System Identification Using the Proper Orthogonal Decomposition with Multiple Loads

The Proper Orthogonal Decomposition (POD) is a method that may be applied to linear and nonlinear structures for extracting important information from a measured structural response. Previous methods of using the POD for system identification typically use the POD for model reduction only and system identification is accomplished via standard methods. A method for using the POD-based identification of a reduced order system model independently of other methods has been published but may only be applied to lightly damped systems with a diagonal mass matrix. This paper extends the applicability of the POD-based identification method by using data from multiple applied loads to remove these constraints. Mode summation techniques are applied to a truncated summation of proper orthogonal modes to find an analytical expression for the proper orthogonal coordinate histories, which are time modulations of the proper orthogonal modes in the measured response. The proper orthogonal coordinate histories are modified to reflect the modulation of proper orthogonal modes in response to a new forcing function by numerical deconvolution and convolution techniques using multiple load cases. The new method is shown to accurately predict the forced response of simple linear and nonlinear beam models when compared with results obtained by the finite element method. Examples are given to show that the new method is more accurate than the previous POD-based identification method for both undamped and damped systems.