Improved energy graph-based visualisation fault detection and isolation — A spectral theorem approach

This paper illustrates how the energy graph-based visualisation (EGBV) fault detection and isolation (FDI) method may be interpreted in terms of the spectral theorem to gain insight into the sensitivity and robustness performance of the method. It is shown that the EGBV monitoring structure can be decomposed into components of varying importance. A formula is proposed as a guideline for informed component removal. These principles are applied to a practical heated two-tank process. It is shown that lesser-weighted components exhibit noisy behaviour and, when removed, increase the robustness of EGBV. Additionally, the computational requirements for the EGBV method and its fault signatures are reduced. It is also shown that retaining smaller components provides the benefit of improved sensitivity. Therefore, a trade-off exists between sensitive and robust process monitoring. Furthermore, it is acknowledged that component removal may compromise the resolution of EGBV’s fault signatures and so, a formula is derived to verify its resolution integrity.