Presentation on theme: "George M. Coghill The Morven Framework. Motivation To provide properly constructive, constraint based qualitative simulation Retain QR ethos To alleviate."— Presentation transcript:
Motivation To provide properly constructive, constraint based qualitative simulation Retain QR ethos To alleviate the problem of spurious behaviours General purpose QR Why a Framework –No system is suitable for all situations –Permits testing and comparison of approaches –Consists in modular constituents
Constituents Predecessors –Variables are represented as vectors –Models are distributed over differential planes –Fuzzy quantity spaces are utilised –Empirical knowledge can be incorporated. Specific to Morven –Transitions only generated for state variables –Constructive (assynchronous) simulation –Fuzzy Vector Envisionment –Different approach to prioritisation –Discrete time (synchronous) simulation
The Morven Framework Constructive Non-constructive Simulation Envisionment Synchronous Asynchronous
Fuzzy Qualitative Reasoning Motivation Integration of qualitative and vague quantitative information - captured in the nature of fuzzy sets Ability to utilise and calculate temporal information in a qualitative simulator To include empirically derived information into a qualitative simulator
4-tuple fuzzy numbers (a, b, ) precise and approximate useful for computation x A (x) 1 0 a x (a) A (x) 1 0 a b x (b) A (x) 1 0 a- a x a+ (c) A (x) 1 0 a- b+ ab (d) A convenient fuzzy representation
Fuzzy Quantity Spaces A (x) 10 x 0.20.4 0.6 0.8-0.8-0.6 -0.4 -0.2 0
Transition Rules Intermediate Value Theorem (IVT) –States that for a continuous system, a function joining two points of opposite sign must pass through zero. Mean Value Theorem (MVT) –Defines the direction of change of a variable between two points. [++][+o][+-] [o+][oo][o-] [-+][-o][- -]
Single Tank System V qiqi qoqo plane 0 q O = kV V = q i - q O plane 1 q O = kV V = q i - q O plane 2 q O = kV V = q i - q O
Single Compartment System plane 0 k10x1 = k10.x1 x1 = u - k10x1 plane 1 k10x1 = k10.x1 x1 = u - k10x1 plane 2 k10x1 = k10.x1 x1 = u - k10x1 1 u k 10.x 1
Possible States statevectorstatevector 1+ + + +22+ - o + 2+ + + o23+ - o o 3+ + + -24+ - o - 4+ + o +25+ - - + 5+ + o o26+ - - o 6+ + o -27+ - - - 7+ + - +28o + + + 8+ + - o29o + + o 9+ + - -30o + + - 10+ o + +31o + o + 11+ o + o32o + o o 12+ o + -33o + o - 13+ o o +34o + - + 14+ o o o35o + - o 15+ o o -36o + - - 16+ o - +37o o + + 17+ o - o38o o + o 18+ o - -39o o + - 19+ - + +40o o o + 20+ - + o41o o o o 21+ - + -
Soundness and Completeness Sound –Guarantees to find all possible behaviours of system Incomplete –Unfortunately also finds non-existent (spurious) behaviours Still useful for ascertaining that a dangerous state cannot be reached. Large research effort to remove spurious behaviours –we will skim the surfarce of the surface!
Single Tank System: Ramp Input V qiqi qoqo t qiqi Input: Stepped Ramp plane 0 q O = kV V = q i - q O plane 1 q O = kV V = q i - q O plane 2 q O = kV V = q i - q O
Representational Primitives (2) Functional primitives –More specific than M+/- relations, though still incomplete –Compiled (tabular) set of fuzzy if-then rules - permits incusion of empirical information Derivative primitive
The Approximation Principle The Approximation principle facilitates the mapping of the result of a fuzzy operation onto the values in the quantity space of the result variable. A measure of the Goodness of Approximation is achieved by means of a Distance Metric d(A, A) = [(power(A)-power(A)) 2 +(centre(A)-(centre(A)) 2 ] 0.5 power([a,b, = 0.5[2(a+b) + centre([a,b, = 0.5[a+b]
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