system with small-amplitude white noise, solve for the transfer function, and then use this assumed linear system transfer function for random load spectrum iteration. However, because of the linear system assumption, the solved linear system transfer function is not the actual nonlinear system transfer function, resulting in a large number of load spectrum iteration steps, slow convergence, significantly increased iteration time, and a longer overall test cycle. This diminishes the advantage of short test cycles for vibration test specimens. Furthermore, the increased number of iterations can lead to overtesting of the test specimen.

[0004] In addition, in traditional random load spectrum iteration, the evaluation of the iteration effect relies on only the root mean square error as a single indicator, ignoring indicators such as frequency domain and counting, which leads to an incomplete evaluation of the iteration results and inaccurate evaluation results. Summary of the Invention

[0005] The purpose of this invention is to provide a random load spectrum iteration method based on transfer function nonlinear correction to solve the problems mentioned in the background art.

[0006] This invention relates to a random load spectrum iterative algorithm, which is particularly suitable for vibration testing of components controlled by electromagnetic or hydraulic vibration test benches, road simulation testing, and aircraft vibration simulation, and belongs to the field of random vibration testing.

[0007] To achieve the above objectives, the present invention provides the following technical solution: a random load spectrum iteration method based on transfer function nonlinear correction, comprising:

[0008] Target load spectrum processing and statistical analysis;

[0009] Initial transfer function identification;

[0010] Nonlinear correction iteration of transfer function;

[0011] Multi-dimensional error calculation and integration.

[0012] Furthermore, the target load spectrum processing and statistical analysis also include:

[0013] The target load spectrum signal is processed, including resampling, filtering, mean removal, and trend term removal;

[0014] Perform statistical analysis on the processed target signal to analyze the maximum and minimum values ​​of the target signal;

[0015] Load spectrum is extracted according to operating conditions.

[0016] Furthermore, initial transfer function identification also includes:

[0017] Identify the transfer function of the experimental system according to the linear system assumption theory;

[0018] Based on the test frequency range, use an appropriate level of white noise signal to drive the test operation, and make the amplitude of the response signal between the maximum and minimum values ​​of the target signal;

[0019] The transfer function of the linear system assumption is identified by calculation using the white noise driving signal and the response signal.

[0020] Furthermore, the nonlinear correction iteration of the transfer function also includes:

[0021] Calculate the initial drive signal command and estimate the response signal based on the initial transfer function;

[0022] The test run is driven by the initial drive signal to obtain the actual response signal, and the actual drive signal is collected at the same time.

[0023] The linear transfer function is nonlinearly corrected, which includes three correction methods: driving channel correction, response channel correction, and hybrid correction.

[0024] The modified transfer function is applied to the next load spectrum iteration, and so on, continuously modifying and iterating the transfer function to ensure that the transfer function continuously corrects itself as the number of iterations increases, so as to approach the true characteristics.

[0025] Furthermore, nonlinear corrections to the linear transfer function also include:

[0026] For system nonlinearity caused by the driving channel, the transfer function is corrected by applying driving correction.

[0027] For system nonlinearity caused by the response channel, the transfer function is corrected by applying response correction;

[0028] For system nonlinearities caused by the driving channel and the response channel, a hybrid correction is applied to correct them simultaneously.

[0029] Furthermore, for the system nonlinearity caused by the driving channel, the application of driving correction to modify the transfer function also includes:

[0030] The formula for calculating the nonlinearity ratio of the drive channel is as follows:

[0031]

[0032] In the formula, K i+1 D represents the nonlinear correction ratio of the drive channel in the (i+1)th iteration; i (ω) represents the actual driving signal acquired during the i-th iteration; X i (ω) represents the drive signal command during the i-th iteration;

[0033] The nonlinearity of the driving channel is corrected for the transfer function used in the (i+1)th iteration, and the calculation formula is as follows:

[0034]

[0035] In the formula, This represents the inverse function of the transfer function used in the (i+1)th iteration after modification; Let represent the inverse function of the transfer function used in the i-th iteration.

