Showing papers on "Optimal design published in 1995"

Bayesian Experimental Design: A Review

Abstract: This paper reviews the literature on Bayesian experimental design. A unified view of this topic is presented, based on a decision-theoretic approach. This framework casts criteria from the Bayesian literature of design as part of a single coherent approach. The decision-theoretic structure incorporates both linear and nonlinear design problems and it suggests possible new directions to the experimental design problem, motivated by the use of new utility functions. We show that, in some special cases of linear design problems, Bayesian solutions change in a sensible way when the prior distribution and the utility function are modified to allow for the specific structure of the experiment. The decision-theoretic approach also gives a mathematical justification for selecting the appropriate optimality criterion.

Sizing, Shape, and Topology Design Optimization of Trusses Using Genetic Algorithm

Abstract: A procedure is developed for the combined sizing, shape, and topology design of space trusses. Discrete and continuous values are used to define the cross-sectional areas of the members. The nodal locations are treated as continuous design variables using the hybrid natural approach for shape optimal design. Element connectivity and boundary conditions are treated as Boolean design variables in the context of topology design. The traditional genetic algorithm is modified to handle the problem formulation. Simple concepts are used to accelerate convergence and reduce the computational effort. Numerical examples are solved to illustrate the proposed methodology. Several conclusions drawn from the research results are presented along with some thoughts on computational strategies.

Optimal Design via Curve Fitting of Monte Carlo Experiments

Abstract: This article explores numerical methods for stochastic optimization, with special attention to Bayesian design problems. A common and challenging situation occurs when the objective function (in Bayesian applications, the expected utility) is very expensive to evaluate, perhaps because it requires integration over a space of very large dimensionality. Our goal is to explore a class of optimization algorithms designed to gain efficiency in such situations, by exploiting smoothness of the expected utility surface and borrowing information from neighboring design points. The central idea is that of implementing stochastic optimization by curve fitting of Monte Carlo samples. This is done by simulating draws from the joint parameter/sample space and evaluating the observed utilities. Fitting a smooth surface through these simulated points serves as estimate for the expected utility surface. The optimal design can then be found deterministically. In this article we introduce a general algorithm for cu...

Design, fabrication and testing of fixed-valve micro-pumps

Abstract: Micro-fluidic systems rely on positive displacement pumps to move fluid due to the low Reynolds numbers encountered at flow rates that are typically in a range around 100 µl/min. These pumps are usually reciprocating devices due to limitations of rotating machinery at small scales. Valves for micro-pumps are not necessarily scaled-down macro-valve designs. Existing designs range from passive membranes to complex thermally-controlled active devices. A simpler idea and one that may be more applicable to particulate-laden fluids is a valve that is fixed in shape. Such a valve operates solely by the differential pressure characteristics in each flow direction, which are caused by the flow through it. Such fixed or no-moving-parts (NMP) valves are attractive due to their simplicity of fabrication but have not been studied in enough detail to determine optimal designs. We present design and testing techniques for use in developing efficient NMP valves and for comparing various designs. These techniques were applied to diffuser and valvular conduit designs etched on silicon. Valve performance was characterized by flow resistance and by diodicity, which is the ratio of pressure losses in the reverse to forward direction. Techniques for measuring diodicity in steady and transient flow were developed, and both viscous and dynamic loss contributions to valve performance were analyzed. Computational techniques were used to demonstrate their use in the design of efficient valves.

The use of observability and controllability gramians or functions for optimal sensor and actuator location in finite-dimensional systems

Abstract: In this paper, we discuss the optimal location of sensors and actuators for both linear and nonlinear dynamical systems, in both the continuous-time and discrete-time case, on the basis of observability and controllability functions. The optimal location of sensors can be viewed as the problem of maximizing the output energy generated by a given state. On the other hand, the optimal location of actuators can be viewed as the problem of minimizing the input energy required to reach a given state. Such design problems occur in many applications, such as the control of distributed parameter systems, arising in mechanical, hydraulic or chemical processes. In this paper, some new results on observability and controllability functions for nonlinear systems are also provided. Furthermore, we propose a general procedure for computing the optimal design parameters, based on both integer programming and a branch and bound method, suitable for large-scale systems. The effectiveness of this approach is demonstrated for a practical example.

