• Nuclear Engineering and Technology
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• v.43 no.6
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• pp.531-546
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• 2011

The backward differentiation formula (BDF) method is applied to a three-dimensional reactor kinetics calculation for efficient yet accurate transient analysis with adaptive time step control. The coarse mesh finite difference (CMFD) formulation is used for an efficient implementation of the BDF method that does not require excessive memory to store old information from previous time steps. An iterative scheme to update the nodal coupling coefficients through higher order local nodal solutions is established in order to make it possible to store only node average fluxes of the previous five time points. An adaptive time step control method is derived using two order solutions, the fifth and the fourth order BDF solutions, which provide an estimate of the solution error at the current time point. The performance of the BDF- and CMFD-based spatial kinetics calculation and the adaptive time step control scheme is examined with the NEACRP control rod ejection and rod withdrawal benchmark problems. The accuracy is first assessed by comparing the BDF-based results with those of the Crank-Nicholson method with an exponential transform. The effectiveness of the adaptive time step control is then assessed in terms of the possible computing time reduction in producing sufficiently accurate solutions that meet the desired solution fidelity.

• Journal of Information Processing Systems
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• v.16 no.4
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• pp.832-844
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• 2020

The degree of dispersion of a random variable can be described by the variance, which reflects the distance of the random variable from its mean. However, the time complexity of the traditional variance calculation algorithm is O(n), which results from full calculation of all samples. When the number of samples increases or on the occasion of high speed signal processing, algorithms with O(n) time complexity will cost huge amount of time and that may results in performance degradation of the whole system. A novel multi-step recursive algorithm for variance calculation of the time-varying data series with O(1) time complexity (constant time) is proposed in this paper. Numerical simulation and experiments of the algorithm is presented and the results demonstrate that the proposed multi-step recursive algorithm can effectively decrease computing time and hence significantly improve the variance calculation efficiency for time-varying data, which demonstrates the potential value for time-consumption data analysis or high speed signal processing.

• Korean Journal of Optics and Photonics
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• v.10 no.5
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• pp.405-412
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• 1999

We propose an effective algorithm, which can predict the detailed behavior of the intensity-modulated high speed optical signal after propagating through an optical fiber. The alogrithm is based on the SSF (Split Step Fourier) Method, however, the step size is automatically calibrated in each calculation step to reduce the number of calculations within given round-off error bound. Applying the algorithm to the 2.5 Gbps 100 km transmission and 10 Gbps 40 km transmission simulations, we achieved the calculation time reduction by maximum 1/120 and 1/56 of the calculation time by using the SSF fixed step algorithm previously known. The root-mean-square of the round-off error was kept within -30 dB compared to the signal level throughout the calculation.

• Journal of Korea Foundry Society
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• v.14 no.5
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• pp.412-418
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• 1994

Efficient algorithm for the solidification simulation by FDM is described from the practical point of views. If a proper time step ${\Delta}t$ is selected, the calculation is accelerated by implicit algorithm with the temperature recovery method of latent heat method. The implicit routine in the calculation is processed by SOR method(relaxation factor＝1.5, truncation error＝$10^{-4}$). The calculation is more accelerated by linear-interpolated explicite algorithm with a time step larger than the minimum value of the time step. This explicit method, which is applicable to the practical casting simulation problems, produces almost same results with about 40% faster calculation speed compared with the conventional explicit method.

• Structural Engineering and Mechanics
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• v.81 no.5
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• pp.591-606
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• 2022

When the friction pendulum system and shear keys work together to resist the ground motion, which inclined inputs (non 45°) to the bridge structure, the shear keys in XY direction will be sheared asynchronously, endowed the friction pendulum system with a violent curvilinear motion on the sliding surface during earthquakes. In view of this situation, firstly, this paper abandons the equivalent linearization model of friction and constructs a Spring-Coulomb friction plane isolation system with XY shear keys, and then makes a detailed mechanical analysis of the movement process of friction pendulum system, next, this paper establishes the mathematical model of structural time history response calculation by using the step-by-step integration method, finally, it compiles the corresponding computer program to realize the numerical calculation. The results show that the calculation method in this paper takes advantage of the characteristic that the friction force is always µmg, and creatively uses the "circle making method" to express the change process of the friction force and resultant force of the friction pendulum system in any calculation time step, which can effectively solve the temporal nonlinear action of the plane friction; Compared with the response obtained by the calculation method in this paper, the peak values of acceleration response and displacement response calculated by the unidirectional calculation model, which used in the traditional research of the friction pendulum system, are smaller, so the unidirectional calculation model is not safe.

