A nonlinear data processing method and its application for vehicle water entry impact simulation

Abstract

The present invention relates to a method and application for processing nonlinear data of a vehicle entering water impact simulation, which combines transient modal analysis of water impact, Butterworth low-pass filtering and Ensemble Empirical Mode Decomposition (EEMD) to process nonlinear data such as impact load, pressure and stress obtained by simulation. The method first uses EEMD to decompose the original data to obtain IMF components of various orders, and obtains the filtered results by recombining the low-frequency IMF components. Then, the original data is filtered by selecting a suitable low-pass filter frequency through transient modal analysis of water impact. Finally, the low-pass filter result is compared and analyzed with the results of each recombined IMF, and finally a suitable recombined result is selected as the final filtering result. Starting from the essential characteristics of the impact data, the present invention can accurately obtain the filtering results of the nonlinear data of water impact without setting other parameters except the white noise amplitude and the number of times white noise is added.

Description

Technical Field

[0001] The present invention belongs to a method for analyzing high-speed water entry impact simulation data, and relates to a method and application for processing nonlinear data of a vehicle water entry impact simulation, which is suitable for the post-processing process of nonlinear data such as impact load, pressure, stress, etc. obtained by numerical simulation of a vehicle high-speed water entry. Background Art

[0002] The engineering applications of vehicle entry research are closely related to our daily lives. From seaplane landings and the impact of ships and waves to the entry of air-dropped torpedoes and the launch of underwater weapons, the application value of water entry research is reflected everywhere. The high-speed entry of a vehicle into water is a typical fluid-structure interaction problem and a transient and highly nonlinear mechanical process. To understand the typical physical laws of this process, theoretical research, numerical simulation, and experimental research are required. Compared with theoretical and experimental research, numerical simulation has the advantages of being shorter, less expensive, and applicable to various complex environments. Therefore, numerical simulation has become a common method used by scholars at home and abroad to conduct related research.

[0003] During the numerical study, the transient nonlinear characteristics of the impact of a high-speed vehicle entering water caused the impact load, pressure, and stress data to exhibit high-frequency oscillations and multiple peaks. The high-frequency components may be caused by the vibration of the vehicle shell under the impact, which interferes with the data analysis. Therefore, it is necessary to filter out the high-frequency vibration response components in the impact signal. The commonly used method for extracting low-frequency impact signals is the Butterworth low-pass filter method. This method can filter out the high-frequency vibration response of the structure while retaining the high-frequency components of the impact load. However, the selection of the filter frequency is often based on past experience, which is subjective and uncertain. A filter frequency that is too high or too low will cause signal distortion, resulting in large errors in the filtering results. Figure 1 The impact load coefficients of a vehicle under certain operating conditions are filtered using the Butterworth low-pass filter method. As the filter frequency increases from low to high, significant differences in both the curve trend and the peak value of the waveform are observed. Artificially selecting the filter frequency can render the results unreliable. Therefore, it is necessary to propose a reliable post-processing method for nonlinear numerical simulation data.

[0004] Patent publication number CN 110987145 A proposes a high-speed water impact signal analysis method based on EEMD. This method first decomposes the original signal using the EEMD method, then performs Burg power spectrum analysis on the IMF components. Next, based on the rigid body's modal analysis, the high-frequency portion of the rigid body's vibration is obtained. Finally, the high-frequency IMF components are filtered out of the original signal as needed, and the remaining IMF components are reconstructed to obtain the filtered signal. This patent applies to impact acceleration signals measured by internal sensors during water impact tests and is not fully applicable to nonlinear data obtained from simulations. First, Burg power spectrum analysis of the IMF components obtained from simulation data fails to produce the expected results. The power spectra of each order of IMF coincide with the coordinate axes, making it impossible to infer the reconstruction order based on the number of peaks in the power spectrum. Second, while modal analysis of the rigid body is performed to obtain the critical frequency p, the patent does not describe the specific steps for obtaining the critical frequency p, nor does it provide criteria for selecting the critical frequency p. Finally, during the actual water entry process, the vehicle is an elastic body, and modal analysis using a rigid body ignores the impact of the initial water entry conditions on the modal analysis results. It should also be noted that the results obtained from free and fixed modes are different, and the fixed mode results are affected by the fixed position and fixed area, which raises questions about the accuracy of the critical frequency p. Since the critical frequency p is the basis for the final reconstruction order, this raises questions about the accuracy of the final results. Therefore, while fully considering feasibility and specific operating conditions such as water entry speed and angle, this paper proposes a post-processing method for nonlinear data from numerical simulations of high-speed water entry of vehicles. Summary of the Invention

