Frequency Domain Identification of Multi-Input, Multi-Output Systems Considering Physical Relationships between Measured Variables

Abstract

This paper presents a new frequency domain identification method for multi-input, multi-output (MIMO) systems. Based on experimentally determined frequency response function data, rational polynomial transfer function models of structural systems are identified. Known physical relationships between the measured variables are incorporated in this MIMO frequency domain identification method. The method has three stages: (1) an initial estimation model is generated using a linear least-squares method, (2) the Steiglitz–McBride method is applied to improve the initial estimation model, and (3) a maximum likelihood estimator is optimized using the Levenberg–Marquardt method. For verification of the method, two experimental studies are conducted using shaking table tests; one is the system identification of a smart base-isolated structure employing a magnetorheological (MR) damper, and the other is for an actively controlled two-story, bench-scale building employing an active mass driver. Using the developed method, system models of the experimental structures are estimated, and simulated time histories for the models are compared with measured responses. These comparisons demonstrate that the proposed method is quite effective and robust for system identification of MIMO systems. A graphic user interface program, named