Fault diagnosis approach based on Volterra models

Abstract The fault diagnosis schemes are roughly divided into two major categories: signal analysis and modeling method. Compared with the signal analysis approaches, the availability of suitable models of machines could be exploited more conveniently, which allows a more precise and reliable fault identification. In this paper, a modeling fault diagnostic approach based on Volterra series for rotating machinery is presented. After a brief review of the Volterra series theory, the process of the new diagnostic approach and the identification method of Volterra kernels are introduced in detail. The computer simulation verifies its feasibility and validity. Then, this novel method based on Volterra modeling is employed for the fault diagnosis of a rotor-bearing system. Through investigating the changes of generalized frequency response functions of the system under different states, the faults are identified successfully. Finally, the laboratory experimental results verify its effectiveness.

[1]  S. Billings,et al.  Mapping non-linear integro-differential equations into the frequency domain , 1990 .

[2]  Gary G. R. Green,et al.  Calculation of the Volterra kernels of non-linear dynamic systems using an artificial neural network , 1994, Biological Cybernetics.

[3]  Reinhard Männer,et al.  Towards an Optimal Mutation Probability for Genetic Algorithms , 1990, PPSN.

[4]  Sang-Won Nam,et al.  Application of higher order spectral analysis to cubically nonlinear system identification , 1994, IEEE Trans. Signal Process..

[5]  Paolo Pennacchi,et al.  Use of modal representation for the supporting structure in model-based fault identification of large rotating machinery. part 1-theoretical remarks , 2006 .

[6]  Keith Worden,et al.  A harmonic probing algorithm for the multi-input Volterra series , 1997 .

[7]  S. A. Billings,et al.  An investigation into the characteristics of non-linear frequency response functions. Part 1: Understanding the higher dimensional frequency spaces , 2005 .

[8]  Jonathan M. Nichols,et al.  Second-order spectra for quadratic nonlinear systems by Volterra functional series: Analytical description and numerical simulation , 2008 .

[9]  S. A. Billings,et al.  An investigation into the characteristics of non-linear frequency response functions. Part 2: New analysis methods based on symbolic expansions and graphical techniques , 2005 .

[10]  John J. Grefenstette,et al.  Optimization of Control Parameters for Genetic Algorithms , 1986, IEEE Transactions on Systems, Man, and Cybernetics.

[11]  Paolo Pennacchi,et al.  Some Results in Model Based Transverse Crack Identification in Rotor Systems , 2000 .

[12]  S. Billings,et al.  Frequency response functions for nonlinear rational models , 1995 .

[13]  K. Dejong,et al.  An analysis of the behavior of a class of genetic adaptive systems , 1975 .

[14]  Rajarshi Das,et al.  A Study of Control Parameters Affecting Online Performance of Genetic Algorithms for Function Optimization , 1989, ICGA.

[15]  L. Chua,et al.  Measuring Volterra kernels (II) , 1989 .

[16]  David Rees,et al.  Probing signals for measuring nonlinear Volterra kernels , 1995, Proceedings of 1995 IEEE Instrumentation and Measurement Technology Conference - IMTC '95.

[17]  Leon O. Chua,et al.  Measuring Volterra kernels , 1983 .

[18]  W. Rugh.  Nonlinear System Theory: The Volterra / Wiener Approach , 1981 .

[19]  Paolo Pennacchi,et al.  Accuracy of modelling and identification of malfunctions in rotor systems: experimental results , 2000 .

[20]  M. Schetzen.  The Volterra and Wiener Theories of Nonlinear Systems , 1980 .

[21]  D. E. Goldberg,et al.  Genetic Algorithms in Search , 1989 .