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This thesis summarizes the author’s developments of combustion models and multi-objective optimization methods for gasoline and diesel engines. The combustion models belong to the family of zero-dimensional stochastic reactor models introduced in the 1990s to improve the prediction of emissions with detailed chemistry in partially stirred reactors.
The first part introduces the fundamentals of the physical and chemical models describing the combustion process. As a novelty, k−ε turbulence models were implemented in the stochastic reactor model to predict the turbulent time and length scales in gasoline and diesel engines. This development allowed an improvement of the models for convective heat transfer, fuel evaporation, gas exchange across the valves, turbulent flame propagation and crevice flow, which depend on the turbulent time and length scales.
In the second part, the multi-objective optimization platform for automatic training of the stochastic reactor model is presented. The optimization method considers multiple operating points to find a set of model parameters that predict performance and emissions over the entire engine map. The Non-domination Sorting Genetic Algorithm II is combined with the stochastic reactor model and response surface models to find the best Pareto front. Multi-criteria decision making is used to select the best designs from the Pareto front.
Finally, the third part of this thesis deals with the validation of the stochastic reactor model and the multi-objective optimization platform. For this purpose, experiments of two single-cylinder research engines with spark ignition, one passenger car engine with compression ignition and one heavy duty engine with compression ignition are used. For the spark ignition engines, a set of model parameters was found that predicts well the power and emissions over the whole engine map. The calculated turbulent kinetic energy, dissipation, and angular momentum follow the trends of the three-dimensional computational fluid dynamic simulations to a good approximation for various operating points. For the two compression ignition engines, the prediction of combustion progress and nitrogen oxide emissions are in good agreement with the experiments. Larger discrepancies were found for the prediction of carbon monoxide and unburned hydrocarbon. Optimization of the soot model parameters improves the prediction of soot mass for operating points throughout the engine map.
Water injection is investigated for turbocharged spark-ignition engines to reduce knock probability and enable higher engine efficiency. The novel approach of this work is the development of a simulation-based optimization process combining the advantages of detailed chemistry, the stochastic reactor model and genetic optimization to assess water injection. The fast running quasi-dimensional stochastic reactor model with tabulated chemistry accounts for water effects on laminar flame speed and combustion chemistry. The stochastic reactor model is coupled with the Non-dominated Sorting Genetic Algorithm to find an optimum set of operating conditions for high engine efficiency. Subsequently, the feasibility of the simulation-based optimization process is tested for a three-dimensional computational fluid dynamic numerical test case. The newly proposed optimization method predicts a trade-off between fuel efficiency and low knock probability, which highlights the present target conflict for spark-ignition engine development. Overall, the optimization shows that water injection is beneficial to decrease fuel consumption and knock probability at the same time. The application of the fast running quasi-dimensional stochastic reactor model allows to run large optimization problems with low computational costs. The incorporation with the Non-dominated Sorting Genetic Algorithm shows a well-performing multi-objective optimization and an optimized set of engine operating parameters with water injection and high compression ratio is found.
This dissertation is a compilation of four self-contained research articles that focus on selected subjects in the field of energy economics.
The first article focuses on the competitiveness of offshore wind in mature markets. In this work, we harmonise auction results based on the auction design features. We show that offshore wind power generation can be considered commercially competitive in mature markets without subsidy. Furthermore, once auction results are harmonised, we observe similar expected revenue streams of wind farms across countries. This finding means that different auction designs can fairly reflect the actual costs of developing wind farms and thus translate cost reductions into lower bids.
The second article explores the impacts of uncertainty in integrated electricity and gas system optimization models. We address the trade-off that the energy research community faces on a daily basis, i.e., whether to neglect uncertainty when constructing an energy system model and accept a suboptimal solution or to incorporate uncertainty and increase model complexity. Our research aims to bring a systematic understanding of which parametric uncertainties most substantially affect long-term planning decisions in energy system models.
In the third article, we focus on seasonal flexibility in the European natural gas market. We develop a market optimization model to simulate the operation of the gas market over a long period. This allows us to explore structural trends in market development, which are driven by changing supply and demand fundamentals. Our work contributes to the methodological question of how to measure the contributions of different flexibility options.
Finally, the fourth article investigates the value of Projects of Common Interest—gas infrastructure projects supported by EU public funds—in maintaining gas system resilience amid cold-winter demand spikes and supply shortages. For this purpose, we develop the first application of adaptive robust optimization to gas infrastructure expansion planning. The model endogenously identifies the unfortunate realizations of unknown parameters and suggests the optimal investments strategies to address them. We find that (i) robust solutions point to consistent preferences for specific infrastructure projects, (ii) the real-world construction efforts have been focused on the most promising projects, and (iii) most projects are unlikely to be realized without financial support.