A computational market model for distributed configuration design

Abstract: A precise market model for a well-defined class of distributed configuration design problems is presented. Given a design problem, the model defines a computational economy to allocate basic resources to agents participating in the design. The result of running these “design economies” constitutes the market solution to the original problem. After defining the configuration design framework, the mapping to computational economies and the results to date are described. For some simple examples, the system can produce good designs relatively quickly. However, analysis shows that the design economies are not guaranteed to find optimal designs, and some of the major pitfalls are identified and discussed. Despite known shortcomings and limited explorations thus far, the market model offers a useful conceptual viewpoint for analyzing distributed design problems.

Optimal Model-Based Decomposition of Powertrain System Design

Abstract: Optimal design of large engineering systems modeled as nonlinear programming problems remains a challenge because increased size reduces reliability and speed of numerical optimization algorithms. Decomposition of the original model into smaller coordinated submodels is desirable or even necessary. The article presents a methodology for optimal model-based decomposition of design problems, whether or not initially cast as optimization models. The overall model is represented by a hypergraph that is optimally partitioned into weakly-connected subgraphs satisfying partitioning constraints. The formulation is robust enough to account for computational demands and resources, and the strength of interdependencies between the design relations contained in the model. This decomposition methodology is applied to a vehicle powertrain system design model consisting of engine, torque converter, transmission, and wheel-tire assemblies, with 87 design relations and 119 design and state/behavior variables.

D-Optimum Designs for Heteroscedastic Linear Models

Abstract: The methods of optimum experimental design are applied to models in which the variance, as well as the mean, is a parametric function of explanatory variables. Extensions to standard optimality theory lead to designs when the parameters of both the mean and the variance functions, or the parameters of only one function, are of interest. The theory also applies whether the mean and variance are functions of the same variables or of different variables, although the mathematical foundations differ. The example studied is a second-order two-factor response surface for the mean with a parametric nonlinear variance function. The theory is used both for constructing designs and for checking optimality. A major potential for application is to experimental design in off-line quality control.

Optimal Designs for Identifying the Degree of a Polynomial Regression

Abstract: If an experimenter wants to determine the degree of a polynomial regression on the basis of a sample of observations, Anderson showed that the following method is optimal. Starting with the highest (specified) degree the procedure is to test in sequence whether the coefficients are 0. In this paper optimal designs for Anderson's procedure are determined explicitly. The optimal design maximizes the minimum power of a given set of alternatives.

Design of Optimal Four-Wheel Steering System

Abstract: SUMMARY Optimal design of the four wheel steering (4WS) system of the ground vehicle is studied. 4WS vehicles with the optimal control scheme are considered first. General formulation of the optimal control law is developed based on the linear quadratic regulator theory. The vehicle speed function (VSF) based 4WS vehicle with a simple feedback controller is considered as a special case of the optimal system. Two new designs of the VSF 4WS system are proposed and their performances are compared with the optimal 4WS systems and the existing VSF 4WS system. The first system is designed for the maximum stability while the second system is designed to emulate the response of the optimal 4WS vehicle. Advantages of the new VSF designs are discussed.

Utilizing genetic algorithms for the optimal design of electromagnetic devices

Abstract: The application of genetic algorithms (GAs) to the design optimization of electromagnetic devices is presented. The method is applied to a magnetizer to design its pole face. Optimization is sought to achieve a desired magnetic flux density distribution in the device. The shape of the pole face is constructed from the control points by means of uniform nonrational b-splines. The results obtained signify the efficiency of the method.

A Geometric Approach to Optimal Design for One‐Parameter Non‐Linear Models

Abstract: SUMMARY A geometric framework for constructing optimal Bayesian designs and maximin designs for non-linear models with a single unknown parameter and a prior distribution on that parameter, which is restricted in that it comprises exactly two points of support, is presented. The approach is illustrated by means of selected examples involving logistic regression and the simple exponential model, and its applicability to the construction of optimal designs for models with uncontrolled variation and to model robust designs is also demonstrated. In addition, the method is shown to provide some valuable insights into the general properties of optimal Bayesian designs for non-linear models.

