MIMO LMS-ARMAX IDENTIFICATION OF VIBRATING STRUCTURES—PART I: THE METHOD

Abstract

A comprehensive linear multi stage autoregressive moving average with exogenous excitation (LMS-ARMAX) method for effective multiple-input multiple-output (MIMO) structural dynamics identification in the presence of noise is introduced. The method consists of (a) a vector ARMAX representation of an appropriate form, (b) effective LMS parameter estimation, (c) statistical order selection/validation, and (d) a digital dispersion analysis (DA) methodology for effective modal characterization. The LMS-ARMAX method overcomes many of the difficulties that had rendered MIMO ARMAX identification difficult in the past, featuring modest computational complexity, high accuracy, guaranteed algorithmic and model stability, and thus applicability to higher-dimensional problems and lightly damped structures, accurate modal parameter extraction, and effective distinction of structural from ‘extraneous’ modes. A critical assessment of the LMS-ARMAX method under various noise conditions, as well as comparisons with a simpler ARX version and the ERA (Eigensystem Realization Algorithm), are undertaken based upon experimental vibration data obtained from a scale aircraft skeleton structure. The paper is divided into two parts: The LMS-ARMAX method is presented in the first, and its critical assessment and comparisons in the second.