Abstract

Virtual stochastic sensors (VSS) enable the reconstruction of unobserved behavior of discrete or hybrid stochastic systems from observable output. Augmented stochastic Petri nets (ASPN) are user models for VSS and describe discrete stochastic models that produce discrete output symbols based on the transitions or system states. Hybrid ASPN (H-ASPN) can describe hybrid stochastic systems with continuous quantities that are influenced by and interact with the discrete system parts, producing samples of these continuous system quantities as observable output. Real-world systems often contain both of these types of observable output. In household energy models, the total consumption is a continuous quantity that can be sampled regularly. Additionally, the usage behavior of some appliances might be known in advance or can be monitored easily, resulting in observable discrete symbols. Being able to utilize both of these for behavior reconstruction, promises better re-sults than using either one alone. In this paper, we describe an extended H-ASPN paradigm for modeling symbol output as well as sample measurement for partially observable hybrid stochastic systems. We demonstrate the paradigm on a small non-intrusive appliance load monitoring (NIALM) example and test the behavior reconstruction. The extended H-ASPN modeling paradigm enables faster and more reliable behavior reconstruction results, when using both observable symbols and samples. The experimental results indicate that extended H-ASPN could lead the way to practically feasible VSS for hybrid systems.