• International Journal of Aeronautical and Space Sciences
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• v.3 no.2
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• pp.46-58
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• 2002

An inverse method is introduced to construct benchmark problems for the numerical solution of initial value problems. Benchmark problems constructed through this method have a known exact solution, even though analytical solutions are generally not obtainable. The solution is constructed such that it lies near a given approximate numerical solution, and therefore the special case solution can be generated in a versatile and physically meaningful fashion and can serve as a benchmark problem to validate approximate solution methods. A smooth interpolation of the approximate solution is forced to exactly satisfy the differential equation by analytically deriving a small forcing function to absorb all of the errors in the interpolated approximate solution. A multi-variable orthogonal function expansion method and computer symbol manipulation are successfully used for this process. Using this special case exact solution, it is possible to directly investigate the relationship between global errors of a candidate numerical solution process and the associated tuning parameters for a given code and a given problem. Under the assumption that the original differential equation is well-posed with respect to the small perturbations, we thereby obtain valuable information about the optimal choice of the tuning parameters and the achievable accuracy of the numerical solution. Illustrative examples show the utility of this method not only for the ordinary differential equations (ODEs) but for the partial differential equations (PDEs).

• Transactions of Materials Processing
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• v.6 no.5
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• pp.386-394
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• 1997

The analysis of the springback is done based on the stress of sheet after forming. Therfore, it is important to get the accurate stress from forming analysis. In this study, some parameters that influence on the accuracy of the springback estimation are investigated. Discretization of sheet and tools, choice of penalty constant and damping in contact treatment, and tool speed scaling are chosen as parameters. As a numerical example, the 2D draw bending benchmark problem of the NUMISHEET'93 is used. Also, the springback results of the s-rail benchmark problem of the NUMISHEET'96 are presented.

• Journal of the Korean Professional Engineers Association
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• v.22 no.3
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• pp.5-13
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• 1989

A major problem of stopwatch time study is how to do for the accurate and consistent performance rating, which is one of the critical variables to determine the accuracy of work measurement and should be still dependent upon time observer's judgement. Therefore the time observer's ability for the performance rating is very important, and must be improved by correct training method and procedure. This paper developed a new benchmark and benchmark-observation method for the effective performance rating training of assembling and machining operations. The trainees' ability in the accuracy and consistency of the performance rating ,improved significantly after being trained by subject method. The percentage improvement in rating accuracy and consistency values was 34.7% and 49% respectively. In addition, benchmark-practice method for the performance rating training is not significant, so it is proofed that the skill of a certain operation is not important for the improvement of the rating ability.

• Journal of Korean Institute of Industrial Engineers
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• v.33 no.1
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• pp.86-98
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• 2007

This paper presents a heuristic algorithm for the traveling salesman problem with time windows (TSPTW). Aniterative insertion algorithm as a constructive search heuristic and a hybrid meta heuristic combining simulatedannealing and tabu search with the randomized selection of 2-interchange and a simple move operator as animproving search heuristic are proposed, Computational tests performed on 400 benchmark problem instancesshow that the proposed algorithm generates optimal or near-optimal solutions in most cases. New best knownheuristic values for many benchmark problem sets were obtained using the proposed approach.

• Smart Structures and Systems
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• v.6 no.1
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• pp.17-27
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• 2010

The approach to damage detection and localization adopted in this paper is based on a statistical comparison of models built from the response time histories collected at different stages during the structure lifetime. Some of these time histories are known to have been recorded when the structural system was undamaged. The consistency of the models associated to two different stages, both undamaged, is first recognized. By contrast, the method detects the discrepancies between the models from measurements collected for a damaged situation and for the undamaged reference situation. The damage detection and localization is pursued by a comparison of the SSE (sum of the squared errors) histograms. The validity of the proposed approach is tested by applying it to the analytical benchmark problem developed by the ASCE Task Group on Structural Health Monitoring (SHM). In the paper, the results of the benchmark studies are presented and the performance of the method is discussed.

