Showing papers on "Optimal design published in 2002"

Shape optimization by the homogenization method

Abstract: In the context of shape optimization, we seek minimizers of the sum of the elastic compliance and of the weight of a solid structure under specified loading. This problem is known not to be well-posed, and a relaxed formulation is introduced. Its effect is to allow for microperforated composites as admissible designs. In a two-dimensional setting the relaxed formulation was obtained in [6] with the help of the theory of homogenization and optimal bounds for composite materials. We generalize the result to the three dimensional case. Our contribution is twofold; first, we prove a relaxation theorem, valid in any dimensions; secondly, we introduce a new numerical algorithm for computing optimal designs, complemented with a penalization technique which permits to remove composite designs in the final shape. Since it places no assumption on the number of holes cut within the domain, it can be seen as a topology optimization algorithm. Numerical results are presented for various two and three dimensional problems.

Optimal designs for space-time linear precoders and decoders

Abstract: We introduce a new paradigm for the design of transmitter space-time coding that we refer to as linear precoding. It leads to simple closed-form solutions for transmission over frequency-selective multiple-input multiple-output (MIMO) channels, which are scalable with respect to the number of antennas, size of the coding block, and transmit average/peak power. The scheme operates as a block transmission system in which vectors of symbols are encoded and modulated through a linear mapping operating jointly in the space and time dimension. The specific designs target minimization of the symbol mean square error and the approximate maximization of the minimum distance between symbol hypotheses, under average and peak power constraints. The solutions are shown to convert the MIMO channel with memory into a set of parallel flat fading subchannels, regardless of the design criterion, while appropriate power/bits loading on the subchannels is the specific signature of the different designs. The proposed designs are compared in terms of various performance measures such as information rate, BER, and symbol mean square error.