[0005] Technical problems to be solved

[0006] In order to avoid the shortcomings of the prior art, the present invention proposes a nonlinear data processing method and application for vehicle water entry impact simulation to achieve filtering of the simulated nonlinear data.

[0007] Technical Solution

[0008] A nonlinear data processing method for simulating a water impact of a vehicle is characterized by the following steps:

[0009] Step 1: Perform EEMD decomposition on the nonlinear data f(t) obtained from the water impact simulation of the vehicle, and obtain the original data consisting of each order IMFi and the residual ε n express:

[0010]

[0011] Where: N is the number of times white noise is added to the EEMD decomposition, and the residual ε n is the margin;

[0012] Step 2: Remove the first i-order high-frequency IMF components IMFi from the original signal and reconstruct the remaining low-frequency IMF components to obtain the reconstruction results of each order Reconstruct ii; Reconstruct 2 is the result obtained by removing IMF1 and IMF2 and reconstructing the remaining IMF3 to IMFN, and so on:

[0013]

[0014] Step 3: Perform transient modal analysis of the water impact on the vehicle, obtain the Butterworth low-pass filter frequency, and use this frequency to low-pass filter the original data to obtain a comparison curve;

[0015] Step 4: Compare the reconstructed curve in step 2 with the Butterworth low-pass filter curve obtained in step 3, and select the closest reconstruction result Reconstruct i as the final filtering result;

[0016] The comparison is carried out in the following order:

[0017] First, select the first m Reconstruct i curves whose peak values ​​are closest to the peak values ​​of the Butterworth low-pass filter curve;

[0018] Then, among the m Reconstruct i curves, the curve with the inflection point closest to the inflection point of the Butterworth low-pass filter curve is selected;

[0019] If a unique Reconstruct i curve has not been selected, the one closest to the peak pulse width of the Butterworth low-pass filter curve is selected as the final filtering result.

[0020] The nonlinear data f(t) includes but is not limited to original data of axial, normal and radial load coefficients, and also includes but is not limited to nonlinear data of pressure, stress and bending moment.

[0021] The original data including but not limited to axial, normal and radial load coefficients, and the processing method for nonlinear data including but not limited to pressure, stress and bending moment are processed respectively according to steps 1 to 3 to obtain respective final filtering result data graphs.

[0022] The degree N and the remainder ε in the EEMD n The amplitude ε of white noise has the following empirical formula: It means that the more times white noise is added, the closer the final result is to the true value.

[0023] The center frequencies of the IMFs in the EEMD are from high to low and meet the following two conditions:

[0024] 1. The number of extreme points and zero-crossing points of the decomposed IMF components must be equal or differ by at most one; the extreme points include maximum and minimum values;

[0025] 2. At any time, the mean of the upper envelope determined by the local maximum and the lower envelope determined by the local minimum is zero, that is, the components are locally symmetric with respect to the time axis.

[0026] The process of obtaining the comparison curve in step 3 is as follows: taking the peak moment of the curve in the reconstruction result of step 2 as the peak moment of the water entry impact, considering the water entry speed and angle, locating the water entry simulation cavitation cloud map under the working condition to this moment, that is, obtaining the area of ​​the elastomeric vehicle affected by the water entry impact, and using the wetted area of ​​this area as the fixed position in the modal analysis to carry out the transient modal analysis of the water entry impact; obtaining the first m-order modes and the corresponding vibration shapes; finding the natural frequency corresponding to the second-order bending mode, and using this frequency to perform Butterworth low-pass filtering on the original data to obtain the comparison curve.

[0027] A use of the method for processing nonlinear data of a vehicle entering water impact simulation is characterized by being used for processing nonlinear data of a vehicle entering water impact simulation.

