A Multiple-Input Multiple-Output Cepstrum

TL;DR

This paper generalizes scalar cepstrum coefficients to MIMO systems using Smith-McMillan form, enabling model-free analysis of system poles and zeros from input/output data, with applications to fault detection in industrial processes.

Contribution

It introduces a method to compute MIMO cepstrum coefficients from data, extending scalar cepstrum concepts to multi-input multi-output systems for system analysis.

Findings

MIMO cepstrum detects faults even with controller compensation

Method verified on systems with known poles and zeros

Applied to real industrial process data

Abstract

This paper extends the concept of scalar cepstrum coefficients from single-input single-output linear time invariant dynamical systems to multiple-input multiple-output models, making use of the Smith-McMillan form of the transfer function. These coefficients are interpreted in terms of poles and transmission zeros of the underlying dynamical system. We present a method to compute the MIMO cepstrum based on input/output signal data for systems with square transfer function matrices (i.e. systems with as many inputs as outputs). This allows us to do a model-free analysis. Two examples to illustrate these results are included: a simple MIMO system with 3 inputs and 3 outputs, of which the poles and zeros are known exactly, that allows us to directly verify the equivalences derived in the paper, and a case study on realistic data. This case study analyses data coming from a (model of) a non-isothermal continuous stirred tank reactor, which experiences linear fouling. We analyse normal and faulty operating behaviour, both with and without a controller present. We show that the cepstrum detects faulty behaviour, even when hidden by controller compensation. The code for the numerical analysis is available online.