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• PROPORTIONAL PROBABILISTIC SELECTION METHOD
Because of the high selective pressure
1
associated with it, the probabilistic selection of individuals according to their fitness value runs the risk of pre-
mature convergence of a population. That is, the “best” individuals become dominant and hence start to inbreed
2
. •
CROSSOVER RECOMBINATION Crossover recombination randomly swaps single values bits or segments of
the parameter vectors of two dissimilar individuals, aiming to combine the best features from both individuals and thus creating a better offspring.
Although most GAs use mutation along with crossover recombination, almost exclusively crossover recombination is used to assure the diversity
and broadening of the population.
Evolution Strategies ESs
Using normally distributed mutations to modify the real-valued parameter vectors, the emphasis in ESs is equally placed on mutation and recombination as search
operators. Moreover, the simultaneous adjustment extended optimization of the strategy parameters and the parameter vector itself further distinguishes the ESs
from other GAs.
Unlike in GAs, the selection operators in ESs are deterministic and the parent and offspring population sizes usually differ from each other. That is, the number of par-
ents is less or equal the number of offspring and thus the worst performing individ- uals i.e. the ones with the lowest measure of quality of an offspring generally don’t
procreate.
Evolutionary Programming EP
Similar to ESs, the EP algorithms use normally distributed mutations and extend the evolutionary process to the strategy parameters as well. Emphasizing mutation while
neglecting the recombination of individuals, EP algorithms drop the implicit assumption that the fitness value is linked to parts of the parameter vector, as is usu-
ally assumed for GAs and ESs.
Further studies on applications, advantages and disadvantages of the various opti- mization algorithms used in EP are given in [6][30][89], whereas [35][50][60][81] pro-
vide the fundamentals for the various approaches.
1.
Selective Pressure
- probability of the best individual being selected compared to the average prob- ability of selection of all individuals
2.
Inbreeding
- mating of nearly identical individuals, reduces the diversity of the population and hence increases the risk of premature convergence.
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3 A
PPROACHES AND
E
QUIPMENT
After briefly defining the system and introducing the objectives of the study, detailed information on both the “modelknowledge based” and “black-box” approaches
are given in the first part of this chapter. The second part subsequently documents the equipment used, i.e. both computer soft-hardware and the three distinct IC
engines and utilized measurement techniques.
3.1 System Objectives
The combustion of a Common-Rail DI diesel engine, as characterized by the rate of heat release and the nitrogen oxide and soot emissions, serves as a measure for the
subsequently described comparative investigation. Given the general engine and operating condition specifications as inputs, the actual ROHR and specific NO
x
and soot emissions are defined as outputs.
The objectives of the study are the fast and reliable prediction of the system out- puts for three distinct types of engines, more specifically an automotive, a heavy-
duty and a two-stroke marine diesel engine. Additionally, the investigation includes the comparison of two dissimilar approaches for modeling; the “model or knowl-
edge based” and “black-box” approaches. As there are at least two optimization sequences necessary to get from initiation to an optimized simulated engine operat-
ing map, a concept for the interaction of modeling and optimization is derived.
3.2 “ModelKnowledge Based” Approach
The model or knowledge based approach in this context refers to a physical and chemical description of the underlying system, derived from both fundamental
theory and phenomenological experience. As stated in the objectives, the description of the system i.e. the basic models should allow for fast and reliable predictions of
the system outputs. In other words: the models used in this approach need to be as complex as necessary and as simple as possible at the same time. Hence, given the
restrictions and requirements, only phenomenological models c.f. Section 2.1.2, p. 7 are used in this study.
Physical and chemical models - phenomenological ones in particular - inherently need to be calibrated to fit the actual system. The model or knowledge based
approach hence consists of two optimization parts, the model calibration a.k.a. model optimization and the system or process optimization. The quality of the
18
model calibration thereby significantly affects the outcome of the subsequent search for the system optimum.
3.2.1 “ModelingOptimization” Scheme
Based on experience from joint experimental and numerical combustion engine RD projects, such as [59] and [83], a fundamental modeling and optimization
scheme is derived to profit from the mutual advantages of both subjects. Along with the distinction
between modeling and optimization, the strict subdivision of exper- imental data into calibration and verification parts
thereby assures the formal cor- rectness of the approach. Although the objectives of the two optimization parts in
the scheme, the “model calibration” and the “system optimization”, differ, the opti- mization algorithms do not need to be dissimilar.
Fig. 3.1 ModelingOptimization Scheme
Starting from available experimental knowledge of the system, there is an itera- tive process of modeling, calibration and verification to derive an appropriate model
of the system. Given an appropriate model, the iteration between the numerical opti- mization and the experimental validation allows for both the optimization of the
system outcome and a profound understanding of the application Figures 3.1.
3.2.2 Application Examples
As the proposed modelingoptimization scheme by itself is not restricted to diesel engine combustion systems only, it has successfully been applied to other applica-
tions using the same procedures, e.g. evolutionary algorithms as optimization method.
EXPERIMENTS SIMULATIONS
M O
D E
L IN
G
O P
T IM
IZ A
T IO
N
Knowledge Model
Validation Calibration
Verification Opt imization
EXPERIMENTS SIMULATIONS
M O
D E
L IN
G
O P
T IM
IZ A
T IO
N
Knowledge Model
Validation Calibration
Verification Opt imization
