A new algorithm for adaptive threshold generation in robust fault detection based on a sliding window and global optimization

Robust fault detection based on envelopes generated using a parameter bounded model has been studied from several approaches. But none of the existing approaches can produce the exact system envelopes without increasing the uncertainty over the system states, or at least, approximate envelopes controlling the degree of uncertainty added by the envelope generation algorithm. This paper presents a new approach based on global optimization and the sliding window paradigm. The optimal length of the sliding window can be determined analytically and it has been proved that its length is the order of settling time of the system. The paper focuses on solving the problems of global optimization resulting after applying the new envelope generation algorithm. Several approaches to solve this global optimization problem are proposed. At the end of the paper these techniques are compared using an example. The main objective of the paper is to determine a global optimization technique suitable to solve the optimization problems that appear after applying the envelope generation algorithm, using the less possible time because this algorithm should operate in real time.