Motivated by computing functionals of high-dimensional, potentially metastable diffusion processes, this thesis studies robustness issues appearing in the numerical approximation of expectation values and their gradients. A major challenge being high variances of corresponding estimators, we investigate importance sampling of stochastic processes for improving statistical properties and provide novel nonasymptotic bounds on the relative error of corresponding estimators depending on deviations from optimality. Numerical strategies that aim to come close to those optimal sampling strategies can be encompassed in the framework of path space measures, and minimizing suitable divergences between those measures suggests a variational formulation that can be addressed in the spirit of machine learning. A key observation is that while several natural choices of divergences have the same unique minimizer, their finite sample properties differ vastly. We provide the novel log-variance divergence, which turns out to have favorable robustness properties that we investigate theoretically and apply in the context of path space measures as well as in the context of densities, for instance offering promising applications in Bayesian variational inference.
Aiming for optimal importance sampling of diffusions is (more or less) equivalent to solving Hamilton-Jacobi- Bellman PDEs and it turns out that our numerical methods can be equally applied for the approximation of rather general high-dimensional semi-linear PDEs. Motivated by stochastic representations of elliptic and parabolic boundary value problems we refine variational methods based on backward SDEs and provide the novel diffusion loss, which can be related to other state-of-the-art attempts, while offering certain numerical advantages.
Stochastic modelling of biochemical reaction networks is getting more and more popular. Throughout the past decades typical biological models increased in their size and complexity, because of advances in systems and molecular biology, in particular through the high-throughput omic technologies. Here biochemical networks of different levels of detail are modelled, starting with simple chemical reactions and signal transduction networks, up to individual cells and entire organisms. This increases the demand for efficient analysis methods.
A Petri net is a mathematical modelling language for the description of concurrent behaviour of distributed systems. Its advantage is the ease of scalability of the models, which relates to the network’s state space, as well as the structure of the network itself.
In this work, we recall several stochastic simulation algorithms, e.g., exact as well as approximate methods. Furthermore, we introduce an approach to improve the efficiency of stochastic simulation for large and dense networks by a new approximate stochastic simulation algorithm called discrete-time leap method. We depict the wide range of simulative analyses of complex stochastic systems ranging from trace generation to the computation of transient solutions and steady state distributions. We set forth advanced analysis of stochastic models by means of simulative model checking. For the use of simulative model checking, we integrate the continuous stochastic (reward) logic (CS(R)L) and the probabilistic linear-time temporal logic with constraints (PLTLc). Simulative model checking has some limitations compared to the numerical methods, e.g., in principle it is possible to consider nested probabilistic formulas in CS(R)L, but not practical, since the calculation is not feasible in a reasonable period of time. In addition to the transient analysis, the steady state analysis is often of interest; therefore we have implemented two on-the-fly steady state detection methods. The first one is based on a “sample batch means” algorithm and is used in the linear-time temporal logic. The second approximates the steady state distribution and checks for convergence. We apply the aforementioned techniques to several case studies from systems biology and technical systems.
The main contributions of this thesis to scientific knowledge are the development of the discrete-time leap method for the simulation of stochastic models, the approximations of transient solutions and steady state distributions by use of stochastic simulation for stochastic models and Markov reward models, the development of an infinite time horizon model checking algorithm exploiting the steady state property for PLTLc and CSL, and the first simulative model checking algorithm for CSRL incorporating state and impulse rewards. All presented algorithms and methods are implemented in the advanced analysis tool MARCIE.
The work described in this report can be broadly divided into two sections. The first section considers two export features. We describe how the export for stochastic Petri nets to SBML level 1 has been added to the Petri net modelling and simulation tool Snoopy. This task was accomplished by making appropriate changes to the existing export code to generate SBML level 2. Also we demonstrate in detail, how the direct export for coloured Petri nets to both levels (i.e. 1 and 2) of SBML was realised. The next section summarises the performed comparison of different stochastic simulation tools for biochemical reaction networks. We first compare BioNetGen and SSC with each other by performing simulations on non-coloured Petri nets. Then, we compare the remaining four tools, i.e. Cain, Marcie, Snoopy and Stochkit with each other by performing simulation on coloured Petri nets.
This work builds on results by Aman Sinha [19].
This report compares some stochastic simulation tools for biochemical reaction networks. The stochastic simulation tools are selected on the basis of some selection criteria. Simulations are performed for the different stochastic simulation tools on different benchmark models. This report gives an overview of how the comparison is carried out for the chosen tools.
The tools are compared on a common evaluation protocol. The evaluation protocol comprises a set of benchmark models along with the parameters which are provided as input to the tools. The benchmark models are represented as Petri nets and fed in SBML (System Biology Markup Language) to the different tools. Experiments are performed on each tool and the results are recorded. The tools are finally compared based on the comparison criteria.