• Journal of the Korean Mathematical Society
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• v.53 no.5
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• pp.1037-1056
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• 2016

In this paper, we define the concepts of commute proximally, dominate proximally, weakly dominate proximally, proximal generalized ${\varphi}$-contraction and common best proximity point in probabilistic Menger space. We prove some common best proximity point and common fixed point theorems for dominate proximally and weakly dominate proximally mappings in probabilistic Menger space under certain conditions. Finally we show that proximal generalized ${\varphi}$-contractions have best proximity point in probabilistic Menger space. Our results generalize many known results in metric space.

• Smart Structures and Systems
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• v.10 no.2
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• pp.89-110
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• 2012

This study was intended to efficiently perform the probabilistic optimal safety assessment of steel cable-stayed bridges (SCS bridges) using stochastic finite element analysis (SFEA) and expected life-cycle cost (LCC) concept. To that end, advanced probabilistic finite element algorithm (APFEA) which enables to execute the static and dynamic SFEA considering aleatory uncertainties contained in random variable was developed. APFEA is the useful analytical means enabling to conduct the reliability assessment (RA) in a systematic way by considering the result of SFEA based on linearity and nonlinearity of before or after introducing initial tensile force. The appropriateness of APFEA was verified in such a way of comparing the result of SFEA and that of Monte Carlo Simulation (MCS). The probabilistic method was set taking into account of analytical parameters. The dynamic response characteristic by probabilistic method was evaluated using ASFEA, and RA was carried out using analysis results, thereby quantitatively calculating the probabilistic safety. The optimal design was determined based on the expected LCC according to the results of SFEA and RA of alternative designs. Moreover, given the potential epistemic uncertainty contained in safety index, failure probability and minimum LCC, the sensitivity analysis was conducted and as a result, a critical distribution phase was illustrated using a cumulative-percentile.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.59 no.8
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• pp.1366-1373
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• 2010

Purpose of the electric power system planning and operation is to supply the electric energy to customers continuously and economically. With the mutual exclusive laws of nature between reliability and economic, finding the meeting point is very important but not easy. Commonly the probabilistic reliability indices of the electric power systems are represented with negatively. And the effectiveness of FACTS on the probabilistic reliability could not be reflected with common methods. In this paper, a method to evaluate the probabilistic arrival power at each load point is presented. With this new proposed method, probabilistic reserve margin at load points can be calculated and which can be used with positive reliability index also. Using the P-V analysis, the voltage stability is considered in reliability evaluation. It is expected that the proposed method will be useful expecially in reliability evaluation of electric power system which has voltage restriction.

• The Magazine of the IEIE
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• v.36 no.11
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• pp.66-82
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• 2009

Probabilistic atlases for the human brain structure are more suitable than single brain atlases for representing population anatomy. In this study, we hypothesized the group-specific probabilistic atlas for accurate characteristic feature coding. Our proposed method for a new group comparison study, using a subpopulation specific probabilistic atlas, was based on this hypothesis. A knowledge-based automatic labeling technique using nonlinear registration was applied to encode group-specific regional probabilistic information. Direct atlas-based comparison using volume counting above the probability threshold, distance measurement and correlation analysis were performed based on the probabilistic atlas. Here, we applied this method for comparison between Korean and occidental groups. The results showed that this method could provide simple but intuitive regions of interest-based group analysis for the entire cortex area.

• Geomechanics and Engineering
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• v.6 no.6
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• pp.545-560
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• 2014

For slope stability analysis, an alternative to the classical limit equilibrium method (LEM) of slices is the shear strength reduction method (SRM), which can be integrated into finite element analysis or finite difference analysis. Recently, probabilistic analysis of earth slopes has been very attractive because it is capable to take the soil uncertainty into account. However, the SRM is less commonly extended to probabilistic framework compared to a variety of probabilistic LEM analysis of earth slopes. To overcome some limitations that hinder the development of probabilistic SRM stability analysis, a new procedure based on recursive algorithm FORM with sensitivity analysis in the space of original variables is proposed. It can be used to deal with correlated non-normal variables subjected to implicit limit state surface. Using the proposed approach, a probabilistic finite element analysis of the stability of an existing earth dam is carried out in this paper.

