Karhunen-Loeve decomposition for reducing the order and monitoring the dynamics of coupled oscillators

Karhunen-Loeve - KL modes are used to discretize the dynamics of a four-bay linear truss. This is achieved by defining global KL modal amplitudes and employing the orthogonality relations between KL modes that are inherent in the KL decomposition. It is found that the KL-based low-order models can capture satisfactory the transient dynamics of the truss, even when only a limited number of them is used for the order reduction. A comparison between the exact and low-order dynamics in the frequency domain reveals that the low-order models capture the leading resonances of the truss. A series of experiments with a practical three-bay truss is then performed to validate the theoretical KL decomposition. A comparison between theory and experiment indicates agreement between the predicted and realized dominant KL mode shapes, but less so in the higher order modes. The reasons for this discrepancy between theory and experiment are discussed, and possible applications of the KL-based order reduction to passive and active control of practical large-scale flexible systems are outlined.