Showing papers on "Optimal design published in 1997"

On the Design of Compliant Mechanisms Using Topology Optimization

Abstract: This paper presents a method for optimal design of compliant mechanism topologies. The method is based on continuum-type topology optimization techniques and finds the optimal compliant mechanism topology within a given design domain and a given position and direction of input and output forces. By constraining the allowed displacement at the input port, it is possible to control the maximum stress level in the compliant mechanism. The ability of the design method to find a mechanism with complex output behavior is demonstrated by several examples. Some of the optimal mechanism topologies have been manufactured, both in macroscale (hand-size) made in Nylon, and in microscale (<.5mm)) made of micromachined glass.

Model-Oriented Design of Experiments

Abstract: 1 Some Facts From Regression Analysis.- 1.1 The Linear Model.- 1.2 More about the Information Matrix.- 1.3 Generalized Versions of the Linear Regression Model.- 1.4 Nonlinear Models.- 2 Convex Design Theory.- 2.1 Optimality Criteria.- 2.2 Some Properties of Optimality Criteria.- 2.3 Continuous Optimal Designs.- 2.4 The Sensitivity Function and Equivalence Theorems.- 2.5 Some Examples.- 2.6 Complements.- 3 Numerical Techniques.- 3.1 First Order Algorithm:D-criterion.- 3.2 First Order Algorithm: The General Case.- 3.3 Finite Sample Size.- 4 Optimal Design under Constraints.- 4.1 Cost Constraints.- 4.2 Constraints for Auxiliary Criteria.- 4.3 Directly Constrained Design Measures.- 5 Special Cases and Applications.- 5.1 Designs for Time-Dependent Models.- 5.2 Regression Models with Random Parameters.- 5.3 Mixed Models and Correlated Observations.- 5.4 Design for "Contaminated" Models.- 5.5 Model Discrimination.- 5.6 Nonlinear Regression.- 5.7 Design in Functional. Spaces.- A Some Results from Matrix Algebra.- B List of Symbols.- References.

Optimal design in random-effects regression models

Abstract: SUMMARY An approach is proposed to optimal design of experiments for estimating randomeffects regression models. The population designs are defined by the number of subjects and the individual designs to be performed. Cost functions associated with individual designs are incorporated. For a given maximal cost, an algorithm is proposed for finding the statistical population design that maximises the determinant of the Fisher information matrix of the population parameters. The Fisher information matrix is formulated for linear models and normal distributions. The approach is applied to the design of an optimal experiment in toxicokinetics using a first-order linearisation of the model. Several cost functions and designs of various orders are studied. An example illustrates the optimal population designs and the increased efficiency of some optimal designs over more standard designs.

A Bayesian variable-selection approach for analyzing designed experiments with complex aliasing

Abstract: Experiments using designs with complex aliasing patterns are often performed—for example, twolevel nongeometric Plackett-Burman designs, multilevel and mixed-level fractional factorial designs, two-level fractional factorial designs with hard-to-control factors, and supersaturated designs. Hamada and Wu proposed an iterative guided stepwise regression strategy for analyzing the data from such designs that allows entertainment of interactions. Their strategy provides a restricted search in a rather large model space, however. This article provides an efficient methodology based on a Bayesian variable-selection algorithm for searching the model space more thoroughly. We show how the use of hierarchical priors provides a flexible and powerful way to focus the search on a reasonable class of models. The proposed methodology is demonstrated with four examples, three of which come from actual industrial experiments.

Designing Experiments with Respect to ‘Standardized’ Optimality Criteria

Abstract: We introduce a new class of `standardized' optimality criteria which depend on `standardized' covariances of the least squares estimators and provide an alternative to the commonly used criteria in design theory. Besides a nice statistical interpretation the new criteria satisfy an extremely useful invariance property which allows an easy calculation of optimal designs on many linearly transformed design spaces.

GeneAS: A Robust Optimal Design Technique for Mechanical Component Design

Abstract: A robust optimal design algorithm for solving nonlinear engineering design optimization problems is presented. The algorithm works according to the principles of genetic algorithms (GAs). Since most engineering problems involve mixed variables (zero-one, discrete, continuous), a combination of binary GAs and real-coded GAs is used to allow a natural way of handling these mixed variables. The combined approach is called GeneAS to abbreviate Genetic Adaptive Search. The robustness and flexibility of the algorithm come from its restricted search to the permissible values of the variables. This also makes the search efficient by requiring a reduced search effort in converging to the optimum solution. The efficiency and ease of application of the proposed method are demonstrated by solving four mechanical component design problems borrowed from the optimization literature. The proposed technique is compared with traditional optimization methods. In all cases, the solutions obtained using GeneAS are better than those obtained with the traditional methods. These results show how GeneAS can be effectively used in other mechanical component design problems.

