Detecting structural changes with ARMA processes

In this paper, we discuss the application of autoregressive moving average (ARMA) processes in structural health monitoring. For this aim, we consider a linear system of differential equations driven by white noise, which could be seen as a continuous time model of an engineering structure under ambient excitation. A single component of the solution of such a system reflects the position or velocity of a fixed point of the observed structure. We first show that every such component behaves like an ARMA process. These considerations are illustrated by an example, where we show how the natural frequencies can be calculated from the process coefficients. However, the main focus of the paper lies in the detection of structural changes with ARMA processes. For this purpose, we propose a new distance measure that relies on the one-step prediction errors and some sampling strategies. Two case studies are included, which serve to demonstrate the performance of the proposed method. The first one is an off-duty steel truss railway bridge, followed by an in-depth study of an aluminium shear frame construction. In the latter case scenario, we show that the distance measure increases with increasing damage extent.