• Computational Structural Engineering
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• v.10 no.4
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• pp.315-325
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• 1997

This paper describes the application of discretized continuum-type optimality criteria (DCOC) and the development of optimum design program for the multispan partially prestressed concrete beams. The cost of construction as objective function which includes the costs of concrete, prestressing steel, non-prestressing steel and formwork is minimized. The design constraints include limits on the maximum deflection, flexural and shear strengths, in addition to ductility requirements, and upper and lower bounds on design variables as stipulated by the design Code. Based on Kuhn-Tucker necessary conditions, the optimality criteria are explicitly derived in terms of the design variables-effective depth, eccentricity of prestressing steel and non-prestressing steel ratio. The prestressing profile is prescribed by parabolic functions. The self-weight of the structure is included in the equilibrium equation of the real system, as is the secondary effect resulting from the prestressing force. An iterative procedure and computer program for updating the design variables are developed. Two numerical examples of multispan PPC beams with rectangular cross-section are solved to show the applicability and efficiency of the DCOC-based technique.

• The Korean Journal of Applied Statistics
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• v.25 no.3
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• pp.485-501
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• 2012

This research is to find a design D that minimizes forecast variance in d dimensions over the candidate space ${\chi}$. We want a robust design since we may not know the specific covariance structure. We seek a design that minimizes a coverage criterion and hope that this design will provide a small forecast variance even if the covariance structure is unobservable. The details of an exchange or swapping algorithm and several properties of the parameters of coverage criterion with the unknown correlation structures are discussed.

• Communications for Statistical Applications and Methods
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• v.2 no.2
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• pp.376-386
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• 1995

Designs for polynomial approximation to the unknown response function are considered. Optimality criteria are monotone functions of the mean squared error matrix of the least squares estimator. They correspond to the classical A-, D-, G- and Q-optimalities. Optimal first order designs are chosen from the invariant designs and then compared with optimal second order designs.

• Journal of Korean Society for Quality Management
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• v.40 no.4
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• pp.431-440
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• 2012

Purpose: In this paper we propose modified Notz designs which are useful to experimenters who want to adopt the sequential experimentation strategy and to estimate second-order regression model with as few experimental points as possible. Methods: We first present the design matrices and design points in two or three dimensional spaces for such small sized second-order designs as small composite, hybrid, and Notz designs. Modified Notz designs are proposed and compared with some response surface designs in terms of the total number of experimental points, the estimation capability criteria such as D- and A-optimality. Results: When sequential experimentation is necessary, the modified Notz designs are recommendable. Conclusion: The result of this paper will be beneficial to experimenters who need to do experiments more efficiently, especially for those who want to reduce the time of experimentation as much as possible to develop cutting-edge products.

• Journal of the Society of Naval Architects of Korea
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• v.47 no.1
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• pp.58-66
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• 2010

Topology design optimization is a method to determine the optimal distribution of material that yields the minimal compliance of structures, satisfying the constraint of allowable material volume. The method is easy to implement and widely used so that it becomes a powerful design tool in various disciplines. In this paper, a large-scale topology design optimization method is developed using the efficient adjoint sensitivity and optimality criteria methods. Parallel computing technique is required for the efficient topology optimization as well as the precise analysis of large-scale problems. Parallelized finite element analysis consists of the domain decomposition and the boundary communication. The preconditioned conjugate gradient method is employed for the analysis of decomposed sub-domains. The developed parallel computing method in topology optimization is utilized to determine the optimal structural layout of human powered vessel.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.16 no.1
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• pp.59-68
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• 2003

An optimization Program is developed to produce new topologies of plane structures under multiload case. A four-node finite element is used in the response analysis to reduce the computation time and to ultimately achieve practical topology optimization. The bilinear finite element is prone to produce chequer-boarding phenomenon and a simple filtering process is therefore adopted. An artificial material model is employed to represent the structural material and the resizing algorithm based on the optimality criteria is adopted to update the material density parameter during optimization process. With newly developed optimization program, the comparison study has been made between single and multiload cases and its results are described in this paper. From numerical results, it appears that multiload case should be considered to achieve the practical topology optimization.

