• The Korean Journal of Applied Statistics
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• v.22 no.1
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• pp.171-179
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• 2009

In this paper we studied the effective approximations to the distribution of the sum of products of normal variables. Based on the saddlepoint approximations to the quadratic forms, the suggested approximations are very accurate and easy to use. Applications to the FSK (Frequency Shift Keying) communication are also considered.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.26 no.1
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• pp.33-40
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• 2014

Reliability analysis of jacket type offshore wind turbine (OWT) support structure under extreme ocean environmental loads was performed. Limit state function (LSF) of OWF support structure is defined by using structural dynamic response at mud-line. Then, the dynamic response is expressed as the static response multiplied by dynamic response factor (DRF). Probabilistic distribution of DRF is found from response time history under design significant wave load. Band limited beta distribution is used for internal friction angle of ground soil. Wind load is obtained in the form of thrust force from commercial code called GH_Bladed and then, applied to tower hub as random load. In a numerical example, the response surface method (RSM) is used to express LSF of jacket type support structure for 5MW OWF. Reliability index is found using first order reliability method (FORM).

• Journal of the Korean earth science society
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• v.32 no.3
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• pp.249-264
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• 2011

A multi-Gaussian kriging approach extended to space-time domain is presented for uncertainty modeling as well as time-series mapping of environmental variables. Within a multi-Gaussian framework, normal score transformed environmental variables are first decomposed into deterministic trend and stochastic residual components. After local temporal trend models are constructed, the parameters of the models are estimated and interpolated in space. Space-time correlation structures of stationary residual components are quantified using a product-sum space-time variogram model. The ccdf is modeled at all grid locations using this space-time variogram model and space-time kriging. Finally, e-type estimates and conditional variances are computed from the ccdf models for spatial mapping and uncertainty analysis, respectively. The proposed approach is illustrated through a case of time-series Particulate Matter 10 ($PM_{10}$) concentration mapping in Incheon Metropolitan city using monthly $PM_{10}$ concentrations at 13 stations for 3 years. It is shown that the proposed approach would generate reliable time-series $PM_{10}$ concentration maps with less mean bias and better prediction capability, compared to conventional spatial-only ordinary kriging. It is also demonstrated that the conditional variances and the probability exceeding a certain thresholding value would be useful information sources for interpretation.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.22 no.4
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• pp.299-306
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• 2009

Design optimization is a method to find optimum point which minimizes the objective function while satisfying design constraints. The conventional optimization does not consider the uncertainty originated from modeling or manufacturing process, so optimum point often locates on the boundaries of constraints. Reliability based design optimization includes optimization technique and reliability analysis that calculates the reliability of the system. Reliability analysis can be classified into simulation method, fast probability integration method, and moment-based reliability method. In most generally used MPP based reliability analysis, which is one of fast probability integration method, if many MPP points exist, cost and numerical error can increase in the process of transforming constraints into standard normal distribution space. In this paper, multiplicative decomposition method is used as a reliability analysis for RBDO, and sensitivity analysis is performed to apply gradient based optimization algorithm. To illustrate whole process of RBDO mathematical and engineering examples are illustrated.

• Journal of the Korean Geophysical Society
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• v.3 no.3
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• pp.161-174
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• 2000

Bayesian inversion is a stable approach to infer the subsurface structure with the limited data from geophysical explorations. In geophysical inverse process, due to the finite and discrete characteristics of field data and modeling process, some uncertainties are inherent and therefore probabilistic approach to the geophysical inversion is required. Bayesian framework provides theoretical base for the confidency and uncertainty analysis for the inference. However, most of the Bayesian inversion require the integration process of high dimension, so massive calculations like a Monte Carlo integration is demanded to solve it. This method, though, seemed suitable to apply to the geophysical problems which have the characteristics of highly non-linearity, we are faced to meet the promptness and convenience in field process. In this study, by the Gaussian approximation for the observed data and a priori information, fast Bayesian inversion scheme is developed and applied to the model problem with electric well logging and dipole-dipole resistivity data. Each covariance matrices are induced by geostatistical method and optimization technique resulted in maximum a posteriori information. Especially a priori information is evaluated by the cross-validation technique. And the uncertainty analysis was performed to interpret the resistivity structure by simulation of a posteriori covariance matrix.

• Journal of the Korean association of regional geographers
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• v.17 no.4
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• pp.432-442
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• 2011

Climatic variables such as temperature and precipitation tend to vary both in space and in time simultaneously. Thus, it is necessary to include space-time autocorrelation into conventional spatial interpolation methods for reliable time-series mapping. This paper introduces and applies space-time variogram modeling and space-time kriging to generate time-series temperature maps using hourly Automatic Weather System(AWS) temperature observation data for a one-month period. First, temperature observation data are decomposed into deterministic trend and stochastic residual components. For trend component modeling, elevation data which have reasonable correlation with temperature are used as secondary information to generate trend component with topographic effects. Then, space-time variograms of residual components are estimated and modelled by using a product-sum space-time variogram model to account for not only autocorrelation both in space and in time, but also their interactions. From a case study, space-time kriging outperforms both conventional space only ordinary kriging and regression-kriging, which indicates the importance of using space-time autocorrelation information as well as elevation data. It is expected that space-time kriging would be a useful tool when a space-poor but time-rich dataset is analyzed.