Efficient sampling technique for optimization under uncertainty

Abstract: The concept of robust design involves identification of design settings that make the product performance less sensitive to the effects of seasonal and environmental variations. This concept is discussed in this article in the context of batch distillation column design with feed stock variations, and internal and external uncertainties. Stochastic optimization methods provide a general approach to robust/parameter design as compared to conventional techniques. However, the computational burden of these approaches can be extreme and depends on the sample size used for characterizing the parametric variations and uncertainties. A novel sampling technique is presented that generates and inverts the Hammersley points (an optimal design for placing n points uniformly on a k-dimensional cube) to provide a representative sample for multivariate probability distributions. The example of robust batch-distillation column design illustrates that the new sampling technique offers significant computational savings and better accuracy.

Optimal design of a flexure hinge based XYθ wafer stage

Abstract: Optimal design o1 a XYφ micromotion stage is presented. The stage consists of a monolithic flexure hinge mechanism with three piezoelectric actuators. This paper describes the procedures of selecting parameters for the optimal design. In particular, it presents a mathematical formulation of the optimization problem. Based on the solution of the optimiiation problem, the final design of the stage is also presented. Experimental results indicate that the design procedure is effective, and the designated stage has the total range of 41.5 μm mid 47.8 μm along the X- and Y-axes, respectively, and the maximum yaw motion range of 322.8 aresec (1.565 mrad).

Columnwise-pairwise algorithms with applications to the construction of supersaturated designs

Abstract: Motivated by the construction of supersaturated designs, we develop a class of algorithms called columnwise-pairwise exchange algorithms. They differ from the k-exchange algorithms in two respects: (1) They exchange columns instead of rows of the design matrix, and (2) they employ a pairwise adjustment in the search for a “better” column. The proposed algorithms perform very well in the construction of supersaturated designs both for a single criterion and for multiple criteria. They are also applicable to the construction of designs that are not supersaturated.

Optimal design in psychological research.

Abstract: Psychologists often do not consider the optimality of their research designs. However, increasing costs of using inefficient designs requires psychologists to adopt more efficient designs and to use more powerful analysis strategies. Common designs with many factor levels and equal allocations of observations are often inefficient for the specific questions most psychologists want to answer. Happenstance allocations determined by random sampling are usually even more inefficient and some common analysis strategies can exacerbate the inefficiency. By selecting treatment levels and allocating observations optimally, psychologists can greatly increase the efficiency and statistical power of their research designs. A few heuristic design principles can produce much more efficient designs than are often used. Experimental researchers outside psychology often carefully consider the efficiency of their research designs. For example, the high costs of conducting large-scale experiments with industrial processes has motivated the search for designs that are optimally efficient. As a consequence, a substantial literature on optimal design has developed outside psychology. In contrast, psychologists have not been as constrained by costs, so their research designs have been based on tradition and computational ease. Most psychologists are unaware of the literature on optimal research design; this topic receives little or no attention in popular textbooks on methods and statistics in psychology. Experimental design textbooks offer little if any advice on how many levels of the independent variables to use or on how to allocate observations across those levels to obtain optimal efficiency. When advice is offered, it is usually based on heuristics derived from experience rather than statistical principles. The purpose of this article is to review the basic concepts of optimal design and to illustrate how a few

Optimal design of piezoelectric microstructures

Abstract: Application of piezoelectric materials requires an improvement in their performance characteristics which can be obtained by designing new topologies of microstructures (or unit cells) for these materials The topology of the unit cell (and the properties of its constituents) determines the effective properties of the piezocomposite By changing the unit cell topology, better performance characteristics can be obtained in the piezocomposite Based on this idea, we have proposed in this work an optimal design method of piezocomposite microstructures using topology optimization techniques and homogenization theory The topology optimization method consists of finding the distribution of material phase and void phase in a periodic unit cell, that optimizes the performance characteristics, subject to constraints such as property symmetry and stiffness The optimization procedure is implemented using sequential linear programming In order to calculate the effective properties of a unit cell with complex topology, a general homogenization method applied to piezoelectricity was implemented using the finite element method This method has no limitations regarding volume fraction or shape of the composite constituents Although only two-dimensional plane strain topologies of microstructures have been considered to show the implementation of the method, this can be extended to three-dimensional topologies Microstructures obtained show a large improvement in performance characteristics compared to pure piezoelectric material or simple designs of piezocomposite unit cells

