Time-Domain Errors-in-Variables Identification of Transmissibilities

Transmissibility operators are time-domain operators that model the relationship between outputs of an underlying system. Since real measurements are corrupted by noise, identification of transmissibilities is an errors-in-variables identification problem. This paper applies a bias-compensated recursive least-squares algorithm to errors-in-variables identification of transmissibilities. Noncausal FIR models are used to approximate transmissibility operators. To investigate the accuracy of this approach, we consider data from an acoustic experiment. The goal is to identify the transmissibility operator that models the relationship between measurements from two microphones.

I. Introduction

A transmissibility is a sensor-to-sensor model that describes the relationship between outputs of a system [1]–[3]. The input and output of the transmissibility are referred to as “pseudo-input” and “pseudo-output”, respectively. Transmissibilities are used in applications such as structural health monitoring, fault detection, and fault localization, and are typically used in applications where the excitation signal is unknown or cannot be measured [4]–[10]. If a model of the underlying system is available, then the transmissibility of interest can be constructed mathematically. Otherwise, the transmissibility can be identified from the available measurements of the pseudo-input and pseudo-output.