Showing papers on "Optimal design published in 2010"

Adaptive design optimization: A mutual information-based approach to model discrimination in cognitive science

Abstract: Discriminating among competing statistical models is a pressing issue for many experimentalists in the field of cognitive science. Resolving this issue begins with designing maximally informative experiments. To this end, the problem to be solved in adaptive design optimization is identifying experimental designs under which one can infer the underlying model in the fewest possible steps. When the models under consideration are nonlinear, as is often the case in cognitive science, this problem can be impossible to solve analytically without simplifying assumptions. However, as we show in this letter, a full solution can be found numerically with the help of a Bayesian computational trick derived from the statistics literature, which recasts the problem as a probability density simulation in which the optimal design is the mode of the density. We use a utility function based on mutual information and give three intuitive interpretations of the utility function in terms of Bayesian posterior estimates. As a proof of concept, we offer a simple example application to an experiment on memory retention.

Shape-Preserving Response Prediction for Microwave Design Optimization

Abstract: A shape-preserving response prediction methodology for microwave design optimization is introduced. The presented technique allows us to estimate the response of the microwave structure being optimized (fine model) using a computationally cheap representation of the structure (coarse model). The change of the coarse model response is described by the translation vectors corresponding to certain (finite) number of characteristic points of the response. These translation vectors are subsequently used to predict the response change of the fine model. The presented method has very good generalization capability and it is not based on any extractable parameters, which makes it easy to implement. Applications for microwave design optimization are discussed. The robustness of the proposed approach is demonstrated by extensive comparison with space mapping, which is one of the most efficient optimization approaches in microwave engineering so far.

Choice-Based Conjoint Analysis: Models and Designs

Abstract: Introduction Conjoint Analysis (CA) Discrete Choice Experimentation (DCE) Random Utility Models The Logistic Model Contributions of the Book Some Statistical Concepts Principles of Experimental Design Experimental versus Treatment Design Balanced Incomplete Block Designs and 3-Designs Factorial Experiments Fractional Factorial Experiments Hadamard Matrices and Orthogonal Arrays Foldover Designs Mixture Experiments Estimation Transformations of the Multinomial Distribution Testing Linear Hypotheses Generic Designs Introduction Four Linear Models Used in CA and DCE Brands-Only Designs Attribute-Only Designs Brands-Plus-Attributes Designs Brands, Attributes, and Interaction Design Estimation and Hypothesis Testing Appendix: Logit Analysis of Traditional Conjoint Rating Scale Data Designs with Ordered Attributes Introduction Linear, Quadratic, and Cubic Effects Interaction Components: Linear and Quadratic An Illustration Pareto Optimal Designs Inferences on Main Effects Inferences on Main Effects in 2m Experiments Inferences on Interactions Orthogonal Polynomials Substitution Rate of Attributes Reducing Choice Set Sizes Introduction Subsetting Choice Sets Subsetting Levels into Overlapping Sets Subsetting Attributes into Overlapping Sets Designs Generated from a BIBD Cyclic Construction: s Choice Sets of Size s Each for an ss Experiment Estimating a Subset of Interactions Availability (Cross-Effects) Designs Introduction Brands-Only Availability Designs Portfolio Designs Brand and One (or More) Attributes Brands and More Than One Attribute Sequential Methods Introduction Sequential Experiment to Estimate All Two- and Three-Attribute Interactions Sequential Methods to Estimate Main Effects and Interactions, Including a Common Attribute in 2m Experiments CA Testing Main Effects and a Two-Factor Interaction Sequentially Interim Analysis Some Sequential Plans for 3m Experiments Mixture Designs Introduction Mixture Designs: CA Example Mixture Designs: DCE Example Mixture-Amount Designs Other Mixture Designs Mixture Designs: Field Study Illustration References Index

Generalized Latin hypercube design for computer experiments

Abstract: Space filling designs, which satisfy a uniformity property, are widely used in computer experiments. In the present paper, the performance of nonuniform experimental designs, which locate more points in a neighborhood of the boundary of the design space, is investigated. These designs are obtained by a quantile transformation of the one-dimensional projections of commonly used space-filling designs. This transformation is motivated by logarithmic potential theory, which yields the arc-sine measure as an equilibrium distribution. The methodology is illustrated for maximin Latin hypercube designs by several examples. In particular, it is demonstrated that the new designs yield a smaller integrated mean squared error for prediction.

