Residual capacity assessment of in-service concrete box-girder bridges considering traffic growth and structural deterioration

Yuanyuan Liu,Junyong Zhou,Jianxu Su,Junping Zhang 국제구조공학회 2023 Structural Engineering and Mechanics, An Int'l Jou Vol.85 No.4

The existing concrete bridges are time-varying working systems, where the maintenance strategy should be planned according to the time-varying performance of the bridge. This work proposes a time-dependent residual capacity assessment procedure, which considers the non-stationary bridge load effects under growing traffic and non-stationary structural deterioration owing to material degradations. Lifetime bridge load effects under traffic growth are predicated by the nonstationary peaks-over-threshold (POT) method using time-dependent generalized Pareto distribution (GPD) models. The nonstationary structural resistance owing to material degradation is modeled by incorporating the Gamma deterioration process and field inspection data. A three-span continuous box-girder bridge is illustrated as an example to demonstrate the application of the proposed procedure, and the time-varying reliability indexes of the bridge girder are calculated. The accuracy of the proposed non-stationary POT method is verified through numerical examples, where the shape parameter of the time-varying GPD model is constant but the threshold and scale parameters are polynomial functions increasing with time. The case study illustrates that the residual flexural capacities show a degradation trend from a slow decrease to an accelerated decrease under traffic growth and material degradation. The reliability index for the mid-span cross-section reduces from 4.91 to 4.55 after being in service for 100 years, and the value is from 4.96 to 4.75 for the mid-support cross-section. The studied bridge shows no safety risk under traffic growth and structural deterioration owing to its high design safety reserve. However, applying the proposed numerical approach to analyze the degradation of residual bearing capacity for bridge structures with low safety reserves is of great significance for management and maintenance.

POT 방법을 이용한 극치 해수위의 비정상성 빈도해석

정병순,이옥정,김경민,김상단 한국방재학회 2018 한국방재학회논문집 Vol.18 No.7

본 연구에서는 극치 해수위의 비정상성을 반영하기 위하여 Peak-Over-Threshold (POT) 방법에 기초한 빈도해석이 수행되었다. 일반 Pareto 분포(GPD)의 매개변수들 중에서 규모 매개변수가 시간 의존적인 함수로 고려되었다. 부산지점이 연구대상지점으로 선정되었으며, 1976년부터 2015년까지 40년 동안 1시간 단위로 정리된 해수위 자료가 이용되었다. 연 최대치 시계열에 기초한 일반 극치 분포에 의해 추정된 재현기간별 극치 해수위 추정 값과 가장 유사한 결과를 얻을 수 있도록 POT 시계열의 임계값이 결정되었다. 정상성 GPD 모델과 비정상성 GPD 모델을 비교한 결과, 2055년에는 현재보다 재현기간 50년 극치 해수위 추정값이 83 cm 정도 상승할 가능성이 많은 것으로 분석되었다. In this study, frequency analysis based on the Peak-Over-Threshold (POT) method was performed to reflect the non-stationarity of extreme sea level. Of the parameters of the general Pareto distribution (GPD), the scale parameter was considered as a time-dependent function. The Busan site was selected as a study site, and sea level data from 1976 to 2015 (40 years) were collected at 1-hour intervals. The threshold value of the POT time series was determined to obtain extreme sea level estimates as close to those calculated by the generalized extreme value distribution based on the annual maximum time series. By comparing the stationary GPD model with the non-stationary GPD model, it was determined that the estimate of the extreme sea level for the 50-year return period is likely to be increased by approximately 83 cm in 2055.

POT법에 의한 극치풍속분포에 관한 연구

오종섭(Oh, Jong-Seop) 대한건축학회 2011 大韓建築學會論文集 : 構造系 Vol.27 No.10

This study is concerned with the estimation of extreme wind distribution and of wind speeds for return period in the major cities reflecting the recent meteorological data(uncorrelated samples obtained from largest daily data records(1990-2010), largest yearly data samples(1971-2010)). They were standardized homogeneously to the surface roughness category C, and to 10m above ground surface. This study seeks to ascertain whether the any extreme distribution is an appropriate extreme wind speed model by performing statistical analyses based on the "peaks over threshold" approach. This study uses the de Haan method, which was found in previous studies to perform about as well or better than the other methods, and has the advantage of providing estimates of confidence bounds. The analyses provide persuasive evidences that extreme wind speeds are described predominantly by reverse Weibull distribution, which unlike the Gumbel distribution has finite upper tails.