[0036] Furthermore, for the system nonlinearity caused by the response channel, the application of response correction to modify the transfer function also includes:

[0037] The formula for calculating the nonlinearity ratio of the response channel is as follows:

[0038]

[0039] In the formula, M i+1 R represents the nonlinear correction ratio of the transfer function response channel in the (i+1)th iteration; i (ω) represents the actual response signal collected during the i-th iteration; Y i (ω) represents the predicted response signal at the i-th iteration;

[0040] The response channel nonlinearity is proportionally corrected for the transfer function used in the (i+1)th iteration, and the calculation formula is as follows:

[0041]

[0042] Furthermore, for the system nonlinearity caused by the driving channel and the response channel, a hybrid correction is applied to correct it simultaneously, which also includes:

[0043] The calculation is performed using a hybrid correction, which applies a hybrid correction to the nonlinearity of the driving channel and the response channel of the transfer function used in the (i+1)th iteration. The calculation formula is as follows:

[0044]

[0045] Furthermore, multi-dimensional error calculation and integration also include:

[0046] Multi-dimensional error calculation is performed on the iterated response signal, including root mean square error in the time domain, root mean square error in the frequency domain power spectrum, and root mean square error in the level crossing count.

[0047] The calculated errors are integrated using a proportionality coefficient to generate a total error, which is then used to evaluate the iteration effect.

[0048] Furthermore, including:

[0049] Time-domain error: Perform time-domain analysis on the iterated response signal and the expected response signal, and calculate the root mean square error in the time domain, as shown in the following formula:

[0050]

[0051] In the formula, Err time The root mean square error in the time domain; RMS(Y) i ) represents the root mean square value of the response signal; RMS(Y) d ) represents the root mean square value of the desired response signal;

[0052] Frequency domain error: Perform frequency domain analysis on the iterated response signal and the expected response signal to obtain the power spectrum, and calculate the root mean square error of the frequency domain power spectrum, as shown in the following formula:

[0053]

[0054] In the formula, Err psd The root mean square error of the power spectrum; RMS(P) i RMS(P) represents the root mean square value of the power spectrum of the response signal. d ) represents the root mean square value of the power spectrum of the desired response signal;

[0055] Counting dimension error: Counting analysis is performed on the iterated response signal and the expected response signal to obtain the level-through count. The root mean square error of the count power spectrum is calculated using the following formula:

[0056]

[0057] In the formula, Err psd The root mean square error of the power spectrum; RMS(C) i) is the root mean square value of the response signal level count; RMS(C) d The root mean square value of the expected response signal's stage count is denoted as .

[0058] Total Error: Based on the errors in each of the above dimensions, the total error is calculated using the following formula:

[0059] Err=k1·Err time +k2·Err psd +k3·Err count ——Formula (9);

[0060] In the formula, Err is the total error, k1 is the time-domain error proportion coefficient, k2 is the frequency-domain power spectrum error proportion coefficient, and k3 is the penetration counting error proportion coefficient. The requirement is that k1 + k2 + k3 = 1, and the proportion of each error can be customized according to the error dimension that is emphasized in the analysis.

[0061] After each iteration, the error in each dimension is calculated, the total error is obtained, the convergence of the total error is compared, and it is determined whether the iteration result meets the requirements.

[0062] Compared with existing technologies, the beneficial effects of this invention are as follows: Based on the linear time-invariant system assumption iteration, this invention performs nonlinear correction on the transfer function during the iteration process, preserving the system nonlinearity and ensuring that the transfer function used in the iteration is closer to the actual system characteristics. Simultaneously, it performs multi-dimensional error analysis on the iteration results, calculating and normalizing the root mean square error in the time domain, the power spectrum error in the frequency domain, and the stage counting error into a total error. This invention can quickly and effectively apply vibration test systems to iterate random load spectrum signals, reducing the number of iterations. Furthermore, the analysis of the iteration results is more comprehensive and accurate. This invention can effectively shorten the iteration cycle, reduce additional damage to the test specimen, shorten the test cycle, and save test costs. Attached Figure Description

