APRIS: Library and On-Line Tools to Drive Parallel Adaptive and Neural Heuristic to Improve System Identification Precision Juan Antonio Gómez Pulido, Miguel Ángel Vega Rodríguez, Juan Manuel Sánchez Pérez, María Dolores Jaraíz Simón, José María Granado Criado Department of Computer Sciences. University of Extremadura. Cáceres, Spain jangomez@unex.es Abstract—In this paper are shown the methodologies and tools developed to increase the accuracy of the System Identification as method of modelization, simulation and prediction of the behaviour of dynamic systems, so much of the type single- input-single-output as the well known time series. These developments are mainly based on an adaptive parallel algorithm. The adaptive part consists of the evolution of its main parameter through the time, so it self-adjusts to offer good solutions. The parallel part consists of the implementation of processing units of parallel running. The codes have been programmed in Matlab language, organizing themselves in a free and public domain library, which is handled by a set of graphic tools through web services for its on-line control and experimentation. I. MODELING SISO SYSTEMS AND TIME SERIES In many engineering fields (meteorology, economy, physics, etc) it is necessary to obtain mathematical models for studying the behaviour of systems whose equations are not available “a priori”. Our works are focused on two kinds of systems: single-input-single-output (SISO) systems and time series (TS). In these systems u(k) is the sampled input and y(k) is the observed output with period T. When dealing with SISO and TS there are only available its input/output (I/O) signals under observation; its physical structure is not known. This led us to employ planning System Identification (SI) techniques [1] in order to obtain the model. A. ARX Modeling SI tries to find a parametric model of dynamical systems. In this work we consider the polynomial ARX model [2], whose parameters (a i , b j ) are determinated from measured I/O. Then, it is possible to compute the estimated output y e (k) and compare it with the real output y(k), computing the generated error (Eq. 1). y e (k) = [- a 1 •y(k-1) -...- a na •y(k-na)] + [b 1 •u(k-nk) + ...+ b nb •u(k-nk-nb+1)] = T (k) (1) y e (k) is the estimated output; y(k), u(k) are real output and input at present time; y(k-1), u(k-1),... are real outputs and inputs at previous time. The parameters na and nb determine the model size. B. Identification Modes The recursive estimation updates the model in each time k. To more sampled data processed the model has more information about the system behaviour history. We consider SI performed by the Recursive Least Squares (RLS) with forgetting factor ( ) algorithm [3]. It is well known that a major requirement in RLS (and other methods driven by the output prediction error) is the presence of presistent excitation in the input. This algorithm is specified with , initial values and the observed I/O signals {u(k), y(k)}. There is not any fixed value for , even it is often used a value between 0.97 and 0.995 [4]. The cost function F is defined as the value to minimize, as we can see in Eq. 2, where SN is the sample number. F( ) = ∑ - + = = - 1 0 0 ) ( ) ( SN k k k k e k y k y (2) The recursive identification is very useful for predicting the system behaviour when there is a high degree of complexity and variability in the response. As identification advances in the time, the predictions improve using more precise models. For example, we can compute in sample time the system model and then, with this model to simulate the system future behaviour, forwarding real situations. II. IMPROVING PRECISION WITH AN ADAPTIVE HEURISTIC The main parameters of the identification are na (model size) and (forgetting-factor). Both parameters have influence on the precision of prediction results. The forgetting factor is meant to reduce the influence of old data on the model estimation in recursive identification methods; a good (optimal) value for it can improve the identification IEEE MELECON 2006, May 16-19, Benalmádena (Málaga), Spain 1-4244-0088-0/06/$20.00 ©2006 IEEE 425