STRIDE for Structural Identification Using Expectation Maximization: Iterative Output-Only Method for Modal Identification

Abstract

This paper introduces structural identification using expectation maximization (STRIDE), a novel application of the expectation maximization (EM) algorithm and approach for output-only modal identification. The EM algorithm can be used to estimate the maximum likelihood parameters of a state-space model. In this context, the state-space model represents the equation of motion for a linear dynamic system. STRIDE is an iterative procedure that uses Kalman filtering and Rauch-Tung-Striebel (RTS) smoothing equations to produce estimates of the unobserved states; these calculations are based on the observed data and prior estimates of the state-space parameters. With this information, the conditional likelihood of the model is maximized and the state-space parameters are updated at each iteration. Once an iteration meets user-prescribed convergence criterion, the algorithm ends—yielding maximum likelihood estimates (MLE) for the state-space model parameters. The modal properties of the structure are then extracted from these MLE. The performance of STRIDE is compared in detail with eigenvalue realization algorithm-natural excitation technique (ERA-NExT) and eigenvalue realization algorithm-observer Kalman filter identification of output-only systems (ERA-OKID-OO) identification algorithms in the analyses of ambient vibration data from the Northampton Street Bridge and Golden Gate Bridge, both collected using a dense wireless sensor network. A computational comparison shows that STRIDE provides a successful identification at a significantly lower model order than ERA-NExT, ERA-OKID-OO, or auto-regressive (AR), simultaneously requiring fewer cumulative floating point operations than ERA-OKID-OO in both applications.