Research On Some Key Technologies Of Observability Analysis And Application Of Dynamic System

The observability of dynamical systems is an essential characteristic of them which plays an important role in target identification, navigation, operation monitoring and RMS(reliability, maintainability and supportability) work. In this dissertation, investigation was performed on some key technologies of dynamical system observability analysis and application, including judgment and measurement of observability, improvement and persistence of the observability. Innovation works and results are shown as follows:1) Basic methods of observability judgment and measurement for linear systems were studied. The observability judgment method based on Jordan canonical form and detection matrix was studied. Based on this judgment approach, detection matrix optimization method was obtained for linear systems(which include systems with cycle index bigger than 1, i.e. in its Jordan canonical form, different Jordan blocks have same root). For the measurement of observability of linear systems, relationship of singular values of observability Gram matrix and bounds of upper and lower estimation square errorswas studied. A new parameter from observability Gram matrix was presented for the measurement of observability which was able to measure observability of the original states of systems.2) A partial observability concept and relative analysis method was studied. This concept was presented for analyzing the local characteristic of complex systems. The sufficient and necessary condition of partial observability was studied and proved. A partial observability judgment index which is convenient for application was obtained. In order to measure partial observability, the concept of degree of unobservability and its computation method were presented which can be used to measure the states of sets or units of systems.3) A method to select LRU(Line Replaceable Unit) which can develop the system observability was studied. New RMS parameters were presented for LRU selection. When detailed fault detection parameters were not confirmed, a Mean Failure Unobservability concept was employed to substitute Mean Failure Fault Undetected Rate, and LRUs selection was performed by this method. This means can be used to increase system observability sufficiently, and provide a direct RMS tradeoff approach.4) The analysis method of keep the observability of nonlinear systems was studied. Firstly, the influence of coordinate transformation on nonlinear systems has been investigated. The sufficient condition of the observability persistence after coordinate transformation of a kind of nonlinear systems was obtained. Based on above results, a constrained Extended Kalman Filter was presented and investigated. The observability persistence after coordinate transformation of this filter was affirmed. Then a number of parameters of a nonlinear model with more dimensions and strong nonlinearity were successfully identified with this filter.