Sigmoid curves have found broad applicability in biological sciences and biopharmaceutical research during the last decades. A well planned experiment design is essential to accurately estimate the parameters of the model. In contrast to a large literature and extensive results on optimal designs for linear models, research on the design for nonlinear, including sigmoid curve, models has not kept pace. Furthermore, most of the work in the optimal design literature for nonlinear models concerns the characterization of minimally supported designs. These minimal, optimal designs are frequently criticized for their inability to check goodness of fit, as there are no additional degrees of freedom for the testing. This design issue can be a serious problem, since checking the model adequacy is of particular importance when the model is selected without complete certainty. To assess for lack of fit, we must add at least one extra distinct design point to the experiment. The goal of this dissertation is to identify optimal or highly efficient designs capable of checking the fit for sigmoid curve models. In this dissertation, we consider some commonly used sigmoid curves, including logistic, probit and Gompertz models with two, three, or four parameters. We use D-optimality as our design criterion. We first consider adding one extra point to the design, and consider five alternative designs and discuss their suitability to test for lack of fit. Then we extend the results to include one more additional point to better understand the compromise among the need of detecting lack of fit, maintaining high efficiency and the practical convenience for the practitioners. We then focus on the two-parameter Gompertz model, which is widely used in fitting growth curves yet less studied in literature, and explore three-point designs for testing lack of fit under various error variance structures. One reason that nonlinear design problems are so challenging is that, with nonlinear models, information matrices and optimal designs depend on the unknown model parameters. We propose a strategy to bypass the obstacle of parameter dependence for the theoretical derivation. This dissertation also successfully characterizes many commonly studied sigmoid curves in a generalized way by imposing unified parameterization conditions, which can be generalized and applied in the studies of other sigmoid curves. We also discuss Gompertz model with different error structures in finding an extra point for testing lack of fit. / Statistics

Discrete choice experiments are used when choice alternatives can be described in terms of attributes. The objective is to infer the value that respondents attach to attribute levels. Respondents are presented sets of profiles based on attributes specified at certain levels and asked to select the profile they consider best. When the number of attributes or attribute levels becomes large, the profiles in a single choice set may be too numerous for respondents to make precise decisions. One strategy for reducing the size of choice sets is the sub-setting of attributes. However, the optimality of these reduced size choice sets has not been examined in the literature. We examine the optimality of reduced size choice sets for 2^n experiments using information per profile (IPP) as the optimality criteria. We propose a new approach for calculating the IPP of designs obtained by dividing attributes into two or more subsets with one, two, and in general, r overlapping attributes, and compare the IPP of the reduced size designs with the original full designs. Next we examine the IPP of choice designs based on 3^n factorial experiments. We calculate the IPP of reduced size designs obtained by sub-setting attributes in 3^n plans and compare them to the original full designs. / Statistics

Choice-based conjoint experiments are used when choice alternatives can be described in terms of attributes. The objective is to infer the value that respondents attach to attribute levels. This method involves the design of profiles on the basis of attributes specified at certain levels. Respondents are presented sets of profiles called choice sets, and asked to select the one they consider best. Sets with no dominating or dominated profiles are called Pareto Optimal sets. Information Per Profile (IPP) is used as an optimality criteria to compare designs with different numbers of profiles. For a 2^n experiment, the optimality of connected main effects plans based on two consecutive choice sets, Sl and Sl+1, has been examined in the literature. In this thesis we examine the IPP of both consecutive and non-consecutive choice sets and show that IPP can be maximized under certain conditions. We show that non-consecutive choice sets have higher IPP than consecutive choice sets for n ≥ 4. We also examine the optimality of connected first-order-interaction designs based on three choice sets and show that non-consecutive choice sets have higher IPP than consecutive choice sets under certain conditions. Further, we examine the D-, A- and E-optimality of consecutive and non-consecutive PO choice sets with maximum IPP. Finally, we consider 3^n choice experiments. We look for the optimal PO choice sets and examine their IPP, D-, A- and E-optimality, as well as comparing consecutive and non-consecutive choice sets. / Statistics