[0063] Figure 1 This is a flowchart of a random load spectrum iterative method based on transfer function nonlinear correction in an embodiment of the present invention;

[0064] Figure 2 This is a flowchart of the nonlinear correction process for the transfer function in an embodiment of the present invention;

[0065] Figure 3 This is a schematic diagram comparing the initial transfer function and the transfer function after response correction in an embodiment of the present invention;

[0066] Figure 4 This is a schematic diagram of the response channel correction ratio curve in an embodiment of the present invention. Detailed Implementation

[0067] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0068] In the description of this invention, unless otherwise stated, "a plurality of" means two or more; the terms "upper," "lower," "left," "right," "inner," "outer," "front end," "rear end," "head," "tail," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings, and are only for the convenience of describing the invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of the invention. Furthermore, the terms "first," "second," "third," etc., are used for descriptive purposes only and should not be construed as indicating or implying relative importance.

[0069] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "connected" and "linked" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0070] Please refer to the accompanying drawings in the specification. This invention provides a technical solution: such as... Figure 1 As shown, an iterative method for random load spectra based on transfer function nonlinear correction includes the following steps:

[0071] S102, Target load spectrum processing and statistical analysis;

[0072] Specifically, the target load spectrum signal is processed, including resampling, filtering, removing the mean and removing the trend term; statistical analysis is performed on the processed target signal to analyze the maximum and minimum values ​​of the target signal; and the load spectrum is extracted according to the working conditions.

[0073] The load spectrum signal can be a force signal, strain signal, acceleration signal, or displacement signal, etc.

[0074] S104. Initial transfer function identification;

[0075] Specifically, the initial transfer function identification also includes:

[0076] Identify the transfer function of the experimental system according to the linear system assumption theory;

[0077] Based on the test frequency range, use an appropriate level of white noise signal to drive the test operation, and make the amplitude of the response signal between the maximum and minimum values ​​of the target signal;

[0078] The transfer function of the linear system assumption is identified by calculation using the white noise driving signal and the response signal.

[0079] S106, Nonlinear correction iteration of transfer function;

[0080] Specifically, such as Figure 3 As shown, the nonlinear correction iteration of the transfer function also includes:

[0081] Calculate the initial drive signal command and estimate the response signal based on the initial transfer function;

[0082] Here, is the process for correcting the nonlinearity of the transfer function during the iteration.

[0083] The test run is driven by the initial drive signal to obtain the actual response signal, and the actual drive signal is collected at the same time.

[0084] The linear transfer function is nonlinearly corrected, which includes three correction methods: driving channel correction, response channel correction, and hybrid correction.

[0085] The modified transfer function is applied to the next load spectrum iteration, and so on, continuously modifying and iterating the transfer function to ensure that the transfer function continuously corrects itself as the number of iterations increases, so as to approach the true characteristics.

[0086] Specifically, nonlinear corrections to the linear transfer function also include:

[0087] For system nonlinearity caused by the driving channel, the transfer function is corrected by applying driving correction.

[0088] For system nonlinearity caused by the response channel, the transfer function is corrected by applying response correction;

[0089] For system nonlinearities caused by the driving channel and the response channel, a hybrid correction is applied to correct them simultaneously.

[0090] Specifically, for the system nonlinearity caused by the driving channel, the application of driving correction to correct the transfer function also includes:

[0091] The formula for calculating the nonlinearity ratio of the drive channel is as follows:

[0092]

[0093] In the formula, K i+1 D represents the nonlinear correction ratio of the drive channel in the (i+1)th iteration; i(ω) represents the actual driving signal acquired during the i-th iteration; X i (ω) represents the drive signal command during the i-th iteration;

[0094] The nonlinearity of the driving channel is corrected for the transfer function used in the (i+1)th iteration, and the calculation formula is as follows:

[0095]

[0096] In the formula, This represents the inverse function of the transfer function used in the (i+1)th iteration after modification; Let represent the inverse function of the transfer function used in the i-th iteration.