Optimal Reliability Modeling: Principles and Applications

Abstract: PrefaceAcknowledgments1 Introduction11 Needs for Reliability Modeling12 Optimal Design2 Reliability Mathematics21 Probability and Distributions211 Events and Boolean Algebra212 Probabilities of Events213 Random Variables and Their Characteristics214 Multivariate Distributions215 Special Discrete Distributions216 Special Continuous Distributions22 Reliability Concepts23 Commonly Used Lifetime Distributions24 Stochastic Processes241 General Definitions242 Homogeneous Poisson Process243 Nonhomogeneous Poisson Process244 Renewal Process245 Discrete-Time Markov Chains246 Continuous-Time Markov Chains25 Complex System Reliability Assessment Using Fault Tree Analysis3 Complexity Analysis31 Orders of Magnitude and Growth32 Evaluation of Summations33 Bounding Summations34 Recurrence Relations341 Expansion Method342 Guess-and-Prove Method343 Master Method35 Summary4 Fundamental System Reliability Models41 Reliability Block Diagram42 Structure Functions43 Coherent Systems44 Minimal Paths and Minimal Cuts45 Logic Functions46 Modules within a Coherent System47 Measures of Performance48 One-Component System49 Series System Model491 System Reliability Function and MTTF492 System Availability410 Parallel System Model4101 System Reliability Function and MTTF4102 System Availability of Parallel System with Two iid Components4103 System Availability of Parallel System with Two Different Components4104 Parallel Systems with n iid Components411 Parallel-Series System Model412 Series-Parallel System Model413 Standby System Model4131 Cold Standby Systems4132 Warm Standby Systems5 General Methods for System Reliability Evaluation51 Parallel and Series Reductions52 Pivotal Decomposition53 Generation of Minimal Paths and Minimal Cuts531 Connection Matrix532 Node Removal Method for Generation of Minimal Paths533 Generation of Minimal Cuts from Minimal Paths54 Inclusion-Exclusion Method55 Sum-of-Disjoint-Products Method56 Markov Chain Imbeddable Structures561 MIS Technique in Terms of System Failures562 MIS Technique in Terms of System Success57 Delta-Star and Star-Delta Transformations571 Star or Delta Structure with One Input Node and Two Output Nodes572 Delta Structure in Which Each Node May Be either an Input Node or an Output Node58 Bounds on System Reliability581 IE Method582 SDP Method583 Esary-Proschan (EP) Method584 Min-Max Bounds585 Modular Decompositions586 Notes6 General Methodology for System Design61 Redundancy in System Design62 Measures of Component Importance621 Structural Importance622 Reliability Importance623 Criticality Importance624 Relative Criticality63 Majorization and Its Application in Reliability631 Definition of Majorization632 Schur Functions633 L-Additive Functions64 Reliability Importance in Optimal Design65 Pairwise Rearrangement in Optimal Design66 Optimal Arrangement for Series and Parallel Systems67 Optimal Arrangement for Series-Parallel Systems68 Optimal Arrangement for Parallel-Series Systems69 Two-Stage Systems610 Summary7 Thek-out-of-n System Model71 System Reliability Evaluation711 The k-out-of-n:G System with iid Components712 The k-out-of-n:G System with Independent Components713 Bounds on System Reliability72 Relationship between k-out-of-n G and F Systems721 Equivalence between k-out-of-n:G and (n - k + 1)-out-of-n:F Systems722 Dual Relationship between k-out-of-n G and F Systems73 Nonrepairable k-out-of-n Systems731 Systems with iid Components732 Systems with Nonidentical Components733 Systems with Load-Sharing Components Following Exponential Lifetime Distributions734 Systems with Load-Sharing Components Following Arbitrary Lifetime Distributions735 Systems with Standby Components74 Repairable k-out-of-n Systems741 General Repairable System Model742 Systems with Active Redundant Components743 Systems with Load-Sharing Components744 Systems with both Active Redundant and Cold Standby Components75 Weighted k-out-of-n:G Systems8 Design of k-out-of-n Systems81 Properties of k-out-of-n Systems811 Component Reliability Importance812 Effects of Redundancy in k-out-of-n Systems82 Optimal Design of k-out-of-n Systems821 Optimal System Size n822 Simultaneous Determination of n and k823 Optimal Replacement Time83 Fault Coverage831 Deterministic Analysis832 Stochastic Analysis84 Common-Cause Failures841 Repairable System with Lethal Common-Cause Failures842 System Design Considering Lethal Common-Cause Failures843 Optimal Replacement Policy with Lethal Common-Cause Failures844 Nonlethal Common-Cause Failures85 Dual Failure Modes851 Optimal k or n Value to Maximize System Reliability852 Optimal k or n Value to Maximize System Profit853 Optimal k and n Values to Minimize System Cost86 Other Issues861 Selective Replacement Optimization862 TMR and NMR Structures863 Installation Time of Repaired Components864 Combinations of Factors865 Partial Ordering9 Consecutive-k-out-of-n Systems91 System Reliability Evaluation911 Systems with iid Components912 Systems with Independent Components92 Optimal System Design921 B-Importances of Components922 Invariant Optimal Design923 Variant Optimal Design93 Consecutive-k-out-of-n:G Systems931 System Reliability Evaluation932 Component Reliability Importance933 Invariant Optimal Design934 Variant Optimal Design94 System Lifetime Distribution941 Systems with iid Components942 System with Exchangeable Dependent Components943 System with (k - 1)-Step Markov-Dependent Components944 Repairable Consecutive-k-out-of-n Systems95 Summary10 Multidimensional Consecutive-k-out-of-n Systems101 System Reliability Evaluation1011 Special Multidimensional Systems1012 General Two-Dimensional Systems1013 Bounds and Approximations102 System Logic Functions103 Optimal System Design104 Summary11 Other k-out-of-n and Consecutive-k-out-of-n Models111 The s-Stage k-out-of-n Systems112 Redundant Consecutive-k-out-of-n Systems113 Linear and Circular m-Consecutive-k-out-of-n Model114 The k-within-Consecutive-m-out-of-n Systems1141 Systems with iid Components1142 Systems with Independent Components1143 The k-within-(r, s)/(m, n):F Systems115 Series Consecutive-k-out-of-n Systems116 Combined k-out-of-n:F and Consecutive-kc-out-of-n:F System117 Combined k-out-of-mn:F and Linear (r, s)/(m, n):F System118 Combined k-out-of-mn:F, One-Dimensional Con/kc/n:F, and Two-Dimensional Linear (r, s)/(m, n):F Model119 Application of Combined k-out-of-n and Consecutive-k-out-of-n Systems1110 Consecutively Connected Systems1111 Weighted Consecutive-k-out-of-n Systems11111 Weighted Linear Consecutive-k-out-of-n:F Systems11112 Weighted Circular Consecutive-k-out-of-n:F Systems12 Multistate System Models121 Consecutively Connected Systems with Binary System State and Multistate Components1211 Linear Multistate Consecutively Connected Systems1212 Circular Multistate Consecutively Connected Systems1213 Tree-Structured Consecutively Connected Systems122 Two-Way Consecutively Connected Systems123 Key Concepts in Multistate Reliability Theory124 Special Multistate Systems and Their Performance Evaluation1241 Simple Multistate k-out-of-n:G Model1242 Generalized Multistate k-out-of-n:G Model1243 Generalized Multistate Consecutive-k-out-of-n:F System125 General Multistate Systems and Their Performance Evaluation126 SummaryAppendix: Laplace TransformReferencesBibliographyIndex

