Can interval parity relations improve fault diagnosis in complex systems affected by external disturbances? This paper explores the design of such relations for systems described by linear and nonlinear models. The approach is based on the reduced-order model of the original system, deriving relations that are insensitive or minimally sensitive to disturbances. The problem of interval parity relations design for systems described by linear and nonlinear models under the external disturbances is considered. These relations allow for the creation of interval parity relations that reduce sensitivity to external disturbances. By using the reduced-order model of the original system, the interval parity relations are used to solve the problem of fault diagnosis, enhancing the accuracy and reliability of the process. The obtained interval parity relations are used to solve the problem of fault diagnosis. The theoretical results are illustrated with an example, demonstrating the practical application and effectiveness of the proposed method. This research has implications for improving the reliability and safety of various engineering systems by enabling more accurate fault detection and diagnosis, even in the presence of external disturbances.
This paper, published in the International Journal of Adaptive Control and Signal Processing, is directly aligned with the journal's focus on advanced control techniques and signal processing applications. By addressing the design of interval parity relations for fault diagnosis, the article contributes to the field of adaptive control, a core area of interest for the journal.