• Journal of Korean Society for Quality Management
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• v.48 no.4
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• pp.535-552
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• 2020

Purpose: The main theme of this study is to derive a specific quality loss function with multiple characteristics according to the same analytical structure as the single characteristic quality loss function of Taguchi. In other words, it presents an analytical framework for measuring quality costs that can be controlled in practice. Methods: This study followed the analytical methodology through geometric, linear algebraic, and statistical approaches Results: The function suggested by this study is as follows; $$L(x_1,x_2,{\cdots},x_t)={\sum\limits_{i=1}^{t}}k_i\{x_i+{\sum\limits_{j=1}^{t}}\({\rho}_{ij}{\frac{d_i}{d_j}}\)x_j\}x_i$$ Conclusion: This paper derived the quality loss function with multiple quality characteristics to expand the usefulness of the Taguchi quality loss function. The function derived in this paper would be more meaningful to estimate quality costs under the practical situation and general structure with multiple quality characteristics than the function by linear algebraic approach in response surface analysis.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.15 no.12
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• pp.4567-4583
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• 2021

This study proposes an analytical approximation algorithm based on extreme value theory (EVT) for the inverse of the power of the incomplete Gamma function. First, the Gumbel function is used to approximate the power of the incomplete Gamma function, and the corresponding inverse problem is transformed into the inversion of an exponential function. Then, using the tail equivalence theorem, the normalized coefficient of the general Weibull distribution function is employed to replace the normalized coefficient of the random variable following a Gamma distribution, and the approximate closed form solution is obtained. The effects of equation parameters on the algorithm performance are evaluated through simulation analysis under various conditions, and the performance of this algorithm is compared to those of the Newton iterative algorithm and other existing approximate analytical algorithms. The proposed algorithm exhibits good approximation performance under appropriate parameter settings. Finally, the performance of this method is evaluated by calculating the thresholds of space-time block coding and space-frequency block coding pattern recognition in multiple-input and multiple-output orthogonal frequency division multiplexing. The analytical approximation method can be applied to other related situations involving the maximum statistics of independent and identically distributed random variables following Gamma distributions.

• Nuclear Engineering and Technology
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• v.54 no.4
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• pp.1471-1481
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• 2022

This paper aims to present a new method for obtaining an analytical solution for the Kaniadakis Doppler broadening (KDB) function. Also, in this work, we report the computational efficiencies of this solution compared with the numerical one. The solution of the differential equation achieved in this paper is free of approximations and is, consequently, a more robust methodology for obtaining an analytical representation of ψ_k. Moreover, the results show an improvement in efficiency using the analytical approximation, indicating that it may be helpful in different applications that require the calculation of the deformed Doppler broadening function.

• Proceedings of the KSME Conference
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• 2007.05b
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• pp.2250-2254
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• 2007

Comprehensive analytical models focusing on the anode water loss, the cathode flooding, water equilibrium, and water management strategy are developed for polymer electrolyte fuel cells. Analytical solutions presented in this study are compared with two-dimensional computational results and shows a good agreement in predicting those critical characteristics of water. General features of water concentration profile as a function of membrane thickness and current density are presented to illustrate the net effect of the back-diffusion of water from the cathode to anode and the water production by the cathode catalytic reaction on water transport over a fuel cell domain. As one of practical applications, the required humidity level of feed streams for full saturation at the channel outlets are investigated as a function of the physical operating condition. These analytical models can provide good understanding on the characteristic water

• Earthquakes and Structures
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• v.3 no.3_4
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• pp.507-518
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• 2012

It is now widely accepted that the resulting displacement field within elastic, inhomogeneous, anisotropic solids subjected to equipartitioned, uniform illumination from uncorrelated sources, has intensities that follow diffusion-like equations. Typically, coda waves are invoked to illustrate this concept. These waves arrive later as a consequence of multiple scattering and appear at "the tail" (coda, in Latin) of seismograms and are usually considered an example of diffuse field. It has been demonstrated that the average correlations of motions within a diffuse field, in frequency domain, is proportional to the imaginary part of Green's function tensor. If only one station is available, the average autocorrelation is equal to the average squared amplitudes or the average power spectrum and this gives the Green's function at the source itself. Several works address this point from theoretical and experimental point of view. However, a complete and explicit analytical description is lacking. In this work we study analytically some properties of the Green's function, specifically the imaginary part of Green's function for 2D antiplane problems. This choice is guided by the fact that these scalar problems have a closed analytical solution (Kausel 2006). We assume the diffusiveness of the field and explore its analytical consequences.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.17 no.7 s.124
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• pp.579-586
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• 2007

