A Systematic Computational and Experimental Study of the Principal Data-Driven Identification Procedures. Part II: Numerical Analysis and Experimental Testing

This paper is the second part of a two-part research work intended at realizing a systematic computational and experimental analysis of the principal data-driven identification procedures based on the Observer/Kalman Filter Identification Methods (OKID) and the Numerical Algorithms for Subspace State-Space System Identification (N4SID). More specifically, this second paper treats the presentation of the numerical analysis and the experimental testing carried out in this study. To perform a systematic comparison, the identification methods mentioned before are implemented in a general-purpose computer program developed in the MATLAB computational environment. To this end, a simple two-degrees-of-freedom dynamical model of a vibrating mechanical system is considered first as a demonstrative example. The demonstrative example is used to carry out a numerical analysis of the performance of the computational methods of interest for this investigation. Subsequently, an experimental analysis is carried out focusing on a three-dimensional structure that vibrates under the effect of an external source of impulsive excitation. To perform a thorough analysis, the flexible structure employed as an experimental case study is modeled starting from its CAD geometric model and assuming different levels of complexity, which range from a simple three-degrees-of-freedom lumped parameter model to a relatively more complex linear finite element model. In the paper, the mechanical models of the structural system considered as illustrative examples are principally employed for comparing the results arising from the modal analysis. The computational and experimental analysis of these structural models turned out to be useful to trace guidelines for evaluating the effectiveness and the efficiency of the numerical and experimental results obtained from the identification process. In this study, a numerical and experimental analysis of the OKID algorithms and the N4SID methods is developed. Both classes of techniques enable the time-domain state-space system identification, that is, they construct an estimation of the state, input influence, output influence, and direct transmission matrices which characterize the dynamic properties of a mechanical system. The present investigation demonstrates that, if properly tuned, both the OKID methods and the N4SID algorithms lead to consistent numerical and experimental results, even in the case when the input-output measurements used for performing the identification procedure are affected by a certain degree of noise. The numerical and experimental results found in this second part of the research work confirmed the efficacy of the time-domain system identification methodologies described in the first part of the paper.