[0028] Beneficial effects

[0029] This paper proposes a nonlinear data processing method and application for vehicle water impact simulation, combining transient modal analysis of water impact, Butterworth low-pass filtering, and Ensemble Empirical Mode Decomposition (EEMD) to process nonlinear data such as simulated impact loads, pressures, and stresses. The method first decomposes the raw data using EEMD to obtain various-order IMF components. The low-frequency IMF components are then recombined to obtain a filtered result. The raw data is then filtered using transient modal analysis of water impact, selecting an appropriate low-pass filter frequency. Finally, the low-pass filter result is compared and analyzed with the results of the recombined IMFs, and the appropriate recombined result is selected as the final filtered result.

[0030] The present invention has the following beneficial effects: By decomposing the raw data using EEMD, the modal aliasing drawback of the EMD method is overcome. By analyzing the transient modal state of water impact, the influence of different initial water entry conditions on the modal analysis results of the vehicle is considered, resulting in a more accurate Butterworth low-pass filter frequency. Based on the essential characteristics of the impact data, the present invention accurately obtains the nonlinear data filtering results of water impact without requiring any parameters other than the white noise amplitude and the number of times white noise is added. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Figure 1 Butterworth low-pass filter curve of impact load coefficient at different frequencies

[0032] Figure 2 is the raw data of axial, normal and radial load factors

[0033] Figure 3 is the EEMD decomposition result of the axial load coefficient

[0034] Figure 4 is the reconstruction result of the axial load coefficient

[0035] Figure 5 This is the wetted area diagram at the peak moment of water impact

[0036] Figure 6 is the second-order bending mode vibration shape diagram

[0037] Figure 7 Comparison of low-pass filtering and reconstruction results

[0038] Figure 8 Final filtering result diagram DETAILED DESCRIPTION

[0039] The present invention will now be further described with reference to the embodiments and accompanying drawings:

[0040] The technical solution employed in this invention is as follows: Through EEMD decomposition and IMF reconstruction, the nonlinear data of water entry impact is converted into finite-order selectable data. By performing transient modal analysis of water entry impact on the vehicle under specific operating conditions, the Butterworth low-pass filter frequency is obtained, generating comparative reference data. The final filtering result is obtained by comparing the reconstructed data with the low-pass filtered data.

[0041] The specific implementation process is as follows: First, the original data is subjected to EEMD decomposition. The EEMD method decomposes the signal into the sum of a finite number of intrinsic mode functions (IMFs). In the order of decomposition, the center frequencies of the IMFs are ranked from high to low, and the following two conditions are met:

[0042] (1) The number of extreme points (including maxima and minima) and the number of zero-crossing points of the decomposed IMF components must be equal or differ by at most one;

[0043] (2) At any time, the mean of the upper envelope determined by the local maximum and the lower envelope determined by the local minimum is zero, that is, the components are locally symmetric with respect to the time axis.

[0044] The basic processing of the EEMD method is as follows:

[0045] (1) First, a set of white noise α1(t) is added to the signal to be analyzed f(t) to obtain the overall signal F1(t).

[0046] F1(t)=f(t)+α1(t) (1)

[0047] (2) Then, use a cubic spline interpolation function to fit F1(t), ensuring that the spline function passes through all the maximum and minimum points of F1(t). Obtain the upper and lower envelopes of the signal and find the mean of the upper and lower envelopes, m1(t). Calculate the difference, h1(t), between F1(t) and m1(t).

[0048] h1(t)=F1(t)-m1(t) (2)

[0049] (3) Determine whether h1(t) satisfies the two conditions of IMF. If not, take h1(t) as the new overall signal and repeat step (2). The mean of the upper and lower envelopes is recorded as m 1,1 (t), h1(t) and m 1,1 The difference between (t) is denoted as h 1,1 (t).

[0050] h 1,1 (t)=h1(t)-m 1,1 (t) (3)

[0051] Assume that h obtained after k cycles 1,k (t) satisfies the IMF conditions, then h 1,k (t) is the first-order IMF extracted from the overall signal F1(t), denoted as imf1, which is the highest frequency component in F1(t).