Energy demand for buildings has been rising during recent years. Increasing building energy consumption has caused many energy-related problems and environmental issues. The on-site community energy system application is a promising way of providing energy for buildings. Community energy system usage reduces the primary energy consumption and environmental effects of greenhouse gas (GHG) emissions compared to the implementation of the stand-alone energy systems. Furthermore, due to the increase in electricity price and shortage of fossil fuel resources, renewable energies and energy storage technologies could be great alternative solutions to solve energy-related problems. Generally, the energy system might include various technologies such as internal combustion engine, heat recovery system, boiler, thermal storage tank, battery, absorption chiller, ground source heat pump, heating coil, electric chiller, solar photovoltaics (PV) and solar thermal collectors, and seasonal thermal energy storage. The economic, technical and environmental impacts of energy systems depend on the system design and operational strategy. The focus of this thesis is to propose unified frameworks, including the mathematical formulation of all of the components to determine the optimal energy system configuration, the optimal size of each component, and optimal operating strategy. The proposed methodologies address the problems related to the optimal design of the energy system for both deterministic and stochastic cases. By the use of the proposed frameworks, the design of the energy system is investigated for different specified levels of GHG emissions ratio, and the purpose is to minimize the annual total cost. To account for uncertainties and to reduce the computational times and maintain accuracy, a novel strategy is developed to produce scenarios for the stochastic problem. System design is carried out to minimize the annual total cost and conditional value at risk (CVaR) of emissions for the confidence level of 95%. The results demonstrate how the system size changes due to uncertainty and as a function of the operational GHG emissions ratio. It is shown that with the present-day technology (without solar technologies and seasonal storage), the lowest amount of GHG emissions ratio is 37%. This indicates the need for significant technological development to overcome that ratio to be 10% of stand-alone systems. This thesis introduces novel performance curves (NPC) for determining the optimal operation of the energy system. By the use of this approach, it is possible to identify the optimal operation of the energy system without solving complex optimization procedures. The application of the proposed NPC strategy is investigated for various case studies in different locations. The usage of the proposed strategy leads to the best-operating cost-saving and operational GHG savings when compared to other published approaches. It has shown that other strategies are special (not always optimal) cases of the NPC strategy. Based on the extensive literature review, it is found that it is exceptionally complicated to apply the previously proposed models of seasonal thermal energy storage in optimization software. Besides, the high computational time is required to obtain an optimum size and operation of storage from an optimization software. This thesis also proposes a new flexible semi-analytical, semi-numerical methodology to model the heat transfer process of the borehole thermal energy storage to solve the above challenges. The model increases the flexibility of the storage operation since the model can control the process of the storage by also deciding the appropriate storage zone for charging and discharging. / Thesis / Doctor of Engineering (DEng)

Yes / In the wake of the COVID-19 pandemic, social distancing has become an essential element of our daily lives. As a result, the development of technological solutions for the design and re-design of physical spaces with the necessary physical distancing measures is an important problem that must be addressed. In this paper, we show how automatic design optimisation can be used to simulate the layout of physical spaces subject to a given social distancing requirement. We use a well known mathematical technique based on the circle packing to address this challenge. Thus, given the dimensions and the necessary constraints on the physical space, we formulate the design as a solution to a constrained nonlinear optimisation problem. We then solve the optimisation problem to arrive at a number of feasible design solutions from which the user can pick the most desirable option. By way of examples, in this paper, we show how the proposed model can be practically applied. / University of Bradford’s COVID-19 Response Fund, the Spanish Ministry of Science, Innovation, and Universities (Computer Science National Program) under grant #TIN2017-89275-R of the Agencia Estatal de Investigacion and European Funds (AEI/FEDER, UE)

Moore's Law has been used to describe and predict the blossom of IC industries, so increasing the data density is clearly the ultimate goal of all technological development. If the power density of power electronics converters can be analogized to the data density of IC's, then power density is a critical indicator and inherent driving force to the development of power electronics. Increasing the power density while reducing or keeping the cost would allow power electronics to be used in more applications. One of the design challenges of the high-density power converter design is to have high-density magnetic components which are usually the most bulky parts in a converter. Increasing the switching frequency to shrink the passive component size is the biggest contribution towards increasing power density. However, two factors, losses and parasitics, loom and compromise the effect. Losses of high-frequency magnetic components are complicated due to the eddy current effect in magnetic cores and copper windings. Parasitics of magnetic components, including leakage inductances and winding capacitances, can significantly change converter behavior. Therefore, modeling loss and parasitic mechanism and control them for certain design are major challenges and need to be explored extensively. In this dissertation, the abovementioned issues of high-frequency transformers are explored, particularly in regards to high-power converter applications. Loss calculations accommodating resonant operating waveform and Litz wire windings are explored. Leakage inductance modeling for large-number-of-stand Litz wire windings is proposed. The optimal design procedure based on the models is developed. / Ph. D.

