By Fan Yang, Ping Duan, Sirish L. Shah, Tongwen Chen
This short studies techniques of inter-relationship in sleek commercial techniques, organic and social platforms. in particular rules of connectivity and causality inside and among components of a fancy process are taken care of; those principles are of significant significance in analysing and influencing mechanisms, structural houses and their dynamic behaviour, specially for fault prognosis and chance research. Fault detection and isolation for commercial techniques worrying with root motives and fault propagation, the short indicates that, method connectivity and causality details may be captured in ways:
· from procedure wisdom: structural modeling in response to first-principles structural types could be merged with adjacency/reachability matrices or topology types acquired from approach flow-sheets defined in usual codecs; and
· from approach facts: cross-correlation research, Granger causality and its extensions, frequency area equipment, information-theoretical equipment, and Bayesian networks can be utilized to spot pair-wise relationships and community topology.
These equipment depend on the idea of data fusion wherein strategy working facts is mixed with qualitative procedure wisdom, to offer a holistic photograph of the system.
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Additional info for Capturing Connectivity and Causality in Complex Industrial Processes
Biol Cybern 84(6):463–474 3. Fedai M, Drath R (2005) CAEX—a neutral data exchange format for engineering data. ATP Int Autom Technol 3(1):43–51 4. Iri M, Aoki K, O’shima E, Matsuyama H (1979) An algorithm for diagnosis of system failures in the chemical process. Comput Chem Eng 3(1–4):489–493 5. Iri M, Aoki K, O’shima E, Matsuyama H (1980) A graphical approach to the problem of locating the origin of the system failure. J Oper Res Soc Jpn 23(4):295–311 6. Jiang H, Patwardhan R, Shah SL (2009) Root cause diagnosis of plant-wide oscillations using the concept of adjacency matrix.
Xn ) , i = 1, . . 1) where x1 , . . , xn are process variables. By Taylor series expansion near an operating point x10 , · · · , xn0 , we obtain dxi ≈ f i x10 , . . ,xn0 where f i (x10 , . . , xn0 ) = 0. ⎦≈ dt . xn ⎡∂f ∂ f1 ⎤ ⎢ ∂ x1 ∂ xn ⎥ ⎢ . ⎥ ⎢ . ⎥ . ⎥ ⎢ . ⎣∂f ∂ fn ⎦ n ··· ∂ x1 ∂ xn 1 ⎡ ⎤ x1 − x10 ⎢ .. ⎥ ⎣ . ⎦. ,xn0 The Jacobian matrix ⎡∂f 1 ⎢ ∂ x1 ⎢ . J =⎢ ⎢ .. ⎣∂f n ∂ x1 ··· ··· ∂ f1 ⎤ ∂ xn ⎥ .. ⎥ ⎥ . 5) if the nodes correspond to the process variables. Thus the SDG in fact describes the direct influences or sensitivities between process variables.
This constitutes a closed loop. Because the controlled 30 4 Capturing Connectivity and Causality from Process Knowledge Fig. 6 Block diagram of a feedback control loop variable may be affected by some disturbances or be coupled with other system variables, the exogenous plant and variable xi are also added in Fig. 6. Assume that the controlled plant and the controller are both linear amplifiers, namely, proportion elements, with the positive gains k and k y , respectively. 10) = , ⎪ ⎪ dt τ ⎪ ⎪ ⎪ ⎪ ⎩ u D = kc τ D · de , dt where, k p is the positive proportion parameter, τ I and τ D are integral and differential time constants, respectively.
Capturing Connectivity and Causality in Complex Industrial Processes by Fan Yang, Ping Duan, Sirish L. Shah, Tongwen Chen