• Proceedings of the KIEE Conference
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• 1997.07c
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• pp.903-906
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• 1997

When large capacity generation stations that consist of several large units tend to pull out of step from main power system, stabilizing control scheme as emergency control for preventing loss of synchronism of the whole stations with the remaining system is devided into two steps that the first step is to perform on-line prediction for out-of-step and the next step is on-line calculation of the amount of generation shedding for the rest of generators to be in step when out of step is expected. This paper presents on-line prediction scheme for out-of-step based on P-$\delta$ curve estimation using real-time measurement and on-line calculation of generation shedding. The proposed stabilizing scheme was applied to case study of real power system and the results obtained by the method compare well with the results by simulation.

• Journal of Korean Association for Spatial Structures
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• v.22 no.2
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• pp.39-46
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• 2022

Recently, machine learning is widely used to solve optimization problems in various engineering fields. In this study, machine learning is applied to development of a control algorithm for a smart control device for reduction of seismic responses. For this purpose, Deep Q-network (DQN) out of reinforcement learning algorithms was employed to develop control algorithm. A single degree of freedom (SDOF) structure with a smart tuned mass damper (TMD) was used as an example structure. A smart TMD system was composed of MR (magnetorheological) damper instead of passive damper. Reward design of reinforcement learning mainly affects the control performance of the smart TMD. Various hyper-parameters were investigated to optimize the control performance of DQN-based control algorithm. Usually, decrease of the time step for numerical simulation is desirable to increase the accuracy of simulation results. However, the numerical simulation results presented that decrease of the time step for reward calculation might decrease the control performance of DQN-based control algorithm. Therefore, a proper time step for reward calculation should be selected in a DQN training process.

• Atmosphere
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• v.33 no.4
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• pp.331-341
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• 2023

A numerical forecasting models usually predict future states by performing time integration considering fixed static time-steps. A time-step that is too long can cause model instability and failure of forecast simulation, and a time-step that is too short can cause unnecessary time integration calculations. Thus, in numerical models, the time-step size can be determined by the CFL (Courant-Friedrichs-Lewy)-condition, and this condition acts as a necessary condition for finding a numerical solution. A static time-step is defined as using the same fixed time-step for time integration. On the other hand, applying a different time-step for each integration while guaranteeing the stability of the solution in time advancement is called an adaptive time-step. The adaptive time-step algorithm is a method of presenting the maximum usable time-step suitable for each integration based on the CFL-condition for the adaptive time-step. In this paper, the adaptive time-step algorithm is applied for the Korean Integrated Model (KIM) to determine suitable parameters used for the adaptive time-step algorithm through the monthly verifications of 10-day simulations (during January and July 2017) at about 12 km resolution. By comparing the numerical results obtained by applying the 25 second static time-step to KIM in Supercomputer 5 (Nurion), it shows similar results in terms of forecast quality, presents the maximum available time-step for each integration, and improves the calculation efficiency by reducing the number of total time integrations by 19%.

• Explosives and Blasting
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• v.36 no.3
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• pp.10-18
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• 2018

The dynamic behaviour of the rock mass under the dynamic load is different from the static application of the maximum load of the same size. An experimental approach to investigating rock behavior under dynamic loads is more difficult than that under static conditions in control of dynamic loads, measurement and analysis of the results. Numerical methods are less constrained by performing the experiments numerically, rather than experimental ones, so they can be very powerful analytical tool at the design stage. However, even if the algorithms of the analysis method are appropriate, careful analysis is required because the calculation results may vary largely depending on input data and boundary conditions. In this paper, when investigating the behavior of rock structures under dynamic load numerically, the effects of boundary conditions, dynamic load and calculation time step, and dynamic load characteristics on the calculation results were reviewed to provide guidance on setting up boundary conditions and calculation time step related to dynamic analysis.

• Journal of the Korea institute for structural maintenance and inspection
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• v.27 no.5
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• pp.75-83
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• 2023

As part of a study to analyze the excessive camber occurring in prestressed concrete railway bridges, this paper presents a calculation method and analysis results for the creep coefficient which defines the increase in camber of a concrete structure over time. Using the creep coefficient formula of the design code, the coefficient is obtained by applying the climatic conditions (relative humidity and temperature) of 12 regions in Korea. The effects of differences in climatic conditions by region and starting time of load on the creep coefficient are analyzed. In order to properly calculate the creep, most of which occurs in the early stages of loading, a detailed analysis is performed by applying a time step analysis method to consider varying climate conditions through loaded period. The creep coefficient obtained by applying the average climate conditions of the region is similar to the average of the creep coefficients obtained by time step analysis. Through time step analysis, it is shown that the offset and overlap effects of relative humidity and temperature on the creep coefficient and the climate effect at the time of initial loading can be appropriately represented.