Monotonicity analysis for constructing qualitative models (2004) [2 citations — 2 self]
Abstract:
Abstract. Qualitative models are more suitable than classical quantitative models in many tasks like Model-based Diagnosis (MBD), explaining system behavior, and designing novel devices from first principles. Monotonicity is an important feature to leverage when constructing qualitative models. Detecting monotone pieces robustly and efficiently from sensor or simulation data remains an open problem. This paper introduces an approach based on scale-dependent monotonicity: the notion that monotonicity can be defined relative to a scale. Real-valued functions defined on a finite set of reals e.g. the sensor data the simulation results, can be partitioned into quasi-monotone segments, i.e. segments monotone with respect to nonzero scale. We can identify the extrema of the quasi-monotone segments. This paper then uses this method to abstract qualitative models from simulation models for the purpose of diagnosis. It shows that using monotone analysis, the abstracted qualitative model is not only sound, but also parsimonious because it generates few landmarks. Qualitative models are more suitable than classical quantitative models in solving many problems. Qualitative models are used in tasks such as diagnosis [7], explaining system behavior [4, 6, 8], and designing novel devices from first principles [9]. Building a qualitative model for a complex system requires significant knowledge and is a time consuming process. Thus automatic construction of qualitative model is a well motivated topic. This paper studies how to construct qualitative models from scattered data, such as sensor data or simulation data. The main contributions of this paper are: – Our technique is shown to be robust and computational efficient at detecting monotone pieces from scattered data. – We provide algorithms to generate the landmarks and abstract the model from the monotonicity analysis. – The resulting qualitative model is shown to support diagnosis of dynamic faults.
Citations
| 536 | Qualitative process theory – Forbus - 1984 |
| 366 | Qualitative simulation – Kuipers - 1986 |
| 73 | An Online Algorithm for Segmenting Time Series – Keogh, Chu, et al. - 2001 |
| 13 | Automated abstraction of numerical simulation models - theory and practical experience – Struss - 2002 |
| 11 | Induction of qualitative tree – Suc, Bratko - 2001 |
| 8 | Approximation complexity for piecewise monotone functions and real data – Brooks - 1994 |
| 8 | Deriving qualitative deviations from matlab models – Console, Correndo, et al. - 2003 |
| 8 | Qualitative model abstraction for diagnosis – Yan - 2003 |
| 7 | A toolbox integrating model-based diagnosability analysis and automated generation of diagnostics – Dressler, Struss - 2003 |
| 6 | Interaction-based invention: designing devices from first principles – Williams - 1992 |
