A comparison of equation-based modeling with Bayesian network modeling for engineering applications

Modeling and Simulation is an important tool in Systems Engineering, Current practice is to use an equation-based approach. Equation-based models can require extensive time and money to construct high fidelity models that accurately represent the real world. The goal of this research is to explore alternate methods of creating accurate models and simulations that can be done rapidly and at much lower cost. The research compared engineering modeling applications for time of construction and the accuracy between equation-based models and Bayesian networks. The derivative method, a multivariate approach to discretizing continuous data was proposed and compared to four current search and score methods. The comparison found little difference in performance between different methods of discretization while the derivative method was much faster. The research software also integrated a neural network into the Bayesian network construction. The neural network strengthens the data set by predicting missing values or areas were data were incomplete. Improved performance was also demonstrated by use of Gaussian smoothing of the probability tables of Bayesian network nodes. The comparison found that human judgment Bayesian networks took longer to build and were less accurate than equation-based models. Bayesian networks created using formulae had approximately the same time of construction and accuracy as equation-based models. Computer-generated Bayesian networks were both faster (95% confidence) to construct and more accurate (95% confidence) than equation-based models. An important assumption in this comparison was that the data to construct the computer-generated network already existed. To optimize the model construction process, the research developed integration software and demonstrated that Bayesian networks or influence diagrams and equation-based models could be integrated together. The research also demonstrated that equation-based simulation could be used to train an influence diagram which decisions resulted in optimal outcomes. The research goal was exceeded by demonstrating not only that computer-generated Bayesian network models can be constructed in less time and with less human labor resulting in significantly less cost, but that improved accuracy is achieved simultaneously.