• Journal of the Korea Institute of Information and Communication Engineering
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• v.26 no.11
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• pp.1623-1629
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• 2022

Matrix multiplication is a fundamental operation widely used in science and engineering. There is an approximate matrix multiplication method as a way to reduce the amount of computation of matrix multiplication. Approximate matrix multiplication determines an appropriate probability distribution for selecting columns and rows of matrices, and performs approximate matrix multiplication by selecting columns and rows of matrices according to this distribution. Probability distributions are generated by considering both matrices A and B participating in matrix multiplication. In this paper, we propose a method to generate a probability distribution that selects columns and rows of matrices to be used for approximate matrix multiplication, targeting only matrix A. Approximate matrix multiplication was performed on 1000×1000 ~ 5000×5000 matrices using existing and proposed methods. The approximate matrix multiplication applying the proposed method compared to the conventional method has been shown to be closer to the original matrix multiplication result, averaging 0.02% to 2.34%.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.29 no.3A
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• pp.199-207
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• 2009

In this paper, new vehicular load model is developed for reliability-based bridge design code. Rational load model and statistical properties of loads are important for developing reliability-based design code. In the previous paper, truck weight data collected at eight locations using WIM or BWIM system are analyzed to calculate the maximum truck weights for specified bridge lifetime. Probability distributions of upper 20% total truck weight are assumed as Extreme Type I (Gumbel Distribution) and 100 years maximum weights are estimated by linear regression. In this study, effects of multiple presence of trucks are analyzed. Probability of multiple presence of trucks are estimated and corresponding multiple truck weights are calculated using the same probability distribution function as in the previous paper. New vehicular live load model are proposed for span length from 10 m to 200 m. New model is compared with current Korean model and various load models of other countries.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.28 no.2B
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• pp.225-236
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• 2008

The techniques to calculate the probability precipitation for the design of hydrological projects can be determined by the point frequency analysis and the regional frequency analysis. Probability precipitation usually calculated by point frequency analysis using rainfall data that is observed in rainfall observatory which is situated in the basin. Therefore, Probability precipitation through point frequency analysis need observed rainfall data for enough periods. But, lacking precipitation data can be calculated to wrong parameters. Consequently, the regional frequency analysis can supplement the lacking precipitation data. Therefore, the regional frequency analysis has weaknesses compared to point frequency analysis because of suppositions about probability distributions. In this paper, rainfall observatory in Korea did grouping by cluster analysis using position of timely precipitation observatory and characteristic time rainfall. Discordancy and heterogeneity measures verified the grouping precipitation observatory by the cluster analysis. So, there divided rainfall observatory in Korea to 6 areas, and the regional frequency analysis applies index-flood techniques and L-moment techniques. Also, the probability precipitation was calculated by the regional frequency analysis using variable kernel density function. At the results, the regional frequency analysis of the variable kernel function can utilize for decision difficulty of suitable probability distribution in other methods.

• Journal of Energy Engineering
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• v.23 no.3
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• pp.36-41
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• 2014

The world's overall need for natural gas (NG) has been growing up fast, especially in the residential sector. The better the estimation of residential NG consumption (RNGC) distribution, the better decision-making for a residential NG policy such as pricing, demand estimation, management options and so on. Approximating the distribution of RNGC is complicated by zero observations in the sample. To deal with the zero observations by allowing a point mass at zero, a mixture model of RNGC distributions is proposed and applied. The RNGC distribution is specified as a mixture of two distributions, one with a point mass at zero and the other with full support on the positive half of the real line. The model is empirically verified for household RNGC survey data collected in Korea. The mixture model can easily capture the common bimodality feature of the RNGC distribution. In addition, when covariates were added to the model, it was found that the probability that a household has non-expenditure significantly varies with some variables. Finally, the goodness-of-fit test suggests that the data are well represented by the mixture model.

• Korean Management Science Review
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• v.31 no.2
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• pp.1-13
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• 2014

In almost all of the organizations, the cost for acquiring and maintaining the inventory takes a considerable portion of the management budget, and thus a certain constraint is set upon the budget itself. The previous studies on inventory control for each item that aimed to improve the fill rate, backorder, and the expenditure on inventory are fitting for the commercially-operated SCM, but show some discrepancies when they are applied to the spare parts for repairing disabled systems. Therefore, many studies on systematic approach concept considering spare parts of various kinds simultaneously have been conducted to achieve effective performance for the inventory control at a lower cost, and primarily, METRIC series models can be named. However, the past studies were limited when dealing with the probability distributions for representing the situation on demand and transportation of the parts, with the (S-1, S) inventory control policy, and so on. To address these shortcomings, the Continuous Time Markov Chain (CTMC) model, which considers the phase-type distributions and the (s, Q) inventory control policies to best describe the real-world situations inclusively, is presented in this study. Additionally, by considering the cost versus the system availability, the optimization of the inventory level, based on this model, is also covered.