[0097] Specifically, for the system nonlinearity caused by the response channel, applying response correction to the transfer function also includes:

[0098] The formula for calculating the nonlinearity ratio of the response channel is as follows:

[0099]

[0100] In the formula, M i+1 R represents the nonlinear correction ratio of the transfer function response channel in the (i+1)th iteration; i (ω) represents the actual response signal collected during the i-th iteration; Y i (ω) represents the predicted response signal at the i-th iteration;

[0101] The response channel nonlinearity is proportionally corrected for the transfer function used in the (i+1)th iteration, and the calculation formula is as follows:

[0102]

[0103] Specifically, for the system nonlinearity caused by the driving channel and the response channel, a hybrid correction is applied to correct it simultaneously, which also includes:

[0104] The calculation is performed using a hybrid correction, which applies a hybrid correction to the nonlinearity of the driving channel and the response channel of the transfer function used in the (i+1)th iteration. The calculation formula is as follows:

[0105]

[0106] S108, Multi-dimensional error calculation and integration.

[0107] Specifically, multi-dimensional error calculation and integration also includes:

[0108] Multi-dimensional error calculation is performed on the iterated response signal, including root mean square error in the time domain, root mean square error in the frequency domain power spectrum, and root mean square error in the level crossing count.

[0109] The calculated errors are integrated using a proportionality coefficient to generate a total error, which is then used to evaluate the iteration effect.

[0110] Among these methods, using the total error to evaluate the iteration effect is fast, effective, and comprehensive.

[0111] Specifically, multidimensional errors include time-domain error, frequency-domain error, and counting error;

[0112] Time-domain error: Perform time-domain analysis on the iterated response signal and the expected response signal, and calculate the root mean square error in the time domain, as shown in the following formula:

[0113]

[0114] In the formula, Err time The root mean square error in the time domain; RMS(Y) i ) represents the root mean square value of the response signal; RMS(Y) d ) represents the root mean square value of the desired response signal;

[0115] Frequency domain error: Perform frequency domain analysis on the iterated response signal and the expected response signal to obtain the power spectrum, and calculate the root mean square error of the frequency domain power spectrum, as shown in the following formula:

[0116]

[0117] In the formula, Err psd The root mean square error of the power spectrum; RMS(P) i RMS(P) represents the root mean square value of the power spectrum of the response signal. d ) represents the root mean square value of the power spectrum of the desired response signal;

[0118] Counting dimension error: Counting analysis is performed on the iterated response signal and the expected response signal to obtain the level-through count. The root mean square error of the count power spectrum is calculated using the following formula:

[0119]

[0120] In the formula, Err psd The root mean square error of the power spectrum; RMS(C) i ) is the root mean square value of the response signal level count; RMS(C) d The root mean square value of the expected response signal's stage count is denoted as .

[0121] Total Error: Based on the errors in each of the above dimensions, the total error is calculated using the following formula:

[0122] Err=k1•Err time +k2·Err psd+k3·Err count ——Formula (9);

[0123] In the formula, Err is the total error, k1 is the time-domain error proportion coefficient, k2 is the frequency-domain power spectrum error proportion coefficient, and k3 is the penetration counting error proportion coefficient. The requirement is that k1 + k2 + k3 = 1, and the proportion of each error can be customized according to the error dimension that is emphasized in the analysis.

[0124] After each iteration, the errors in each dimension are calculated, the total error is obtained, and the convergence of the total error is compared to determine whether the iteration result meets the requirements. The total error fully considers the time-domain overlap, frequency-domain power spectrum and the number of counts, making the error estimation more accurate.

[0125] The iterative method of this invention will be further illustrated below using a 24-channel vehicle axle coupling road simulation test as an example:

[0126] In the experiment, the vehicle was connected and fixed to the test bench by shaft coupling. The six-component force signal of the wheel was iterated, and the nonlinear correction of the transfer function of the test system was applied by response correction.

