• Communications for Statistical Applications and Methods
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• v.31 no.3
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• pp.349-363
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• 2024

Compositional data refers to data where the sum of the values of the components is a constant, hence the sample space is defined as a simplex making it impossible to apply statistical methods developed in the usual Euclidean vector space. A natural approach to overcome this restriction is to consider an appropriate transformation which moves the sample space onto the Euclidean space, and log-ratio typed transformations, such as the additive log-ratio (ALR), the centered log-ratio (CLR) and the isometric log-ratio (ILR) transformations, have been mostly conducted. However, in scenarios with sparsity, where certain components take on exact zero values, these log-ratio type transformations may not be effective. In this work, we mainly suggest an alternative transformation, that is the square-root transformation which moves the original sample space onto the directional space. We compare the square-root transformation with the log-ratio typed transformation by the simulation study and the real data example. In the real data example, we applied both types of transformations to the USG% data obtained from NBA, and used a density based clustering method, DBSCAN (density-based spatial clustering of applications with noise), to show the result.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.10 no.3
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• pp.1-6
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• 1990

The dynamic behaviour of a four-span continuous girder railway bridge subjected to multiple support excitations is investigated using the response spectrum method. Small-amplitude oscillations and linear-elastic material behaviour are assumed. Soil-structure interaction effects are disregarded and only the out-of-plane response of the bridge is considered. The results of the response spectrum analysis are compared with those from a time history analysis. Different combination rules for the superposition of modal maxima as well as supports are employed, such as square-root-of-sum-squares, double sum and p-norm methods.

• Journal of the Korean Society of Safety
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• v.29 no.6
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• pp.166-171
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• 2014

Nuclear power plants are equipped with the reactor trip system (RTS) and the engineered safety features actuation system (ESFAS) to improve safety on the normal operation. In the event of the design basis accident (DBA), a various of post accident monitor(PAM)systems support to provide important details (e.g. Containment pressure, temperature and pressure of reactor cooling system and core exit temperature) to determine action of main control room (MCR). Operator should be immediately activated for the accident mitigation with the information. Especially, core exit temperature is a critical parameter because the operating mode converts from normal mode to emergency mode when the temperature of core exit reaches $649^{\circ}C$. In this study, uncertainty which was caused by exterior environment, characteristic of thermocouple/connector and accuracy of calibrator/indicator was evaluated in accordance with ANSI-ISA 67.04. The square root of the sum of square (SRSS) methodology for combining uncertainty terms that are random and independent was used in the synthesis. Every uncertainty that may exist in the hardware which is used to measure the core exit temperature was conservatively applied and the associative relation between the elements of uncertainty was considered simultaneously. As a result of uncertainty evaluation, the channel statistical allowance (CSA) of single channel of core exit temperature was +1.042%Span. The range of uncertainty, -0.35%Span ($-4.05^{\circ}C$) ~ +2.08%Span($24.25^{\circ}C$), was obtained as the operating criteria of core exit temperature.

• Environmental and Resource Economics Review
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• v.9 no.3
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• pp.461-487
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• 2000

Kang et al. (1999) computed a composite environmental index in Korea by practicing the survey for environmental experts. They used the weighted sum form among feasible aggregation forms. In this study, we carry out the survey for both experts and non-experts to see the degree of differences of the weights for nine types of environmental problems between two groups. In addition, we apply different aggregation forms such as linear sum, weighted sum, root-sum-power, root-mean-square forms and compare these four outcomes. We found no significant discrepancy in the trends of composite indices. In case we rely on the weights provided by the experts, the composite index, on average, has been increased annually by about 7.2% over the 1986~1997 period, which informs us that overall environmental quality in 1997 has been worse than in 1986 by about 1.8 times.

• Proceedings of the Korean Society of Propulsion Engineers Conference
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• 2007.04a
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• pp.258-261
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• 2007

The objective of this paper is to examine the ways in which to implement MEPS method for setting the design and operational limits in order to provide the guaranteed performance of the aircraft engine. Direct adder arithmetically added and related with the effects of ambient humidity, engine quality, throttle set tolerance and deterioration, etc is described with the random adder added in root square sum. The method was applied on the preliminary design of 4,000Ib class turbofan engine and the MEPS for engine component design and operational margin was generated.

