• The Korean Journal of Applied Statistics
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• v.15 no.2
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• pp.297-310
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• 2002

Liang and Zeger proposed generalized estimating equations(GEE) for analyzing repeated data which is discrete or continuous. GEE model can be extended to model for repeated categorical data and its estimator has asymptotic multivariate normal distribution in large sample sizes. But GEE is based on large sample asymptotic theory. In this paper, we study the properties of GEE estimators for repeated ordinal data in small sample sizes. We generate ordinal repeated measurements for two groups using two methods. Through Monte Carlo simulation studies we investigate the empirical type 1 error rates, powers, relative efficiencies of the GEE estimators, the effect of unequal sample size of two groups, and the performance of variance estimators for polytomous ordinal response variables, especially in small sample sizes.

• Computers and Concrete
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• v.9 no.5
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• pp.327-340
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• 2012

The search for a design that meets both performance and safety, with minimal cost and lesser environmental impact was always the goal of structural engineers. In general, the design of conventional reinforced concrete structures is an iterative process based on rules of thumb established from the personal experience and intuition of the designer. However, such procedure makes the design process exhaustive and only occasionally leads to the best solution. In such context, this work presents the development and implementation of a mathematical formulation for obtaining optimal sections of reinforced concrete columns subjected to uniaxial flexural compression, based on the verification of strength proposed by the Brazilian standard NBR 6118 (ABNT 2007). To minimize the cost of the reinforced concrete columns, the Simulated Annealing optimization method was used, in which the amount and diameters of the reinforcement bars and the dimensions of the columns cross sections were considered as discrete variables. The results obtained were compared to those obtained from the conventional design procedure and other optimization methods, in an attempt to verify the influence of resistance class, variations in the magnitudes of bending moment and axial force, and material costs on the optimal design of reinforced concrete columns subjected to uniaxial flexural compression.

• Advances in Computational Design
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• v.2 no.4
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• pp.313-331
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• 2017

In this study, teaching-learning based optimization (TLBO) is improved by incorporating model of multiple teachers, adaptive teaching factor, self-motivated learning, and learning through tutorial. Modified TLBO (MTLBO) is applied for simultaneous topology, shape, and size optimization of space and planar trusses to study its effectiveness. All the benchmark problems are subjected to stress, displacement, and kinematic stability constraints while design variables are discrete and continuous. Analyses of unacceptable and singular topologies are prohibited by seeing element connectivity through Grubler's criterion and the positive definiteness. Performance of MTLBO is compared to TLBO and state-of-the-art algorithms available in literature, such as a genetic algorithm (GA), improved GA, force method and GA, ant colony optimization, adaptive multi-population differential evolution, a firefly algorithm, group search optimization (GSO), improved GSO, and intelligent garbage can decision-making model evolution algorithm. It is observed that MTLBO has performed better or found nearly the same optimum solutions.

• Steel and Composite Structures
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• v.28 no.4
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• pp.427-438
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• 2018

Static stability is a decisive factor in the design of domes. Stability-related external factors, such as load and supports, are incorporated into structural vulnerability theory by the definition of a relative rate of joint well-formedness ($r_r$). Hence, the instability mechanism of domes can be revealed. To improve stability, an optimization model against instability, which takes the maximization of the lowest $r_r$ ($r_{r,min}$) as the objective and the discrete member sections as the variables, is established with constraints on the design requirements and steel consumption. Optimizations are performed on two real-life Kiewitt-6 model domes with a span of 23.4 m and rise of 11.7 m, which are initially constructed for shaking table collapse test. Well-formedness analyses and stability calculation (via arc-length method) of the models throughout the optimization history demonstrate that this proposed method can effectively enhance $r_{r,min}$ and optimize the static stability of shell-like structures. Additionally, seismic performance of the optimum models subjected to the same earthquake as in the shaking table test is checked. The supplemental simulations prove that the optimum models are superior to the original models under earthquake load as well.

• Proceedings of the Korean Society For Composite Materials Conference
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• 2002.10a
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• pp.233-236
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• 2002

An efficient method was developed in this study to obtain optimal stacking sequences, thicknesses, and minimum weights of stiffened laminated composite shells under combined loading conditions and stiffener layouts using genetic algorithms (GAs) and finite element analyses. Among many parameters in designing composite laminates determining a optimal stacking sequence that may be formulated as an integer programming problem is a primary concern. Of many optimization algorithms, GAs are powerful methodology for the problem with discrete variables. In this paper the optimal stacking sequence was determined, which gives the maximum critical buckling load factor and the minimum weight as well. To solve this problem, both the finite element analysis by ABAQUS and the GA-based optimization procedure have been implemented together with an interface code. Throughout many parametric studies using this analysis tool, the influences of stiffener sizes and three different types of stiffener layouts on the stacking sequence changes were throughly investigated subjected to various combined loading conditions.

