Interval estimation-based fault detection for time-delay parabolic systems

Abstract

Parabolic partial differential equations (PPDEs) are essential in practical engineering applications, and interval estimation methods offer an effective framework for fault detection in these systems. However, research on fault detection for time-delayed PPDEs using interval estimation remains limited. In this paper, we propose a new fault detection strategy for time-delay PPDE with uncertainties. The detection thresholds are designed within the framework of a two-step interval estimation method. First, we estimate the bounds of the auxiliary function through descriptive approach and inequality techniques. Then, we derive the detection threshold through the bounds of the auxiliary function and peak-to-peak analysis techniques. Finally, an example of a shallow geothermal system demonstrates the effectiveness of the proposed method.