[0127] Based on the statistical values ​​of the load spectrum signal collected by the vehicle at the test site, a white noise drive signal of corresponding magnitude is generated. The white noise drives the test bench to run, excites the vehicle to vibrate, collects the six-component force signal of the wheels, and then calculates the initial transfer function of the test system under the linear system assumption.

[0128] like Figure 2 As shown, the driving signal for the first iteration is calculated from the expected response and the initial transfer function, and the predicted response signal for the first iteration is also calculated. The first driving signal drives the experimental system to run, and the actual response signal for the first iteration is collected. The nonlinear correction scaling matrix for the transfer function in the second iteration is calculated from the predicted and actual response signals of the first iteration. Using the nonlinear correction scaling matrix and the initial transfer function, the system transfer function applied to the second iteration after one correction can be calculated. This process is repeated, continuously applying the predicted and actual response signals from the previous iteration to perform nonlinear corrections on the transfer function used in the previous iteration for use in the next iteration. See [link to previous step]. Figure 3 The solid line represents the initial transfer function of the vertical force on the left front wheel of the test system, while the dashed line represents the comparison of the transfer function after more than ten nonlinear corrections during the iterative testing of the test system on a rocky road surface at a certain test site. (See also...) Figure 4 , which is the correction ratio for the left front wheel vertical response channel when performing the first nonlinear correction on the initial transfer function.

[0129] After more than ten iterations of the pebble load case, the errors in each dimension of the vertical load channel are: Err time =7.2%, Errpsd =9.6%, Err count =10.5%. Taking the error percentage coefficients for each dimension as k1 = 0.5, k1 = 0.3, and k1 = 0.2, the total error is calculated as follows:

[0130] Err=0.5×7.2%+0.3×9.6%+0.2×10.5%=8.58%

[0131] During the more than ten iterations of this working condition, the errors in each dimension were calculated after each iteration, the total error was obtained, and the convergence of the total error was compared to determine whether the iteration results met the requirements. This total error fully considers the time-domain overlap, frequency-domain power spectrum, and the number of load counts, resulting in a more accurate error estimation.

[0132] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A random load spectrum iterative method based on transfer function nonlinear correction, characterized in that, include: Target load spectrum processing and statistical analysis; Initial transfer function identification; Nonlinear correction iteration of transfer function; Calculate the initial drive signal command and estimate the response signal based on the initial transfer function; The test run is driven by the initial drive signal to obtain the actual response signal, and the actual drive signal is collected at the same time. The linear transfer function is nonlinearly corrected, which includes three correction methods: driving channel correction, response channel correction, and hybrid correction. The modified transfer function is applied to the next load spectrum iteration, and so on, to continuously modify and iterate the transfer function, ensuring that the transfer function continuously modifies itself as the number of iterations increases, so as to approach the true characteristics. The nonlinear correction of the linear transfer function includes: For system nonlinearity caused by the driving channel, the transfer function is corrected by applying driving correction. For system nonlinearity caused by the response channel, the transfer function is corrected by applying response correction; For system nonlinearities caused by the driving channel and the response channel, a hybrid correction is applied to correct them simultaneously.

2. Multi-dimensional error calculation and integration; Multi-dimensional error calculation is performed on the iterated response signal, where, Multidimensional errors include root mean square error in the time domain, root mean square error in the frequency domain power spectrum, and root mean square error in the level crossing count. The calculated errors are integrated using a proportionality coefficient to generate a total error, which is then used to evaluate the iteration effect.

3. The iterative method for random load spectra based on transfer function nonlinear correction according to claim 1, characterized in that, Target load spectrum processing and statistical analysis also include: The target load spectrum signal is processed, including resampling, filtering, mean removal, and trend term removal; Perform statistical analysis on the processed target signal to analyze the maximum and minimum values ​​of the target signal; extract the load spectrum according to the working conditions.

