Cascade alarm systems: A study on singular value analysis

This paper introduces a novel alarm system designed for use with both Independent and Identically Distributed (IID) and non-IID variables. The proposed algorithm, termed the Cascade Alarm System (CAS), utilizes the largest singular value of the signal as the basis for fault detection, employing k alarm subsystems. The greatest singular values extracted from the Lagged Covariance Matrix (LCM) of a sliding window constitute the output of the first alarm subsystem. The CAS offers two primary advantages. First, each subsystem independently generates its own alarm signal, resulting in a more flexible multilevel architecture. Second, the multilevel structure, founded on singular value decomposition (SVD), exhibits a filtering property that enhances its resilience to noise and inaccuracies. The maximum singular value effectively captures the essential information of the signal, ensuring that the filtering capabilities of the proposed method do not significantly compromise the performance of the alarm system or the integrity of critical signal information. The experimental results from the implementation of the proposed alarm system under various fault conditions demonstrate satisfactory performance. Additionally, the performance of the Cascade Alarm System has been compared with leading contemporary alarm system design methodologies, including median, moving average filters, delay timers, Cumulative Sum Control Chart (CUSUM), and serial method.