[0052] (4) Extract imf1 from F1(t) to obtain the residual r1(t).

[0053] r1(t)=F1(t)-h 1,k (t)=F1(t)-imf1 (4)

[0054] Take r1(t) as the new original signal, repeat steps (2) and (3) to extract the second-order IMF, denoted as imf2. Repeat this cycle to extract the first n-order IMF, denoted as imf n .

[0055]

[0056] Adding the equations in equation 5 together gives the decomposition result of the overall signal F1(t). The overall signal F1(t) is decomposed into various order IMFs and the residual r n (t) and.

[0057]

[0058] (5) Add a set of different white noises α2(t) to the analyzed signal f(t) to obtain the overall signal F2(t). Repeat steps (2), (3) and (4) to obtain the corresponding IMFs of various orders.

[0059]

[0060] After adding white noise for the jth time, IMFs of various orders are obtained.

[0061]

[0062] A total of N white noises are added, and the IMFs of each order are averaged to obtain the IMFs of each order of the final signal, which are recorded as IMFi.

[0063]

[0064] Then the original signal f(t) can be obtained by the order IMFi and the residual ε n express.

[0065]

[0066] The number N, the remainder ε n The amplitude ε of white noise has the following empirical formula:

[0067]

[0068] The more times white noise is added, the closer the final result is to the true value. In the present invention, N=200 and ε=0.15 are taken. Thus, the IMF components of various orders from high to low frequencies have been obtained.

[0069] In the second step, the first i-order high-frequency IMF components (IMFi) are removed from the original signal, and the remaining low-frequency IMF components are reconstructed to obtain the reconstruction results of each order, Reconstruct ii. For example, Reconstruct 1 is the result of removing IMF1 and reconstructing the remaining IMF2 to IMFN; Reconstruct 2 is the result of removing IMF1 and IMF2 and reconstructing the remaining IMF3 to IMFN, and so on.

[0070]

[0071] The third step is to perform a transient modal analysis of the vehicle's water entry impact, obtain the Butterworth low-pass filter frequency, and use this frequency to perform a low-pass filter on the original data. In addition to strong nonlinearity, the curves of water entry impact load, pressure, and stress also have the characteristics of high peak value and short pulse width. They reach a peak value at the moment the vehicle hits the water, and then drop rapidly. In the study of high-speed water entry, the peak value of the water entry impact data is one of the data we are most concerned about. Therefore, it is reasonable to conduct a transient modal analysis of the vehicle at the peak moment and apply the obtained results to the Butterworth low-pass filter of the overall curve. The specific method is as follows: select the peak moment of the curve in the reconstruction result of the second step as the peak moment of water entry impact, consider the water entry speed and angle, and locate the water entry simulation cavitation cloud map under this working condition to this moment, so as to obtain the area of ​​the elastomeric vehicle affected by water entry impact, use the wetted area of ​​this area as the fixed position in the modal analysis, and conduct a transient modal analysis of water entry impact. Obtain the first m-order modes and the corresponding vibration shapes. According to the research conclusions of Dr. Shi Yao, the water entry impact of the vehicle mainly excites the second-order bending mode. [1] . Find the natural frequency corresponding to the second-order bending mode, and use this frequency to perform Butterworth low-pass filtering on the original data to obtain a comparison curve. It should be noted that in the result curve of the second step reconstruction, there is a slight deviation between the peak moments of each order curve Reconstruct i. At the same time, due to the influence of the simulation data storage interval and grid size, there is also a certain error in the fixed position of the transient modal analysis of water entry impact. Therefore, the result of this step cannot be directly used as the final filtering result, and can only be used as comparison data.

[0072] The research of Shi Yao during her doctoral period is: Research on the characteristics of cavitation and impact load of rotating body vehicle entering water at high speed[D]. Northwestern Polytechnical University, 2016.

[0073] In the last step, the reconstructed curve obtained in the second step is compared with the Butterworth low-pass filter curve obtained in the third step. A comparative analysis is performed from the aspects of the curve change trend, curve details and peak size, and the closest reconstruction result Reconstruct i is selected as the final filtering result.

