Diagnosis (05) Qualitative Reasoning Alban Grastien alban.grastien@rsise.anu.edu.au
Issue System We consider system that are dynamic continuous Difficulties The evolution of the system is described by complex equations, based on algebraic equations (that model the behaviour) and differential equation (that model the dynamics), potentially chaotic. Computing accurate values can be very expensive, or even impossible.
Qualitative Reasoning Goal Predict the system behaviour without resorting to numeric values. Explain system behaviour (diagnosis). QR AI community ( cf. QR proceedings).
Model A physical system is considered as a set of variables. The state evolves from one equilibrium point to another. Static models provide an image of the system’s equilibrium states. Dynamic models give a description of the transitory states between two equilibriums.
Example B A Two tanks of infinite height partially filled with a liquid and connected at their bottom.
Variables B A Amount of water in each tank: WA and WB (0 or +) Level of water in each tank: LA and LB ( mLx or +) Pressure of the water at the bottom of each tank: PA and PB ( mPx or +) Flow from tank A to tank B: A → B (-, 0, or +)
Static Model B A LA ր when WA ր (LB ր when WB ր ). PA ր when LA ր (PB ր when LB ր ). A → B ր when PA ր , and ց when PB ր . State WA + ; WB + ; LA + ; LB + ; PA + ; PB + ; A → B -
Dynamic Model B A WA ր when A → B ≤ 0 and ց when A → B ≥ 0. WB ր when A → B ≥ 0 and ց when A → B ≤ 0 .
Evolution of the System From the current state and the dynamic, determine which variables (potentially) evolve, how these variable evolve (increase or decrease), which new values the variables can reach. The evolution of a variable can be ambiguous: - 0 + - - - ? 0 - 0 + + ? + +
Possible Evolutions of this System B A Initial State WA + ; WB + ; LA + ; LB + ; PA + ; PB + ; A → B - Three Possible Next States WA + ; WB + ; LA + ; LB + ; PA + ; PB + ; A → B 0 WA + ; WB 0 ; LA + ; LB mLB ; PA + ; PB mPB ; A → B - WA + ; WB 0 ; LA + ; LB mLB ; PA + ; PB mPB ; A → B 0
Other Example B C A What happens after ? WA + ; WB + ; WC + ; LA + ; LB + ; LC + ; PA + ; PB + ; PC + ; A → B - ; B → C -
Diagnosis Given the model of the system, observations on some variables, determine the values of the faulty variables. The model leads to a finite-state machine. Diagnosis techniques include techniques used for diagnosis of discrete-event systems.
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