Frequency Based Optimal Input Signal Determination for ARX Parameter Estimation of Constraint Systems

Abstract

Modern parametric based eigensystem realization algorithms (ERA) used in system identification algorithms depend heavily on the quality of the estimated parameters. Generally, parameters are estimated experimentally by exciting all the modes of the system. The generated input/output data is processed using least-squares or maximum likelihood algorithms to fit the parameters of the assumed model to the gathered data. Since the locations of the system modes are not known at the beginning of the system identification experiment, band-limited white noise signals are used as the input. Input design or experimental design for system identification addresses the input signal computation for optimum parameter estimation. Constraint systems, such as commonly found in biomedical engineering applications, represent a particular challenge to the input design algorithm. This paper presents a novel approach that induces learning into the input design computation and allows for considerations of the given constraints of the system. In particular, the proposed algorithm adapts to the information gathered during the first step of the identification experiment and uses this gained information to form a new input that targets the system modes. The input signal starts with a band-limited white noise and based on the response uses the frequency information contained in the preliminary estimated ARX model to shape the new input signal. This new input is computed such that more energy is directed towards the system modes. Since the objective is to accurately estimate the ARX model parameters and therefore the system model, the preliminary estimated ARX parameters posses some uncertainty. The optimization of the new input signal is accomplished using a simple Genetic Algorithm. Simulation results indicate the proposed piecewise adaptive input design algorithm performs well compared to the general white noise based estimation results

Application of Genetic Algorithms to Observer Kalman Filter Identification

“…Two systems were used to simulate the proposed noise filter. The first system is an overdamped second order system (Thumati and Schoen, 2005):…”