Parity relations for linear uncertain dynamic systems

Robust Fault Diagnosis of Nonlinear Systems Using Interval Constraint Satisfaction and Analytical Redundancy Relations

“…Definition 3.1 (Consistency for sets of ARRs): Given a set of ARRs expressed according to (12) and a sequence of measured system inputsũ k and outputs y k at time k, the set of ARRs is consistent with those measurements and the known bounds of uncertain parameters and noises if there exist valid sequences (with values inside their corresponding intervals) for these uncertain variables that simultaneously satisfy the ARRs, i.e.…”

“…Exit (Fault detected) 11: end if 12: end for solving an ICSP whose variables are the ones involved in (10), their domains are given by (14) and the constraints correspond to the ARRs in (12), and checking whether the obtained result is the empty set. This procedure is summarized in Algorithm 1.…”

“…This paper can be considered an adaptation of the non-linear ARR approach proposed in [11] in the case that noise and model parameters are modelled in the set-membership context and included in the ARRs. In case of linear systems, [12] has suggested the evaluation of uncertain ARRs generated using the parity space approach using set computations. However, to the best of the authors' knowledge, the fault detection problem in presence of bounded uncertainty has not been considered before by using parity equations and ICSPs within the non-linear context.…”

Fault diagnosis and fault tolerant control using set-membership approaches: Application to real case studies

“…But, time invariance in uncertain parameters being to be preserved, an -order MA parity equation should be used (Tornil et al, 2003). Finally, Ploix and Adrot (2006) proposed a method to obtain the interval parity equations directly from the state-space using the Chow-Wilsky scheme.…”

“…Seminal papers suggesting this approach are the one by Horak (1988) in the time domain and that by Emami-Naeini et al (1988) in the frequency domain. This passive approach has been developed lately by several researches but still is under development, see for example (Adrot and Flaus, 2008;Armengol et al, 2008;Fagarasan et al, 2004;Hamelin and Sauter, 2000;Ploix and Adrot, 2006;Puig et al, 2006;Rambeaux, 2000;Sainz et al, 2002). This approach has also been integrated with qualitative reasoning tools (coming from the AI community), see, e.g., the tools CA∼EN (Travé-Massuyes et al, 2001;Escobet et al, 2001), SQualTrack (Armengol et al, 2008) or MOSES (Rinner and Weiss, 2004).…”