Identification of Continuous-time Noise Models

The goal of operational modal analysis is to estimate the resonance frequencies and damping ratios of mechanical structures (bridge, air plane, building ...) from their response to non-measurable external forces induced by e.g. the wind, earth quakes, traffic, turbulence ... The classical approach for identifying these physical parameters consists in straightforward discrete-time ARMA modeling of the true continuous-time process from discrete-time data (Peeters and De Roeck, 2001). Refined discrete-time approximations are proposed in Walhlberg et al. (1993), Söderström et al. (1997), and Fan et al. (1999). In this paper we model the continuous-time noise processes using the frequency domain BoxJenkins framework developed in Ljung (1999) for data collected in open loop. The advantages of this modeling approach are (i) it is exact for a realistic class of continuous-time noise processes, (ii) it can handle time domain as well as frequency domain data.