Gradient-based optimization of a multi-orifice asynchronous injection system in a diesel engine using an adaptive cost function

Document Type

Conference Proceeding

Publication Date



Department of Mathematical Sciences; Department of Computer Science


A gradient-based optimization tool has been developed and, in conjunction with a CFD code, utilized in the search of optimal fuel injection strategies. The approach taken uses a steepest descent method with an adaptive cost function, where the line search is 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 tool is demonstrated for a non-road version of the Sulzer S20 DI diesel engine which, for these simulations, is equipped with a multi-orifice, asynchronous injection system. This system permits an independent timing of the fuel pulses, and each orifice has its own diameter and injection direction. Optimizations have been performed for a two fuel pulse strategy, where the optimization parameters include the start of the injections, the injection durations, the size of the nozzle orifices and the injection directions. It has been demonstrated that this new injection method has a large potential for reducing emissions while maintaining a low fuel consumption. In addition, in comparison with other non-gradient-based techniques, the optimization approach used in this study is computationally very efficient.

Publisher's Statement

Copyright © 2006 SAE International. Publisher’s version of record: https://doi.org/10.4271/2006-01-1551

Publication Title

SAE Technical Papers