Multiobjective Shape Design in Electricity and Magnetism

Abstract: Preface. 1 INTRODUCTION. 2 INVERSE PROBLEMS AND ERROR MINIMISATION. 2.1 A Copernican revolution: direct and inverse problems. 2.2 Insidiousness of inverse problems. 2.3 Classification of inverse problems. 2.4 Green formula and Fredholm equation. 2.5 Solving inverse problems by minimising a functional. 2.6 Constrained minimisation. 2.7 Local vs global search. 2.8 Evolutionary computing. 2.9 Solving inverse problems by means of rectangular systems of algebraic equations. 3 A PARETIAN APPROACH TO MOSD THEORY. 3.1 Need of a multiobjective formulation. 3.2 Multiobjective formulation of a design problem. 3.3 Paretian optimality. 4 FIELD MODELS AND SHAPE DESIGN. 4.1 Maxwell equations in differential form. 4.2 Wave, diffusion and steady-state equations in terms of vectors. 4.3 Wave, diffusion and steady-state equations in terms of potentials. 4.4 Boundary and transmission conditions. 4.5 Insidiousness of direct problems. 4.6 Field-based inverse problems. 4.7 More insidious difficulties. 4.8 A unifying view of analysis and synthesis. 5 SOLVING MULTIOBJECTIVE OPTIMISATION PROBLEMS. 5.1 Classical methods of multiobjective optimisation. 5.2 Classical vs Paretian formulation. 5.3 Evolutionary methods of multiobjective optimisation. 5.4 Multi-objective evolution strategy (MOESTRA). 5.5 The gradient-balance method for 2D problems. 6 A FIELD-BASED BENCHMARK. 6.1 A twofold meaning of benchmarking. 6.2 Test problem: shape design of a magnetic pole. 6.3 The test problem simplified. 6.4 Criticism to Pareto optimality in the static case. 7 STATIC MOSD. 7.1 A bibliographic insight. 7.2 FEM-assisted optimal design. 7.3 Test problem: a priori analysis of the objective space. 7.4 Optimisation strategies and results. 7.5 Processing clusters. 7.6 The test problem solved by means of the GB method. 7.7 An industrial case study: permanent-magnet alternator. 8 MOVING ALONG THE PARETO FRONT. 8.1 John optimality. 8.2 Reconsidering the industrial case study. 8.3 Exploring the Pareto front. 8.4 Optimising along the front. 9 SENSITIVITY ANALYSIS AND MOSD. 9.1 Discrete sets and perturbation domains. 9.2 Case study: superconducting magnetic-bearing design. 9.3 Design optimisation of the PM-HTSC interaction. 9.4 An inexpensive evaluation of sensitivity. 9.5 Results. 10 NON-CONFLICTING MULTIPLE OBJECTIVES. 10.1 Case study: a system for magnetic induction tomography. 10.2 Design problem. 10.3 Analysis problem. 10.4 Optimal shape design of the MIT antenna. 11 HIGHER-ORDER DIMENSIONALITY. 11.1 Case study: an electrostatic micromotor. 11.2 Field analysis: doubly-connected domain. 11.3 Field synthesis and rotor shape design. 11.4 Results. 11.5 A criterion for decision making. 12 MULTI-SCALE EVOLUTION STRATEGY. 12.1 Industrial electromagnetic design. 12.2 A multi-scale evolutionary search. 12.3 Permanent-magnet alternator design. 12.4 Results. 13 GAME THEORY AND MOSD. 13.1 From Pareto front to Nash equilibrium. 13.2 Theoretical background. 13.3 Analytical validation. 13.4 Numerical implementation. 13.5 Case study: permanent-magnet motor design. 14 DYNAMIC MOSD. 14.1 From static to dynamic conditions. 14.2 Theoretical background. 14.3 An analytical benchmark. 14.4 Criticism to dynamic Pareto optimality. 14.5 Numerical benchmark. 14.6 Direct problem. 14.7 Design problem. 14.8 Auxiliary inverse problems. 14.9 Main inverse problem: synthesising the device geometry. 14.10 Computational aspects. 14.11 Results I. 14.12 The design problem revisited: recovering steady state from time evolution. 14.13 Results II. 15 AN INTRODUCTION TO BAYESIAN PROBABILITY THEORY. 15.1 Bayesian conception of probability. 15.2 Prior distributions. 15.3 Bayesian inference vs maximum likelihood. 15.4 Bayesian non-parametric problems. 15.5 Model choice. 16 A BAYESIAN APPROACH TO MULTIOBJECTIVE OPTIMISATION. 16.1 Reasons for a new approach. 16.2 Weak regularity. 16.3 Local Bayesian formulation. 16.4 Integral Bayesian formulation. 16.5 Computation of the Bayesian terms. 16.6 Bayesian imaging. 17 BAYESI

