Application of Improved HHT Algorithm in Missile Working Mode Identification

doi:10.3969/j.issn.1009-086x.2022.03.005

Abstract

Abstract:

The key to improving the accuracy of vibration mode identification is to improve the separation accuracy of dense natural modes. Based on the analysis of the sieving results of ensemble empirical mode decomposition （EEMD）， this paper proposes a multi-noise method. The improved sieving algorithm， combined with the Hilbert Transform（HT） method， is applied to the identification of missile operating modes. Compared with the sieving results of empirical mode decomposition and ensemble empirical mode decomposition algorithms， the new algorithm reduces the error and effectively suppresses the phenomenon of modal aliasing. Compared with the logarithmic decay method， the Hilbert transform is used for mode identification， which improves the parameter identification accuracy， and can identify the variation law of natural frequency with time， which is more suitable for analyzing the time-varying missile working mode. This research can provide a reference for solving the modal aliasing problem in signal processing.

Key words: improved ensemble empirical mode decomposition（EEMD） algorithm, mode identification, Hilbert transform, modes aliasing, end effect

摘要：

提高振动模态辨识精度的关键在于提高密集固有模态的分离精确度，基于对集合经验模态分解（ensemble empirical mode decomposition, EEMD）筛分结果的分析，提出了一种多次加噪的改进筛分算法，与希尔伯特变换（Hilbert transform, HT）相结合，应用于导弹工作模态辨识。与经验模态分解、集合经验模态分解算法的筛分结果相比，新方法降低了误差，有效抑制了模态混叠现象。较之对数衰减法，利用希尔伯特变换进行模态辨识，提高了参数辨识精度，同时可以辨识出固有频率随时间变化趋势，更适合分析具有时变性的导弹工作模态。该研究可为信号处理中解决模态混叠问题提供参考。

关键词: 改进EEMD算法, 模态辨识, 希尔伯特变换, 模态混叠, 端点效应

CLC Number:

TJ76

Jin-song XIE, Lin XUE, Qing-feng GAO. Application of Improved HHT Algorithm in Missile Working Mode Identification[J]. Modern Defense Technology, 2022, 50(3): 32-39.

谢金松, 薛林, 高庆丰. 改进HHT算法在导弹工作模态辨识中的应用[J]. 现代防御技术, 2022, 50(3): 32-39.

Figures/Tables 13

Fig.1 Flowchart of EEMD algorithm

Fig.2 Flowchart of improved EEMD algorithm

Fig.3 The missile is simplified to Euler-Bernoulli beam

Table 1 Missile body parameters

弹长

l / m m

弹径

d / m m

体密度

ρ/（kg·m^-3）

弹性模量

E / M P a

压心位置

x / m m

Table 1 Missile body parameters

弹长

l / m m

弹径

d / m m

体密度

ρ/（kg·m^-3）

弹性模量

E / M P a

压心位置

x / m m

3 762

223

1 757

10 000

1 570

Fig.4 Vibration signal measured by accelerometer

Fig.5 Decomposition results of EMD

Fig.6 Decomposition results of EEMD

Fig.7 Decomposition results of improved EEMD

Table 2 Decomposition accuracy of each algorithm

算法

一阶

模态

二阶

模态

三阶

模态

Fig.8 Identification process of peak logarithmic attenuation

Fig.9 Variation trend of the logarithm of the first oder IMF amplitude

Fig.10 Variation trend of the instantaneous frequency of first oder IMF

Table 3 Identification results of each algorithm

参数	一阶模态	二阶模态	三阶模态
频率真实值/Hz	41.24~41.96	114.56~116.57	224.54~228.49
对数衰减辨识结果/Hz	44.43	122.74	237.52
HHT辨识结果/Hz	41.13~42.04	114.72~117.84	223.82~226.91
阻尼比真实值	0.008 5	0.022 1	0.033 2
对数衰减辨识结果	0.007 4	0.024 1	0.035 4
HHT辨识结果	0.008 0	0.023 9	0.034 7

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