Improved acceleration integration method based on Welch power spectrum
LI Zhanquan1,CHEN Taicong1,2,3
1. School of Civil Engineering and Transportation, South China University of Technology, Guangzhou 510641, China;
2. State Key Laboratory of Subtropical Building Science, Guangzhou 510641, China; 3. Pazhou Lab, Guangzhou 510335, China
Abstract:For the integration of noisy acceleration signals, the newly developed effective frequency band method has greatly improved the integration accuracy and noise immunity compared with the traditional frequency cutoff method. However, multiple frequency ranges for analysis need to be artificially specified and the adaptation to high noise is still poor, which is not conducive to engineering practice. Based on the Welch power spectrum of acceleration signals, an improved effective frequency band method is proposed. Firstly, with the Welch power spectrum curve, the 5%-peak threshold and the neighboring trough frequencies are integrated and applied to achieve the automatic definition of multiple frequency ranges for analysis. Following that, two different morphological fitting methods based on the Welch power spectrum curve and the Welch power spectrum squared curve, respectively, are proposed to realize the automatic identification of the effective frequency bands. Finally, the corresponding velocity and displacement signals are obtained through frequency-domain integration within the effective frequency bands. Through numerical simulation examples, the integration effects of the original effective frequency band method and the improved method are examined comparatively under multi-frequency excitation and random excitation. The results show that, in contrast to the original method, the improved method can realize the whole-process automatic analysis of acceleration integration, and the noise immunity is further enhanced, in which the Welch power spectrum curve based morphological fitting is applicable to the case of multi-frequency excitation under high noise, as well as the Welch power spectrum squared curve based one to the case of random excitation.
Key words: acceleration integration; frequency domain integration; effective frequency band; Welch power spectrum
李展铨1,陈太聪1,2,3. 基于Welch功率谱的加速度积分改进方法研究[J]. 振动与冲击, 2022, 41(18): 41-46.
LI Zhanquan1,CHEN Taicong1,2,3. Improved acceleration integration method based on Welch power spectrum. JOURNAL OF VIBRATION AND SHOCK, 2022, 41(18): 41-46.
[1] Ignace M, Andre R B, Arijit S, et al. System identification of UCSD-NHERI shake-table test of two-story structure with cross-laminated timber rocking walls [J]. Journal of Structural Engineering, 2021, 147(4): 04021018.
[2] Prawin J, Anbarasan R. A novel Mel-frequency cepstral analysis based damage diagnostic technique using ambient vibration data [J]. Engineering Structures, 2021, 228: 111552.
[3] Joseph M. Seismic performance and retrofit evaluation of reinforced concrete structures [J]. ACI Structural Journal, 1997, 123(1): 3-10.
[4] Lee K, Foutch D A. Performance evaluation of new steel frame buildings for seismic loads [J]. Earthquake Engineering and Structural Dynamics, 2002, 31(3): 653-670.
[5] Phani A S, Woodhouse J. Experimental identification of viscous damping in linear vibration [J]. Journal of Sound and Vibration, 2009, 319: 832-849.
[6] Pintelon R, Schoukens J. Real-time integration and differentiation of analog-signals by means of digital filtering [J]. IEEE Transactions on Instrument and Measurement, 1990, 39(6): 923-927.
[7] 徐庆华. 试采用FFT方法实现加速度、速度与位移的相互转换[J]. 振动、测试与诊断, 1997, (04): 30-34.
XU Qinghua. The conversion of acceleration, velocity and displacement realized by FFT method [J]. Journal of Vibration, Measurement & Diagnosis, 1997, (04): 30-34.
[8] Brandt A, Brincker R. Integrating time signals in frequency domain - Comparison with time domain integration [J]. Measurement, 2014, 58: 511-519.
[9] 方新磊, 郝伟, 陈宏. 基于频域滤波的加速度信号处理[J]. 仪表技术与传感器, 2012, 4: 94-96.
FANG Xinlei, HAO Wei, CHEN Hong. Acceleration signal processing based on frequency domain filtering [J]. Instrument Technique and Sensor, 2012, 4: 94-96.
[10] 陈太聪, 张奇. 基于频谱能量形态拟合的加速度积分方法研究[J]. 振动与冲击, 2019, 38(13): 7-12+20.
CHEN Taicong, ZHANG Qi. Acceleration integration method based on frequency spectral energy morphological fitting [J]. Journal of Vibration and Shock, 2019, 38(13): 7-12+20.
[11] 杨婧,程乃平,倪淑燕. Welch算法在弱信号检测中的性能分析[J]. 计算机仿真, 2020, 37(5): 235-240.
YANG Jing, CHENG Naiping, NI Shuyan. Performance analysis of Welch algorithm in weak signal detection [J]. Computer Simulation, 2020, 37(5): 235-240.
[12] 王福杰, 潘宏侠. MATLAB中几种功率谱估计函数的比较分析与选择[J]. 电子产品可靠性与环境试验, 2009, 27(06): 28-31.
WANG Fujie, PAN Hongxia. Analysis and selection of several power spectrum estimation functions in MATLAB [J]. Electronic Product Reliability and Environmental Testing, 2009, 27(06): 28-31.
[13] 周臻,孟少平,吴京. 预应力双层柱面网壳的风振响应与整体风振系数研究[J]. 工程力学, 2011, 28(10): 124-132.
ZHOU Zhen, MENG Shaoping, WU Jing. The wind-induced response and global wind vibration coefficient of prestressed double-layer cylindrical reticulated shells [J]. Engineering Mechanics, 2011, 28(10): 124-132.
[14] 房建, 雷晓燕, 练松良. 合-武客运专线轨道不平顺谱特性实测分析[J]. 铁道学报, 2015, 37(7): 79-85.
FANG Jian, LEI Xiaoyan, LIAN Songliang. Analysis on characteristics of track irregularity spectrum of Hefei-Wuhan passenger dedicated line [J]. Journal of the China Railway Society, 2015, 37(7): 79-85.
[15] 白永福, 高翔, 张伟, 奚冲霄, 王凌. 海拉尔台阵数据功率谱分析[J]. 防灾减灾学报, 2020, 36(2): 49-55.
BAI Yongfu, GAO Xiang, ZHANG Wei, XI Chongxiao, Wang Ling. Analysis of the array data power spectrum in Hailar [J]. Journal of Disaster and Reduction, 2020, 36(2): 49-55.
[16] 李德保, 陆秋海. 工程振动试验分析[M]. 北京: 清华大学出版社, 2004.
LI Debao, LU Qiuhai. Engineering Vibration Test Analysis [M]. Beiiingg: Tsinghua UniveIsity Press, 2004.
[17] 叶其孝, 沈永欢. 实用数学手册[M]. 北京: 科学出版社, 2006.
YE Qixiao, SHEN Yonghuan. Practical Mathematics Handbook [M]. Beijing: Science Press, 2006.
[18] Ang H-S A, Tang W H. Probability Concepts in Engineering: Emphasis on Applications to Civil and Environmental Engineering (2nd Edition) [M]. New York: John Wiley & Sons, 2007.
[19] Han S. Measuring displacement signal with an accelerometer [J]. Journal of Mechanical Science and Technology, 2010, 24(6): 1329-1335.