Identifiability of process coefficients for technical failure diagnosis

Estimation of process coefficients of time-continuous models has turned out to be a viable method to detect failures in dynamic systems at an early stage of their development. In order to plan and configure an effective diagnostic system based on estimation methods there has to be a theory which supplies the minimum of instrumentation to estimate a given set of process coefficients. The second question which arises is the identifiability of process coefficients with given models and instrumentation. Identifiability is a concept which has been extensively studied in the past from different points of view, although the problems were mostly formulated in a state space representation. Here a different procedure was chosen: The idea was to translate the information contained in a block diagram of a linear or nonlinear process model into a system of equations in such a way, that a general method for the derivation of the estimation equations could be provided. The estimated parameters are mostly nonlinear functions of the process coefficients. On the basis of the chosen representation an identifiability theorem for the process coefficients was obtained in order to have a practical method for the design of modern diagnostic systems. Several examples are given to illustrate the procedure.