Model determination for nonlinear state-based system identification

• Published in: Nonlinear dynamics Vol. 63; no. 4; pp. 735 - 753
• Main Authors: Kolodziej, Jason R., Mook, D. Joseph
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.03.2011; Springer Nature B.V
• Subjects: Algorithms; Analysis of variance; Automotive Engineering; Classical Mechanics; Computer simulation; Control; Correlation analysis; Dynamical Systems; Engineering; Mechanical Engineering; Nonlinear dynamics; Nonlinear systems; Nonlinearity; Original Paper; Regression; Regression analysis; Routines; State estimation; System dynamics; System identification; Variance analysis; Vibration; State estimation; Nonlinear systems; Identification
• ISSN: 0924-090X; 1573-269X
• DOI: 10.1007/s11071-010-9834-z

A complete methodology for robust nonlinear system identification is derived and illustrated through example. A proven state estimation algorithm is utilized in conjunction with a modified version of a stepwise regression approach to successfully determine the nonlinear dynamics in a “known” truth simulation without a priori knowledge of the system model. First, Minimum Model Error (MME) estimation is derived and illustrated through example. MME is a robust state estimation routine that provides, in addition to smooth states, an estimate of the unmodeled system dynamics is determined from noisy measurement data of known variance. Next, an Analysis of Variance (ANOVA) model correlation routine where a modified version of a forward stepwise procedure is derived and implemented. The ANOVA approach to model acceptance is well documented primarily in social science literature, but has been sparsely written about for engineering applications. This paper shows a significant improvement in nonlinear model identification when used in conjunction with MME estimation.