Data-driven forecasting schemes: evaluation and applications.

INTRODUCTION

A reliable multi-step forecasting tool is very useful to a wide array of real-world applications to predict the future states of a dynamic system. In industrial applications, for example, forecast information can be used to schedule repairs and maintenance for important fabrication facilities so as to prevent production performance degradation, malfunction, or even catastrophic failures. A robust predictor is also critically needed in applications such as time consuming operations (e.g., material property testing), structure remaining life estimation, and earthquake forecasting. System state forecasting utilizes some available observations to predict the future states of a dynamic system. The representative observations can be derived from different information carriers, such as vibration, temperature, and acoustic measurement data, by using appropriate signal processing techniques.

Several techniques have been proposed in the literature for time series prediction (1). The classical approaches are the use of stochastic (or the extended) models (2), (3); However, an accurate analytical model is usually difficult to derive for a complex dynamic system, especially under noisy and uncertain environment such as in real-world industrial applications. Since the last decade, more interests in time series forecasting have focused on the use of knowledge-based data-driven paradigms, such as various neural networks (NNs) (4-6) and neural fuzzy (NF) paradigms (7-9). Even though the data-driven predictors have demonstrated their superior potential in many applications over the classical numerical models, as a matter of fact, these currently available predictors are mainly for one-step-ahead prediction in real applications. Advanced research needs to be done in several aspects before a multi-step-ahead predictor can be effectively applied to real-time industrial applications. Correspondingly, the objectives of this work are to 1) evaluate the input patterns on the performance of multi-step prediction paradigms, 2) improve convergence for a recurrent NF predictor by adopting a hybrid training technique, and 3) implement the proposed recurrent NF predictor for real-world applications.

MATERIALS AND METHODS

The knowledge-based data-driven forecasting tools interested in this work include feedforward NN, recurrent NN, as well as a weighted recurrent NF scheme that is an extension to that as proposed in (8). A brief description is given in this section for these related predictors, as well as the suggested hybrid training technique.

Recurrent NN Predictor: System state forecasting is to predict the future states of a dynamic system based on its current and some previous states. Since the performance of a knowledge-based data drive forecasting scheme is directly related to its reasoning structure (or the number of network parameters), to facilitate the comparison study among different predictors, the number of the network parameters will be kept comparable.

The network architecture of the recurrent NN predictor is as shown in Fig. 1. Consider (n+1) input state variables {[x.sub.0] [x.sub.-s] ... [x.sub.-ns]}, which represent the current ( [x.sub.0] ) and the previous states of a dynamic system with a time step s. If ten inputs are employed in the input layer, that is, n = 9, ten nodes will be used in the recurrent context layer. The s-step-ahead state, [x.sub.+s], will be given from the output node. In total, there are 151 parameters to be updated in this predictor: 100 input weights ([w.sub.ij.sup.1]), 10 output weights ([w.sub.ij.sup.2]), 10 recurrent weights ([w.sub.ij.sup.3]), and …