Multi-Objective Surrogate-Assisted Stochastic Optimization for Engine Calibration

Abstract

A surrogate-assisted optimization approach is an attractive way to reduce the total computational budget for obtaining optimal solutions. This makes it special for its application to practical optimization problems requiring a large number of expensive evaluations. Unfortunately, all practical applications are affected by measurement noises, and not much work has been done to address the issue of handling stochastic problems with multiple objectives and constraints. This work tries to bridge the gap by demonstrating three different frameworks for performing surrogate-assisted optimization on multi-objective constrained problems with stochastic measurements. To make the algorithms applicable to real-world problems, heteroscedastic (nonuniform) noise is considered for all frameworks. The proposed algorithms are first validated on several multi-objective numerical problems (unconstrained and constrained) to verify their effectiveness and then applied to the diesel engine calibration problem, which is expensive to perform and has measurement noises. A gt-suite model is used to perform the engine calibration study. Three control parameters, namely, variable geometry turbocharger (VGT) vane position, exhaust-gas-recirculating (EGR) valve position, and the start of injection (SOI), are calibrated to obtain the tradeoff between engine fuel efficiency performance (brake specific fuel consumption (BSFC)) and NOx emissions within the constrained design space. The results show that all three proposed extensions can handle the problems well with different measurement noise levels at a reduced evaluation budget. For the engine calibration problem, a good approximation of the optimal region is observed with more than 80% reduction in the evaluation budget for all the proposed methodologies.

Stochastic Bayesian optimization for predicting borderline knock

“…However in the context of multi-objective with stochastic functions, there are two challenges of calculating expected improvement: (1) expensive calculation due to multi-variable integration in improvement function and (2) the current best solution is not well defined for stochastic case with exact values unknown. Based on the promising work developed in references, 12,16,25 the standard EI functions E I i ( i = 1 , 2 , . . . , m ) are extended to a single augmented matrix-based EI (AMEI) function to counter these two issues for multi-objective stochastic case. The closed expression of AMEI function for the n th unknown design vector x n is formulated by equation (9) below.…”

“…The high potential efficiency of SMAO process has been validated in terms of low cost and fast convergence by using classical test problems 12 and SMAO has been used for different applications such as groundwater reactive transport 13 and aerodynamic problems 14 with limited applications to automotive industry. Recently, Pal et al 15,16 successfully optimized the diesel engine calibration process using the SMAO method. To the authors’ best knowledge, this paper is the first time to utilize the SMAO method for predicting borderline knock limit.…”

Data-driven model-based calibration for optimizing electrically boosted diesel engine performance

“…Considering the multiobjective constraint problem with non-uniform noise variance, a comparative simulation study between three stochastic surrogate-assisted optimization approaches can be found in our previous work. 25 This work aims to demonstrate the advantage of using the stochastic surrogate-assisted optimization approaches for performing complex engine calibration on an actual experimental setup. This study focuses on performing steady-state calibrations.…”

“…For the current work, the surrogate-assisted optimization method, also known as Bayesian optimization, is used as it has shown its ability to significantly reduce the computational burden in identifying the global optimal regions. 9–12…”

“…Considering the multiobjective constraint problem with non-uniform noise variance, a comparative simulation study between three stochastic surrogate-assisted optimization approaches can be found in our previous work. 25…”