Optimal Design for Multinomial Choice Experiments

Abstract: The author derives D-optimal designs for main-effects, multinomial choice experiments using attribute levels as design parameters. The design solutions are similar to standard main-effects designs except that one attribute is used to manipulate response probabilities. The manipulator is key to implementing optimal designs in practice.

Centered L 2 -discrepancy of random sampling and Latin hypercube design, and construction of uniform designs

Abstract: In this paper properties and construction of designs under a centered version of the L2-discrepancy are analyzed. The theoretic expectation and variance of this discrepancy are derived for random designs and Latin hypercube designs. The expectation and variance of Latin hypercube designs are significantly lower than that of random designs. While in dimension one the unique uniform design is also a set of equidistant points, low-discrepancy designs in higher dimension have to be generated by explicit optimization. Optimization is performed using the threshold accepting heuristic which produces low discrepancy designs compared to theoretic expectation and variance.

On the theory of optimal sensor placement

Abstract: On the Theory of Optimal Sensor Placement An optimal sensor placement is defined as a sensor configuration that achieves the minimum capital cost while observing prespecified performance criteria. Previous formulations of this problem have resulted in the definition of a mixed-integer nonlinear program (MINLP) with dimensions dependent on the value of the integer decision variables. The main contribution of this work is an equivalent reformulation of the design problem such that the dimension of the NLP is independent of all decision variables. Additionally, the traditional sensor-placement problem, based on static process conditions, is extended to linear dynamic processes. The final contribution is the exact conversion of the general NLP into a convex program through the use of linear matrix inequalities. The aggregation of these results show that the sensor-placement problem can be solved globally and eficiently using standard interior-point and branch-and-bound search algorithms.

Tuned mass dampers for response control of torsional buildings

Abstract: This paper presents an approach for optimum design of tuned mass dampers for response control of torsional building systems subjected to bi-directional seismic inputs. Four dampers with fourteen distinct design parameters, installed in pairs along two orthogonal directions, are optimally designed. A genetic algorithm is used to search for the optimum parameter values for the four dampers. This approach is quite versatile as it can be used with different design criteria and definitions of seismic inputs. It usually provides a globally optimum solution. Several optimal design criteria, expressed in terms of performance functions that depend on the structural response, are used. Several sets of numerical results for a torsional system excited by random and response spectrum models of seismic inputs are presented to show the effectiveness of the optimum designs in reducing the system response. Copyright © 2002 John Wiley & Sons, Ltd.

The optimal design of blocked and split-plot experiments

Abstract: Introduction * Advanced Topics in Optimal Design * Compound Symmetric Error Structure * Optimal Designs in the Presence of Random Block Effects * Optimal Designs for Quadratic Regression on One Variable and Blocks of Size Two * Constrained Split-Plot Designs * Optimal Split-Plot Designs in the Presence of Hard-to-Change Factors * Optimal Split-Plot Designs * Two-level Factorial and Fractional Factorial Designs

Non-parametric optimal design in dose finding studies

Abstract: We describe a non-parametric optimal design as a theoretical gold standard for dose finding studies. Its purpose is analogous to the Cramer-Rao bound for unbiased estimators, i.e. it provides a bound beyond which improvements are not generally possible. The bound applies to the class of non-parametric designs where the data are not assumed to be generated by any known parametric model. Whenever parametric assumptions really hold it may be possible to do better than the optimal non-parametric design. The goal is to be able to compare any potential dose finding scheme with the optimal non-parametric benchmark. This paper makes precise what is meant by optimal in this context and also why the procedure is described as non-parametric.

Constrained robust optimal design using a multiobjective evolutionary algorithm

Abstract: A major fraction of evolutionary optimization methods aims to find solutions that maximize performance. However, a solution that solely maximizes performance is of no practical use as it may be too sensitive to parametric variations (nonuniform material properties, inexact physical dimensions, uncertainties in loading and operating conditions, etc.). Furthermore, for design problems with constraints, a robust solution needs to be feasible and remain feasible under parametric variations. In this paper, a new evolutionary algorithm is proposed that is capable of handling constrained robust optimal design problems. A multiobjective formulation is introduced that considers an individuals' performance, the mean performance of its neighbors and the standard deviation of its neighbors' performance as three objectives for optimization. In order to handle feasibility, an innovative constraint-handling scheme based on the Pareto concept is introduced that considers an individual's self-feasibility and its neighborhood feasibility. Robust optimal solutions to two engineering design examples are reported in this paper. Results of simulations are also presented to illustrate the differences between an optimal solution and a robust optimal solution.