Optimal three‐stage designs for phase II cancer clinical trials

Abstract: The objective of a phase II cancer clinical trial is to screen a treatment that can produce a similar or better response rate compared to the current treatment results. This screening is usually carried out in two stages as proposed by Simon. For ineffective treatment, the trial should terminate at the first stage. Ensign et al. extended two-stage optimal designs to three stages; however, they restricted the rejection region in the first stage to be zero response, and the sample size to at least 5. This paper extends Simon's two-stage to a three-stage design without these restrictions, and provides tables for both optimal and minimax designs. One can use the three-stage design to reduce the expected sample size when the treatment is not promising a priori and when the accrual rate is slow. The average reduction in size from a two-stage to three-stage design is 10 per cent.

Multidisciplinary Optimization of a Supersonic Transport Using Design of Experiments Theory and Response Surface Modeling

Abstract: The presence of numerical noise in engineering design optimization problems inhibits the use of many gradient-based optimization methods. This numerical noise may result in the inaccurate calculation of gradients which in turn slows or prevents convergence during optimization, or it may promote convergence to spurious local optima. The problems created by numerical noise are particularly acute in aircraft design applications where a single aerodynamic or structural analysis of a realistic aircraft configuration may require tens of CPU hours on a supercomputer. The computational expenses of the analyses coupled with the convergence difficulties created by numerical noise are significant obstacles to performing aircraft multidisciplinary design optimization. To address these issues, a procedure has been developed to create noise-free algebraic models of subsonic and supersonic aerodynamic performance qualities for use in the optimization of high-speed civil transport (HSCT) aircraft configurations. This procedure employs methods from statistical design of experiments theory and response surface modeling to create the noise-free algebraic models. Results from a sample HSCT design problem involving ten variables are presented to demonstrate the utility of this method.

Toward optimal structured light patterns

Abstract: A methodology for the optimal design of projection patterns for stereometric structured light systems is presented. The similarity as well as the difference between the design of projection patterns and the design of optimal signals for digital communication are discussed. The design of K projection patterns for a structured light system with L distinct planes of light is shown to be equivalent to the placement of L points in a K dimensional space subject to certain constraints. optimal design in the MSE sense is defined, but shown to lead to an intractable multi-parameter global optimization problem. Intuitively appealing suboptimal solutions derived from the family of K dimensional space-filling Hilbert curves are obtained. Preliminary experimental results are presented.

Experimental Design for Sensitivity Analysis, Optimization and Validation of Simulation Models

Abstract: This chapter gives a survey on the use of statistical designs for what-if analysis in simula- tion, including sensitivity analysis, optimization, and validation/verification. Sensitivity analysis is divided into two phases. The first phase is a pilot stage, which consists of screening or searching for the important factors among (say) hundreds of potentially important factors. A novel screening technique is presented, namely sequential bifurcation. The second phase uses regression analysis to approximate the input/output transformation that is implied by the simulation model; the resulting regression model is also known as a metamodel or a response surface. Regression analysis gives better results when the simu- lation experiment is well designed, using either classical statistical designs (such as frac- tional factorials) or optimal designs (such as pioneered by Fedorov, Kiefer, and Wolfo- witz). To optimize the simulated system, the analysts may apply Response Surface Metho- dology (RSM); RSM combines regression analysis, statistical designs, and steepest-ascent hill-climbing. To validate a simulation model, again regression analysis and statistical designs may be applied. Several numerical examples and case-studies illustrate how statisti- cal techniques can reduce the ad hoc character of simulation; that is, these statistical techniques can make simulation studies give more general results, in less time. Appendix 1 summarizes confidence intervals for expected values, proportions, and quantiles, in termi- nating and steady-state simulations. Appendix 2 gives details on four variance reduction techniques, namely common pseudorandom numbers, antithetic numbers, control variates or regression sampling, and importance sampling. Appendix 3 describes jackknifing, which may give robust confidence intervals.

A mixed design approach for probabilistic structural durability

Abstract: In this paper, a mixed approach for probabilistic structural durability design of mechanical systems is proposed. In this approach, a deterministic design optimization that considers structural crack initiation and crack propagation lives at critical points of the structural component as design constraints is performed first. After an optimal design is obtained, a reliability analysis is performed to ascertain if the deterministic optimal design is reliable. If the probability of the failure of the deterministic optimal design is found to be acceptable, a reliability-based design approach that employs a set of interactive design steps, such as trade-off analysis and what-if study, is used to obtain a near-optimal design that is reliable with an affordable computational cost. A 3-D tracked vehicle roadarm is employed to demonstrate the feasibility of the proposed approach.