• The Korean Journal of Applied Statistics
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• v.20 no.2
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• pp.267-280
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• 2007

Various single-valued design optimality criteria such as D-, G-, and V-optimality are used often in constructing optimal experimental designs for mixture experiments in a constrained region R where lower and upper bound constraints are imposed on the ingredients proportions. Even though they are optimal in the strict sense of particular optimality criterion used, it is known that their performance is unsatisfactory with respect to the prediction capability over a constrained region. (Vining et at., 1993; Khuri et at., 1999) We assume the quadratic polynomial model as the mixture response surface model and are interested in finding efficient designs in the constrained design space for a mixture. In this paper, we make an expanded list of candidate design points by adding interior points to the extreme vertices, edge midpoints, constrained face centroids and the overall centroid. Then, we want to propose a robust design with respect to D-optimality, G-optimality, V-optimality and distance-based U-optimality. Comparing scaled prediction variance quantile plots (SPVQP) of robust designs with that of recommended designs in Khuri et al. (1999) and Vining et al. (1993) in the well-known examples of a four-component fertilizer experiment as well as McLean and Anderson's Railroad Flare Experiment, robust designs turned out to be superior to those recommended designs.

• Communications for Statistical Applications and Methods
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• v.9 no.3
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• pp.619-627
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• 2002

It is unpractical for the optimal design theory based on the given model and assumption to be applied to the real-world experimentation. Particularly, when the experimenter feels it necessary to consider multiple objectives in experimentation, its modified version of optimality criteria is indeed desired. The constrained optimal design is one of many methods developed in this context. But when the number of constraints exceeds two, there always exists a problem in specifying the lower limit for the efficiencies of the constraints because the “infeasible solution” issue arises very quickly. In this paper, we developed a sequential approach to tackle this problem assuming that all the constraints can be ranked in terms of importance. This approach has been applied to the polynomial regression model.

• Communications for Statistical Applications and Methods
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• v.23 no.2
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• pp.119-129
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• 2016

A new sampling method is introduced based on the idea of a ranked set sampling scheme in which taken samples in each set are dependent on previous ones. Some theoretical results are presented and distribution-free confidence intervals are derived for the quantiles of any continuous population. It is shown numerically that the proposed sampling scheme may lead to 95% confidence intervals (especially for extreme quantiles) that cannot be found based on the ordinary ranked set sampling scheme presented by Chen (2000) and Balakrishnan and Li (2006). Optimality aspects of this scheme are investigated for both coverage probability and minimum expected length criteria. A real data set is also used to illustrate the proposed procedure. Conclusions are eventually stated.

• Structural Engineering and Mechanics
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• v.70 no.3
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• pp.367-380
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• 2019

The paper concerns topology and geometry optimization of statically determinate beams with arbitrary number of supports. The optimization problem is treated as a bi-criteria one, with the objectives of minimizing the absolute maximum bending moment and the maximum deflection for a uniform gravity load. The problem is formulated and solved using the Pareto optimality concept and the lexicographic ordering of the objectives. The non-dominated sorting genetic algorithm NSGA-II and the local search method are used for the optimization in the Pareto sense, whereas the genetic algorithm and the exhaustive search method for the lexicographic optimization. Trade-offs between objectives are examined and sets of Pareto-optimal solutions are provided for different topologies. Lexicographically optimal beams are found assuming that the maximum moment is a more important criterion. Exact formulas for locations and values of the maximum deflection are given for all lexicographically optimal beams of any topology and any number of supports. Topologies with lexicographically optimal geometries are classified into equivalence classes, and specific features of these classes are discussed. A qualitative principle of the division of topologies equivalent in terms of the maximum moment into topologies better and worse in terms of the maximum deflection is found.