MMSE Based Transceiver Designs in Closed-Loop Non-Regenerative MIMO Relaying Systems

Abstract: In this paper, we propose a new design strategy based on the minimum mean-squared error (MMSE) in closed-loop non-regenerative multiple-input multiple-output relaying systems. Instead of conventional singular value decomposition based methods, we address the problem for joint MMSE design in a different approach using the Wiener filter solution which leads to simple derivations of the optimal MMSE designs. First, allowing the channel state information (CSI) at the source, we provide a new closed form solution for a source-relay-destination joint MMSE design by extending existing relay-destination joint MMSE designs. Second, for the limited feedback scenario, we address a codebook design criteria for the multiple streams preceding design with respect to the MMSE criterion. From our design strategy, we observe that compared to conventional non-regenerative relaying systems, the source or the destination only needs to know the CSI corresponding to its own link such as the source-to-relay or the relay-to-destination in view of the MMSE. Simulation results show that the proposed design gives about 7.5 dB gains at a bit error rate of 10-4 over existing relay-destination joint MMSE schemes and we can get close to the optimal unquantized schemes with only a few feedback bits.

A parametric level-set approach for topology optimization of flow domains

Abstract: Traditional methods based on an element-wise parameterization of the material distribution applied to the topology optimization of fluidic systems often suffer from slow convergence of the optimization process, as well as robustness issues at increased Reynolds numbers. The local influence of the design variables in the traditional approaches is seen as a possible cause for the slow convergence. Non-smooth material distributions are suspected to trigger premature onset of instationary flows which cannot be treated by steady-state flow models. In the present work, we study whether the convergence and the versatility of topology optimization methods for fluidic systems can be improved by employing a parametric level-set description. In general, level-set methods allow controlling the smoothness of boundaries, yield a non-local influence of design variables, and decouple the material description from the flow field discretization. The parametric level-set method used in this study utilizes a material distribution approach to represent flow boundaries, resulting in a non-trivial mapping between design variables and local material properties. Using a hydrodynamic lattice Boltzmann method, we study the performance of our level-set approach in comparison to a traditional material distribution approach. By numerical examples, the parametric level-set approach is validated through comparison with traditional material distribution based methods. While the parametric level-set approach leads to similar optimal designs, the present study reveals no general improvements of the convergence of the optimization process and of the robustness of the nonlinear flow analyses when compared to the traditional material distribution approach. Instead, our numerical experiment suggests that a continuation method operating on the volume constraint is needed to achieve optimal designs at higher Reynolds numbers.

Monotonic convergence of a general algorithm for computing optimal designs

Abstract: Monotonic convergence is established for a general class of multiplicative algorithms introduced by Silvey, Titterington and Torsney [Comm. Statist. Theory Methods 14 (1978) 1379–1389] for computing optimal designs. A conjecture of Titterington [Appl. Stat. 27 (1978) 227–234] is confirmed as a consequence. Optimal designs for logistic regression are used as an illustration.

