Global optimization of a two-pulse fuel injection strategy for a diesel engine using interpolation and a gradient-based method

Document Type

Conference Proceeding

Publication Date



Department of Mathematical Sciences


A global optimization method has been developed for an engine simulation code and utilized in the search of optimal fuel injection strategies. This method uses a Lagrange interpolation function which interpolates engine output data generated at the vertices and the intermediate points of the input parameters. This interpolation function is then used to find a global minimum over the entire parameter set, which in turn becomes the starting point of a CFD-based optimization. The CFD optimization is based on a steepest descent method with an adaptive cost function, where the line searches are performed with a fast-converging backtracking algorithm. The adaptive cost function is based on the penalty method, where the penalty coefficient is increased after every line search. The parameter space is normalized and, thus, the optimization occurs over the unit cube in higher-dimensional space. The application of this optimization method is demonstrated for a non-road version of the Sulzer S20 DI diesel engine equipped with a common rail injection system. Optimizations have been performed for a two fuel pulse injection strategy, where the optimization parameters include the start of the injections and the injection durations. It has been demonstrated that this optimization method is computationally efficient and has a big potential for finding optimal engine operating conditions which reduce emissions while maintaining a low fuel consumption.

Publisher's Statement

Copyright © 2007 SAE International. Publisher’s version of record: https://doi.org/10.4271/2007-01-0248

Publication Title

SAE Technical Papers