Interval-based validation of a nonlinear estimator

TL;DR

This paper introduces an interval-based validation method for nonlinear estimators that guarantees maximum error bounds, enhancing safety and reliability in engineering decision-making processes.

Contribution

It proposes a novel interval analysis approach using the Moore-Skelboe algorithm to validate nonlinear estimators, including neural networks, with guaranteed error bounds.

Findings

Provides guaranteed maximum error bounds for nonlinear estimators

Validates neural network estimators with interval-based guarantees

Enhances reliability of model-based decision making in engineering

Abstract

In engineering, models are often used to represent the behavior of a system. Estimators are then needed to approximate the values of the model's parameters based on observations. This approximation implies a difference between the values predicted by the model and the observations that have been made. It creates an uncertainty that can lead to dangerous decision making. Interval analysis tools can be used to guarantee some properties of an estimator, even when the estimator itself doesn't rely on interval analysis (Adam, 2019) (Adam, 2015). This paper contributes to this dynamic by proposing an interval-based and guaranteed method to validate a nonlinear estimator. It is based on the Moore-Skelboe algorithm (van Emden, 2004). This method returns a guaranteed maximum error that the estimator will never exceed. We will show that we can guarantee properties even when working with non-guaranteed estimators such as neural networks.