A stochastic design optimization methodology to reduce emission spread in combustion engines

摘要

This paper introduces a method for efficiently solving stochastic optimization problems in the field of engine calibration.The main objective is to make more conscious decisions during the base engine calibration process by considering the systemuncertainty due to component tolerances and thus enabling more robust design, low emissions, and avoiding expensiverecalibration steps that generate costs and possibly postpone the start of production. The main idea behind the approach is tooptimize the design parameters of the engine control unit (ECU) that are subject to uncertainty by considering the resultingoutput uncertainty. The premise is that a model of the system under study exists, which can be evaluated cheaply, and thesystem tolerance is known. Furthermore, it is essential that the stochastic optimization problem can be formulated such thatthe objective function and the constraint functions can be expressed using proper metrics such as the value at risk (VaR). Themain idea is to derive analytically closed formulations for the VaR, which are cheap to evaluate and thus reduce the computationaleffort of evaluating the objective and constraints. The VaR is therefore learned as a function of the input parametersof the initial model using a supervised learning algorithm. For this work, we employ Gaussian process regression models.To illustrate the benefits of the approach, it is applied to a representative engine calibration problem. The results show asignificant improvement in emissions compared to the deterministic setting, where the optimization problem is constructedusing safety coefficients. We also show that the computation time is comparable to the deterministic setting and is orders ofmagnitude less than solving the problem using the Monte-Carlo or quasi-Monte-Carlo method.