• Geomechanics and Engineering
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• v.24 no.4
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• pp.399-406
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• 2021

It is a key issue in the tunnel design to evaluate the stability of the excavation face. Two efficient analytical models in the context of the limit equilibrium method (LEM) and the limit analysis method (LAM) are used to carry out the deterministic calculations of the safety factor. The safety factor obtained by these two models agrees well with that provided by the numerical modelling by FLAC 3D, but consuming less time. A simple probabilistic approach based on the Mote-Carlo Simulation technique which can quickly calculate the probability distribution of the safety factor was used to perform the probabilistic analysis on the tunnel face stability. Both the cumulative probabilistic distribution and the probability density function in terms of the safety factor were obtained. The obtained results show the effectiveness of this probabilistic approach in the tunnel design.

• Journal of KIISE
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• v.44 no.3
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• pp.239-245
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• 2017

Probabilistic grammar is used in natural language processing, and the parse result of the grammar has to preserve the probability of the original grammar. As for the representative parsing method, LL parsing and LR parsing, the former preserves the probability information of the original grammar, but the latter does not. A characteristic of a probabilistic parsing automaton has been studied; but, currently, the generating model of probabilistic parsing automata has not been known. The paper provides a model of probabilistic parsing automata based on the single state parsing automata. The generated automaton preserves the probability of the original grammar, so it is not necessary to test whether or not the automaton is probabilistic parsing automaton; defining a probability function for the automaton is not required. Additionally, an efficient automaton can be constructed by choosing an appropriate parameter.

• Structural Engineering and Mechanics
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• v.64 no.4
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• pp.413-426
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• 2017

Probabilistic methods are used in engineering where a computational model contains random variables. The proposed method under development: Direct Optimized Probabilistic Calculation (DOProC) is highly efficient in terms of computation time and solution accuracy and is mostly faster than in case of other standard probabilistic methods. The novelty of the DOProC lies in an optimized numerical integration that easily handles both correlated and statistically independent random variables and does not require any simulation or approximation technique. DOProC is demonstrated by a collection of deliberately selected simple examples (i) to illustrate the efficiency of individual optimization levels and (ii) to verify it against other highly regarded probabilistic methods (e.g., Monte Carlo). Efficiency and other benefits of the proposed method are grounded on a comparative case study carried out using both the DOProC and MC techniques. The algorithm has been implemented in mentioned software applications, and has been used effectively several times in solving probabilistic tasks and in probabilistic reliability assessment of structures. The article summarizes the principles of this method and demonstrates its basic possibilities on simple examples. The paper presents unpublished details of probabilistic computations based on this method, including a reliability assessment, which provides the user with the probability of failure affected by statistically dependent input random variables. The study also mentions the potential of the optimization procedures under development, including an analysis of their effectiveness on the example of the reliability assessment of a slender column.

• Journal of the Korean Society of Industry Convergence
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• v.23 no.5
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• pp.799-807
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• 2020

This paper deals with identification of probabilistic design using reliability based robust optimization in structure design of automatic salt collector. The thickness sizing variables of main structure member in the automatic salt collector were considered the random design variables including the uncertainty of corrosion that would be an inevitable hazardousness in the saltern work environment. The probabilistic constraint functions were selected from the strength performances of the automatic salt collector. The reliability based robust optimum design problem was formulated such that the random design variables were determined by minimizing the weight of the automatic salt collector subject to the probabilistic strength performance constraints evaluating from reliability analysis. Mean value reliability method and adaptive importance sampling method were applied to the reliability evaluation in the reliability based robust optimization. The three sigma level quality was considered robustness in side constraints. The probabilistic optimum design results according to the reliability analysis methods were compared to deterministic optimum design results. The reliability based robust optimization using the mean value reliability method showed the most rational results for the probabilistic optimum structure design of the automatic salt collector.

• Journal of Institute of Control, Robotics and Systems
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• v.21 no.4
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• pp.367-371
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• 2015

In this paper, a novel localization method for a monocular camera is proposed by using a feature-based probabilistic map. The localization of a camera is generally estimated from 3D-to-2D correspondences between a 3D map and an image plane through the PnP algorithm. In the computer vision communities, an accurate 3D map is generated by optimization using a large number of image dataset for camera pose estimation. In robotics communities, a camera pose is estimated by probabilistic approaches with lack of feature. Thus, it needs an extra system because the camera system cannot estimate a full state of the robot pose. Therefore, we propose an accurate localization method for a monocular camera using a probabilistic approach in the case of an insufficient image dataset without any extra system. In our system, features from a probabilistic map are projected into an image plane using linear approximation. By minimizing Mahalanobis distance between the projected features from the probabilistic map and extracted features from a query image, the accurate pose of the monocular camera is estimated from an initial pose obtained by the PnP algorithm. The proposed algorithm is demonstrated through simulations in a 3D space.