---
title: "Polynomial Temporal Band Sequences for Analog Diagnosis"
authors:
  - "Étienne Loiez"
  - "Patrick Taillibert"
doi: ""
url: "https://ijcai.org/proceedings/1997/70"
pdf: "https://ijcai.org/proceedings/1997/0070.pdf"
venue: "Proceedings of the Fifteenth International Joint Conference on Artificial Intelligence"
year: 1997
pages: "474-478"
track: "Diagnosis and Qualitative Reasoning"
keywords:
---

# Polynomial Temporal Band Sequences for Analog Diagnosis

Étienne Loiez, Patrick Taillibert

*Proceedings of the Fifteenth International Joint Conference on Artificial Intelligence*, pages 474-478.

## Abstract

In [Loiez and Taillibert 96a] we proposed a new way to model components and physical quantities in the framework of Model-based Diagnosis applied to analog systems. Components were represented by equations of the form " f+g'=O " where f and g are functions of observable quantities of the system to be diagnosed ; observations were represented by temporal band sequences (sets of consecutive trapezoids encompassing the observations); consistency checking was done by integration. The present paper generalizes the observation representation to temporal bands defined by any polynomial function. It shows that this extension not only allows a better approximation of observations but also that models of components can now be represented by equations relating derivatives of any order (f+g'+h"+ ... =O) and involving any polynomial functions, which improves dramatically the ease of modeling analog systems.