Bayesian design criteria: Computation, comparison, and application to a pharmacokinetic and a pharmacodynamic model

Abstract: In this paper 3 criteria to design experiments for Bayesian estimation of the parameters of nonlinear models with respect to their parameters, when a prior distribution is available, are presented: the determinant of the Bayesian information matrix, the determinant of the preposterior covariance matrix, and the expected information provided by an experiment. A procedure to simplify the computation of these criteria is proposed in the case of continuous prior distributions and is compared with the criterion obtained from a linearization of the model about the mean of the prior distribution for the parameters. This procedure is applied to two models commonly encountered in the area of pharmacokinetics and pharmacodynamics: the one-compartment open model with bolus intravenous single-dose injection and theEmax model. They both involve two parameters. Additive as well as multiplicative gaussian measurement errors are considered with normal prior distributions. Various combinations of the variances of the prior distribution and of the measurement error are studied. Our attention is restricted to designs with limited numbers of measurements (1 or 2 measurements). This situation often occurs in practice when Bayesian estimation is performed. The optimal Bayesian designs that result vary with the variances of the parameter distribution and with the measurement error. The two-point optimal designs sometimes differ from the D-optimal designs for the mean of the prior distribution and may consist of replicating measurements. For the studied cases, the determinant of the Bayesian information matrix and its linearized form lead to the same optimal designs. In some cases, the pre-posterior covariance matrix can be far from its lower bound, namely, the inverse of the Bayesian information matrix, especially for theEmax model and a multiplicative measurement error. The expected information provided by the experiment and the determinant of the pre-posterior covariance matrix generally lead to the same designs except for theEmax model and the multiplicative measurement error. Results show that these criteria can be easily computed and that they could be incorporated in modules for designing experiments.

Design of high-order digital differentiators using L/sub 1/ error criteria

Abstract: This paper considers the optimal design of high order digital differentiators in the L/sub 1/ sense. Conventionally, using L/sub 1/ error criterion for this design problem results in a nonlinear optimization problem since the corresponding objective function contains an absolute error function. We first reformulate the design problem as a linear programming problem in the frequency domain. To avoid the requirement of huge computation load and storage space when using linear programming based algorithms, we present a method based on a modification of Karmarkar's algorithm to solve the design problem so that an analytical weighted least-squares (WLS) solution formula can be obtained. This leads to a very efficient procedure for the considered design problem. Computer simulations show that the designed differentiators can achieve more accurate wideband differentiation than those designed by using L/sub 2/ and Chebyshev (minimax) error criteria. >

The Use of the Second Law of Thermodynamics in Process Design

Abstract: The importance of using the second law of thermodynamics in the design of heat exchangers, heat exchanger networks, and processes in general, is discussed. The optimal {Delta}T at a refrigerated heat exchanger is considered from a second law viewpoint. It is shown that the use of minimum total annualized cost as the single optimizing factor is unsatisfactory. Total annualized costs are based on predicted costs of fuel, equipment, and capital, which are uncertain at best. Instead of a singular or ``global optimum`` {Delta}T, there is a range of optimal {Delta}Ts over which the total annualized cost is essentially the same, but within which the distribution between cost of capital and cost of energy is significantly different. In selecting a design {Delta}T, this distribution of costs should also be considered. The possibility of only one singular, or global optimum, solution for complex processes is also considered from a philosophical viewpoint, and is again rejected. The existence and identification of design decisions which unnecessarily waste thermodynamic availability (physical exergy) are discussed and identified as ``second law errors.`` Elimination of a second law error from a design guarantees an improved design. An optimal design, which may be any one of a numerous setmore » of optimal designs, will result when all second law errors are eliminated. A design procedure to develop optimal process designs, using such thermodynamic insights, is proposed.« less

D-Optimal Designs for Generalized Linear Models

Abstract: This paper develops some simple methods for obtaining D-optimal designs for generalized linear models with multiple design variables In some important cases the numerical complexity can be reduced to that of the two parameter case regardless of the original dimension The form and properties of the obtained D-optimal designs are illustrated and discussed through a few interesting examples

Response surface bandits

Abstract: In this paper we define a response surface bandit as the sequential design problem that maximizes an expected bandit utility but where the outcomes y n are continuous and can be related through a response surface to a set of controllable variables x n = (x 1n , x 2n ,..., x kn ). We link this problem to other traditional optimization problems from industrial engineering and to the traditional bandit problem. We consider two approaches to the problem. The first is based on a myopic sequential design. The second approach uses the best design out of a family of designs related to upper bounds for the predicted surface; the family includes myopic and sequential versions of D-optimal designs. These approaches can be generalized to more broadly defined sequential problems.

