A model‐based failure times identification for a system governed by a 2D parabolic partial differential equation

Abstract

Abstract This research focuses on the identification of failure times in thermal systems governed by partial differential equations, a task known for its complexity. A new model‐based diagnostic approach is presented that aims to accurately identify failing heat sources and accurately determine their failure times, which is crucial when multiple heat sources fail and there is a delay in detection by distant sensors. To validate the effectiveness of the approach, a comparative analysis is carried out with an established method based on a Bayesian filter, the Kalman filter. The aim is to provide a comprehensive analysis, highlighting the advantages and potential limitations of the methodology. In addition, a Monte Carlo simulation is implemented to assess the impact of sensor measurements on the performance of this new approach.

Keywords

• conjugate gradient methods
• fault diagnosis
• heat transfer
• identification
• Kalman filters
• parabolic equations