Detailed or Complex Models

9 RANS simulations are currently employed in a majority of the cases for the sake of simplicity and available computation time [8], whereas predominantly LES and DNS simulations are used in fundamental research studies [33][61]. Owing to the limited understanding and the complexity of the reaction chemistry at a fundamental level, there is considerable activity in this field of research, includ- ing studies on hydrocarbon reaction mechanisms [9] or turbulence-chemistry inter- actions [107]. Applications Examples Compared to empirical and phenomenological models, the generality of detailed complex models makes it possible to comply with almost any kind of problem. Depending on the intention, and hence the level of sophistication, the models are commonly used to gain insight into the governing processes, provide information of local in-cylinder phenomena or evaluate new combustion technologies. • HEAT TRANSFER Gosman and Watkins applied computational fluid dynamic simulations for turbulent in-cylinder flows including a one-dimensional gas-wall heat trans- fer model [36]. Given the present LES and DNS turbulence models avail- able, the model accuracy is no longer restricted in terms of the turbulent flow field resolution. • RATE OF HEAT RELEASE COMBUSTION Focusing on the combustion itself, numerous approaches, such as the char- acteristic time scale models by Magnussen et al. [65], the flamelet approach by Peters et al. [76] or the Conditional Moment Closure CMC model by Bilger et al. [12] exist. Details about the advantages and disadvantages of each of these models, as well as a general survey on multidimensional com- bustion modeling are given by [92]. • EMISSIONS As the thermal nitric oxide formation based on the Zeldovich mechanism is included in most commercially available engine simulation codes, the main emphasis in nitrogen oxide emission studies is on prompt NO, NO 2 and N 2 O formation, and catalytic removal processes e.g. Miller [68]. There is still only a limited understanding of the fundamental governing physical and chemical processes to be considered for the modeling of engine out soot emissions [55]. Although it is derived for laminar premixed flames, the model by Frenklach and Wang [31], using detailed kinetics for acetylene pyrolysis and the growth of polycyclic aromatic hydrocarbons PAHs, is being studied for engine applications [58]. 10

2.2 Artificial Neural Networks

Inspired by biological nervous systems - such as the human brain, where informa- tion is transmitted and stored in groups of interconnected neurons 1 - Artificial Neural Networks ANNs employ clusters of small and simple information process- ing units a.k.a. artificial neurons to mimic the natural learning process and thereby acquire knowledge. Similar to the human brain, ANNs operate like “black box” models, as they do not require detailed information about the basic system being observed. ANNs “learn” the relationship between input and output parameters by “studying” given data, and “store” the knowledge in the interconnections, or rather the associated weights akin to the synapses efficacy in biological neural systems. Basic Structures Definitions In a simplified model of an artificial neuron, the given inputs are weighted, added up and passed through an activation function e.g. a threshold, linear or sigmoid 2 func- tion to produce an output signal, as shown in Figure 2.2. Combining several artifi- cial neurons in a network architecture, similar neurons are generally arranged in layers that are labeled as input, hidden and output layers a.k.a. multi-layer network architecture. During the training mode of an ANN, an appropriate learning algo- rithm e.g. backpropagation 3 is used to modify the interconnection weights such that, given selected inputs, the network attempts to produce the desired outputs. Fig. 2.2 Model of an Artificial Neuron With Interconnections 1. Neuron - primary cell of the nervous system, consisting of a cell body, the axon single long activa- tion fiber out of the cell body and multiple dentdrites receptive nerve fibers 2. Sigmoid - curved in two directions, viz. shaped like the letter S c.f. Figure 2.2 3. Backpropagation - abbreviation for “backwards propagation of errors” x 1 x 2 x n x j w i1 w i2 w ij w in Σ ... ... Act ivat ion Funct ion α i y i = α i Σ x j · w ij y i INPUTS Weight s Summat ion OUTPUT x 1 x 2 x n x j w i1 w i2 w ij w in Σ ... ... Act ivat ion Funct ion α i y i = α i Σ x j · w ij y i INPUTS Weight s Summat ion OUTPUT 11 Types of Artificial Neural Networks