Optimal Design of Water Distribution Systems Using an NLP Method

Abstract: In this study, a nonlinear programming approach using the successive quadratic programming optimization technique is developed for the optimal design of a pipeline network for water supply systems. The proposed method eliminates the equality constraints describing the hydraulics by a suitable choice of dependent and independent variables. The dependent variables are chosen based on graph theoretic decomposition of the network structure. This makes it possible to compute analytically the reduced constraints, objective function gradients, and reduced Hessian in a very efficient manner. This method of decomposition ensures that the nodal and loop balances are exactly satisfied and is robust for any initial starting point, able to handle incorrect initial flow directions. The method gives solutions comparable to the previous optimal solutions for the design of new as well as expansion of existing water distribution networks.

Optimal repeated measurements designs: the linear optimality equations

Abstract: In approximate design theory, necessary and sufficient conditions that a repeated measurements design be universally optimal are given as linear equations whose unknowns are the proportions of subjects on the treatment sequences. Both the number of periods and the number of treatments in the designs are arbitrary, as is the covariance matrix of the normal response model. The existence of universally optimal "symmetric" designs is proved; the single linear equation which the proportions satisfy is given. A formula for the information matrix of a universally optimal design is derived.

An automated approach for the optimal design of heat exchangers

Abstract: This paper presents an efficient strategy based on simulated annealing (SA), an algorithmic procedure for large-scale combinatorial optimization problems, for the optimal design of heat exchangers. The general heat exchanger design problem can be posed as a large-scale discrete optimization problem, and SA was found to be well suited for this type of heat exchanger design problem. A methodology based on a command procedure has been developed to run the HTRI design program coupled to the annealing algorithm, iteratively. At first, initial runs were made using the command procedure developed to determine the key annealing parameters. These parameters were then used to study several test cases pertaining to the general heat exchanger design problem involving infeasible configurations and vibration constraints. The analyses were performed using two different objective functions namely, total heat transfer area and a linearized purchased cost index. Lastly, the variable set governing the different configurations was extended to incorporate a larger set of design variables. It was observed that, in almost all cases, the optimum designs obtained using the simulated annealing algorithm yielded better performance or cost functions compared to the base case (Amoco) designs. It has also been shown that an improvement in heat exchanger designs is achievable by extending the variable set to include a larger set of design alternatives. Simulated annealing offers great computational savings (in terms of CPU time) as a search strategy and has been found to be a robust technique for the optimal design of heat exchangers subject to process infeasibilities and vibration constraints.

Optimal design of reinforced concrete beams using genetic algorithms

Abstract: This paper presents a method for optimizing the design of reinforced concrete beams subject to a specified set of constraints. A new model of optimization is proposed, leading to more realistic and practical designs. As there are an infinite number of possible beam dimensions and reinforcement ratios that yield the same moment of resistance, it becomes difficult to achieve the least-cost design by conventional iterative methods. We present a method based upon a search technique using genetic algorithms. Several applications show how our system provides more realistic designs than other methods based on mathematical programming techniques. Also, we show our results of experimenting with several representation schemes for the genetic algorithm, and the methodology that we used to adjust its parameters — i.e. population size, crossover and mutation rates and maximum number of generations—so that it produces a reasonable answer in a short period of time. A prototype of this system is currently being tested at our school, to see its potential use as a tool for real-world applications.

Effects of structural uncertainties on tmd design: a reliability-based approach

Abstract: This study investigates the effects of structural uncertainties on the design and performance evaluation of passive tuned mass dampers (TMD) used for vibration control. A probabilistic optimal design methodology is presented in which time-invariant uncertain structural parameters are modelled by random variables with prescribed probability distribution. Unlike conventional TMD designs based on minimizing the mean-square response, a reliability-based performance index is considered in the proposed design which properly accounts for uncertainties in load and structural models. An approximate asymptotic expansion is used to compute the multidimensional reliability integrals arising in the proposed optimal design methodology. Accuracy and effectiveness issues are addressed by comparing results obtained using this approximation with corresponding results obtained by numerical integration. The importance of structural uncertainties is demonstrated by applying the methodology to a single degree of freedom structure subjected to broadband excitations that are modelled by stationary white noise. It is found that the consideration of structural uncertainties improves substantially the robustness of the TMD design. Also, the reliability-based TMD-design methodology results into significantly larger structural reliability compared to that obtained by the conventional design approach based on minimizing the mean-square response.