동아시아 통화 포트폴리오의 의존성과 위험측정

조광조(Kwang-Jo JO) 조선대학교 지식경영연구원 2008 기업과 혁신연구 Vol.1 No.2

본 연구는 미국 달러를 중심으로 한 동아시아 통화 포트폴리오의 의존성과 위험(VaR, ES)을 Copula를 이용하여 실증 분석하였다. 분석결과 첫째, 달러대 싱가포르 달러환율과 달러대 말레이시아 링기트환율의 상호의존성이 가장 높게 나타났다. 둘째, 달러대 동아시아국가들의 환율은 외환위기를 겪으면서 환율의 극단적 의존성이 커졌다. 셋째, Gumbel Copula, Galambos Copula, Husler and reiss Copula, Twan Copula, bb5 Copula중 Twan Copula의 왼쪽 꼬리와 오른쪽 꼬리의 AIC지수가 가장 낮아 GPD모형에 가장 적합한 것으로 나타났다. 넷째, 달러대 홍콩달러환율과 달러대 싱가포르 달러환율의 포트폴리오가 위험척도인 VaR및 ES가 가장 작았다. 다섯째, 각국 환율포트폴리오의 의존성과 VaR 및 ES가 어느정도 상관관계가 있는 것으로 나타났다. This paper presents an application of copula methodology in modelling joint distributions with fat tails. We select Peaks-Over-Threshold(POT) method and use Generalized Pareto Distribution(GPD) as the marginal distribution, We use the Gumbel Copula, Galambos Copula, Husler and reiss Copula, Twan Copula, bb5 Copula. We fit these copulas to daily Currencies portfolio returns of East Asia countries and use upper and lower tail dependence. Empirical result show that asymptotic dependence exist between $/SIN$ and $/MAL. And such dependence become stronger after Asian Financial Crisis. The twan copula is clearly a better fit to the bivariate returns than another copula. The portfolio VaR of $/hongkong $ and $/singapore $ are means that with 5% probability, the portfolio could lose 0.231006% or more in one day. If the return is less than 0.231006%, then, average, the loss is 0.347388%.

동아시아 통화 포트폴리오의 의존성과 위험측정 - Copula접근방법을 중심으로

조광조(Kwang-Jo Jo) 한국경제통상학회 2006 경제연구 Vol.24 No.2

  본 연구는 동아시아 금융위기 전후 상황에서 Copula를 이용하여 통화 포트폴리오의 의존성과 위험(VaR, ES)을 실증 분석하였다. 분석결과 첫째, 원화대 달러환율과 원화대 홍콩달러 환율의 상호의존성이 가장 높게 나타났다. 둘째, 동아시아국들은 외환위기를 겪으면서 국가들간의 환율의 극단적 의존성이 확연히 커졌다. 셋째, Gumbel Copula, Galambos Copula, Husler and reiss Copula, Twan Copula, bb5 Copula중 Twan Copula의 왼쪽 꼬리와 오른쪽 꼬리의 AIC지수가 가장 낮아 GPD모형에 가장 적합한 것으로 나타났다. 넷째, 원화대 홍콩달러환율과 원화대 싱가포르 달러환율의 포트폴리오가 위험척도인 VaR와 ES가 가장 작아 위험이 적은 것을 의미한다. 다섯째, 각국 환율포트폴리오의 의존성과 VaR 및 ES가 어느정도 상관관계가 있는 것으로 나타났다.   This paper presents an application of copula methodology in modelling joint distributions with fat tails. We select Peaks-Over-Threshold(POT) method and use Generalized Pareto Distribution(GPD) as the marginal distribution, We use the Gumbel Copula, Galambos Copula, Husler and reiss Copula, Twan Copula, bb5 Copula. We fit these copulas to daily Currencies portfolio returns of East Asia countries and use upper and lower tail dependence.<BR>  Empirical result show that asymptotic dependence exist between ?/$ and ?/hongkong$. And such dependence become stronger after Asian Financial Crisis. The twan copula is clearly a better fit to the bivariate returns than another copula. The portfolio VaR of ?/hongkong $ and ?/singapore $ are means that with 5% probability, the portfolio could lose 0.241489% or more in one day. If the return is less than -0.241489%, then, average, the loss is 0.501958%.

Estimating extreme tail risk measures with generalized Pareto distribution

Park, M.H.,Kim, J.H.T. North-Holland Pub. Co ; Elsevier Science Ltd 2016 Computational statistics & data analysis Vol.98 No.-

<P>The generalized Pareto distribution (GPD) has been widely used in modelling heavy tail phenomena in many applications. The standard practice is to fit the tail region of the dataset to the GPD separately, a framework known as the peaks-over-threshold (POT) in the extreme value literature. In this paper we propose a new GPD parameter estimator, under the POT framework, to estimate common tail risk measures, the Value-at-Risk (VaR) and Conditional Tail Expectation (also known as Tail-VaR) for heavy-tailed losses. The proposed estimator is based on a nonlinear weighted least squares method that minimizes the sum of squared deviations between the empirical distribution function and the theoretical GPD for the data exceeding the tail threshold. The proposed method properly addresses a caveat of a similar estimator previously advocated, and further improves the performance by introducing appropriate weights in the optimization procedure. Using various simulation studies and a realistic heavy-tailed model, we compare alternative estimators and show that the new estimator is highly competitive, especially when the tail risk measures are concerned with extreme confidence levels. (C) 2015 Elsevier B.V. All rights reserved.</P>