4. The iterative method for random load spectra based on transfer function nonlinear correction according to claim 1, characterized in that, Initial transfer function identification also includes: Identify the transfer function of the experimental system according to the linear system assumption theory; Based on the test frequency range, use an appropriate level of white noise signal to drive the test operation, and make the amplitude of the response signal between the maximum and minimum values ​​of the target signal; The transfer function of the linear system assumption is identified by calculation using the white noise driving signal and the response signal.

5. The iterative method for random load spectra based on transfer function nonlinear correction according to claim 1, characterized in that, For system nonlinearities caused by the driving channel, the transfer function is corrected by applying driving correction, which also includes: The formula for calculating the nonlinearity ratio of the drive channel is as follows: -- Official (1); In the formula, K i+1 D represents the nonlinear correction ratio of the drive channel in the (i+1)th iteration; i (ω) represents the actual driving signal acquired during the i-th iteration; X i (ω) represents the drive signal command during the i-th iteration; The nonlinearity of the driving channel is corrected for the transfer function used in the (i+1)th iteration, and the calculation formula is as follows: --Official (2); In the formula, (ω) represents the inverse function of the transfer function used in the (i+1)th iteration after correction; (ω) represents the inverse function of the transfer function used in the i-th iteration.

6. The iterative method for random load spectra based on transfer function nonlinear correction according to claim 4, characterized in that, For system nonlinearities caused by the response channel, applying response correction to the transfer function also includes: The formula for calculating the nonlinearity ratio of the response channel is as follows: -- Official (3); In the formula, M i+1 R represents the nonlinear correction ratio of the transfer function response channel in the (i+1)th iteration; i (ω) represents the actual response signal collected during the i-th iteration; Y i (ω) represents the predicted response signal at the i-th iteration; The response channel nonlinearity is proportionally corrected for the transfer function used in the (i+1)th iteration, and the calculation formula is as follows: —Official (4).

7. The iterative method for random load spectra based on transfer function nonlinear correction according to claim 5, characterized in that, For system nonlinearities caused by the driving and response channels, a hybrid correction method is applied to correct them simultaneously, which also includes: The calculation is performed using a hybrid correction, which applies a hybrid correction to the nonlinearity of the driving channel and the response channel of the transfer function used in the (i+1)th iteration. The calculation formula is as follows: — Official (5).

8. The iterative method for random load spectra based on transfer function nonlinear correction according to claim 1, characterized in that, include: Time-domain error: Perform time-domain analysis on the iterated response signal and the expected response signal, and calculate the root mean square error in the time domain, as shown in the following formula: — Equation (6); In the formula, Err time The root mean square error in the time domain; RMS(Y) i ) represents the root mean square value of the response signal; RMS(Y) d ) represents the root mean square value of the desired response signal; Frequency domain error: Perform frequency domain analysis on the iterated response signal and the expected response signal to obtain the power spectrum, and calculate the root mean square error of the frequency domain power spectrum, as shown in the following formula: -- Official (7); In the formula, Err psd The root mean square error of the power spectrum; RMS(P) i RMS(P) represents the root mean square value of the power spectrum of the response signal. d ) represents the root mean square value of the power spectrum of the desired response signal; Counting dimension error: Counting analysis is performed on the iterated response signal and the expected response signal to obtain the level-through count. The root mean square error of the count power spectrum is calculated using the following formula: -- Official (8); In the formula, Err count The root mean square error of the counting power spectrum; RMS(C) i ) is the root mean square value of the response signal level count; RMS(C) d The root mean square value of the expected response signal's stage count is denoted as . Total Error: Based on the errors in each of the above dimensions, the total error is calculated using the following formula: -- Official (9); In the formula, Err is the total error, k1 is the time-domain error ratio coefficient, k2 is the frequency-domain power spectrum error ratio coefficient, and k3 is the level-passing counting error ratio coefficient. It is required that k1+k2+k3=1, and the ratio of each error can be customized according to the error dimension that is emphasized in the analysis. After each iteration, the error in each dimension is calculated, the total error is obtained, the convergence of the total error is compared, and it is determined whether the iteration result meets the requirements.

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