• Nuclear Engineering and Technology
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• v.33 no.3
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• pp.270-282
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• 2001

A simple measure of uncertainty importance based on normalized metric distance to quantify the entire change of cumulative distribution functions (CDFs) has been developed for use in probability safety assessments (PSAs). The metric distance measure developed in this study reflects the relative impact of distributional changes of inputs on the change of an output distribution, white most of the existing uncertainty importance measures reflect the magnitude of relative contribution of input uncertainties to the output uncertainty. Normalization is made to make the metric distance measure a dimensionless quantity. The present measure has been evaluated analytically for various analytical distributions to examine its characteristics. To illustrate the applicability and strength of the present measure, two examples are provided. The first example is an application of the present measure to a typical problem of a system fault tree analysis and the second one is for a hypothetical non-linear model. Comparisons of the present result with those obtained by existing uncertainty importance measures show that the metric distance measure is a useful tool to express the measure of uncertainty importance in terms of the relative impact of distributional changes of inputs on the change of an output distribution.

• Wind and Structures
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• v.30 no.6
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• pp.575-595
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• 2020

The characteristics of winds associated with tropical cyclones are of great significance in many engineering fields. This paper presents an investigation of wind characteristics over a coastal urban terrain based on field measurements collected from multiple cup anemometers and ultrasonic anemometers equipped at 13 height levels on a 356-m-high meteorological tower in Shenzhen during severe Typhoon Hato. Several wind quantities, including wind spectrum, gust factor, turbulence intensity and length scale as well as wind profile, are presented and discussed. Specifically, the probability distributions of fluctuating wind speeds are analyzed in connection with the normal distribution and the generalized extreme value distribution. The von Karman spectral model is found to be suitable to depict the energy distributions of three-dimensionally fluctuating winds. Gust factors, turbulence intensity and length scale are determined and discussed. Moreover, this paper presents the wind profiles measured during the typhoon, and a comparative study of the vertical distribution of wind speeds from the field measurements and existing empirical models is performed. The influences of the topography features and wind speeds on the wind profiles were investigated based on the field-measured wind records. In general, the empirical models can provide reasonable predictions for the measured wind speed profiles over a typical coastal urban area during a severe typhoon.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.33 no.8
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• pp.745-752
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• 2009

In robust design, the mean and variance of design performance are frequently used to measure the design performance and its robustness under uncertainties. In this paper, we present the Gauss-type quadrature formula as a rigorous method for mean and variance estimation involving arbitrary input distributions and further extend its use to robust design optimization. One dimensional Gauss-type quadrature formula are constructed from the input probability distributions and utilized in the construction of multidimensional quadrature formula such as the tensor product quadrature (TPQ) formula and the univariate dimension reduction (UDR) method. To improve the efficiency of using it for robust design optimization, a semi-analytic design sensitivity analysis with respect to the statistical moments is proposed. The proposed approach is applied to a simple bench mark problems and robust topology optimization of structures considering various types of uncertainty.

• Journal of applied mathematics & informatics
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• v.18 no.1_2
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• pp.497-503
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• 2005

This paper presents characterizations on the independence of the exponential and Pareto distributions by record values. Let ${X_{n},\;n {\ge1}$ be a sequence of independent and identically distributed(i.i.d) random variables with a continuous cumulative distribution function(cdf) F(x) and probability density function(pdf) f(x). $Let{\;}Y_{n} = max{X_1, X_2, \ldots, X_n}$ for n \ge 1. We say $X_{j}$ is an upper record value of ${X_{n},{\;}n\ge 1}, if Y_{j} > Y_{j-1}, j > 1$. The indices at which the upper record values occur are given by the record times {u(n)}, n \ge 1, where u(n) = $min{j|j > u(n-1), X_{j} > X_{u(n-1)}, n \ge 2}$ and u(l) = 1. Then F(x) = $1 - e^{-\frac{x}{a}}$, x > 0, ${\sigma} > 0$ if and only if $\frac {X_u(_n)}{X_u(_{n+1})} and X_u(_{n+1}), n \ge 1$, are independent. Also F(x) = $1 - x^{-\theta}, x > 1, {\theta} > 0$ if and only if $\frac {X_u(_{n+1})}{X_u(_n)}{\;}and{\;} X_{u(n)},{\;} n {\ge} 1$, are independent.

• Journal of Korean Society for Quality Management
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• v.18 no.1
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• pp.129-147
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• 1990

This study is to refer to the optimization problems when the stress and strength follow the time dependent model, considering a decision making process in the design methodology from reliability viewpoint. Reliability of a component can be expressed and computed if the probability distributions for the stress and strength in the time dependent case are known. The factors which determine the parameters of the distributions for stress and strength random variables can be controlled in design problems. This leads to the problem of finding the optimal values of these parameters subject to resources and design constraints. This paper is to present techniques for solving the optimization problems at the design stage like as minimizing the total cost to be spent on controlling the stress and strength parameters for random variables subject to the constraint that the component must have a specified reliability, alternatively, maximizing the component reliability subject to certain constraints on amount of resources available to control the parameters. The derived expressions and computations of reliability in the time dependent case and some optimization models of these cases are discussed. The special structure of these models is exploited to develop the optimization techniques which are illustrated by design examples.