Frequency and time domain analysis of model order reduction techniques

Abstract

Model order reduction techniques are commonly employed for dynamic simulation of large models and creating superelements. "Component Mode Synthesis ", "Quasi-Static Mode Synthesis ", nonlinear least squares and "Subspace-Based" identification methods are studied in time and frequency domains by using Finite Element Methods. In literature, phase errors of model order reduction techniques are commonly ignored, whereas it is an indication of performance of these methods and plays an important role in response of dynamical systems. It is observed that in general nonlinear least squares and "Subspace-Based" identification methods have better performance than "Component Mode Synthesis" and "Quasi-Static Mode Synthesis" methods; however, as the size of problems increases, the nonlinear least squares method may have convergence problems and "Subspace-Based" identification method may yield estimated models having large orders. Time response of the methods, in which convergence satisfied in frequency ranges, can not be able to fit with that of the exact system. Therefore, IRI, forward difference and Newmark time integration methods are developed on the base of discrete equivalent principle and used as a model order reduction techniques. Those methods can give good results when the active degrees-of-freedom are selected as the degrees-of-freedom to which forces and/or moments are applied.

Özet

Model derecesi düşürme teknikleri büyük boyutlu dinamik simülasyonlarda işlem zamanını azaltmak ve süper eleman yaratmak amacıyla kullanılmaktadır. Bu çalışmada, Sonlu Elemanlar Metodu (SEM) kullanılarak popüler model derecesi düşürme tekniklerinden "Component Mode Synthesis (CMS)", "Quasi-Static Mode Synthesis (QSM) ", Doğrusal olmayan en küçük kareler metodu(DOEK) ve Alt uzay temelli "Subspace-Based" tanımlama (AUT) metotları frekans ve zaman uzayında yapısal bir problem üzerinde incelendi. DOEK metodu ile AUT metotlarının, CMS ve QSM metotlarından daha iyi sonuçlar verdiği, fakat model derecesi arttıkça DOEK metodunun yakınsamadığı ve AUT metodunun yüksek dereceden modeller uydurduğu görülmüştür. Çalışmanın ikinci bölümünde ayrık eşdeğerlik prensibine göre geliştirilen "Impulse Response Invariant (IRI) ", İleri Farklar ve Newmark zaman entegrasyon metotları model derecesi düşürme tekniği olarak kullanıldı.