[0074] The comparison is carried out in the following order:

[0075] First, select the first m Reconstruct i curves whose peak values ​​are closest to the peak values ​​of the Butterworth low-pass filter curve;

[0076] Then, among the m Reconstruct i curves, the curve with the inflection point closest to the inflection point of the Butterworth low-pass filter curve is selected;

[0077] If a unique Reconstruct i curve has not been selected, the one closest to the peak pulse width of the Butterworth low-pass filter curve is selected as the final filtering result.

[0078] Specific implementation examples Figure 2 The raw data for the axial, normal and radial load factors are shown. Figure 3 The EEMD decomposition results of the axial load coefficient are shown. Figure 4 The reconstruction results of the axial load coefficient for each order are shown. Figure 5 Shows the wetted area at the peak moment of water impact. Figure 6 The second-order bending mode shape of the vehicle at the peak impact moment is shown. Figure 7 The results of low-pass filtering and reconstruction are compared. Figure 8 The final filtered result is shown.

[0079] Take the case where the vehicle enters the water at a speed of 150m / s and an entry angle of 60° as an example. Figure 2 The raw data for the axial, normal, and radial load coefficients exhibit high-frequency oscillations and multiple peaks, representing typical nonlinear data. This interferes with data analysis. The nonlinear data processing method for water impact simulation presented in this disclosure is then used to filter the data.

[0080] According to the above process, first proceed to the first step. Figure 2 The axial impact load coefficient in the EEMD is processed, and the results are as follows Figure 3 As shown in the figure, raw represents the original data before decomposition. After EEMD decomposition, 12 IMF components and the residual r are generated. The first five IMF components are characterized by high frequency and short wavelength. The subsequent IMF components gradually decrease in frequency and increase in wavelength, demonstrating that the impact load contains both high-frequency and low-frequency components. The residual curve r is a monotonically changing curve, showing the final trend of the original signal, namely, the stable value of the axial load coefficient is approximately 0.3.

[0081] Then, the second step is to remove the high-frequency IMF components from the original signal and reconstruct the remaining IMF components to obtain the filtered result. Figure 4 is the axial filtering result obtained after reconstruction, and Reconstruct i represents the result of reconstructing the remaining low-frequency components after removing the first i-order IMF components. Comparing the reconstruction curves, it can be found that the reconstruction results after removing the first three-order IMF components gradually reduce the high-frequency signal, but still do not meet the analysis requirements. The reconstruction results after removing the first seven to twelve orders, while free of high-frequency signals, gradually lose details and suffer severe distortion. In contrast, the reconstruction results after removing the first four to six-order IMF components almost eliminate the high-frequency signal, basically meeting the analysis requirements.

[0082] In the third step, in order to further select the appropriate filtering results in Reconstruct 4 to Reconstruct 6, the transient modal analysis of the vehicle entering the water is performed. The peak time of the curve of Reconstruct 4 to Reconstruct 6 in the reconstruction results of the second step is about 0.8ms, which is taken as the peak time of the water entry impact. The water entry simulation cavitation cloud map under this working condition is located at this time, and the following is obtained: Figure 5 The wetted area diagram at the peak moment of water entry impact is shown in the figure. The wetted area of ​​this area is used as a fixed position in the modal analysis to carry out the transient modal analysis of water entry impact. The results of the first 30 modes and vibration shapes are shown in Table 1. The 26th mode of the aircraft under this working condition is the second-order bending, with a natural frequency of 140.4Hz and a vibration shape as shown in the figure. Figure 6 The raw data were filtered using the Butterworth low-pass filter method, where the filter cutoff frequency was set at 140 Hz based on the natural frequency of the second-order bending mode.

[0083] Table 1 Partial results of the first 30 modal analysis of the aircraft

[0084]

[0085] The last step is to compare the low-pass filtering results with the results of Reconstruct 4 to Reconstruct 6. The comparison chart is as follows: Figure 7 As shown in the figure, the Recon5 and BW140 curves are the closest in terms of change trend, curve details, and peak size. Therefore, Recon5 is selected as the final filtering result.

