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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.
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Keywords:
- chaotic excitation /
- directional Lyapunov exponent /
- fault detection /
- single input single output system
[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 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 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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[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 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 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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