Time-Domain Analysis of Sensor-to-Sensor Transmissibility Operators with Application to Fault Detection.

Abstract

In some applications, multiple measurements are available, but the driving input that gives rise to those outputs may be unknown. This raises the question as to whether it is possible to model the response of a subset of sensors based on the response of the remaining sensors without knowledge of the driving input. To address this issue, we develop time-domain sensor-to-sensor models that account for nonzero initial conditions. The sensor-to-sensor model is in the form of a transmissibility operator, that is, a rational function of the differentiation operator. What is essential in defining the transmissibility operator is that it must be independent of both the initial condition and inputs of the underlying system, which is assumed to be time-invariant. The development is carried out for both single-input, single-output and multi-input, multi-output transmissibility operators. These time-domain sensor-to-sensor models can be used for diagnostics and output prediction. We show that transmissibility operators may be unstable, noncausal, and of unknown order. Therefore, to facilitate system identification, we consider a class of models that can approximate transmissibility operators with these properties. This class of models consists of noncausal finite impulse response models based on a truncated Laurent expansion. These models are shown to approximate the Laurent expansion inside the annulus between the asymptotically stable pole of largest modulus and the unstable pole of smallest modulus. By delaying the measured pseudo output relative to the measured pseudo input, the identified finite impulse response model is a noncausal approximation of the transmissibility operator. The causal (backward-shift) part of the Laurent expansion is asymptotically stable since all of its poles are zero, while the noncausal (forward-shift) part of the Laurent expansion captures the unstable and noncausal components of the transmissibility operator. This dissertation also develops a time-domain framework for both single-input, single-output and multi-input, multi-output transmissibilities that account for nonzero initial conditions for both force-driven and displacement-driven structures. We show that motion transmissibilities in force-driven and displacement-driven structures are equal when the locations of the forces and prescribed displacements are identical.PhDAerospace EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/113623/1/khaledfj_1.pd