A Systematic Computational and Experimental Study of the Principal Data-Driven Identification Procedures. Part I: Analytical Methods and Computational Algorithms

This paper is the first part of a two-part research work aimed at performing 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). Considering the approach proposed in this work, the state-space model of a mechanical system can be identified with the OKID and N4SID methods. Additionally, the second-order configuration-space dynamical model of the mechanical system of interest can be estimated with the MKR (Mass, Stiffness, and Damping matrices) and PDC (Proportional Damping Coefficients) techniques. In particular, this first paper concentrates on the description of the fundamental analytical methods and computational algorithms employed in this study. In this investigation, numerical and experimental analyses of two fundamental time-domain system identification techniques are performed. To this end, the main variants of the OKID and the N4SID methods are examined in this study. These two families of numerical methods allow for identifying a first-order state-space model of a given dynamical system by directly starting from the time-domain experimental data measured in input and output to the system of interest. The basic steps of the system identification numerical procedures mentioned before are described in detail in the paper. As discussed in the manuscript, from the identified first-order state-space dynamical models obtained using the OKID and N4SID methods, a second-order configuration-space mechanical model of the dynamic system under consideration can be subsequently obtained by employing another identification algorithm described in this work and referred to as the MKR method. Furthermore, by using the second-order dynamical model obtained from experimental data, and considering the hypothesis of proportional damping, an effective technique referred to as the PDC method is also introduced in this investigation to calculate an improved estimation of the identified damping coefficients. In this investigation, a numerical and experimental comparison between the OKID methods and the N4SID algorithms is proposed. Both families of methodologies allow for performing the time-domain state-space system identification, namely, they lead to an estimation of the state, input influence, output influence, and direct transmission matrices that define the dynamic behavior of a mechanical system. Additionally, a least-square approach based on the PDC method is employed in this work for reconstructing an improved estimation of the damping matrix starting from a triplet of estimated mass, stiffness, and damping matrices of a linear dynamical system obtained using the MKR identification procedure. The mathematical background thoroughly analyzed in this first research work serves to pave the way for the applications presented and discussed in the second research paper.