Probabilistic interval predictor based on dissimilarity functions

TL;DR

This paper introduces a novel probabilistic interval prediction method for dynamical systems using dissimilarity functions and past measurements, generalizing classical estimation techniques with validated numerical examples.

Contribution

It proposes a new methodology that estimates probabilistic intervals based on dissimilarity functions, encompassing traditional methods like the multivariable normal distribution.

Findings

Effective in predicting probabilistic intervals for dynamical systems

Generalizes classical estimation methods

Validated through numerical examples and comparisons

Abstract

This work presents a new methodology to obtain probabilistic interval predictions of a dynamical system. The proposed strategy uses stored past system measurements to estimate the future evolution of the system. The method relies on the use of dissimilarity functions to estimate the conditional probability density function of the outputs. A family of empirical probability density functions, parameterized by means of two scalars, is introduced. It is shown that the proposed family encompasses the multivariable normal probability density function as a particular case. We show that the presented approach constitutes a generalization of classical estimation methods. A validation scheme is used to tune the two parameters on which the methodology relies. In order to prove the effectiveness of the presented methodology, some numerical examples and comparisons are provided.