A Metric for Modal Truncation in Model Reduction Problems Part 1: Performance and Error Analysis

Paper in proceeding, 2014

The strength of the modal based reduction approach resides in its simplicity, applicability to treat moderate- size systems and also in the fact that it preserves the original system pole locations. However, the main restriction has been in the lack of reliable techniques for identifying the modes that dominate the input-output relationship. To address this problem, an enhanced modal dominancy approach for reduction of second-order systems is presented. Briefly stated, a modal reduction approach is combined with optimality considerations such that the difference between the frequency response function of the full and reduced modal model is minimized in H2 sense. A modal ranking process is performed without solving Lyapunov equations. In the first part of this study, a literature survey on different model reduction approaches and a theoretical investigation of the modified modal approach is presented. The error analysis of the proposed dominancy metric is carried out. Furthermore, the performance of the method is validated for a lightly damped structure and the results are compared with other dominancy metrics. Finally the optimality of the obtained reduced model is discussed and the results are compared with the optimum solution.