By Steven X. Ding
Data-driven layout of Fault prognosis and Fault-tolerant keep an eye on structures provides simple statistical method tracking, fault prognosis, and keep an eye on equipment and introduces complicated data-driven schemes for the layout of fault analysis and fault-tolerant keep watch over platforms catering to the wishes of dynamic commercial methods. With ever expanding calls for for reliability, availability and defense in technical strategies and resources, method tracking and fault-tolerance became vital concerns surrounding the layout of computerized keep watch over structures. this article exhibits the reader how, because of the fast improvement of knowledge expertise, key strategies of data-driven and statistical strategy tracking and keep an eye on can now turn into commonplace in commercial perform to handle those matters. to permit for self-contained learn and facilitate implementation in genuine purposes, very important mathematical and regulate theoretical wisdom and instruments are integrated during this ebook. significant schemes are offered in set of rules shape and tested on commercial case platforms. Data-driven layout of Fault prognosis and Fault-tolerant regulate platforms can be of curiosity to strategy and regulate engineers, engineering scholars and researchers with a regulate engineering background.
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Additional info for Data-driven Design of Fault Diagnosis and Fault-tolerant Control Systems
We assume that m > n, the covariance matrix Σ and matrix A √ Rm×n are known. Our task is to detect faults in the measurement space, which is modeled by ⎤ 0, y = Ax + f + ∂, f = f 1 ⇒= 0, fault-free . 43) There are different ways to approach this problem. Recall that m > n. Then, we can find A⊥ √ R(m−n)×n so that A⊥ A = 0 =∈ A⊥ y = A⊥ ( f + ∂) := f¯ + ∂¯ . 44) In this way, our detection problem is reduced to the FD-P1 and can be solved using the tools introduced in Sect. 4. On the other hand, it is evident that by this detection scheme only those faults can be detected, which satisfy A⊥ f ⇒= 0.
Recall that m > n. Then, we can find A⊥ √ R(m−n)×n so that A⊥ A = 0 =∈ A⊥ y = A⊥ ( f + ∂) := f¯ + ∂¯ . 44) In this way, our detection problem is reduced to the FD-P1 and can be solved using the tools introduced in Sect. 4. On the other hand, it is evident that by this detection scheme only those faults can be detected, which satisfy A⊥ f ⇒= 0. That means, the fault detectability is poor. Next, we consider an alternative solution on the assumption that A is leftinvertible. Let xˆ be a least squares (LS) estimation, that is, ⎦ xˆ = A T A −1 A T y.
Y N , and calculate y¯ N = 1 N N yi , Σˆ = i=1 S2: Set Jth,T 2 Jth,T 2 = 1 N −1 N (yi − y¯ N ) (yi − y¯ N )T , Σˆ −1 i=1 m N2 − 1 FΔ (m, N − m). 38) S3: Make a decision ⎤ J ≤ Jth,T 2 =∈ fault-free . 3 Fault Detection Using Q Statistic In the T 2 statistic, computation of the inverse matrix of Σˆ is necessary. By a high ˆ such a computation may cause numerical dimensional and often ill-conditional Σ, trouble in practice. 39) 36 3 Basic Statistical Fault Detection Problems is widely accepted in practice and applied in the multivariate analysis technique.