Optimal Porosity Distribution for Minimized Ohmic Drop across a Porous Electrode

Abstract: This paper considers the design of spatially varying porosity profiles in next-generation electrodes based on simultaneous optimization of a porous-electrode model. Model-based optimal design not including the solid-phase intercalation mechanism is applied to a porous positive electrode made of lithium cobalt oxide, which is commonly used in lithium-ion batteries for various applications. For a fixed amount of active material, optimal grading of the porosity across the electrode was found to decrease the ohmic resistance by 15%‐33%, which in turn increases the electrode capacity to hold and deliver energy. The optimal porosity grading was predicted to have 40% lower variation in the ohmic resistance to variations in model parameters due to manufacturing imprecision or capacity fade. The results suggest that the potential for the simultaneous model-based design of electrode material properties that employ more detailed physics-based first-principles electrochemical engineering models to determine optimal design values for manufacture and experimental evaluation. © 2010 The Electrochemical Society. DOI: 10.1149/1.3495992 All rights reserved. Electrochemical power sources have had significant improvements in design and operating range and are expected to play a vital role in the future in automobiles, power storage, military, and space applications. Lithium-ion chemistry has been identified as a preferred candidate for high-power/high-energy secondary batteries. Applications for batteries range from implantable cardiovascular defibrillators operating at 10 A current to hybrid vehicles requiring pulses of up to 100 A. Today, the design of these systems have been primarily based on i matching the capacity of anode and cathode materials; ii trial-and-error investigation of thickness, porosity, active material, and additive loading; iii manufacturing convenience and cost; iv ideal expected thermal behavior at the system level to handle high currents; and v detailed microscopic models to understand, optimize, and design these systems by changing one or few parameters at a time. Traditionally, macroscopic models have been used to optimize the electrode thickness or spatially uniform porosity in lithium-ion battery design. Many applications of mathematical modeling to design Li-ion batteries are available in the literature. 1-10 An approach to identify the optimal values of system parameters such as electrode thickness has been reported by Newman and co-workers. 2,5-10 Simplified models based on porous-electrode theory can provide analytical expressions to describe the discharge of rechargeable lithium-ion batteries in terms of the relevant system parameters. Newman and co-workers 2,5-8 have utilized continuum electrochemical engineering models for design and optimization as a tool for the identification of system limitations from the experimental data. Equations were developed that describe the time dependence of potential as a function of electrode porosity and thickness, the electrolyte and solid-phase conductivities, specific ampere-hour capacity, separator conductivity and thickness, and current density. Analysis of these equations yields the values of electrode porosity and electrode thickness so as to maximize the capacity for discharge to a given cutoff potential. 2 Simplified models based on porous-electrode theory were used to describe the discharge of rechargeable lithium batteries and derive analytical expressions for the cell potential, specific energy, and average power in terms of the relevant system parameters. The resulting theoretical expressions were used for design and optimization purposes and for the identification of system limitations from experimental data. 5 Studies were performed by comparing the Ragone plots for a range of design parameters. A single curve in a Ragone plot involves hundreds of simulations wherein the applied current is varied over a wide range of magnitude. Ragone plots for different configurations are obtained by changing the design parameters e.g., thickness one at a time and by keeping the other parameters at constant values. This process of generating a Ragone plot is quite tedious, and typically Ragone curves reported in the literature are not smooth due to computational constraints. Batteries are typically designed only to optimize the performance at the very first cycle of operation of the battery, whereas in practice most of the battery’s operation occurs under significantly degraded conditions. Further, multivariable optimization is not computationally efficient using most first-principles models described in the literature. A reformulated model 11,12 is sufficiently computationally efficient to enable the simultaneous optimal design of multiple parameters over any number of cycles by including the mechanisms for capacity fade. Further, this model can be used to quantify the effects of model uncertainties and variations in the design parameters on the battery performance. Recently, such an application was reported in which the utilization averaged over 1000 cycles was maximized for a battery design obtained by simultaneous optimization of the applied current density I and thickness of the separator and the two electrodes ls,ln,lp for cycle 1, and the effects of variations in these four design parameters due to imprecise manufacturing were investigated. 13 The battery design optimized for cycle 1 did not maximize the cycle-averaged utilization. This paper designs spatially varying porosity profiles in porous electrodes based on simultaneous optimization applied to a porouselectrode model. The next section describes the simple electrochemical porous-electrode model used in this study. Then different methods for the simultaneous optimization of model parameters are discussed. The optimization procedure used in this study is then described, followed by the results and discussion and conclusions.

