指向Lyapunov指数及其在单输入单输出系统故障检测中的应用

杨东东; 马红光; 徐东辉; 刘浩淼

doi:10.7498/aps.63.220505

摘要

针对单输入单输出系统的故障检测, 采用混沌振荡器作为激励源, 并利用非一致延迟时间法对被测系统输出时间序列进行相空间重构. 在相空间中平衡点附近定义了指向Lyapunov指数, 并用其对被测系统输出在相空间中平衡点附近特征结构进行分析, 实现了对单输入单输出系统的故障检测. 仿真结果表明, 被测系统的参数变化将会引起相空间中平衡点附近特征结构的改变, 指向Lyapunov指数对其变化敏感.

关键词:

In this paper, for the fault detection of a single-input single-output (SISO) system, we use chaotic oscillator to generate the excitation of the system under test (SUT), and use non-uniform method to reconstruct the phase space of the output time series. Directional Lyapunov exponent is defined around the equilibrium point in the phase space, and it is used to analyze the eigen-structure of the output phase space around its equilibrium point, thus the fault detection of the SISO system is realized. The simulation results show that parameter changes of the SUT will affect the phase space structure around its equilibrium point, and the directional Lyapunov exponent is sensitive to these changes.

Keywords:

作者及机构信息

1.
第二炮兵工程大学, 西安 710025

基金项目: 国家自然科学基金(批准号:61174207)资助的课题.

Authors and contacts

1.
The Second Artillery Engineering University, Xi'an 710025, China

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 61174207).

参考文献

[1]	Isermann R, Balle P 1997 Control Eng. Pract. 5 709
[2]	Logan D, Mathew J 1996 Mech. Syst. Signal Pr. 10 241
[3]	Yang D D, Ma H G, Xu D H, Feng X W 2014 Acta Phys. Sin. 63 120508 (in Chinese) [杨东东, 马红光, 徐东辉, 冯晓伟 2014 物理学报 63 120508]
[4]	Li Q H, Tan J Y 2011 Chin. Phys. B 20 040505
[5]	Mandelbrot B B 1985 Phys. Scripta 32 257
[6]	Nichols J M, Todd M D, Wait J R 2003 Smart. Mater. Struct. 12 580
[7]	Todd M D, Erickson K, Chang L, Lee K, Nichols J M 2004 Chaos 14 387
[8]	Xia H C, Zhan Y Q 2004 Acta Phys. Sin. 53 1299 (in Chinese) [夏恒超, 詹永麒 2004 物理学报 53 1299]
[9]	Nichols J M, Trickey S T, Todd M D, Virgin L N 2003 Meccanica 38 239
[10]	Nichols J M, Nichols C J, Todd M D, Seaver M, Trickey S T, Virgin L N 2004 Smart. Mater. Struct. 13 241
[11]	So P, Ott E, Sauer T 1997 Phys. Rev. E 55 5398
[12]	Branicki M, Wiggins S 2005 Physica D 212 271
[13]	Tanaka M L, Ross S D 2009 Nonlinear Dynam. 58 1
[14]	Kugiumtzis D 1996 Physica D 95 13
[15]	Melbourne I, Stuart A M 2011 Nonlineartiy 24 1361
[16]	Rossler O E 1976 Phys. Lett. A 57 397
[17]	Judd K, Mees A 1998 Physica D 120 273
[18]	Nichkawde C 2013 Phys. Rev. E 87 022905
[19]	Li W 1990 J. Stat. Phys. 60 823

施引文献

[1]	Isermann R, Balle P 1997 Control Eng. Pract. 5 709
[2]	Logan D, Mathew J 1996 Mech. Syst. Signal Pr. 10 241
[3]	Yang D D, Ma H G, Xu D H, Feng X W 2014 Acta Phys. Sin. 63 120508 (in Chinese) [杨东东, 马红光, 徐东辉, 冯晓伟 2014 物理学报 63 120508]
[4]	Li Q H, Tan J Y 2011 Chin. Phys. B 20 040505
[5]	Mandelbrot B B 1985 Phys. Scripta 32 257
[6]	Nichols J M, Todd M D, Wait J R 2003 Smart. Mater. Struct. 12 580
[7]	Todd M D, Erickson K, Chang L, Lee K, Nichols J M 2004 Chaos 14 387
[8]	Xia H C, Zhan Y Q 2004 Acta Phys. Sin. 53 1299 (in Chinese) [夏恒超, 詹永麒 2004 物理学报 53 1299]
[9]	Nichols J M, Trickey S T, Todd M D, Virgin L N 2003 Meccanica 38 239
[10]	Nichols J M, Nichols C J, Todd M D, Seaver M, Trickey S T, Virgin L N 2004 Smart. Mater. Struct. 13 241
[11]	So P, Ott E, Sauer T 1997 Phys. Rev. E 55 5398
[12]	Branicki M, Wiggins S 2005 Physica D 212 271
[13]	Tanaka M L, Ross S D 2009 Nonlinear Dynam. 58 1
[14]	Kugiumtzis D 1996 Physica D 95 13
[15]	Melbourne I, Stuart A M 2011 Nonlineartiy 24 1361
[16]	Rossler O E 1976 Phys. Lett. A 57 397
[17]	Judd K, Mees A 1998 Physica D 120 273
[18]	Nichkawde C 2013 Phys. Rev. E 87 022905
[19]	Li W 1990 J. Stat. Phys. 60 823

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