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By F.C. Oglesby

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7 Notes and References 19 • the norm-based residual evaluation initiated by Emami-naeini et al. [58] • the FDI system synthesis and design in the norm-based residual evaluation framework by Ding et al. [38]. Chapter 3 Modelling of Technical Systems The objective of this chapter is to introduce typical models for the mathematical description of dynamic systems. As sketched in Fig. 1, we consider systems consisting of a process, also known as plant, actuators and sensors. The systems may be, at different places, disturbed during their operation.

In their pioneering work, Emami-naeini et al. proposed to use the root-mean-square (RMS) norm for the residual evaluation purpose and derived, based on the residual evaluation function, an adaptive threshold, also called threshold selector. This scheme has been applied to detect faults in dynamic systems with disturbances and model uncertainties. Encouraged by this promising idea, researchers have applied this concept to deal with residual evaluation problems in the H∞ framework, where the L2 norm is adopted as the residual evaluation function.

9397 56 D= . 0653 . 77), the influences of road bank angle αx , vehicle body roll angle φR and roll rate pc have not been taken into account. Moreover, sensor noises are inevitable. Generally, sensor noises can be modelled as steady stochastic process with zero mean Gaussian distribution. But, in vehicle systems, the variance or standard variance of sensor noises cannot be modelled as constant, since at different driving situations, the sensor noises are not only caused by the sensor own physical or electronic characteristic, but also strongly disturbed by the vibration of vehicle chassis.

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