The comparison of designs for sequential clinical trials with covariate information

Abstract: coin type for the sequential allocation of treatments in a clinical trial. One important characteristic is the loss, which measures the increase in the variance of parameter estimates due to the imbalance caused by randomization. The other important characteristic is the selection bias measuring the probability of correctly guessing which treatment is to be allocated next. The combination of these two measures leads to the elucidation of admissible designs. Simulations provide clear plots of the behaviour of the designs and make it possible to distinguish good designs from those which are less good.

Genetic algorithm for discrete-sizing optimal design of trusses using the force method

Abstract: In the process of discrete-sizing optimal design of truss structures by Genetic Algorithm (GA), analysis should be performed several times. In this article, the force method is employed for the analysis. The advantage of using this method lies in the fact that the matrices corresponding to particular and complementary solutions are formed independently of the mechanical properties of members. These matrices are used several times in the process of the sequential analyses, increasing the speed of optimization. The second feature of the present method is the automatic nature of the prediction of the useful range of sections for a member from a list of profiles with a large number of cross-sections. The third feature consists of a contraction process developed to increase the efficiency of the GA by which an optimal design for the first sub-string associated with member cross-sections is obtained. Improved designs are achieved in subsequent cycles by reducing the length of sub-strings. Copyright © 2002 John Wiley & Sons, Ltd.

Fisher information matrix for non-linear mixed-effects models: evaluation and application for optimal design of enoxaparin population pharmacokinetics.

Abstract: We address the problem of the choice and the evaluation of designs in population pharmacokinetic studies that use non-linear mixed-effects models. Criteria, based on the Fisher information matrix, have been developed to optimize designs and adapted to such models. We optimize designs under different constraints and evaluate them for a population pharmacokinetics study, within a new phase III trial of enoxaparin, a low molecular weight heparin. To do this, we approximate the expression of the Fisher information matrix for non-linear mixed-effects models including the residual error variance as a parameter to be estimated. We use the Fedorov-Wynn algorithm to minimize the inverse of the determinant of this matrix as required by the D-optimality criterion. Two optimal designs, as well as a design defined by pharmacologists, are evaluated by the simulation of 30 replicated data sets with NONMEM; all designs involve 220 patients with four measurements per patient. We also evaluate the relevance of the standard errors of estimation given from the Fisher information matrix by comparison with those given by NONMEM. The three designs provide more precise population parameter estimates; the optimal design gives the best precision and offers a simple clinical implementation. The expected standard errors given by the information matrix are close to those obtained by NONMEM on the simulation. Moreover, the proposed criterion of D-optimality appears to be a good measure to compare designs for population studies.

Topics in Optimal Design

Abstract: Scope of the Monograph * Optimal Regression Designs in Symmetric Domains * Optimal Regression Designs in Asymmetric Factor Domains * Optimal Regression Designs for Covariates' Models with Structured Intercept Parameter * Stochastic Distance Optimality * Designs in the Presence of Trends * Additional Selected Topics

Shape optimization of supersonic turbines using global approximation methods

Abstract: There is growing interest to adopt supersonic turbines for rocket propulsion. However, this technology has not been actively investigated in the United States for the last three decades. To aid design improvement, a global optimization framework combining the radial-basis neural network (NN) and the polynomial response surface (RS) method is constructed for shape optimization of a two-stage supersonic turbine, involving O(10) design variables. The design of the experiment approach is adopted to reduce the data size needed by the optimization task. The combined NN and RS techniques are employed. A major merit of the RS approach is that it enables one to revise the design space to perform multiple optimization cycles. This benefit is realized when an optimal design approaches the boundary of a predefined design space. Furthermore, by inspecting the influence of each design variable, one can also gain insight into the existence of multiple design choices and select the optimum design based on other factors such as stress and materials consideration.

