WANG Chun-chang， GU Qiang， AN Xiao-hong

(College of Mechatronic Engineering, North University of China, Taiyuan 030051, China)

王春常， 顧 強(qiáng)， 安曉紅

(中北大學(xué) 機(jī)電工程學(xué)院， 山西 太原 030051)

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Analysis of penetration acceleration signal based on wavelet transformation

WANG Chun-chang， GU Qiang， AN Xiao-hong

(CollegeofMechatronicEngineering,NorthUniversityofChina,Taiyuan030051,China)

In order to analyze the composition and frequency distribution of acceleration signal in the process of projectile penetrating, this paper uses wavelet transform to decompose penetration acceleration signal to get the distribution of penetration acceleration signal in different frequency bands. Compared with the ideal acceleration signal curve and its characteristics, it can be concluded that the frequency range of the acceleration signal in the axis of the projectile and the vibration frequency range of the projectile are 31.25-62.5 kHz and 62.5-125 kHz, respectively. Finally, the penetration acceleration signal curve is obtained by Simulink.

penetration process; wavelet transform; acceleration; frequency distribution

0 Introduction

Hard target penetration ammunition is an important means to fight the high valuable hard targets such as ground buildings, bridges, airport runways, underground storehouses, command center, etc. Hard target fuse uses high g acceleration sensor to identify the change of penetration environment and then the ammunition can attack the targets more efficiently[1-2]. Therefore, the acceleration signal has significant influence on the performance of hard target penetration ammunition.

The main means of measuring penetration acceleration signal is to install the recorder inside the projectile. By reading the data from the recorder, we can realize the reconstruction and analysis of acceleration signal[3]. However, because of intense vibration and complex physical changes of the projectile body in the process of penetrating, lots of high frequency signals produce, which results in the acceleration signal of the recorder inevitably overlaying interference signals and makes the collected data have a great deviation from the ideal penetration acceleration signal curve[4-8]. In order to analyze the penetration acceleration signal accurately, this paper uses wavelet transform to decompose the penetration acceleration signal and then extracts corresponding penetration acceleration signal curve.

1 Penetration acceleration signal characteristics

According to the characteristics of penetration acceleration signal, including short action time, large peak pulse amplitude and long average acceleration duration, a model is established for penetration acceleration signal,

(1)

wherea(t) is the axial acceleration in the process of penetrating, which is just the acceleration signal collected by the recorder. As seen from the model, the penetration acceleration signal mainly consists ofalow frequency(t) andavibration(t), wherealow frequency(t) is the signal resulting from resistance emerging in the process of target medium penetrating, shown as a pulse signal superimposed by infinitesimally small perturbations in the whole process of penetrating.avibration(t) is the vibration signal generated in the process of penetrating, including horizontal and vertical vibration signals, andainterference(t) is the main interference signal in the environment.

The ideal curve ofa(t) is shown in Fig.1. When the bullet enters the target, negative acceleration continually increases, but it remains basically unchanged after fully entering into the target. When it leaves the target, acceleration will increase sharply and then decrease rapidly under the influence of Stokes viscosity resistance. Finally, it has a shot-term increasing process as a result of energy release between the mass block and the spring in the senor. This process is usually not considered.

In reality, the penetration acceleration signal curve obtained by the signal acquisition system is similar to the curve in Fig.2. The vibration of the projectile, sensor installation, internal collision and other factors lead to large fluctuation. The broken line is a simplified graphic of ideal acceleration curve.

Fig.1 Ideal penetration acceleration signal curve

Fig.2 Actual penetration acceleration signal curve

2 Wavelet transform

The wavelet transform can decompose the signal into the sum of a series of the wavelet functions obtained through the translation and scale changes of wavelet basic function, thus superimposition function can approximate the signal.

