Showing papers on "Optimal design published in 2000"

The Theory of the Design of Experiments

Abstract: SOME GENERAL CONCEPTS Types of Investigation Observational Studies Some Key Terms Requirements in Design Interplay between Design and Analysis Key Steps in Design A Simplified Model A Broader View AVOIDANCE OF BIAS General Remarks Randomization Retrospective Adjustment for Bias Some More on Randomization More on Causality CONTROL OF HAPHAZARD VARIATION General Remarks Precision Improvement by Blocking Matched Pairs Randomized Block Design Partitioning Sums of Squares Retrospective Adjustment for Improving Precision Special Models of Error Variation SPECIALIZED BLOCKING TECHNIQUES Latin Squares Incomplete Block Designs Cross-Over Designs FACTORIAL EXPERIMENTS: BASIC IDEAS General Remarks Example Main Effects and Interactions Example: Continued Two-Level Factorial Systems Fractional Factorials Example FACTORIAL EXPERIMENTS: FURTHER DEVELOPMENTS General Remarks Confounding in 2k Designs Other Factorial Systems Split Plot Designs Nonspecific Factors Designs for Quantitative Factors Taguchi Methods Conclusion OPTIMAL DESIGN General Remarks Some Simple Examples Some General Theory Other Optimality Criteria Algorithms for Design Construction Nonlinear Design Space-Filling Designs Bayesian Design Optimality of Traditional Designs SOME ADDITIONAL TOPICS Scale of Effort Adaptive Designs Sequential Regression Design Designs for One-Dimensional Error Structure Spatial Designs APPENDIX A: Statistical Analysis APPENDIX B: Some Algebra APPENDIX C: Computational Issues Each chapter also contains Bibliographic Notes plus Further Results and Exercises

An algorithm for the construction of “ D -optimal” experimental designs

Abstract: This paper presenm the algorithm “DETMAX” whose purpose is to construct experimental designs that are “D-optimal.” These are designs for which the determinant of X'X is maximum, where X is the “matrix of independent variables” in the usual linear model y = Xβ + e. Although the algorithm does not guarantee D-optimality, it has performed well in many cases where D-optimal designs are known. Five examples are given, illustrating the use of DETMAX to construct designs “from scratch” and to augment existing data. A FORTRAN listing is available on request.

Design of Nonlinear Framed Structures Using Genetic Optimization

Abstract: In this paper we present a genetic algorithm (GA)-based optimization procedure for the design of 2D, geometrical, nonlinear steel-framed structures. The approach presented uses GAs as a tool to achieve discrete nonlinear optimal or near-optimal designs. Frames are designed in accordance with the requirements of the AISC-LRFD specification. In this paper, we employ a group selection mechanism, discuss an improved adapting crossover operator, and provide recommendations on the penalty function selection. We compare the differences between optimized designs obtained by linear and geometrically nonlinear analyses. Through two examples, we will illustrate that the optimal designs are not affected significantly by the P-Δ effects. However, in some cases we may achieve a better design by performing nonlinear analysis instead of linear analysis.

Response Surface Techniques for Diffuser Shape Optimization

Abstract: The design of incompressible diffusers for maximum pressure recovery is used to demonstrate the utility of response surface approximations for design optimization of eow devices. Two examples involving two and eve design variables are treated, with the diffuser wall shapes described by polynomials and B-splines. In both cases monotonicity conditions drastically reduce the design space. In this irregularly shaped space, a pool of designs is selected by a D-optimality criterion and analyzed by a e nite volume computational euid dynamics (CFD) code. Quadratic polynomial response surfaces are then e tted to the pressure recovery coefe cients. To improve the prediction accuracy, uncertain regressor terms and possible outlier design points are excluded based on statistical tests. A standard optimization algorithm is used to e nd the optimal diffuser design from the response surface approximations. The optimum diffusers exhibit minimal e ow separation and yield similar wall shapes for the two parameterizations. A main asset of the response surface optimization approach lies in the smoothing of noisy response functions.Therefore, theissueofnumericalnoiseinCFD results basedon theuseof two different analysis codes is addressed.