Optimal design of passive energy dissipation systems based on H∞ and H2 performances

Abstract: Passive energy dissipation devices (EDDs), such as viscous dampers, viscoelastic dampers, etc., have been used to effectively reduce the dynamic response of civil infrastructures, such as buildings and bridges, subject to earthquakes and strong winds. The design of these passive energy dissipation devices (EDDs) involves the determination of the optimal locations and the corresponding capacities. In this paper, we present two optimal design methodologies for passive EDDs based on active control theories, including H∞ and H 2 performances, respectively. The optimal design methodologies presented are capable of determining the optimal locations and the corresponding capacities of EDDs. Emphasis is placed on the application of linear matrix inequality (LMI) for the effective design of passive EDDs using the popular MATLAB toolboxes. One important advantage of the proposed approaches is that the computation of the structural response is not needed in the design process. The proposed optimal design methodologies have been applied to: (i) a 10-storey building and a 24-storey building both subject to earthquake excitations, and (ii) a 76-storey wind-excited benchmark building, to demonstrate the advantages of the proposed design methodologies over the conventional equal capacity design.

Optimal asymmetric one‐sided group sequential tests

Abstract: SUMMARY We extend the optimal symmetric group sequential tests of Eales & Jennison (1992) to the broader class of asymmetric designs. Two forms of asymmetry are considered, involving unequal type I and type II error rates and different emphases on expected sample sizes at the null and alternative hypotheses. We discuss the properties of our optimal designs and use them to assess the efficiency of the family of tests proposed by Pampallona & Tsiatis (1994) and two families of one-sided tests defined through error spending functions. We show that the error spending designs are highly efficient, while the easily implemented tests of Pampallona & Tsiatis are a little less efficient but still not far from optimal. Our results demonstrate that asymmetric designs can decrease the expected sample size under one hypothesis, but only at the expense of a significantly larger expected sample size under the other hypothesis.

Design of Computer Experiments for Metamodel Generation

Abstract: We review the use of statistical design and analysis of computer experiments (DACE) for the generation of parsimonious, surrogate models, also known as metamodels. Such metamodels are used to replace cpu- or memory-intensive, discretized approximations that often arise in MEMS and MOEMS. Emphasis is placed on optimal designs.

Optimal crossover designs in a model with self and mixed carryover effects

Abstract: We consider a variant of the usual model for crossover designs with carryover effects. Instead of assuming that the carryover effect of a treatment is the same regardless of the treatment in the next period, the model assumes that the carryover effect of a treatment on itself is different from the carryover effect on other treatments. For the traditional model, optimal designs tend to have pairs of consecutive identical treatments; for the model considered here, they tend to avoid such pairs. Practitioners have long expressed reservations about designs that exhibit such pairs and about the traditional model. The new model provides an attractive alternative that leads to appealing optimal designs.

Design and analysis of computer experiments when the output is highly correlated over the input space

Abstract: To build a predictor, the output of a deterministic computer model or “code” is often treated as a realization of a stochastic process indexed by the code's input variables. The authors consider an asymptotic form of the Gaussian correlation function for the stochastic process where the correlation tends to unity. They show that the limiting best linear unbiased predictor involves Lagrange interpolating polynomials; linear model terms are implicitly included. The authors then develop optimal designs based on minimizing the limiting integrated mean squared error of prediction. They show through several examples that these designs lead to good prediction accuracy.

Flexibility analysis and design using a parametric programming framework

Abstract: This article presents a new framework, based on parametric programming, that unifies the solution of the various flexibility analysis and design optimization problems that arise for linear, convex, and nonconvex, nonlinear systems with deterministic or stochastic uncertainties. This approach generalizes earlier work by Bansal et al. It allows (1) explicit information to be obtained on the dependence of the flexibility characteristics of a nonlinear system on the values of the uncertain parameters and design variables; (2) the critical uncertain parameter points to be identified a priori so that design optimization problems that do not require iteration between a design step and a flexibility analysis step can be solved; and (3) the nonlinearity to be removed from the optimization subproblems that need to be solved when evaluating the flexibility of systems with stochastic uncertainties.

Optimal design of number and locations of actuators in active vibration control of a space truss

Abstract: This paper presents the optimal design methodology of number and locations of actuators in active vibration control of a space truss using multiple piezoelectric ceramic stack actuators. The eigenvalue distribution of the energy correlative matrix of the control input force is applied to determine the optimal number of actuators required, and genetic algorithms (GAs) are adopted to search for the optimal locations of actuators. The results show that the disturbance acting on a structure is a key factor in determining the optimal number and locations of actuators in active structural vibration control, and a global and efficient optimization solution of multiple actuator locations can be obtained using the GAs.