Through wavelet transform, an original signal can be decomposed into high frequency part and low frequency part. The low frequency part usually contains main features of the signal and the high frequency part contains the signal details or difference. By decomposing the original signal into the low frequency part, a plurality of low frequency signals are obtained. We can get the original signal based on analysis of the characteristics of the low frequency signals.

In wavelet transform, the selection of wavelet basis function is very important. For the same original signal, if different wavelet basis functions are adopted, the wavelet components also will be different. There is no standard theory for selection of the best wavelet basic function, which is generally decided in accordance with the characteristics of wavelet basic function, features of the detected signal and specific requirements. In the process of wavelet transformation, the similar shape features between the signal waveform and wavelet basic function will be amplified, and the greatly different signal features will be suppressed. Therefore, the wavelet coefficients can indicate the similarity of the wavelet basic function and processed signal.

The commonly used wavelets include Haar wavelet, Daubechies wavelet, Biorthogonal wavelet, and so on. Daubechies wavelet has good compact support, smooth and nonlinear phase characteristics. Therefore, in the analysis of blasting, earthquakes, penetration and other non-stationary signals, we usually use Daubechies wavelet, which has a variety of sequences according to the difference of the positive integerN. What is commonly used in vibration signals is db3, db4 and db8.

3 Penetration acceleration signal

3.1 Acquisition of penetration acceleration signal

The target material is A30 steel and the size is

whereLis length,Wis width andTis thickness.

The length of penetration projectile is 640 mm and its weight is 47 kg. Armor piercing shell penetrates through the steel target at the speed of 483.66 m/s and finally hits into the soil. Data sampling frequency is 160 kHz. The signal frequency spectrum and signal curve are shown in Fig.3.

It can be seen from Fig.3 that the signal curves in the range of 50-180 kHz and the range of 200-280 kHz mutate significantly, while the sampling frequency of data acquisition instrument is 160 kHz. Therefore, the signal mutation in the range of 200-280 kHz can be neglected.

According to the penetration acceleration signal model in Eq.(1), it can be known that one of the two signals is the signal resulting from resistance emerging in the process of target medium penetrating and the other is the vibration signal generated in the process of the projectile penetrating. In order to distinguish the specific distribution range of the signal frequency, we need further analysis.

Fig.3 Original signal and frequency spectrum curves

3.2 Decomposition of penetration signal

According to the characteristics of penetration signal and the questions under discussion, the db4 is selected to decompose the measured penetration acceleration signal. The decomposition has 8 layers. The original signal and approximate signal of each layer (a1-a8) are shown in Fig.4. The details signal of each layer (d1-d8) are show in Fig.5. The enlarged drawings of wavelet decomposition of low frequency a5 and high frequency d4 are shown in Figs.6 and 7, respectively.

Fig.4 Original signal and approximate signals of layers a1-a8

Fig.5 Original signal and detail signals of layers d1-d8

Fig.6 Low frequency a5 by wavelet decomposition

Fig.7 High frequency d4 by wavelet decomposition

3.3 Analysis of penetration acceleration signal

Comparing the approximate signals of eight layers in Fig.4, it can be found that a1-a3 layer signals have violent oscillation, smaller pulse width and larger amplitude variation, which indicates that there are a number of residual interference signals and thus a1-a3 layers are not considered. Though a4 waveform is smooth, there are still many oscillation signals and therefore it is also discarded. Compared with the ideal acceleration signal curve, waveform of a5 is more consistent with the basic characteristics of penetration acceleration signal, therefore the low frequency acceleration signal of projectile is in the range of a5 frequency band. The a6-a8 layer signals have large deviation from the ideal signal curve and therefore they are not considered too. Comparing the detail signals of eight layers in Fig.5, the d1-d3 layer signals have smaller span, more concentrated energy and higher frequency, and thus we can deduce that they belong to high frequency noise signals at the end of penetration, which can be neglected. The d4 layer signal is distributed throughout all the penetration process and the distribution of signal is also averaged. According to the characteristics of vibration signal, namely small amplitude, large signal broadening and high frequency, it can be ensured that the d4 layer signal is projectile vibration signal. The d5-d8 layer signals have larger span and may be a part of the residual penetration acceleration signal, therefore they will not be considered.

