Reachability Analysis of Stochastic Hybrid Systems: A Biodiesel Production System

Reachability analysis of stochastic hybrid systems (SHS) is an important problem because it provides a formal framework to analyze complex systems. Biodiesel production is a realistic biochemical process that can be modeled and analyzed using SHS methods. Analysis of a biodiesel production system is important to understand and analyze because demand for biofuels is growing, and economical, efficient production methods will result in high-quality, lower cost fuel. In this work we present a SHS biodiesel production model which captures the dynamical behavior of the chemical reactions including the effects of temperature control as well as the glycerol settling process which is used to increase the product quality. We compare simulation results obtained using our model with experimental results collected from an actual biodiesel processor to validate and demonstrate the correctness of the model. We also present an exhaustive verification technique based on dynamic programming, and we use the method to analyze the likelihood of quality biodiesel production. Further, we utilize multilevel splitting and Monte Carlo analysis to compute reachability probabilities for the biodiesel system, and we compare the results with the verification method.