A Hybrid Physics-Based and Stochastic Neural Network Model Structure for Diesel Engine Combustion Events

Estimation of combustion phasing and power production is essential to ensuring proper combustion and load control. However, archetypal control-oriented physics-based combustion models can become computationally expensive if highly accurate predictive capabilities are achieved. Artificial neural network (ANN) models, on the other hand, may provide superior predictive and computational capabilities. However, using classical ANNs for model-based prediction and control can be challenging, since their heuristic and deterministic black-box nature may make them intractable or create instabilities. In this paper, a hybridized modeling framework that leverages the advantages of both physics-based and stochastic neural network modeling approaches is utilized to capture CA50 (the timing when 50% of the fuel energy has been released) along with indicated mean effective pressure (IMEP). The performance of the hybridized framework is compared to a classical ANN and a physics-based-only framework in a stochastic environment. To ensure high robustness and low computational burden in the hybrid framework, the CA50 input parameters along with IMEP are captured with a Bayesian regularized ANN (BRANN) and then integrated into an overall physics-based 0D Wiebe model. The outputs of the hybridized CA50 and IMEP models are then successively fine-tuned with BRANN transfer learning models (TLMs). The study shows that in the presence of a Gaussian-distributed model uncertainty, the proposed hybridized model framework can achieve an RMSE of 1.3 x 10(-5) CAD and 4.37 kPa with a 45.4 and 3.6 s total model runtime for CA50 and IMEP, respectively, for over 200 steady-state engine operating conditions. As such, this model framework may be a useful tool for real-time combustion control where in-cylinder feedback is limited.