Mathematical Modeling and Fault Description

This chapter provides an overview on the various fault detection methods, with particular attention to the fault detection and isolation (FDI) techniques. For all of the methods considered, it is essential that the process can be described by a mathematical model. The chapter presents a number of different strategies for solving the quantitative residual generation problem. It provides some considerations on different approaches for representing modeling errors and other uncertain factors via the disturbance term with an estimated distribution matrix. As addressed in a system identification framework, this identified distribution matrix will be used for the design of the disturbance de-coupled residual, in order to solve the robust FDI problem. The fault detection methods mostly require several measurable output signals and make use of the internal analytical redundancy of multivariable systems. Recently, it was proposed to improve their robustness with respect to process parameter changes and unknown input signals.