• Nuclear Engineering and Technology
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• v.52 no.11
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• pp.2422-2430
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• 2020

In order to improve calculational efficiency of the CAPP code in the analysis of the hexagonal reactor core, we have tried to implement a refined AFEN method with transverse gradient basis functions and interface flux moments in the hexagonal geometry. The numerical scheme for the refined AFEN method adopted here is the response matrix method that uses the interface partial currents as nodal unknowns instead of the interface fluxes used in the original AFEN method. Since the response matrix method is single-node based, it has good properties such as good calculational efficiency and parallel computing affinity. Because a refined AFEN method equivalent nonlinear FDM response matrix method tried first could not provide a numerically stable solution, a direct formulation of the refined AFEN response matrix were developed. To show the numerical performance of this response matrix method against the original AFEN method, the numerical error analyses were performed for several benchmark problems including the VVER-440 LWR benchmark problem and the MHTGR-350 HTGR benchmark problem. The results showed a more than three times speedup in computing time for the LWR and HTGR benchmark problems due to good convergence and excellent calculational efficiency of the refined AFEN response matrix method.

• Nuclear Engineering and Technology
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• v.55 no.9
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• pp.3388-3400
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• 2023

Detailed analysis of the neutron pathway through matter inside the nuclear reactor core is exceedingly needed for safety and economic considerations. Due to the constant development of high-performance computing technologies, neutronics analysis using computer codes became more effective and efficient to perform sophisticated neutronics calculations. In this work, a commercial pressurized water reactor (PWR) presented by Virtual Environment for Reactor Applications (VERA) Core Physics Benchmark are modeled and simulated using a high-fidelity simulation of OpenMC code in terms of criticality and fuel pin power distribution. Various problems have been selected from VERA benchmark ranging from a simple two-dimension (2D) pin cell problem to a complex three dimension (3D) full core problem. The development of the code capabilities for reactor physics methods has been implemented to investigate the accuracy and performance of the OpenMC code against VERA SCALE codes. The results of OpenMC code exhibit excellent agreement with VERA results with maximum Root Mean Square Error (RMSE) values of less than 0.04% and 1.3% for the criticality eigenvalues and pin power distributions, respectively. This demonstrates the successful utilization of the OpenMC code as a simulation tool for a whole core analysis. Further works are undergoing on the accuracy of OpenMC simulations for the impact of different fuel types and burnup levels and the analysis of the transient behavior and coupled thermal hydraulic feedback.

• Journal of the Korean Operations Research and Management Science Society
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• v.26 no.2
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• pp.59-68
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• 2001

The job shop scheduling problem is not only NP-hard, but is one of the well known hardest combinatorial optimization problems. The goal of this research is to develop an efficient scheduling method based on hybrid genetic algorithm to address job shop scheduling problem. In this scheduling method, generating method of initial population, new genetic operator, selection method are developed. The scheduling method based on genetic algorithm are tested on standard benchmark job shop scheduling problem. The results were compared with another genetic algorithm0-based scheduling method. Compared to traditional genetic, algorithm, the proposed approach yields significant improvement at a solution.

• Journal of Institute of Control, Robotics and Systems
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• v.7 no.11
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• pp.896-903
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• 2001

This study investigates the use of mixed $H_2/H_{$\infty}$ and $\mu$-synthesis to construct a robust controller for the benchmark problem. The model treated in the problem is a coupled three-inertial system that reflects the dynamics of mechanical vibrations. This kind of problem requires to be satisfied the robust performance (both in the time and frequency-domain specifications). We, first, adopt the mixed $H_2/H_{$\infty}$ theory to design a feedback controller K(s). Next, $\mu$-synthesis method is applied to the overall system to make use of structured parametric uncertainty. This process permits higher levels of controller authority and reduces the conservativeness of the controller. Finally, the feedforward controller is also used to improve the transient response of the output. We confirm that all design specifications except a complementary sensitivity condition can be achieved.

• Smart Structures and Systems
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• v.10 no.4_5
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• pp.485-499
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• 2012

Mode shape expansion is useful in structural dynamic studies such as vibration based structural health monitoring; however most existing expansion methods can not consider the modelling errors in the finite element model and the measurement uncertainty in the modal properties identified from vibration data. This paper presents a reliable approach for expanding mode shapes with consideration of both the errors in analytical model and noise in measured modal data. The proposed approach takes the perturbed force as an unknown vector that contains the discrepancies in structural parameters between the analytical model and tested structure. A regularisation algorithm based on the Tikhonov solution incorporating the L-curve criterion is adopted to reduce the influence of measurement uncertainties and to produce smooth and optimised expansion estimates in the least squares sense. The Canton Tower benchmark problem established by the Hong Kong Polytechnic University is then utilised to demonstrate the applicability of the proposed expansion approach to the actual structure. The results from the benchmark problem studies show that the proposed approach can provide reliable predictions of mode shape expansion using only limited information on the operational modal data identified from the recorded ambient vibration measurements.