Approximation Techniques for Broad-Band Acoustic Radiated Noise Design Optimization Problems

Abstract: This study investigates the applicability of various approximation methods to broadband radiated noise design optimization problems. Low-order series approximations of dynamic response may be used to replace full numerical system solutions to effect significant computer cost savings during design iterations. Also, the ease of evaluating the approximate functions may be further exploited by using global optimization search methods, such as simulated annealing, at individual design iterations. The combination of approximating radiated noise spectra and evaluating the approximate spectra for all possible design alternatives greatly increases the possibility of finding a truly optimal design. The effectiveness of the approximation is measured by considering optimization accuracy, evaluated by the algorithm's ability to find a global or near-global minimum independent of the initial design; computational efficiency, based on the number of numerical design analyses required for convergence; and generality, where the method should be relatively independent of the problem type. Finite element models of three test cases with varying performance goals and design parameters were used to evaluate the optimization methods. Shell thicknesses, shell loss factors, and rib stiffener locations were varied to minimize structural weight and manufacturing costs while lowering broad-band radiated noise levels below a specified goal. First-order Taylor and half-quadratic series approximation optimization approaches were compared to traditional local minimization methods (Modified Method of Feasible Directions and Broydon-Fletcher-Goldfarb-Shanno). For all test cases, the approximation approaches found the global optimum design more frequently than the local minimization methods. Also, the half-quadratic method converged using fewer design evaluations than the first-order Taylor method for most test cases

Optimal design of composite lifting surface for flutter suppression with piezoelectric actuators

Abstract: This paper presents the optimal design of an active flutter suppression system for an adaptive composite lifting surface. Rayleigh-Ritz method is used to develop the equations of motion of a laminated plate-wing model with segmented piezoactuators. A state space aeroservoelastic mathematical model by rational function approximation (RFA) of the unsteady aerodynamic forces is derived. The minimum state method combined with the optimization technique is adapted for RFA. The linear quadratic regulator with output feedback is employed in active control of the system. The thickness and size of the piezoelectric actuators that affect the structural properties as well as the control characteristics are held constant. The optimal placement of piezoelectric actuators for flutter suppression subject to minimize the controller performance index is determined analytically by using the optimization technique. The results show the capability of piezoactuators for the control of wing flutter. Numerical simulations of a model with the optimal actuators placement show a substantial saving in control effort compared with the initial model.

Optimal design of sandwich and laminated composite plates based on the planning of experiments

Abstract: Optimal design problems of sandwich plates with soft core and laminated composite face layers, and multilayered composite plates are investigated. The optimal design problems are solved by using the method of the planning of experiments. The optimization procedure is divided into the following stages: choice of control parameters and establishment of the domain of search, elaboration of plans of experiment for the chosen number of reference points, execution of the experiment, determination of simple mathematical models from the experimental data, design of the structure on the basis of the mathematical models discovered, and finally verification experiments at the point of the optimal solution. Vibration and damping analysis is performed by using a sandwich plate finite elements based on a broken line model. Damping properties of the core and face layers of the plate are taken into account in the optimal design. Modal loss factors are computed using the method of complex eigenvalues or the energy method. Frequencies and modal loss factors of the plate are constraints in the optimal design problem. There are also constraints on geometrical parameters and the bending stiffness of the plate. The mass of the plate is the objective function. Design parameters are the thickness of the plate layers. In the points of experiments computer simulation using FEM is carried out. Using this information, simple mathematical models for frequencies and modal loss factors for the plate are determined. These simple mathematical functions are used as constraints in the nonlinear programming problem, which is solved by random search and the penalty function method. Numerical examples of the optimal design of clamped sandwich and simply supported laminated composite plates are presented. A significant improvement of damping properties of a sandwich plate is observed in comparison with a simple plate of equal natural frequencies.