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... Introduction of Bayesian concepts. TITLE PAGE Slide 1 / 24. Fault Diagnosis: The Introduction of Bayseian Concepts to Signed Digraphs. M.J. Tierney. University of Bristol. ... Introduction of Bayesian concepts. ABSTRACT Slide 2 /24. Purpose of this presentation.
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... Introduction of Bayesian concepts. TITLE PAGE Slide 1/24 Fault Diagnosis: The Introduction of Bayseian Concepts to Signed Digraphs. M.J. Tierney. University of Bristol.
... Introduction of Bayesian concepts. ABSTRACT Slide 2/24 • Purpose of this presentation. • To take conventional SDG approach, and apply probabilistic rules. With examples. • Advantages • Deals with diagnostic instability • Deals with multiple root causes • Richer elicitation of expert knowledge.
... Introduction of Bayesian concepts. CONTENTS Slide 3/24 • Procedure • -A hypothetical example. • - Reformulation of SDG. • -Probabilistic version. • Examples, to illustrate … • - Simultaneous root causes. • - Uncertainty. • - Complexity. • Conclusions and Future Work.
Cao LI mf T Cb m.steam Vpos P ... Introduction of Bayesian concepts. PROCEDURE Slide 4/24 A Hypothetical example. Symptoms - Inadequate conversion or high liquid level.
Ca mf - + + - Vpos Cb LI - + + + ms + P T ... Introduction of Bayesian concepts. PROCEDURE Slide 5/24 SDGs capture cause and effect. Low steam supply low temperature low reaction rate Controller fault high level.
Vpos - Cao LI - mf Low or High Cb P + T + ms Cb_01 ... Introduction of Bayesian concepts. PROCEDURE Slide 6/24 • A) Form a hierarchy from V.pos • Signed paths • Decomposition of loops.
Cause Effect Sign State High High + True Low Low + True High Low - True Low High - True Other False ... Introduction of Bayesian concepts. PROCEDURE Slide 7/24 B) Define a rule for retaining paths (sdgRule)
Vp Vp Cao Cao - - LI LI mf mf - P P Cb Cb + ms ms T T Cb_01 Cb_01 ... Introduction of Bayesian concepts. PROCEDURE Slide 8/24 C) Apply sdgRule and test H(Vpos) B- accept A- reject
... Introduction of Bayesian concepts. PROCEDURE Slide 9/24 D) Postcondition for a diagnosis. Every node is in the hierarchy, or has a clone in the hierarchy, or has a normal signal. Dealing with controllers. A controlled parameter may indicate “OK”, and transmit faults ControllerRule = sdgRule or (P.signal = HIGH and Vpos.signal = HIGH).
... Introduction of Bayesian concepts. PROCEDURE Slide 10/24 • Probabilistic Approach. • The hierarchy facilitates probabilistic approach. • Apply probabilities to paths and nodes outside hierarchy. Cross multiply all these to get P.system. • Eg – a rule for isolated nodes … • signal {high,low} probability = 0.01 • signal {OK, null} probability = 0.99.
Condition Probability SdgRule 0.95 Cause = low, high Effict = low, high 0.60 Both signals OK 0.01 ... Introduction of Bayesian concepts. Slide 11/ 24 … and for paths. Formally … Pdiagnosis = (pi| i.itemType = path i hierarchy) x (pi | i hierarchy)
PORV T LI Pressuriser To turbines. T CORE. SG LI From polishers Auxiliary supply. m ... Introduction of Bayesian concepts. EXAMPLE 1 – TMI. Slide 12/24 Features failure of secondary circuit, auxiliary supply and PORV.
... Introduction of Bayesian concepts. EXAMPLE 1 – TMI. Slide 13/24 Simulated Response.
... Introduction of Bayesian concepts. EXAMPLE 1 – TMI Slide 14/24 The SDG.
... Introduction of Bayesian concepts. EXAMPLE 1– TMI Slide 15/ 24 Test auxiliary Feedwater blockage. Accepted – p ~ 7%
... Introduction of Bayesian concepts. EXAMPLE 1 – TMI Slide 16/24 Test PORV Leak. Rejected.
... Introduction of Bayesian concepts. EXAMPLE 1 Slide 17/24 Probabilistic Test of PORV Leak. P ~1/1,000,000
... Introduction of Bayesian concepts. EXAMPLE 2 FORGING Slide 18/24 Plant Diagram. • Difficulties • Temperature influences phase change • Material properties.
... Introduction of Bayseian concepts. EXAMPLE 2 FORGING Slide 19/24 The SDG.
... Introduction of Bayseian concepts. EXAMPLE 3 Slide 20/ 24 Carbon in ash - factors.. Coal used. Particle size/ grinding. Flow patterns in burner. Tramp air. Air/ fuel distribution to burners. Emissions - particulates + Nox + SOx
Blend Sulphur/ Nitrogen Volatile material content Ash content COAL Grindability Mill wear Classifier set up Coal feeder system MILL MILL PF pipes Air flow factors BURNERS BURNERS Burner layout Burner tilt Burners out-of-service FURNACE Air in-leakage Spatial variation in residence times OFA
... Introduction of Bayseian concepts. EXAMPLE 3 CIA Slide 22/24 An SDG for carbon in Ash Measure CIA, A:F ratio, superheater temps.
... Introduction of Bayseian concepts. CONCLUSIONS Slide 23/24 • We offer a means of representing graphs in a-cyclic form. This allows probabilistic rules. • Advantage of “Auditablity” • Probablistic methods mitigate diagnostic instability, and permit multiple root causes (e.g. TMI). • Specialised rules are frequently needed. • Knowledge from various sources - operators, simulation experiment.
... Introduction of Bayseian concepts. Future Work Slide 24/24 • Future Work. • Hybrid Methods. • Knowledge Elicitation. • Knowledge Transfer. • Quality Assurance. • Human Factors. • Uncertainty. • Good practice.
... Introduction of Bayseian concepts. Example 1 – TMI Slide 25/ .