Extreme Value Analysis of Statistically Independent Stochastic Variables

최용호,연성모,김현조,이동연 한국해양공학회 2019 韓國海洋工學會誌 Vol.33 No.3

An extreme value analysis (EVA) is essential to obtain a design value for highly nonlinear variables such as long-term environmental data for wind and waves, and slamming or sloshing impact pressures. According to the extreme value theory (EVT), the extreme value distribution is derived by multiplying the initial cumulative distribution functions for independent and identically distributed (IID) random variables. However, in the position mooring of DNVGL, the sampled global maxima of the mooring line tension are assumed to be IID stochastic variables without checking their independence. The ITTC Recommended Procedures and Guidelines for Sloshing Model Tests never deal with the independence of the sampling data. Hence, a design value estimated without the IID check would be under- or over-estimated because of considering observations far away from a Weibull or generalized Pareto distribution (GPD) as outliers. In this study, the IID sampling data are first checked in an EVA. With no IID random variables, an automatic resampling scheme is recommended using the block maxima approach for a generalized extreme value (GEV) distribution and peaks-over-threshold (POT) approach for a GPD. A partial autocorrelation function (PACF) is used to check the IID variables. In this study, only one 5 h sample of sloshing test results was used for a feasibility study of the resampling IID variables approach. Based on this study, the resampling IID variables may reduce the number of outliers, and the statistically more appropriate design value could be achieved with independent samples.

Stochastic procedures for extreme wave induced responses in flexible ships

Jensen, Jorgen Juncher,Andersen, Ingrid Marie Vincent,Seng, Sopheak The Society of Naval Architects of Korea 2014 International Journal of Naval Architecture and Oc Vol.6 No.4

Different procedures for estimation of the extreme global wave hydroelastic responses in ships are discussed. Firstly, stochastic procedures for application in detailed numerical studies (CFD) are outlined. The use of the First Order Reliability Method (FORM) to generate critical wave episodes of short duration, less than 1 minute, with prescribed probability content is discussed for use in extreme response predictions including hydroelastic behaviour and slamming load events. The possibility of combining FORM results with Monte Carlo simulations is discussed for faster but still very accurate estimation of extreme responses. Secondly, stochastic procedures using measured time series of responses as input are considered. The Peak-over-Threshold procedure and the Weibull fitting are applied and discussed for the extreme value predictions including possible corrections for clustering effects.

Extreme value modeling of structural load effects with non-identical distribution using clustering

Junyong Zhou,Xin Ruan,Xuefei Shi,Chudong Pan 국제구조공학회 2020 Structural Engineering and Mechanics, An Int'l Jou Vol.74 No.1

The common practice to predict the characteristic structural load effects (LEs) in long reference periods is to employ the extreme value theory (EVT) for building limit distributions. However, most applications ignore that LEs are driven by multiple loading events and thus do not have the identical distribution, a prerequisite for EVT. In this study, we propose the composite extreme value modeling approach using clustering to (a) cluster initial blended samples into finite identical distributed subsamples using the finite mixture model, expectation-maximization algorithm, and the Akaike information criterion; (b) combine limit distributions of subsamples into a composite prediction equation using the generalized Pareto distribution based on a joint threshold. The proposed approach was validated both through numerical examples with known solutions and engineering applications of bridge traffic LEs on a long-span bridge. The results indicate that a joint threshold largely benefits the composite extreme value modeling, many appropriate tail approaching models can be used, and the equation form is simply the sum of the weighted models. In numerical examples, the proposed approach using clustering generated accurate extrema prediction of any reference period compared with the known solutions, whereas the common practice of employing EVT without clustering on the mixture data showed large deviations. Real-world bridge traffic LEs are driven by multi-events and present multipeak distributions, and the proposed approach is more capable of capturing the tendency of tailed LEs than the conventional approach. The proposed approach is expected to have wide applications to general problems such as samples that are driven by multiple events and that do not have the identical distribution.

모조 태풍 합성 재분석 바람장을 이용한 북서태평양 극치 해상풍 추정

김혜인,문일주 한국해양과학기술원 2021 Ocean and Polar Research Vol.43 No.1

In this study, extreme wind speeds in the Western North Pacific (WNP) were estimated using reanalysis wind fields synthesized with an empirical typhoon vortex model. Reanalysis wind data used is the Fifth-generation European Centre for Medium-Range Weather Forecasts (ECMWF) reanalysis (ERA5) data, which was deemed to be the most suitable for extreme value analysis in this study. The empirical typhoon vortex model used has the advantage of being able to realistically reproduce the asymmetric winds of a typhoon by using the gale/storm-forced wind radii information in the 4 quadrants of a typhoon. Using a total of 39 years of the synthesized reanalysis wind fields in the WNP, extreme value analysis is applied to the General Pareto Distribution (GPD) model based on the Peak-Over-Threshold (POT) method, which can be used effectively in case of insufficient data. The results showed that the extreme analysis using the synthesized wind data significantly improved the tendency to underestimate the extreme wind speeds compared to using only reanalysis wind data. Considering the difficulty of obtaining long-term observational wind data at sea, the result of the synthesized wind field and extreme value analysis developed in this study can be used as basic data for the design of offshore structures.