• Transactions of the Korean Society of Machine Tool Engineers
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• v.16 no.1
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• pp.26-32
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• 2007

This study was carried out fusion-welded butt joints in SWS 490A high strength steel subjected to tensile test that load-deflection curve. The windowed or short-time Fourier transform(WFT or STFT) makes possible for the analysis of non-stationary or transient signals into a joint time-frequency domain and the wavelet transform(WT) is used to decompose the acoustic emission(AE) signal into various discrete series of sequences over different frequency bands. In this paper, for acoustic emission signal analysis to use a continuous wavelet transform, in which the Gabor wavelet base on a Gaussian window function is applied to the time-frequency domain. A wavelet transform is demonstrated and the plots are very powerful in the recognition of the acoustic emission features. As a result, the technique of acoustic emission is ideally suited to study variables which control time and stress dependent fracture or damage process in metallic materials.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2009.04a
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• pp.266-271
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• 2009

A modeling method for the modal analysis of a multi-packet blade system having a crack undergoing rotational motion is presented in this paper. Each blade is assumed as a slender cantilever beam. The stiffness coupling effects between blades due to the flexibilities of the disc and the shroud are modeled with discrete springs. Hybrid deformation variables are employed to derive the equations of motion. The flexibility due to crack, which is assumed to be open during the vibration, is calculated basing on a fracture mechanics theory. To obtain more general information, the equations of motion are transformed into dimensionless forms in which dimensionless parameters are identified. The effects of the dimensionless parameters related to the angular speed, the depth and location of a crack on the modal characteristics of the system are investigated with some numerical examples.

• Transactions of the Korean Society of Mechanical Engineers
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• v.19 no.3
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• pp.639-646
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• 1995

The objective of this study is to minimize the weight of a damped anisotropic roto-bearing system considering whirl natural frequency and stability. The system is modeled as an assemblage of rigid disks, flexible shafts and discrete bearings. The system design variables are the crosssectional areas of shaft elements and the properties of bearings. To analyze the system, the polynomial method which is derived by rearranging the calculations performed by a transfer matrix method is adopted. For the optimization, the optimization software IDOL (Integrated Design Optimization Library) which is based on the Augmented Lagrange Multiplier (ALM) method is employed. Also, an analytical design sensitivity analysis of the system is used for high accuracy and efficiency. To demonstrate the usefulness of the proposed optimal design program incorporating analysis, design sensitivity analysis, and optimization modules, a damped anisotropic rotor-bearing system is optimized to obtain 34$ weight reduction.

• Journal of Institute of Control, Robotics and Systems
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• v.3 no.1
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• pp.101-108
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• 1997

The initial token value required to the optimal performance of discrete event systems can be decided by Sum of Delay Time and Synchronic Time ratio, which are new synchronic variables in Timed Place Petri Nets. For the system consisting of two Live-and-Bounded circuits(LB-circuits) fused in common Transition-Transition-Path or common Place-Place-Path, we prove that the Synchronic Time Ratio is the initial token ratio between two LB-circuits to optimally perform system functions. These results are generalized and formulated as a theorem. The initial tokens of a specific place can imply shared resources. Using the theorem, we can decide the minimum number of the shared resources to obtain the optimal performance, and minimize the idling time of resources. As an example, an automated assembly system is modeled by Timed Place Petri Net, and the initial tokens to achieve the optimal system performance are identified. All the values are verified by simulation.

• The Korean Journal of Applied Statistics
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• v.17 no.3
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• pp.535-545
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• 2004

The clustering method suggested in this paper produces clusters based on the 'rules of variables' by merging the 'training' and the identically structured reference data and then by filtering it to obtain the clusters of the 'training data' through the use of the 'tree classification model'. The reference dataset is generated by spatially contrasting it to the 'training data' through the 'reverse arcing' algorithm to effectively identify the clusters. The strength of this method is that it can be applied even to the mixture of continuous and discrete types of 'training data' and the performance of this algorithm is illustrated by applying it to the simulated data as well as to the actual data.