Michael Heiss

Multiplication-free radial basis function network

For the purpose of adaptive function approximation, a new radial basis function network is proposed which is nonlinear in its parameters. The goal is to reduce significantly the computational effort for a serial processor, by avoiding multiplication in both the evaluation of the function model and the computation of the parameter adaptation. The approximation scheme makes use of a grid-based Gaussian basis function network. Due to the local support of digitally implemented Gaussian functions the function representation is parametric local and therefore well suited for an online implementation on a microcomputer. A gradient descent based nonlinear learning algorithm is presented and the convergence of the algorithm is proved.

Lernen linear interpolierter Kennlinien

Automatic actualization of input-output-maps is appreciated when the control of a slowly time variant system is based on these input-output-maps. The paper presents a learning algorithm which is easy to realize and which requires only rough information about the actual deviation of the map. The input-output-map is represented by linear interpolation between the interpolation nodes. In order to update some point of the map, the change request at this point is divided into two parts for the two neighboring interpolation nodes, in a way that the closer the node the more it is changed. It is shown that the algorithm is equivalent to the LMS-algorithm for on-line parameter identification of linear basis functions. The convergence of the algorithm is proven, the behavior is analyzed and illustrated by examples

A Detailed Analysis of the Initiation of Abnormal Combustion with Reaction Kinetics and Multi-cycle Simulation

For highly boosted gasoline engines with direct injection (DI) the operating conditions with lowest fuel consumption are restricted by irregular combustion like knocking. Therefore, the initiation mechanism for knocking was the subject of this research work. A 4-cylinder DI test engine that was provided by GM Europe was set up at the institute’s test bench. Experimental data at low speed at the knock limit (2–3 knock events per 100 cycles) were the basis for numerical investigations. A 1D multi-cycle simulation of gas-exchange and combustion was applied to calculate the in-cylinder properties and charge composition for the knocking cycles. Additionally, a CFD-simulation was carried out in order to obtain the spatial in cylinder distribution of temperature, mixture and residual gas. These results served to set up a stochastic reactor model including the full chemistry of the low and high temperature combustion. The model was initialised with the boundary conditions of the knocking cycle and the temperature and concentration distributions from the CFD-simulation. This method enabled the analysis of knocking combustion on the basis of chemical principles. The results of the multi-cycle analysis showed that important charge properties like the charge temperature at inlet valve closing or the internal residual gas fraction were within a narrow range over all cycles. Furthermore it could be shown that the burn duration for converting 2 % of the fuel mass correlated with cycles showing autoignition. All cycles with an accelerated early flame development showed an irregular heat release later on during the combustion phase. A detailed modelling of this behaviour was carried out for the stochastic reactor model. It could be shown that only with an initial reactor temperature distribution according to the CFD simulation, which included hot regions, the autoignition occurred as early as in the measurement. The formation of typical intermediate species for the low temperature oxidation leading to autoignition could be described. Finally, a possibility was shown to introduce quasi-spatial information of the flame propagation into the zero dimensional reactor model. In this way critical regions for knocking were identified in accordance with optical measurements of knock sources on the test bench. Most theoretical investigations on abnormal combustion are based on a simplified approach considering the mean cycle for a given operating point. However, abnormal combustion never occurred for the mean cycle but rather for a very early cycle. For that reason, this work focused especially on the detailed reconstruction of a measured knocking cycle with reaction kinetics. Considering the effect of temperature inhomogeneities and flame propagation on knock initiation in a stochastic reactor model is thereby a new and innovative approach.

Kennfelder in der Regelungstechnik

Input-output maps are applied in the field of automatic control in multiple ways. An overview of these different classes of applications is given, independently of whether the input-output map is implemented as a neural network, as a fuzzy controller, or is realized in a conventional manner.

Ein kennfeldorientiertes Konzept für Fuzzy-Regler

A map-based concept for a fuzzy controller is presented with the goal to take advantage of both, the idea of fuzzy control and the classical controller properties like a smooth control surface and a limited gain of the controller. A further demand was to provide a concept of such a transparency that it is easy to set up the rule base. This is realizable with the following properties: the conservation of straight lines, the conservation of monotony, and in particular the fact, that the control surface can be represented by a linear combination of so called fuzzy basis functions. It is shown that the classical fuzzy concepts do not share these properties. Two special cases are of particular practical interest: using B-splines as membership functions, and the class of single-overlapping membership functions. These cases are analyzed in detail and the most important properties are proved