• International Journal of Safety
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• v.7 no.1
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• pp.26-29
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• 2008

The purpose of this study is the measurement of whole-body vibration for different road surfaces. Experimental measurements were taken on asphalt, cement, and off-road surfaces as defined by ISO 2631-1. Each experiment was conducted under the same set of conditions (measurement duration, times, speed, vehicle type). Measurement duration was 10 minutes and 3 separate measurements were taken on each road surface. Vehicle speed was 60km/h. In accordance with ISO 2631-1, an acceleration sensor is set up between the driver's seat and the human body. For evaluation, RMS(root-mean-square) values were taken as suggested by ISO 2631-1. The results suggest "health guidance caution zones", and the evaluation was based on obtaining the vector sum with "health guidance caution zones".

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2006.11a
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• pp.361-365
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• 2006

In order to predict method of blasting vibration in ground and it's resident located around blasting field in urban area, blasting vibration characteristics were measured the vibration velocity(cm/sec), vibration acceleration($cm/sec^2$), vibration acceleration level(dB) and vibration level(dB(V)). The charged powder were used to 1.25kg and measuring sites were 25 points front 4m to 90m at the ground. The correlation of vibration velocity, vibration acceleration, vibration acceleration level and vibration level by square root scaled distance and cube root scaled distance were investigated. The correlation of PPV(peak particle velocity) velocity by SRSD(square root scaled distance) and CRSD(cube root scaled distance) was 0.85 and 0.86 and the correlation of PVS(peak vector sum) velocity by SRSD and CRSD was 0.82. Also vibration acceleration, vibration acceleration level and vibration level by SRSD and CRSD was 0.61, 0.62 and 0.82, respectively. As results, the vibration velocity and vibration level(dB(V)) was showed good correlation, but the vibration acceleration and vibration acceleration level was not showed good correlation.

• Journal of the Korean Mathematical Society
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• v.57 no.4
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• pp.1019-1030
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• 2020

Efficient computation of r-th root in 𝔽_q has many applications in computational number theory and many other related areas. We present a new r-th root formula which generalizes Müller's result on square root, and which provides a possible improvement of the Cipolla-Lehmer type algorithms for general case. More precisely, for given r-th power c ∈ 𝔽_q, we show that there exists α ∈ 𝔽_q^r such that $$Tr{\left(\begin{array}{cccc}{{\alpha}^{{\frac{({\sum}_{i=0}^{r-1}\;q^i)-r}{r^2}}}\atop{\text{ }}}\end{array}\right)}^r=c,$$ where $Tr({\alpha})={\alpha}+{\alpha}^q+{\alpha}^{q^2}+{\cdots}+{\alpha}^{q^{r-1}}$ and α is a root of certain irreducible polynomial of degree r over 𝔽_q.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1999.10a
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• pp.233-240
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• 1999

A general procedure is presented here to develope seismic design and analysis method for cable-supported bridges like suspension bridges subjected to ground motion. For representing a numerical model of suspension bridges. a new approach which satisfy design conditions for the initial equilibrium state of suspension bridges. without any nonlinear iterations. is proposed. The dynamic behavior of that model is verified by free vibration analysis. This study uses the response spectrum analysis to determine the Peak response of a suspension bridge to earthquake-induced ground motion. The SRSS(Square Root of Sum of Square). modal combination rule, is adopted for each direction, longitudinal and transverse. To illustrate the potential applicability for the seismic design of suspension bridges, a numerical example is presented in which the dynamic response of the Nam-hae suspension bridge subjected to earthquake

• Journal of Korean Society of Water and Wastewater
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• v.18 no.3
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• pp.351-356
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• 2004

Selecting appropriate G values in flocculator operation is important to produce high quality filter effluent in water treatment plants. However, misunderstanding and misleading of G calculation for the case of having power sources more than one or many paddles with one power source in a flocculation basin sometimes have led to low performance in flocculation. Theoretical analysis confirmed that the total G value in one flocculation unit having power sources more than one or with many paddles is the root-square of the sum of square of individual G value. This analysis also can give a simple calculation method of G value for designers and operators in fields.