Task-Dependent Qualitative Model Abstraction

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Presentation transcript:

Task-Dependent Qualitative Model Abstraction Martin Sachenbacher September 2003

On-board, Real-time Environments

Qualitative Model Abstraction Map real-valued constraints to finite domains Problem: Find adequate distinctions avoid unnecessary details

Interchangeability [Freuder 91] Domain values val1, val2 are interchangeable, iff exchanging val1, val2 preserves solutions Task-independent form of abstraction v2 R val1 val' val2 v1

Task-Dependent Abstraction Idea: “Relaxed” version of interchangeability that keeps only distinctions essential for a given task Granularity of observations and solutions Ç = = Robs R R Ç Robs

Task-Dependent Abstraction Observable Distinctions Partition defining granularity of observations tobs tobs (Robs) Ç = = Robs R R Ç Robs

Task-Dependent Abstraction Target Distinctions Partition defining granularity of solutions tobs ttarg ttarg(R Ç tobs(Robs)) tobs (Robs) Ç = = Rext(v) R R(v) Ç Rext(v)

Task-Dependent Abstraction Induced Abstraction (Maximal) partition preserving solutions tind(R) tind Induced tobs ttarg ? ttarg(R Ç tobs(Robs)) Ç = = Rext(v) tobs (Robs) R R(v) Ç Rext(v)

Qualitative Abstraction Problem Find domain abstraction tind for R such that " Robs Adequacy: ttarg(R Ç tobs(Robs)) = ttarg(tind(R) Ç tind(tobs(Robs))) Simplicity: any abstraction of tind is not adequate Definition of Properties “Obs-complete”, iff each possible Robs can occur “Sol-complete”, iff each possible solution can occur

Determining Induced Abstractions tobs

Determining Induced Abstractions , ttarg tobs

Determining Induced Abstractions 1 1 2 1 2 3 1 1,3 2 4 1 1,3 2

Determining Induced Abstractions Partition S 1 1,3 2

Theorem Induced abstraction tind formed by intersection of interchangeable values for each element of S Partition S val2 val1 1 1,3 2

Results [Sachenbacher et al. 01] On-board Vehicle Diagnosis Application Observable distinctions: sensor values Target distinction: threshold for air/fuel ratio 

Discussion Conclusions Current Work Generalizes notion of interchangeability Increases efficiency and/or fidelity of models Facilitates re-usability of model for several tasks Current Work Extend to probabilistic models Extend to quantitative constraints Extend to dynamic models (transitions) Frame as (pareto-) optimization problem

Material Pedal Position Sensor Example

Example: Pedal Position Sensor Potentiometer Switch Pedal vleft vright vleft vright On-board Diagnosis requires distinction corresponding to switching point Battery vpot vswitch Control Unit