Analytical method to analyze the effect of tolerance on the modal characteristic of multi-body systems in dynamic equilibrium position is suggested in this paper. Monte-Carlo method is conventionally employed to perform the tolerance analysis. However, Monte-Carlo method spends too much time for analysis and has a greater or less accuracy depending on sample condition. To resolve these problems, an analytical method is suggested in this paper. Sensitivity equations for damped natural frequencies and the transfer function are derived at the dynamic equilibrium position. By employing the sensitivity information of mass, damping and stiffness matrices, the sensitivities of damped natural frequencies and the transfer function can be calculated.

• Journal of Power Electronics
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• v.13 no.4
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• pp.552-557
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• 2013

This paper proposed an analytical model for the distributed magnetic field analysis of interior permanent magnet-type blush-less direct current motors under the stator-turn fault condition using the winding function theory. Stator-turn faults cause significant changes in electric and magnetic characteristic. Therefore, many studies on stator-turn faults have been performed by simulation of the finite element method because of its non-linear characteristic. However, this is difficult to apply to on-line fault detection systems because the processing time of the finite element method is very long. Fault-tolerant control systems require diagnostic methods that have simple processing systems and can produce accurate information. Thus analytical modeling of a stator-turn fault has been performed using the winding function theory, and the distributed magnetic characteristics have been analyzed under the fault condition. The proposed analytical model was verified using the finite element method.

• Journal of the Institute of Electronics Engineers of Korea TC
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• v.48 no.8
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• pp.1-6
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• 2011

In this paper, another analytical approach for dual-hop amplify-and-forward(AF) relay systems is proposed over Rayleigh fading channels. Previous approaches derived the moment generating function(MGF) by using the cumulative distribution function(CDF) or probability density function(PDF) of the received signal-to-noise ratio(SNR) for source-relay-destination(S-R-D) link. Then, the average symbol error rate is expressed based on derived MGFs. In this paper, another new approach is proposed. It means that the MGF is directly derived by utilizing PDFs of both source-relay(S-R) and relay-destination(R-D) links. Additionary, the newly derived MGF is compared and analyzed with previous ones. Furthermore, simulation results are presented to validate the accuracy of proposed analytical expression. Based on this, it is confirmed that the proposed analytical approach can be a another solution for dual-hop AF relay systems.

• Advances in concrete construction
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• v.1 no.4
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• pp.319-340
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• 2013

This paper presents a comparative study on the double-K fracture parameters of concrete obtained using four existing analytical methods such as Gauss-Chebyshev integral method, simplified Green's function method, weight function method and simplified equivalent cohesive force method. Two specimen geometries: three point bend test and compact tension specimen for sizes 100-500 mm at initial notch length to depth ratios 0.25 and 0.4 are used for the comparative study. The required input parameters for determining the double-K fracture parameters are derived from the developed fictitious crack model. It is found that the cohesive toughness and initial cracking toughness determined using weight function method and simplified equivalent cohesive force method agree well with those obtained using Gauss-Chebyshev integral method whereas these fracture parameters determined using simplified Green's function method deviates more than by 11% and 20% respectively as compared with those obtained using Gauss-Chebyshev integral method. It is also shown that all the fracture parameters related with double-K model are size dependent.

• Journal of Institute of Control, Robotics and Systems
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• v.17 no.9
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• pp.875-881
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• 2011

This paper describes a new method of estimating the gradient of a function with perturbation and correlation. We impose a known periodic perturbation to the input variable and observe the output of the function in order to obtain much richer and more reliable information. By taking the correlation between the input perturbation and the resultant function outputs, we can determine the gradient of the function. The computation of the correlation does not require derivatives; therefore the gradient can be estimated reliably. Robust estimation of the gradient using perturbation/correlation, which is very effective when an analytical solution is not available, is described. To verify the effectiveness of perturbation/correlation based estimation, the results of gradient estimation are compared with the analytical solutions of an example function. The effects of amplitude of the perturbation and number of samplings in a period are investigated. A minimization of a function with the gradient estimation method is performed.