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| By analyzing the Volterra model in frequency domain, i.e. the generalized frequency response functions (GFRF), characteristics of nonlinear system in frequency domain can be realized, and it can be applied to fault diagnosis of nonlinear system. The Volterra model identification and fault diagnosis method are two important aspects of the nonlinear spectral analysis, we have obtained some new significant progresses about these two aspects in recent year. In this paper, the theory and application based on nonlinear spectral analysis are perfectly introduced, and the new progresses are also presented. For identification of Volterra model, by reconstructing the Volterra model as a pseudo-linear combination construction, and using a constrained optimization analysis idea, a fully decoupled Volterra adaptive identification algorithm is firstly presented. The simulation results show that the fully decoupled identification algorithm can effectively improve the convergence speed and precision of adaptive identification, and its convergence process is more stable. For improving robust performance of Volterra model identification, a robust total least mean square adaptive identification algorithm is presented by defining the Volterra total mean squared error and modifying estimated gradient according to the steepest descent principle. The theoretic analysis and simulation results have indicated its excellent performance. In addition, for reducing computation requirements in fault diagnosis based on nonlinear spectral analysis, a new diagnosis method based on multiple preset GFRF models is also presented. In this method, the multiple preset GFRF models are used to describe the corresponding working mode of the system, and the fault can be directly diagnosed according to the matching extend of each preset model to the current working mode of the system. The experiment test has proved this new diagnosis method is effective. |
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| Keywords:VNonlinear system, Nonlinear spectral analysis, Volterra series, fully decoupled identification, robust total least mean square, fault diagnosis, multi preset GRRF model. |
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