Evolving Fuzzy Prediction Intervals in Nonstationary Environments

This work aims at designing a novel evolving fuzzy prediction interval able to model nonlinear time-variant systems. To achieve this goal, we integrate a passive mechanism meant to update the model when new data are available with an active mechanism able to trigger ad-hoc adaptation mechanisms when changes are detected in the data-generating process. The base model considered for this proposal was the prediction interval based on fuzzy numbers, which allow handling the characterization of the uncertainty of a system through additional parameters focused on the computation of the interval width. The performance of the proposed solution has been tested on both synthetic and real data. In this work, the synthetic data was generated from a generic nonlinear time-variant system, while the real data correspond to measurements of solar power generation obtained from photovoltaic panels. The simulation results confirm the effectiveness of the proposed evolving fuzzy prediction interval for modeling systems that present changes in their dynamics over time.

I. Introduction

The use of fuzzy logic systems and neural networks has proliferated in the literature to model systems. Since both types of models are known as universal approximators that can identify relationships between inputs and target (outputs) variables, they are generally used when the system to be modeled follows nonlinear dynamics [1]. Although some fuzzy logic systems like the Takagi-Sugeno fuzzy model and some neural networks like the recurrent neural networks exhibit adequate performances when dealing with dynamical systems, uncertainty is not typically quantified by these approaches. However, having information on the dispersion of possible future model outputs may be more useful from a decision-making point of view. [2], [3] With that purpose, prediction interval models have been proposed to address the problem of quantifying prediction uncertainty. A prediction interval establishes a range around the output of the model, which represents the effect of all the uncertainty present in the system due to modeling errors and the uncertain behavior of disturbance signals.