Wavelet analysis is to extract the signal of each frequency band, therefore the process of wavelet decomposition is the process of low-pass filtering or band-pass filtering of signals. The a1-a8 layer signals are obtained by low-pass filter and d1-d8 layer signals are obtained by band pass filter. From Figs.4 and 5, it can be seen that the a5 layer signal obtained by 62.5 kHz low-pass filtering becomes very smooth and basically reflects the main features of penetration acceleration signal. The layer signal a6 obtained by 31.25 kHz low-pass filtering has a large deviation from the ideal penetration acceleration curve. Therefore, penetration acceleration signal frequency range should be from 31.25 kHz to 62.5 kHz. Because d4 layer signal is the result of 62.5-125 MHz band-pass filtering, the projectile vibration frequency range should be in 62.5-125 MHz.

3.4 Signal simulation

After getting penetration acceleration signal frequency in the range of 31.25-62.5 kHz and vibration frequency of 62.5-125 MHz, we get the filter frequency (62.5 kHz low-pass filter and 62.5-125 MHz band-pass filter) at the same time. Then we start the signal simulation.

We use Simulink for signal simulation. By calling digital filter design module, the band-pass filtering of the initial signal is finished. Finally, we get the penetration acceleration curve, as shown in Fig.8.

Compared with the signal curve in Fig.2, the signal curve in Fig.8 includes most of signal characteristics. Only in the detail part do they have some deviations. When the projectile penetrates into the steel plate, the curve in Fig.8 does not keep smooth as the curve in Fig.1 while begins to fluctuate. When the projectile leaves the steel plate, the curve has some fluctuations being consistent with the characteristics of the ideal penetration acceleration curve, which indicates the energy releasing process between the mass block and the spring in the senor.

Fig.8 Penetration acceleration signal curve

4 Conclusion

The analysis of the acceleration signal in the penetration process and corresponding signal frequency distribution can provide the basis for the subsequent extraction of the acceleration signal, which has great significance to the recognition of target and the control of penetration explosion point. The penetration acceleration signal obtained by Simulink can provide the basis for the stress conditions of the projectile in the process of penetrating.

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基于小波變換的侵徹加速度信號(hào)分析

為了分析彈體在侵徹過(guò)程中加速度信號(hào)的構(gòu)成成分和頻率分布范圍， 利用小波變換對(duì)侵徹加速性信號(hào)進(jìn)行了分解， 分解出侵徹加速度信號(hào)在不同頻段內(nèi)的分布情況。 通過(guò)與理想情況下加速度信號(hào)曲線及加速度信號(hào)本身的信號(hào)特點(diǎn)進(jìn)行對(duì)比， 得出彈體在侵徹過(guò)程中， 在軸線上加速度信號(hào)的頻率范圍和彈體振動(dòng)頻率范圍分別為31.25-62.5 kHz和62.5-125 kHz， 而后利用Simulink獲得侵徹加速度信號(hào)曲線。

侵徹過(guò)程； 小波變換； 加速度； 頻率范圍

WANG Chun-chang， GU Qiang， AN Xiao-hong. Analysis of penetration acceleration signal based on wavelet transformation. Journal of Measurement Science and Instrumentation, 2015, 6(3)： 223-228. [

王春常， 顧 強(qiáng)， 安曉紅

(中北大學(xué) 機(jī)電工程學(xué)院， 山西 太原 030051)

10.3969/j.issn.1674-8042.2015.03.004]

WANG Chun-chang(wcc18334791845@163.com)

1674-8042(2015)03-0223-06 doi： 10.3969/j.issn.1674-8042.2015.03.004

Received date： 2015-06-03

CLD number： TJ430.6 Document code： A