Methodology for the Design of Optimal Chemical Reactors based on the Concept of Elementary Process Functions

Abstract: In this contribution, a methodology for the optimal design of chemical reactors based on the best reaction route in the thermodynamic state space is proposed. This route is obtained by tracking a fluid element on its way through the reactor and manipulating the fluxes into this element. Instead of choosing the reactor design a priori and optimizing the free parameters of the chosen reactor setup, an innovative reactor design is developed based on the optimal flux profiles. Besides classical reactor concepts, this methodology is suited to investigate the potential of different process intensification options such as integration of reaction, cooling and separation in a single apparatus, or the application of high interface areas for heat and mass transfer. The methodology is exemplarily illustrated for the development of a new SO2 oxidation reactor. The residence time as an example for a meaningful objective is minimized, and a reduction of 69% compared to the optimized technical reference case is achieved.

Hybrid Genetic Algorithm and Linear Programming Method for Least-Cost Design of Water Distribution Systems

Abstract: The problems involved in the optimal design of water distribution networks belong to a class of large combinatorial optimization problems. Various heuristic and deterministic algorithms have been developed in the past two decades for solving optimization problems and applied to the design of water distribution systems. Nevertheless, there is still some uncertainty about finding a generally trustworthy method that can consistently find solutions which are really close to the global optimum of this problem. The paper proposes a combined genetic algorithm (GA) and linear programming (LP) method, named GALP for solving water distribution system design problems. It was investigated that the proposed method provides results that are more stable in terms of closeness to a global minimum. The main idea is that linear programming is more dependable than heuristic methods in finding the global optimum, but because it is suitable only for solving branched networks, the GA method is used in the proposed algorithm for decomposing a complex looped network into a group of branched networks. Linear programming is then applied for optimizing every branch network produced by GA from the original looped network. The proposed method was tested on three benchmark least-cost design problems and compared with other methods; the results suggest that the GALP consistently provides better solutions. The method is intended for use in the design and rehabilitation of drinking water systems and pressurized irrigation systems as well.

On the de la Garza phenomenon

Abstract: Deriving optimal designs for nonlinear models is, in general, challenging. One crucial step is to determine the number of support points needed. Current tools handle this on a case-by-case basis. Each combination of model, optimality criterion and objective requires its own proof. The celebrated de la Garza Phenomenon states that under a (p — 1)th-degree polynomial regression model, any optimal design can be based on at most p design points, the minimum number of support points such that all parameters are estimable. Does this conclusion also hold for nonlinear models? If the answer is yes, it would be relatively easy to derive any optimal design, analytically or numerically. In this paper, a novel approach is developed to address this question. Using this new approach, it can be easily shown that the de la Garza phenomenon exists for many commonly studied nonlinear models, such as the Emax model, exponential model, three- and four-parameter log-linear models, Emax-PK1 model, as well as many classical polynomial regression models. The proposed approach unifies and extends many well-known results in the optimal design literature. It has four advantages over current tools: (i) it can be applied to many forms of nonlinear models; to continuous or discrete data; to data with homogeneous or nonhomogeneous errors; (ii) it can be applied to any design region; (iii) it can be applied to multiple-stage optimal design and (iv) it can be easily implemented.

Parametric Design of a Waterjet Pump by Means of Inverse Design, CFD Calculations and Experimental Analyses

