Eigensystem Realization With Modified Genetic Algorithm for System Identification of Noise Corrupted Processes

Abstract

The results of real world application of system identification (SI) algorithms are always affected by the process and measurement noise associated with the system to be identified and the measurement set-up. A small signal to noise ratio generally results into poor and sometimes unusable dynamical models. Missing system dynamics and characteristics in the inferred system model may cause undesirable and sometimes harmful control laws. Robust control is one avenue to avoid causing undesirable system performance due to the large model uncertainties. In this paper, an alternative approach is presented. In particular, a proof is given that no dynamic controller can reduce the noise influence in linear system identification. Eigensystem Realization Algorithms (ERA) used commonly in the Observer Kalman Filter Identification (OKID) algorithm allows for the discrimination between noise and system modes based on the magnitude of the singular values. Having a large noise content embedded in the input/output data is reflected by large singular values for the noise and system modes. This leaves them indistinguishable from each other. Hence the number and exact selection of the system modes using the traditional Eigensystem realization and the DC realization algorithm is impracticable. A new selection scheme is proposed for the Eigensystem realization portion of the OKID algorithm. The selection is done using a modified Genetic Algorithm (GA). The GA uses a cost function based on the step response, which is addition data to the random data collected from the experiment. The GA proposed adapts the probability density function for the selection scheme of the mating chromosomes based on the approximated cost gradient. Simulation results of the proposed algorithm in comparison with the traditional used method are presented. The results indicate an improved ability to extract system models from very noise data.

Application of System Identification for Modeling the Dynamic Behavior of Axial Flow Compressor Dynamics

“…In addition to the system's response, there is noise, unmodeled system dynamics, and responses from auxiliary systems that are coupled with the system to be identified. As there is no method to separate the given impulse response from coupled noise, unmodeled dynamics, and auxiliary system responses, we propose to imbed an optimization into the eigensystem realization (ERA) algorithm given by [8]. The optimization is done using an Enhanced Tabu Search (ETS) algorithm.…”

“…The ARMAX model and ARX model parameters are then utilized to construct a Hankel matrix, representing the sampled impulse response of the system relating tip air injection to pressure rise coefficient. A singular value decomposition of the Hankel matrix is performed for an eigensystem realization (ERA, [7,8]) resulting in a state-space description of the coupling dynamics. However, prior to performing the state-space realization, a heuristic optimization algorithm is 2 International Journal of Rotating Machinery introduced to optimize the singular values with respect to the measured output data.…”