[0086] The processing process of normal and radial directions is the same as that of axial direction, so the process will not be repeated. The final filtering result obtained by the method of the present invention is as follows: Figure 8 As shown in Figure 3, the curve retains the details of the water entry impact and filters out high-frequency interference data, providing a feasible filtering solution for the nonlinear impact data obtained from the high-speed water entry simulation of the vehicle.

Claims

1. A nonlinear data processing method for simulating the impact of a vehicle entering water, characterized in that Here are the steps: Step 1: Perform EEMD decomposition on the nonlinear data f(t) obtained from the water impact simulation of the vehicle, and obtain the original data consisting of each order IMFi and the residual ε n express: Where: N is the number of times white noise is added to the EEMD decomposition, and the residual ε n is the margin; Step 2: Remove the first i-order high-frequency IMF components IMFi from the original signal and reconstruct the remaining low-frequency IMF components to obtain the reconstruction results of each order Reconstruct ii; Reconstruct 2 is the result obtained by removing IMF1 and IMF2 and reconstructing the remaining IMF3 to IMFN, and so on: Step 3: Perform transient modal analysis of the water impact on the vehicle, obtain the Butterworth low-pass filter frequency, and use this frequency to low-pass filter the original data to obtain a comparison curve; Step 4: Compare the reconstructed curve in step 2 with the Butterworth low-pass filter curve obtained in step 3, and select the closest reconstruction result Reconstruct ii as the final filtering result; The comparison is carried out in the following order: First, select the first m Reconstruct II curves whose peak values ​​are closest to the peak values ​​of the Butterworth low-pass filter curve; Then, among the m Reconstruct II curves, the curve with the inflection point closest to the inflection point of the Butterworth low-pass filter curve is selected; If a unique Reconstruct i curve has not been selected, the one closest to the peak pulse width of the Butterworth low-pass filter curve is selected as the final filtering result.

2. The nonlinear data processing method for simulating the impact of a vehicle entering water according to claim 1, characterized in that: The nonlinear data f(t) includes but is not limited to original data of axial, normal and radial load coefficients, and also includes but is not limited to nonlinear data of pressure, stress and bending moment.

3. The nonlinear data processing method for simulating the impact of a vehicle entering water according to claim 1, characterized in that: Including but not limited to the original data of axial, normal and radial load coefficients, and the processing method of nonlinear data including but not limited to pressure, stress and bending moment, are processed according to steps 1 to 3 respectively to obtain the respective final filtering result data graphs.

4. The nonlinear data processing method for simulating the impact of a vehicle entering water according to claim 1, characterized in that: The degree N and the remainder ε in the EEMD n The amplitude ε of white noise has the following empirical formula: It means that the more times white noise is added, the closer the final result is to the true value.

5. The nonlinear data processing method for simulating the impact of a vehicle entering water according to claim 1, characterized in that: The center frequencies of the IMFs in the EEMD are from high to low and meet the following two conditions:

1. The number of extreme points and zero-crossing points of the decomposed IMF components must be equal or differ by at most one; the extreme points include maximum and minimum values; 2. At any time, the mean of the upper envelope determined by the local maximum and the lower envelope determined by the local minimum is zero, that is, the components are locally symmetric with respect to the time axis.

6. The nonlinear data processing method for simulating the impact of a vehicle entering water according to claim 1, characterized in that: The process of obtaining the comparison curve in step 3 is as follows: taking the peak moment of the curve in the reconstruction result of step 2 as the peak moment of the water entry impact, considering the water entry speed and angle, locating the water entry simulation cavitation cloud map under the working condition to this moment, that is, obtaining the area of ​​the elastomeric vehicle affected by the water entry impact, and using the wetted area of ​​this area as the fixed position in the modal analysis to carry out the transient modal analysis of the water entry impact; obtaining the first m-order modes and the corresponding vibration shapes; finding the natural frequency corresponding to the second-order bending mode, and using this frequency to perform Butterworth low-pass filtering on the original data to obtain the comparison curve.

7. A use of the nonlinear data processing method for simulating a water impact of a vehicle according to any one of claims 1 to 6, characterized in that: Used for processing nonlinear data of vehicle water entry impact simulation.

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