Experimental design is a powerful tool for gathering highly informative observations using a small number of experiments. The demand for smart data collection strategies is increasing due to the need to save time and budget, especially in online experiments and machine learning. However, the traditional experimental design method falls short in systematically assessing changing variables' effects. Specifically within Artificial Intelligence (AI), the challenge lies in assessing the impacts of model structures and training strategies on task performances with a limited number of trials. This shortfall underscores the necessity for the development of novel approaches. On the other side, the optimal design criterion has typically been model-based in classic design literature, which leads to restricting the flexibility of experimental design strategies. However, machine learning's inherent flexibility can empower the estimation of metrics efficiently using nonparametric and optimization techniques, thereby broadening the horizons of experimental design possibilities. In this dissertation, the aim is to develop a set of novel methods to bridge the merits between these two domains: 1) applying ideas from statistical experimental design to enhance data efficiency in machine learning, and 2) leveraging powerful deep neural networks to optimize experimental design strategies. This dissertation consists of 5 chapters. Chapter 1 provides a general introduction to mutual information, fractional factorial design, hyper-parameter tuning, multi-modality, etc. In Chapter 2, I propose a new mutual information estimator FLO by integrating techniques from variational inference (VAE), contrastive learning, and convex optimization. I apply FLO to broad data science applications, such as efficient data collection, transfer learning, fair learning, etc. Chapter 3 introduces a new design strategy called multi-layer sliced design (MLSD) with the application of AI assurance. It focuses on exploring the effects of hyper-parameters under different models and optimization strategies. Chapter 4 investigates classic vision challenges via multimodal large language models by implicitly optimizing mutual information and thoroughly exploring training strategies. Chapter 5 concludes this proposal and discusses several future research topics. / Doctor of Philosophy / In the digital age, artificial intelligence (AI) is reshaping our interactions with technology through advanced machine learning models. These models are complex, often opaque mechanisms that present challenges in understanding their inner workings. This complexity necessitates numerous experiments with different settings to optimize performance, which can be costly. Consequently, it is crucial to strategically evaluate the effects of various strategies on task performance using a limited number of trials. The Design of Experiments (DoE) offers invaluable techniques for investigating and understanding these complex systems efficiently. Moreover, integrating machine learning models can further enhance the DoE. Traditionally, experimental designs pre-specify a model and focus on finding the best strategies for experimentation. This assumption can restrict the adaptability and applicability of experimental designs. However, the inherent flexibility of machine learning models can enhance the capabilities of DoE, unlocking new possibilities for efficiently optimizing experimental strategies through an information-centric approach. Moreover, the information-based method can also be beneficial in other AI applications, including self-supervised learning, fair learning, transfer learning, etc. The research presented in this dissertation aims to bridge machine learning and experimental design, offering new insights and methodologies that benefit both AI techniques and DoE.

Hydrogen fuel cells are devices used to generate electricity from the electrochemical reaction between air and hydrogen gas. An attractive advantage of these devices is that their byproduct is water, which is very safe to the environment. However, hydrogen fuel cells still lack some improvements in terms of increasing their life time and electricity production, decreasing power losses, and optimizing their operating conditions. In this thesis, the cathode part of the hydrogen fuel cell will be considered. This part mainly consists of an air gas channel and a gas diffusion layer. To simulate the fluid dynamics taking place in the cathode, we present two models, a general model and a simple model both based on a set of conservation laws governing the fluid dynamics and chemical reactions. A numerical method to solve these models is presented and verified in terms of accuracy. We also show that both models give similar results and validate the simple model by recovering a polarization curve obtained experimentally. Next, a shape optimization problem is introduced to find an optimal design of the air gas channel. This problem is defined from the simple model and a cost functional, $E$, that measures efficiency factors. The objective of this functional is to maximize the electricity production, uniformize the reaction rate in the catalytic layer and minimize the pressure drop in the gas channel. The impact of the gas channel shape optimization is investigated with a series of test cases in long and short fuel cell geometries. In most instances, the optimal design improves efficiency in on- and off-design operating conditions by shifting the polarization curve vertically and to the right. The second primary goal of the thesis is to analyze mathematical issues related to the introduced shape optimization problem. This involves existence and uniqueness of the solution for the presented model and differentiability of the state variables with respect to the domain of the air channel. The optimization problem is solved using the gradient method, and hence the gradient of $E$ must be found. The gradient of $E$ is obtained by introducing an adjoint system of equations, which is coupled with the state problem, namely the simple model of the fuel cell. The existence and uniqueness of the solution for the adjoint system is shown, and the shape differentiability of the cost functional $E$ is proved.

