Nonlinear System Identification and Its Applications in Fault Detection and Diagnosis

Interest in nonlinear system identification has grown significantly in recent years. It is much more difficult to develop general results than the concern for linear models since the nonlinear model structures are often much more complicated. As a consequence, the thesis only considers two different kinds of models, one is a type of state space model which is described by Itô Stochastic Differential Equations (ISDE), the other one is a nonlinear First Order Plus Dead Time (FOPDT) model. This thesis aims to investigate these two different kinds of nonlinear models and to propose the corresponding methods to deal with their system identifications.
Firstly, the system described by an ISDE model is considered. Extended from conventional stochastic systems, where the random part of the system is often described as a type of normal distribution signal added to the deterministic differential equation, the ISDE model generally consists of not only a structured deterministic part called drift term, but also a structured random part called diffusion term. The model can describe the system in which the random features are correlated with system states (inputs, outputs) and this relationship can be explicitly described by the model itself. The considered nonlinearity of this model can be expressed by the nonlinearity of the system functions. The parameter identification based on a state estimation such as an Extended Kalman Filter (EKF) and Unscented Kalman Filter (UKF), is investigated for this type of model in the thesis. Moreover, a new method by combining Maximum Likelihood (ML) technique plus UKF is proposed and its convergence property with regard to the consistency and normality is also investigated. The developed methods and algorithms are tested and analyzed for a number of numerical cases and then for a space robot system.
Secondly, the system considered is described by a nonlinear FOPDT model. This type of FOPDT model is an extension of the traditional FOPDT model which pre-assumes all the model parameters are constants. The nonlinearity that is defined in the model is reflected in its two categories of varying parameters, namely depending on time variable or some other variables, such as input signal etc. We refer to this type of model as a Time Varying FOPDT (TV-FOPDT) model. At first, the identifiability of the corresponding model is theoretically investigated. Then, the first concern of parameter identification of the considered systems is under assumption that the parameters of TV-FOPDT model are as time dependent. Afterwards, the input dependent parameter identification approach is considered. For these two categories of FOPDT models, the corresponding methods to make the parameters identification are proposed accordingly. Moreover, the proposed methods are further extended to make parameter identification of a kind of multiple inputs model. The proposed methods and algorithms are tested and analyzed for a number of numerical cases and finally applied to study the superheat dynamic in a Danfoss refrigeration system.
The proposed models and methods are further extended for the purpose of Fault Detection and Diagnosis (FDD). In a system where it exists possible parametric fault, if some fault happens, one or several parameters related to fault may change their values. Then the FDD procedure can be performed by identifying these fault related parameters. Afterwards, the decision whether the fault happened or how large the fault is can be made by comparison and analysis based on the estimated values.