Implicit de-noising in hybrid recurrent nets for meta knowledge abduction

Several financial, physical and biological phenomena exhibit random oscillatory and cyclic behaviour generated by a set of casual parameters referred to as meta knowledge (M-K). Given these behaviour time trajectories, recurrent hybrid nets are used to determine the time derivatives of the behaviour and using these to abduct the values of the casual parameters in real time. The recurrent hybrid nets used possess de-noising properties which can set by the designer. This paper investigates sensitivity to noise of 3 meta knowledge abduction algorithms developed in earlier papers using simulation. The effect of measurement noise on the estimation accuracy is considered when the behaviour trajectories are corrupted with random noise. Noise is simulated using random number generator with zero mean and added to the simulated system behaviour. Analysis of the simulation results show varying abilities of the algorithms to cope with the noise perturbations. In some instances high prediction robustness were achieved, other simulations showed high sensitivity to noise.

I. INTRODUCTION

The short-term behaviour of complex biological and physical systems may be approximated by the dynamics of second order systems [D'Azzo et. al, 1995], [Eykoff 1974]. Such systems are sufficiently complex to display the significant features of higher order systems but can be analyzed without excessive computation [Press et. al, 1992], [Beck & Arnold 1977]. Three parameters govern the behaviour of these systems: natural frequency (ω), the damping ratio and the external input (u), and two state variables. In a previous paper [Al-Dabass et. al, 1999], the authors developed and tested 3 parameter estimation algorithms for an equivalent 2^nd order system . The algorithms combine successive 1st order filters of specified cut-off frequencies to provide smoothing and higher order derivative estimation, with non-linear static parameter estimators. Three hybrid methods for parameter estimation were proposed and tested using the following approaches: 1) By using three sets of estimated 1st and 2^nd time derivatives; 2) By using two sets of estimated 1^st 2^nd and 3^rd time derivatives; and 3) By using a single set of estimated 1^st, 2^nd, 3^rd and 4^th time derivatives of the measured output of the system. In this paper the sensitivity of these algorithms to noise is investigated for a range of noise levels.