Suboptimum Maximum Likelihood Estimation of Structural Parameters from Multiple-Excitation Vibration Data

Abstract

In this paper an effective stochastic and multiple-excitation single-response approach to structural dynamics identification is introduced. The proposed approach accounts for many previously unaccounted for aspects of the problem, as it is based on: A proper, special-form, scalar ARMAX-type representation of the structural and noise dynamics; a new Suboptimum Maximum Likelihood (SML) discrete estimation algorithm (Fassois and Lee, 1990); systematic and efficient modeling strategy and model validation procedures; as well as accurate modal parameter extraction that is compatible with the employed model structure and excitation signal forms. In addition to its comprehensiveness, the proposed approach overcomes the well-known limitations of deterministic time-domain methods in dealing with noise-corrupted data records, while also circumventing some of the major difficulties of existing stochastic schemes by featuring guaranteed algorithmic stability, elimination of wrong convergence problems, very modest computational complexity, and minimal operator intervention. The effectiveness of the approach is verified through numerical simulations with noise-corrupted vibration data, and structural systems characterized by well-separated and closely-spaced vibrational modes. Comparisons with the classical Frequency Domain Method (FDM) are also made, and the approach’s advantages over deterministic methods are demonstrated through comparisons with the Eigensystem Realization Algorithm (ERA). Experimental results, where the proposed approach is used for the modal analysis of a flexible beam from laboratory data, are also presented.