Constrained Surrogate-Based Engine Calibration Using Lower Confidence Bound
Anuj Pal, Ling Zhu, Yan Wang, Guoming Zhu
Abstract
Recent automotive technologicaladvancements mainly focus on improving fuel economy with satisfactory emissions, leading to significant increment of engine system complexity, especially for diesel engines. This results in a large number of calibration parameters in control features, making the engine calibration process a challenge and time consuming using the conventional map-based approach. This article proposes a methodology to perform engine calibration using surrogate assisted optimization to reduce calibration effort for diesel engines. A high fidelity GT-Power engine model is used for the current calibration study. The objective is to find the tradeoff relationship between engine efficiency (brake specific fuel consumption) and its <inline-formula><tex-math notation="LaTeX">$NO_x$</tex-math></inline-formula> emissions. Both these objectives are optimized by calibrating three control variables—namely, variable geometry turbocharger vane position, exhaust-gas-recirculating valve position, and the start of injection. Kriging surrogate models are developed for both objectives and constraints, where lower confidence bound is used as an acquisition function with a newly proposed constraint handling method and nondominated sorting algorithm is used for performing optimization. Results from this proposed algorithm demonstrate that the optimal points obtained for both test and actual engine calibration problems are pretty close to their true Pareto optimal front. For the engine calibration problem, more than 85% reduction in total computational budget is observed. Preliminary experimental study results are also presented to compare them with the simulation results, and the optimal tradeoff from both of them indicates a similar trend.