Aerodynamic design using neural networks

Abstract: An aerodynamic design procedure that incorporates the advantages of both traditional response surface methodology (RSM) and neural networks is described. The procedure employs a strategy called parameterbased partitioning of the design space and uses a sequence of response surfaces based on both neural networks and polynomial fits to traverse the design space in search of the optimal solution. This approach results in response surfaces that have both the power of neural networks and the economy of low-order polynomials (in terms of number of simulations needed and network training requirements). Such an approach can handle design problems with many more parameters than would be possible using neural networks alone. The design procedure has been applied to the "blind" redesign of a turbine airfoil from a modern jet engine. This redesign involved the use of 15 design variables. The results obtained are closer to the target design than those obtained using an earlier method with only three design variables. The capability of the method in transforming generic shapes, such as simple curved plates, into optimal airfoils is also demonstrated.

Optimal design of reverse osmosis module networks

Abstract: The structure of individual reverse osmosis modules, the configuration of the module network, and the operating conditions were optimized for seawater and brackish water desalination. The system model included simple mathematical equations to predict the performance of the reverse osmosis modules. The optimization problem was formulated as a constrained multivariable nonlinear optimization. The objective function was the annual profit for the system, consisting of the profit obtained from the permeate, capital cost for the process units, and operating costs associated with energy consumption and maintenance. Optimization of several dual-stage reverse osmosis systems were investigated and compared. It was found that optimal network designs are the ones that produce the most permeate. It may be possible to achieve economic improvements by refining current membrane module designs and their operating pressures.

Heat exchanger design targets for minimum area and cost

Abstract: A methodology is proposed to determine the feasible region for shell and tube heat exchanger designs on a pressure drop diagram. By accounting for operating as well as geometrical constraints, the feasible region is de®ned so as to eliminate trial-and-error during the design activity. Every point on this plot of shellside versus tubeside pressure drop corresponds to a unique design in terms of tube length, shell diameter and baffle spacing. Furthermore, curves may be plotted for designs corresponding to a specified heat exchange area or a given total annual cost. Such curves permit screening of various design options prior to detailed rating of the exchangers, and allow heat exchanger design targets to be established for minimum area or cost. The area target ensures an exchanger of the smallest size with minimum capital cost, whereas the cost target yields the optimum pressure drops accounting for the tradeoff between power consumption and heat exchanger area. The methodology is equation-based and can be conveniently implemented on a computer.

Model-Robust Factorial Designs

Abstract: In industrial experimentation, experimental designs are frequently constructed to estimate all main effects and a few prespecified interactions. The robust-product-design literature is replete with such examples. A major limitation of this approach is the requirement that the experimenter know which interactions are likely to be active in advance. In this article, we develop a class of balanced designs that can be used for estimation of main effects and any combination of up to CJin teractions, where g is specified by the user. We view this as an issue of model-robust design: We construct designs that are highly efficient for all models involving main effects and g (or fewer) interactions. We compare the performances of these designs with the standard alternatives from the class of maximum-resolution fractional factorial designs for several criteria. The comparison reveals that the new designs are surprisingly robust to model misspecification, something that is generally not true for maximum-resolution fr...

Optimal piezo-actuator locations/lengths and applied voltage for shape control of beams

Abstract: Shape control of beams under general loading conditions is implemented using piezoceramic actuators to provide the control forces. The objective of the shape-control is to minimize the maximum deflection of the beam to obtain a min-max deflection configuration with respect to loading and piezo-actuators. In practice, the loading on a beam is a variable quantity with respect to its magnitude, and this aspect can be handled easily by optimizing the magnitude of the applied voltage to achieve the min-max deflection. This property of the smart materials technology overcomes the problem of one-off conventional optimal designs which become suboptimal when the loading magnitude changes. In addition to the magnitude of the applied voltage, the optimal values for the locations and the lengths of the piezo-actuators are determined to achieve the min-max deflection. Due to the complexity of the governing equations involving finite length piezo patches, the numerical results are obtained by the finite-difference method. The analysis of the problem shows the effect of the actuator locations, lengths and the applied voltage on the maximum deflection. The optimal values for the actuator locations and the voltage are determined as functions of the load locations and load magnitudes, respectively. The effect of the actuator length on the min-max deflection is investigated and it is observed that the optimal length depends on the applied voltage. Finally, it is shown that using multiple actuators are more effective than a single actuator in the cases of complicated loading.

Minimax D-Optimal Designs for the Logistic Model

Abstract: Summary. We propose an algorithm for constructing minimax D-optimal designs for the logistic model when only the ranges of the values for both parameters are assumed known. Properties of these designs are studied and compared with optimal Bayesian designs and Sitter's (1992, Biometrics, 48, 1145–1155) minimax D-optimal kk-designs. Examples of minimax D-optimal designs are presented for the logistic and power logistic models, including a dose-response design for rheumatoid arthritis patients.

