Two general linear time-varying system identification methods for multiple-input multiple-output systems are proposed based on the proper orthogonal decomposition (POD). The method applies the POD to express response data for linear or nonlinear systems as a modal sum of proper orthogonal modes and proper orthogonal coordinates (POCs). Drawing upon mode summation theory, an analytical expression for the POCs is developed, and two deconvolution-based methods are devised for modifying them to predict the response of the system to new loads. The first method accomplishes the identification with a single-load-response data set, but its applicability is limited to lightly damped systems with a mass matrix proportional to the identity matrix. The second method uses multiple-load-response data sets to overcome these limitations. The methods are applied to construct predictive models for linear and nonlinear beam examples without using prior knowledge of a system model. The method is also applied to a linear experiment to demonstrate a potential experimental setup and the method's feasibility in the presence of noise. The results demonstrate that while the first method only requires a single set of load-response data, it is less accurate than the multiple-load method for most systems. Although the methods are able to reconstruct the original data sets accurately even for nonlinear systems, the results also demonstrate that a linear time-varying method cannot predict nonlinear phenomena that are not present in the original signals.
|Translated title of the contribution||A Deconvolution-Based Approach to Structural Dynamics System Identification and Response Prediction|
|Pages (from-to)||031010-1 - 031010-8|
|Number of pages||8|
|Journal||Journal of Vibration and Acoustics|
|Publication status||Published - Jun 2008|