Hydrogen fuel cells are devices used to generate electricity from the electrochemical reaction between air and hydrogen gas. An attractive advantage of these devices is that their byproduct is water, which is very safe to the environment. However, hydrogen fuel cells still lack some improvements in terms of increasing their life time and electricity production, decreasing power losses, and optimizing their operating conditions. In this thesis, the cathode part of the hydrogen fuel cell will be considered. This part mainly consists of an air gas channel and a gas diffusion layer. To simulate the fluid dynamics taking place in the cathode, we present two models, a general model and a simple model both based on a set of conservation laws governing the fluid dynamics and chemical reactions. A numerical method to solve these models is presented and verified in terms of accuracy. We also show that both models give similar results and validate the simple model by recovering a polarization curve obtained experimentally. Next, a shape optimization problem is introduced to find an optimal design of the air gas channel. This problem is defined from the simple model and a cost functional, $E$, that measures efficiency factors. The objective of this functional is to maximize the electricity production, uniformize the reaction rate in the catalytic layer and minimize the pressure drop in the gas channel. The impact of the gas channel shape optimization is investigated with a series of test cases in long and short fuel cell geometries. In most instances, the optimal design improves efficiency in on- and off-design operating conditions by shifting the polarization curve vertically and to the right. The second primary goal of the thesis is to analyze mathematical issues related to the introduced shape optimization problem. This involves existence and uniqueness of the solution for the presented model and differentiability of the state variables with respect to the domain of the air channel. The optimization problem is solved using the gradient method, and hence the gradient of $E$ must be found. The gradient of $E$ is obtained by introducing an adjoint system of equations, which is coupled with the state problem, namely the simple model of the fuel cell. The existence and uniqueness of the solution for the adjoint system is shown, and the shape differentiability of the cost functional $E$ is proved.

Hydrogen fuel cells are devices used to generate electricity from the electrochemical reaction between air and hydrogen gas. An attractive advantage of these devices is that their byproduct is water, which is very safe to the environment. However, hydrogen fuel cells still lack some improvements in terms of increasing their life time and electricity production, decreasing power losses, and optimizing their operating conditions. In this thesis, the cathode part of the hydrogen fuel cell will be considered. This part mainly consists of an air gas channel and a gas diffusion layer. To simulate the fluid dynamics taking place in the cathode, we present two models, a general model and a simple model both based on a set of conservation laws governing the fluid dynamics and chemical reactions. A numerical method to solve these models is presented and verified in terms of accuracy. We also show that both models give similar results and validate the simple model by recovering a polarization curve obtained experimentally. Next, a shape optimization problem is introduced to find an optimal design of the air gas channel. This problem is defined from the simple model and a cost functional, $E$, that measures efficiency factors. The objective of this functional is to maximize the electricity production, uniformize the reaction rate in the catalytic layer and minimize the pressure drop in the gas channel. The impact of the gas channel shape optimization is investigated with a series of test cases in long and short fuel cell geometries. In most instances, the optimal design improves efficiency in on- and off-design operating conditions by shifting the polarization curve vertically and to the right. The second primary goal of the thesis is to analyze mathematical issues related to the introduced shape optimization problem. This involves existence and uniqueness of the solution for the presented model and differentiability of the state variables with respect to the domain of the air channel. The optimization problem is solved using the gradient method, and hence the gradient of $E$ must be found. The gradient of $E$ is obtained by introducing an adjoint system of equations, which is coupled with the state problem, namely the simple model of the fuel cell. The existence and uniqueness of the solution for the adjoint system is shown, and the shape differentiability of the cost functional $E$ is proved.