Analysis of Stepped Beam Using Reduced Order Models

Damage detection in complicated engineering systems from vibration measurements typically involves the use of algorithms that are built on the principles of bayesian dynamic state estimation. These methods invariably required the solution of the forward problem a fairly large number of times. For complex engineering systems that are numerically modeled using Finite Element (FE), this can be computationally intensive especially when a single FE run for the problem takes a large time. To alleviate this problem, there is a need for the development of Reduced Order Models (ROMs) that significantly reduce the computational cost associated with solving the forward problem, for a given measure without sacrificing the accuracy. The present study discusses three ROM methods with specific reference to a simple problem. These methods include well-known Component Mode Synthesis (CMS) and System Equivalent Reduction Expansion Process (SEREP) which are applicable only for linear systems, as well as Principal Component Analysis (PCA)—the method which is more general and can be used for nonlinear systems as well. A comparison of the performance of all these methods is carried out for a stepped beam. The FE based results obtained from the full model is treated as the benchmark.