Open AccessSpatial basis functions based fault localisation for linear parabolic distributed parameter systems
Author(s) -
Feng Yun
Publication year - 2020
Publication title -
iet control theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.059
H-Index - 108
eISSN - 1751-8652
pISSN - 1751-8644
DOI - 10.1049/iet-cta.2020.0807
Subject(s) - basis (linear algebra) , truncation (statistics) , fault detection and isolation , eigenfunction , basis function , filter (signal processing) , fault (geology) , residual , distributed parameter system , control theory (sociology) , computation , computer science , truncation error , algorithm , set (abstract data type) , mathematics , differential operator , partial differential equation , mathematical analysis , artificial intelligence , statistics , geometry , eigenvalues and eigenvectors , computer vision , physics , control (management) , quantum mechanics , seismology , actuator , geology , programming language
Fault localisation for distributed parameter systems is as important as fault detection but is seldom discussed in the literature. The main reason is that an infinite number of sensors in the space are needed to construct a distributed residual signal , which is nearly impossible in practice. In this study, a fault detection and localisation filter which only uses a finite number of sensors is initiated based on an approximated ordinary differential equation model. Considering the limitations on computation resources for higher‐order models in practice, a novel set of spatial basis functions is applied to the reduced‐order fault detection and localisation filter design. Under certain conditions, the novel spatial basis functions obtain smaller state truncation error while the order is lower compared to the mostly used eigenfunctions of the spatial operator.