“Artificial Neural Network” Scheme

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3.4 Computational Setup

As the objectives for the present study include a comparative investigation of two approaches for modeling, identical experimental Section 3.5 and computational setups Section 3.4 are used. Table 3.1 lists the main characteristics of the computa- tional setup while details on the selected software packages are provided in Section 3.4.1 et sqq.

3.4.1 Thermodynamic Analysis Simulation

The in-house thermodynamic software package WEG is used to analyze experimen- tal pressure data and predict combustion characteristics using various models simul- taneously [72]. In addition to the classic one- and two-zone approaches for thermodynamic anal- yses, WEG also allows for an arbitrary number of so-called virtual combustion zones. Directly coupled to a characteristic constant or variable airfuel-ratio, the vir- tual combustion zones are intended to reproduce particular combustion phenom- ena, such as the oxygen deficiency at high engine loads or local emission formation. Given experimental pressure data and engineoperating condition specifications 1 , WEG calculates the apparent burn rate, overall engine heat transfer, rate of heat release and gas temperatures. In order to predict the diesel combustion characteristics and exhaust emissions i.e. the thermodynamic simulation, WEG contains three phenomenological mod- els: a rate of heat release Chapter 4, a nitrogen oxide emission Chapter 5 and a soot emission model Chapter 6. Employing the above described modelingoptimi- zation scheme, the external dynamic data exchange 2 interface furthermore allows the WEG thermodynamic simulation models to be used as server applications in the programming language MATLAB. Thus, all optimization algorithms and ANNs used in the present study are programmed in MATLAB. OPERATING SYSTEM Windows XP ® SP2 CPU MEMORY Intel Pentium ® P4, 3 GHz, 1 GB RAM SOFTWARE PACKAGES MATLAB ® R14 SP2, WEG R10, GT-Suite™ 6.1 Tab. 3.1 Computational Setup 1. Engine Specifications - e.g. bore, stroke, compression ratio, inletexhaust valve diameter, etc. Operating Condition Specifications - e.g. engine speed, load, SOI, rate of fuel injected, etc. 2. Dynamic Data Exchange DDE - standard communication command interface between multi- ple applications e.g. MATLAB and WEG in Windows operating systems 22

3.4.2 Artificial Neural Networks

Featuring a modular network representation for commonly used network architec- tures and a comprehensive set of training functions, the MATLAB Neural Network Toolbox 4.0.5 [66] is used to design and simulate the ANNs in this study. Based on the universal approximation theorem by Hornik et al. [51] and following the successful applications in IC engine combustion modeling e.g. [26][41], a multi- layer feed forward network architecture is chosen. Three different networks are designed to approximate the ROHR combustion characteristics and the specific nitrogen oxide and soot exhaust emissions as a function of seven key operating con- dition parameters. An outline of the configuration of the ANN, as well as the param- eters used is provided in Table 3.2 .

3.4.3 Optimization Algorithms

Given an engineering problem, the definition of an appropriate fitness or objective function, as well as the physical or technical constraints of the system parameter val- ues, are crucial to all optimization algorithms. Constraints Parameters in engineering systems, for example the valve timing, laminar flame speed or global AF-ratio in an IC engine, are subject to physical or technical con- straints. As the present study deals with phenomenological models based on physical and chemical parameters e.g. pressure values, temperatures, velocities, etc., the chosen optimization algorithms need to account for equality and inequality parame- ter constraints. Given these constraints, the variable size of the search dimensions asymmetric search space generally has an impact on the search strategy and accord- ingly the efficiency of the optimization algorithms. Details on the different model parameters and their corresponding size ranges are given in Chapter 4 et sqq. ARCHITECTURE Multi-layer feed forward network TRAINING Levenberg-Marquardt algorithm with back-propagation INITIALIZATION Nguyen-Widrow method ACTIVATION FUNCTION Sigmoid hidden neurons linear output neurons INPUTS c m , BMEP, p Inj , Δ t Inj , ϕ SOI , x EGR , λ global OUTPUTS ROHR Characteristics: ϕ SOC , ϕ 10 , ϕ 50 , ϕ 90 , Q max , ... NO x and soot emissions Tab. 3.2 Artificial Neural Network ANN Characteristics