Optimal placement and size of piezoelectric patches on beams from the controllability perspective

Abstract: This paper is concerned with the optimal design of a collocated pair of piezoelectric patch actuators that are surface bonded onto beams. The design involves selecting the optimal locations and sizes (or lengths) of the piezoelectric actuators based on a controllability perspective. The objective function is referred to as the controllability index, which is the singular value of a control matrix. The index measures the input energy required to achieve a desired structural control by the piezoelectric actuators. The controllability index is dependent on the placement and size of the piezoelectric patches, and thus by maximizing the index the designer can obtain the optimal design of the piezoelectric actuator. As illustrations, various beam examples with a pair of piezoelectric patch actuators are solved and the optimal design characteristics of the actuators are examined.

Flexibility analysis and design of linear systems by parametric programming

Abstract: A new, unified theory and algorithms, based on multiparametric programming techniques, for the solution of flexibility analysis and design optimization problems in linear process systems are presented. They are used for the flexibility test and index problems in systems with deterministic parameters, and for the stochastic and expected stochastic flexibility evaluation problems in systems with stochastic parameters. They are computationally efficient and give the explicit dependence of various flexibility metrics on the values of the continuous design variables. The latter feature enables the easy and efficient comparison of design alternatives. It also allows for the compact formulation of design optimization problems that can be solved parametrically to yield the exact algebraic form of the trade-off curve of economics against flexibility. Key features of the proposed approach are demonstrated through both mathematical and process examples.

On the determination of optimal designs for an interference model

Abstract: This paper generalizes Kushner’s method for finding optimal repeated measurements designs to find optimal designs under an interference model. The model we assume is for a one-dimensional layout without guard plots and with different left and right neighbor effects. The resulting optimal designs may need many blocks or may not even exist as a finite design. The results give lower bounds for optimality criteria on finite designs and the design structure can be used to suggest efficient small designs.

Maximization of Manufacturing Yield of Systems with Arbitrary Distributions of Component Values

Abstract: This paper presents a general method for maximizing manufacturing yield when the realizations of system components are independent random variables with arbitrary distributions. Design specifications define a feasible region which, in the nonlinear case, is linearized using a first-order approximation. The method attempts to place the given tolerance hypercube of the uncertain parameters such that the area with higher yield lies in the feasible region. The yield is estimated by using the joint cumulative density function over the portion of the tolerance hypercube that is contained in the feasible region. A double-bounded density function is used to approximate various bounded distributions for which optimal designs are demonstrated on a tutorial example. Monte Carlo simulation is used to evaluate the actual yields of optimal designs.

Projective three-level main effects designs robust to model uncertainty

Abstract: This paper is concerned with designing experiments under the assumption that an analysis strategy is used that considers interactions in addition to main effects. A criterion which averages an approximation to As-efficiency over lower-dimensional projections of the design is introduced to compare designs. A columnwise design procedure is used to construct three-level designs for six factors in 18 runs. The projection efficiencies of these designs are explored and compared with designs obtained from the L 18 orthogonal array. Results are also given for designs with 14 and 17 runs.

Optimal design procedure for a practical induction heating cooker

Abstract: This paper presents a practical optimal design procedure for small induction heating devices. An experimental modeling of the physical properties and a practical simulation technique for the nonsinusoidal input waveform is adopted. The design sensitivity analysis with Levenberg-Marquardt method is used for the optimal design process. The proposed method is applied to an induction heating pan cooker model, and the result is verified by experiment.

Optimal Channel Cross Section with Composite Roughness

Abstract: For channels with composite roughness, an equivalent uniform roughness coefficient and flow geometric elements are used in an optimal design method using the Manning equation. The optimal design problems are formulated in a nonlinear optimization framework with the objective function being a cost function per unit length of the canal. Constraints are the Manning equation, positive values for design variables, and specified values of side slopes or top width. The constrained problem is transformed into an unconstrained problem using the Lagrangian multipliers. To obtain an optimal solution for the resulting unconstrained problem, the first-order necessary conditions for optima are applied. The resulting simultaneous nonlinear equations are solved using the computational methodology developed. This technique is applied to illustrative numerical examples. The evaluations establish the potential applicability of the developed computational methodology for optimal design of open channel cross sections with composite roughness.