Abstract: The present paper describes the parametric design of a mixed-flow water-jet pump. The pump impeller and diffuser geometries were parameterized by means of an inverse design method, while CFD analyses were performed to assess the hydrodynamic and suction performance of the different design configurations that were investigated. An initial pump design was first generated and used as baseline for the parametric study. The effect of several design parameters was then analyzed in order to determine their effect on the pump performance. The use of a blade parameterization, based on inverse design, led to a major advantage in this study, because the three-dimensional blade shape is described by means of hydrodynamic parameters, such as blade loading, which has a direct impact on the hydrodynamic flow field. On the basis of this study, an optimal configuration was designed with the aim of maximizing the pump suction performance, while at the same time, guaranteeing a high level of hydrodynamic efficiency, together with the required mechanical and vibrational constraints. The final design was experimentally tested, and the good agreement between numerical predictions and experimental results validated the design process. This paper highlights the contrasting requirements in the pump design in order to achieve high hydrodynamic efficiency or good cavitation performance. The parametric study allowed us to determine design guidelines in order to find the optimal compromise in the pump design, in cases where both a high level of efficiency and suction performance must simultaneously be achieved. The design know-how developed in this study is based on flow field analyses and on hydrodynamic design parameters. It has therefore a general validity and can be used for similar design applications.

Data mining of Pareto-optimal transonic airfoil shapes using proper orthogonal decomposition

Abstract: A new approach to extract useful design information from Pareto-optimal solutions of optimization problems is proposed and applied to an aerodynamic transonic airfoil shape optimization. The proposed approach enables an analysis of line, face, or volume data of all Pareto-optimal solutions such as shape and flow field by decomposing the data into principal modes and corresponding base vectors using proper orthogonal decomposition (POD). Analysis of the shape and surface pressure data of the Pareto-optimal solutions of an aerodynamic transonic airfoil shape optimization problem showed that the optimized airfoils can be categorized into two families (low drag designs and high lift designs), where the lift is increased by changing the camber near the trailing edge among the low drag designs while the lift is increased by moving the lower surface upward among the high lift designs.

Optimal Design of Sensor Placement in Water Distribution Networks

Abstract: In this study we provide a methodology for the optimal design of water sensor placement in water distribution networks. The optimization algorithm used is based on a simulation-optimization and a s...

Practical considerations for optimal designs in clinical dose finding studies

Abstract: A key objective in the clinical development of a medicinal drug is the determination of an adequate dose level and, more broadly, the characterization of its dose response relationship. If the dose is set too high, safety and tolerability problems are likely to result, while selecting too low a dose makes it difficult to establish adequate efficacy in the confirmatory phase, possibly leading to a failed program. Hence, dose finding studies are of critical importance in drug development and need to be planned carefully. In this paper, we focus on practical considerations for establishing efficient study designs to estimate relevant target doses. We consider optimal designs for estimating both the minimum effective dose and the dose achieving a certain percentage of the maximum treatment effect. These designs are compared with D-optimal designs for a given dose response model. Extensions to robust designs accounting for model uncertainty are also discussed. A case study is used to motivate and illustrate the methods from this paper.

Single-Loop System Reliability-Based Design Optimization Using Matrix-Based System Reliability Method: Theory and Applications

Abstract: This paper proposes a single-loop system reliability-based design optimization (SRBDO) approach using the recently developed matrix-based system reliability (MSR) method. A single-loop method was employed to eliminate the inner-loop of SRBDO that evaluates probabilistic constraints. The MSR method enables us to compute the system failure probability and its parameter sensitivities efficiently and accurately through convenient matrix calculations. The SRBDO/MSR approach proposed in this paper is applicable to general systems including series, parallel, cut-set, and link-set system events. After a brief overview on SRBDO algorithms and the MSR method, the SRBDO/MSR approach is introduced and demonstrated by three numerical examples. The first example deals with the optimal design of a combustion engine, in which the failure is described as a series system event. In the second example, the cross-sectional areas of the members of a statically indeterminate truss structure are determined for minimum total weight with a constraint on the probability of collapse. In the third example, the redistribution of the loads caused by member failures is considered for the truss system in the second example. The results based on different optimization approaches are compared for further investigation. Monte Carlo simulation is performed in each example to confirm the accuracy of the system failure probability computed by the MSR method.

