Identification of failure times for a system governed by a non-linear parabolic partial differential equation

For complex processes whose evolution is described by partial differential equations, the identification of failures is often difficult. In thermal systems, for example, when one or more heating sources fail, the sensors placed at a distance perceive the effect with delay. From these noisy observations, it is then necessary to determine with precision the moment of failure and the possible restart of the heating. As the inverse heat conduction problems are ill-posed, a regularization method has been developed and implemented for non-linear parabolic systems. It allows to detect failures and restarts of one or more sources. In the following, the whole problematic and the method of resolution is presented. Particular attention is paid to the effect of measurement noise on fault identification. Copyright (c) 2022 The Authors. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/)