Experimental Case Study of Stochastic Surrogate-Assisted Engine Calibration

Reducing experimental calibration cost to achieve optimal system performance is challenging, especially for highly nonlinear engine systems. With the advancement and widespread adoption of machine learning methods for control applications, it is now possible to use an intelligent black-box model to efficiently optimize nonlinear control systems without the detailed knowledge of system dynamics. The surrogate-assisted optimization approach has been recently proven to work effectively to reduce the overall experimental budget (cost). However, its application to calibrate and optimize a practical control system experimentally is a challenge due to stochastic system and measurement noises. This article experimentally calibrates and optimizes the control parameters of a 6.7L Ford diesel engine using the stochastic surrogate-assisted optimization automatically based on a stochastic Kriging model, which is the first step toward automating the engine calibration process. Two engine control variables, namely, exhaust gas recirculation valve and variable geometry turbocharger vane positions, are calibrated to obtain a tradeoff between engine efficiency, in terms of brake-specific fuel consumption, and $\text{NO}_{x}$ emissions, utilizing both the deterministic and stochastic surrogate-assisted learning algorithms. Experimental results show a much better representation of the output response surfaces with the stochastic surrogate-assisted optimization than that from the deterministic approach. Note that the stochastic approach helps direct the search toward the global optimal region without wasting the evaluation budget in exploring the local optima, and the deterministic approach cannot effectively handle stochastic system and measurement noises, resulting in overfitting the data. Therefore, to solve a practical optimization problem with noises, stochastic surrogate-assisted optimization is recommended.