Deterministic Learning Theory And Intelligent Diagnosis Of Oscillation Faults

With rapid development of information processing techniques, computer-based learn-ing approaches have received more and more attention. Many learning problems can behandled by static nonlinear mapping approaches, e.g., statistical learning. Recently, byutilizing results from concepts and tools of adaptive control and dynamical systems,Wang etc. propose the deterministic learning (DL) theory, which provides systematicdesign approaches for knowledge acquisition, representation, and utilization in uncertaindynamical environments.The thesis contains three parts. The first part investigates the persistent of excitation(PE) property of radial basis function (RBF) networks. The second part extends the DLtheory to model and control of nonlinear discrete-time systems. The third part proposesan approach for intelligent diagnosis of nonlinear oscillation systems by using the DLtheory.First, we investigate the PE property of RBF networks. Satisfaction of PE conditionis a challenging problem in the areas of identification and adaptive control of nonlinearsystems. This condition is normally di?cult to be verified a priori, while it guaranteesparameter convergence. During the past decade, the PE property of RBF networks hasbeen received continued attention and some interesting results have been obtained. Basedon some recent results on the PE condition, we show that by using RBF networks, foralmost every recurrent trajectory, a partial PE condition, i.e., the PE condition of acertain regression subvector constructed out of the RBFs along the recurrent trajectory,can be satisfied. This partial PE condition can lead to a local accurate NN approximationof the system dynamics.Second, we investigate the temporal data modeling and control problem. Temporaldata mining has attracted a great deal of attention in the industry and society recently, with the propose to find useful information from data. By using the DL result proposedby Wang, Liu, etc., we present a time-invariant representation manner, definition of simi-larity, and a method for rapid recognition for the temporal data sequences. Furthermore,we investigate the DL problem of closed-loop system dynamics during neural network con-trol of nonlinear discrete-time systems. The knowledge can be reused for pattern-basedintelligent control.Third, we propose an intelligent approach for rapid and sensitive detection and iso-lation of nonlinear oscillation faults. The approach consists of two phases: the training(learning) phase and the test (diagnosis) phase. In the training or learning phase, foran oscillation system in both normal and fault modes, the system dynamics underly-ing the normal and fault oscillations are locally-accurately approximated. The obtainedknowledge of system dynamics is stored in constant RBF networks. In the test or di-agnosis phase, rapid detection and isolation are implemented by utilizing the learnedknowledge of system dynamics. The occurrence of a test oscillation fault can be rapidlydetected and isolated according to the smallest residual principle. A rigorous analysis ofthe performance of the proposed scheme is also given. Compared with existing resultson adaptation and online approximation based methods for fault diagnosis, the proposedapproach has the following features: i) knowledge of modeling uncertainty and nonlinearfaults is obtained in the training phase; ii) the learned knowledge is reused to reducemodeling uncertainty, which enhances the robustness, sensitivity of the diagnosis scheme.Moreover, we investigate the fault diagnosis of nonlinear robotic systems and the rapiddetection of rotating stall in axial compressor by using the proposed diagnosis approach.The results presented in this thesis show that the DL theory will provide a newapproach to data-based modeling, control and fault diagnosis.