• East Asian mathematical journal
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• v.36 no.1
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• pp.55-60
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• 2020

We study a probabilistic approach for valuing an exchange option with default risk. The structural model of Klein [6] is used for modeling default risk. Under the structural model, we derive the closed-form pricing formula of the exchange option with default risk. Specifically, we provide the pricing formula of the option with the bivariate normal cumulative function via a change of measure technique and a multidimensional Girsanov's theorem.

• 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 the Korean Institute of Illuminating and Electrical Installation Engineers
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• v.25 no.10
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• pp.87-93
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• 2011

Nonlinear loads including lighting fixtures generate harmonic currents and create distortions on the sinusoidal voltage of the power system. Harmonic field measurements have shown that the harmonic contents of a waveform varies with time. A cumulative probabilistic approach is the most commonly used method to solve time varying harmonics. In this paper the time varying harmonics of lighting loads are evaluated by international harmonic standards(IEC 61000-3-6).

• Structural Engineering and Mechanics
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• v.60 no.1
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• pp.71-90
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• 2016

In this paper, the normalized variable V=(log N-B)(log ${\Delta}{\sigma}-C$-C), as derived from the probabilistic S-N field of Castillo and Canteli, is taken as a reference for calculation of damage accumulation and probability of failure using the Miner number in scenarios of variable amplitude loading. Alternative damage measures, such as the classical Miner and logarithmic Miner, are also considered for comparison between theoretical lifetime prediction and experimental data. The suitability of this approach is confirmed for it provides safe lifetime prediction when applied to fatigue data obtained for riveted joints made of a puddle iron original from the Fao bridge, as well as for data from experimental programs published elsewhere carried out for different materials (aluminium and concrete specimens) under distinct variable loading histories.

• Wind and Structures
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• v.23 no.1
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• pp.75-90
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• 2016

A probabilistic approach that combines structural demand hazard analysis with cumulative damage assessment is presented and applied to a steel tower of a wind turbine. The study presents the step by step procedure to compare the reliability over time of the structure subjected to fatigue, assuming: a) a binomial Weibull annual wind speed, and b) a traditional Weibull probability distribution function (PDF). The probabilistic analysis involves the calculation of force time simulated histories, fatigue analysis at the steel tower base, wind hazard curves and structural fragility curves. Differences in the structural reliability over time depending on the wind speed PDF assumed are found, and recommendations about selecting a real PDF are given.

• Journal of the Korean Institute of Illuminating and Electrical Installation Engineers
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• v.20 no.9
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• pp.54-60
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• 2006

Large steel industries have time-varying nonlinear loads such as electric arc furnaces. These nonlinear loads generate harmonic currents and create distortions on the sinusoidal voltage of the power system. The main objective of the static var compensator is to maintain the rms voltage at the point of common coupling within the limit. In this research, harmonic mitigation studies were conducted with and without the SVC, and time-varying harmonics were evaluated according to the international harmonic standards (IEC 61000-3-6 and IEEE Std. 519) using a cumulative probabilistic approach.

• 한국지구물리탐사학회:학술대회논문집
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• 2003.11a
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• pp.340-343
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• 2003

This study presents a practical procedure for the Bayesian inversion of geophysical data by Markov chain Monte Carlo (MCMC) sampling and geostatistics. We have applied geostatistical techniques for the acquisition of prior model information, and then the MCMC method was adopted to infer the characteristics of the marginal distributions of model parameters. For the Bayesian inversion of dipole-dipole array resistivity data, we have used the indicator kriging and simulation techniques to generate cumulative density functions from Schlumberger array resistivity data and well logging data, and obtained prior information by cokriging and simulations from covariogram models. The indicator approach makes it possible to incorporate non-parametric information into the probabilistic density function. We have also adopted the MCMC approach, based on Gibbs sampling, to examine the characteristics of a posteriori probability density function and the marginal distribution of each parameter. This approach provides an effective way to treat Bayesian inversion of geophysical data and reduce the non-uniqueness by incorporating various prior information.

• Smart Structures and Systems
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• v.15 no.3
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• pp.699-715
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• 2015

A modal parameter based damage sensitive feature (DSF) is defined to mimic the relative change in any diagonal element of the stiffness matrix of a model of a structure. The damage assessment is performed in a statistical pattern recognition framework using empirical complementary cumulative distribution functions (ECCDFs) of the DSFs extracted from measured operational vibration response data. Methods are discussed to perform probabilistic structural health assessment with respect to the following questions: (a) "Is there a change in the current state of the structure compared to the baseline state?", (b) "Does the change indicate a localized stiffness reduction or increase?", with the latter representing a situation of retrofitting operations, and (c) "What is the severity of the change in a probabilistic sense?". To identify a range of normal structural variations due to environmental and operational conditions, lower and upper bound ECCDFs are used to define the baseline structural state. Such an approach attempts to decouple "non-damage" related variations from damage induced changes, and account for the unknown environmental/operational conditions of the current state. The damage assessment procedure is discussed using numerical simulations of ambient vibration testing of a bridge deck system, as well as shake table experimental data from a 4-story steel frame.

• Earthquakes and Structures
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• v.14 no.3
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• pp.203-214
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• 2018

Predictive demand and collapse fragility functions are two essential components of the probabilistic seismic demand analysis that are commonly developed based on statistics with enormous, costly and time consuming data gathering. Although this approach might be justified for research purposes, it is not appealing for practical applications because of its computational cost. Thus, in this paper, Bayesian regression-based demand and collapse models are proposed to eliminate the need of time-consuming analyses. The demand model developed in the form of linear equation predicts overall maximum inter-story drift of the lowto mid-rise regular steel moment resisting frames (SMRFs), while the collapse model mathematically expressed by lognormal cumulative distribution function provides collapse occurrence probability for a given spectral acceleration at the fundamental period of the structure. Next, as an application, the proposed demand and collapse functions are implemented in a seismic fragility analysis to develop fragility and consequently seismic demand curves of three example buildings. The accuracy provided by utilization of the proposed models, with considering computation reduction, are compared with those directly obtained from Incremental Dynamic analysis, which is a computer-intensive procedure.

• Smart Structures and Systems
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• v.30 no.3
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• pp.303-315
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• 2022

The degradation of wheel tread may result in serious hazards in the railway operation system. Therefore, timely wheel defect diagnosis of in-service trains to avoid tragic events is of particular importance. The focus of this study is to develop a novel wheel defect detection approach based on the relevance vector machine (RVM) which enables online detection of potentially defective wheels with trackside monitoring data acquired under different running-speed conditions. With the dynamic strain responses collected by a trackside monitoring system, the cumulative Fourier amplitudes (CFA) characterizing the effect of individual wheels are extracted to formulate multiple probabilistic regression models (MPRMs) in terms of multi-kernel RVM, which accommodate both variables of vibration frequency and running speed. Compared with the general single-kernel RVM-based model, the proposed multi-kernel MPRM approach bears better local and global representation ability and generalization performance, which are prerequisite for reliable wheel defect detection by means of data acquired under different running-speed conditions. After formulating the MPRMs, we adopt a Bayesian null hypothesis indicator for wheel defect identification and quantification, and the proposed method is demonstrated by utilizing real-world monitoring data acquired by an FBG-based trackside monitoring system deployed on a high-speed trial railway. The results testify the validity of the proposed method for wheel defect detection under different running-speed conditions.