Set Membership Estimation Theory, Methods And Their Applications

Although the research work on set membership estimation theory, methods and their applications has achieved some results, there is a lot of work left to be done. Based on analyzing the existing results, further research work is carried out in this dissertation. The research work here focuses on existing methods improvement, new methods presentation, and applications of set membership estimation theory and methods to fault diagnosis. This dissertation is composed of four parts.In the first part, set membership state estimation algorithms by ellipsoids are analyzed and improved. On one hand, the optimal set membership state estimation algorithm by ellipsoids for linear systems is improved, and two numerically stable suboptimal algorithms are proposed. In order to keep the shape-defining matrixes of the ellipsoids positive definite, cholesky decomposition and singular value decomposition are used in their computation. Besides, a subminimal-volume ellipsoid in the observation update is computed to circumvent inverse of ill-conditioned matrix. On the other hand, a square root non-optimal set membership state estimation algorithm by ellipsoids is given, and the parallel computation of state estimation using systolic arrays is schemed. The square root non-optimal algorithm can keep the shape-defining matrixes of the ellipsoids positive definite, so it is also numerically stable. If the state dimension is n, the parallel computation of state estimation using systolic arrays is of O(n) complexity. So the efficiency of computation is improved. Since the processing elements are enabled different functions at different stages, high processor utilization is achieved.In the second part, set membership estimation algorithms by zonotopes are analyzed and improved. Improved outer bound computation methods of intersection of a zonotope and a strip are pointed out based on the original ones. They give new families of zontopes containing the intersection and select the minimal-volume one as the outer bound. And, it can be proved by zonotope volume formulas that the improved outer bound computation methods can give smaller zonotopes than the original ones. Based on the above work, an improved set membership state estimation algorithm by zonotopes and an improved set membership identification algorithm by zonotopes for time-varying parameterized systems are obtained. The improved algorithms are more accurate than the original ones especially in the presence of uniformly heavy-tailed noise.In the third part, set membership identification algorithms based on advanced pattern classifiers are studied systematically. On one hand, the original set membership identification algorithm by least squares support vector machines is improved for better characterization of the feasible parameter sets. In the improved algorithm, a weighted least squares support vector regression is solved to build a model which approximates the complex functional relationship between the weighted l∞norms of the equation-error vectors and the given parameter vectors, and then the approximate feasible parameter set is obtained according to this model and the feasible weighted l∞norms of the equation-error vectors. Besides, an index reflecting the closeness between the approximate boundary and the true boundary is also given to evaluate the results of the proposed algorithm. Comparing with the original algorithm, the improved algorithm has better performance. On the other hand, two new set membership identification algorithms are given by viewing set membership identification as construction a pattern classifier to decide which class a point belongs to. In the two algorithms, supervised locally linear embedding and supervised isomap are combined with nearest mean classifier and k-nearest neighbor classifier respectively to build decision functions in the parameter space. The points in the parameter space can be divided into two classes according to whether they are in the feasible parameter set or not by decision functions. Since the classification errors are small, the set of all the points that are decided to be in the feasible parameter set can well approximate the feasible parameter set.In the fourth part, two fault diagnosis problems for nonlinear systems with unknown but bounded noises are studied. The first problem is about modeling and fault detection for nonlinear discrete-time dynamical systems with unknown but bounded noises. For this problem, a modeling and fault detection method is proposed using set membership identification algorithms and intelligent models such as radial basis function neural networks and Takagi-Sugeno fuzzy models. From system modeling aspect, this method can model nonlinear systems robustly and predict the bounds of the actual system outputs easily. While from fault detection aspect this method can detect abrupt and incipient faults effectively and is more robust than the methods where the thresholds are determined by statistical properties of residual errors. The second problem is about sensor fault detection and isolation of nonlinear discrete-time dynamical systems based on state space models with unknown but bounded noises. First, a set membership state estimation algorithm by ellipsoids for nonlinear systems is proposed. Since the algorithm has light computational load, on-line fault detection and isolation can be realized when it is applied to state estimation. Then, one fault detection method and two fault isolation methods based on set membership state estimation are given. The methods can detect and isolate sensor faults effectively and are more robust than the methods based on extended Kalman filtering.