Multi-criteria analysis of wastewater treatment plant design and control scenarios under uncertainty

Abstract: Wastewater treatment plant control and monitoring can help to achieve good effluent quality, in a complex, highly non-linear process. The Benchmark Simulation Model no. 2 (BSM2) is a useful tool to competitively evaluate plant-wide control on a long-term basis. A method to conduct scenario analysis of process designs by means of Monte Carlo (MC) simulations and multi-criteria evaluation is presented. It is applied to the open loop version of BSM2 and to two closed loop versions, one with a simple oxygen controller and the other one with an ammonium controller regulating the set-point of the oxygen controller (cascade controller). The results show a much greater benefit of the cascade controller compared to the simple controller, both in environmental and economic terms. From an optimal process design point of view, the results show that the volume of the primary clarifier and the anoxic fraction of the reactor volume have an important impact on process performance. The uncertainty analysis of the optimal designs, also performed with MC simulations, highlights the improved and more stable effluent under closed loop control.

Optimal designs for the emax, log-linear and exponential models

Abstract: We derive locally D- and EDp-optimal designs for the exponential, log-linear and three-parameter emax models. For each model the locally D- and ED p -optimal designs are supported at the same set of points, while the corresponding weights are different. This indicates that for a given model, D-optimal designs are efficient for estimating the smallest dose that achieves 100p% of the maximum effect in the observed dose range. Conversely, ED p -optimal designs also yield good D-efficiencies. We illustrate the results using several examples and demonstrate that locally D- and ED p -optimal designs for the emax, log-linear and exponential models are relatively robust with respect to misspecification of the model parameters.

Decomposition Based Stochastic Programming Approach for Polygeneration Energy Systems Design under Uncertainty

Abstract: Polygeneration, a multi-input multioutput energy conversion process which typically involves the coproduction of electricity and liquid synthetic fuels, is a promising technology which offers real potential toward the reduction of excessive energy consumption and consequent greenhouse gas emissions. The optimal design of such a complex and nonlinear process system under inevitable and unpredictable future uncertainty poses great challenges in terms of both modeling and corresponding solution strategies. In this paper, we propose a stochastic programming framework for the optimal design under uncertainty of polygeneration energy systems. On the basis of a detailed mixed-integer nonlinear programming (MINLP) model, proposed in our previous work, a two-stage stochastic programming problem is formulated, which is then converted into a large-scale multiperiod MINLP problem by employing cubature based integration and sampling techniques. A decomposition algorithm is utilized for the efficient solution of the multiperiod problem, which involves iterations between a set of nonlinear subproblems of much smaller size and a master mixed-integer linear programming problem. A case study is then presented, where detailed computational results and comparisons between optimal designs obtained for both the stochastic and deterministic cases are shown.

Multi-Fidelity Multi-Grid Design Optimization of Planar Microwave Structures with Sonnet

Abstract: Simple and reliable algorithm for design optimization of microwave structures with Sonnet em is introduced. The presented methodology exploits coarse-discretization models of the structure of interest, starting from a very coarse grid, and gradually increasing the discretization density. Each model is optimized using a grid-search routine. The optimal design of the current model is used as an initial design for the finer-discretization one. Our methodology is computationally efficient as most of the operations are performed on coarse-discretization models. Two examples of microstrip filter design are given.

Numerical method for shape optimization using T-spline based isogeometric method

Abstract: Numerical methods for shape design sensitivity analysis and optimization have been developed for several decades. However, the finite-element-based shape design sensitivity analysis and optimization have experienced some bottleneck problems such as design parameterization and design remodeling during optimization. In this paper, as a remedy for these problems, an isogeometric-based shape design sensitivity analysis and optimization methods are developed incorporating with T-spline basis. In the shape design sensitivity analysis and optimization procedure using a standard finite element approach, the design boundary should be parameterized for the smooth variation of the boundary using a separate geometric modeler, such as a CAD system. Otherwise, the optimal design usually tends to fall into an undesirable irregular shape. In an isogeometric approach, the NURBS basis function that is used in representing the geometric model in the CAD system is directly used in the response analysis, and the design boundary is expressed by the same NURBS function as used in the analysis. Moreover, the smoothness of the NURBS can allow the large perturbation of the design boundary without a severe mesh distortion. Thus, the isogeometric shape design sensitivity analysis is free from remeshing during the optimization process. In addition, the use of T-spline basis instead of NURBS can reduce the number of degrees of freedom, so that the optimal solution can be obtained more efficiently while yielding the same optimum design shape.