A new approach to evaluate the extreme value distribution （EVD） of the response and reliability of general multi-DOF nonlinear stochastic structures is proposed. The approach is based on the recently developed proba...A new approach to evaluate the extreme value distribution （EVD） of the response and reliability of general multi-DOF nonlinear stochastic structures is proposed. The approach is based on the recently developed probability density evolution method, which enables the instantaneous probability density functions of the stochastic responses to be captured. In the proposed method, a virtual stochastic process is first constructed to satisfy the condition that the extreme value of the response equals the value of the constructed process at a certain instant of time. The probability density evolution method is then applied to evaluate the instantaneous probability density function of the response, yielding the EVD. The reliability is therefore available through a simple integration over the safe domain. A numerical algorithm is developed using the Number Theoretical Method to select the discretized representative points. Further, a hyper-ball is imposed to sieve the points from the preceding point set in the hypercube. In the numerical examples, the EVD of random variables is evaluated and compared with the analytical solution. A frame structure is analyzed to capture the EVD of the response and the dynamic reliability. The investigations indicate that the proposed approach provides reasonable accuracy and efficiency.展开更多
The bootstrap method is one of the new ways of studying statistical math which this article uses but is a major tool for studying and evaluating the values of parameters in probability distribution.Our research is con...The bootstrap method is one of the new ways of studying statistical math which this article uses but is a major tool for studying and evaluating the values of parameters in probability distribution.Our research is concerned overview of the theory of infinite distribution functions.The tool to deal with the problems raised in the paper is the mathematical methods of random analysis(theory of random process and multivariate statistics).In this article,we introduce the new function to find out the bias and standard error with jackknife method for Generalized Extreme Value distributions.展开更多
Due to global warming and diminishing ice cover in Arctic regions,the northern sea route(NSR)has attracted increasing attention in recent years.Extreme cold temperatures and high wind speeds in Arctic regions present ...Due to global warming and diminishing ice cover in Arctic regions,the northern sea route(NSR)has attracted increasing attention in recent years.Extreme cold temperatures and high wind speeds in Arctic regions present substantial risks to vessels operating along the NSR.Consequently,analyzing extreme temperature and wind speed values along the NSR is essential for ensuring maritime operational safety in the region.This study analyzes wind and temperature data spanning 40 years,from 1981 to 2020,at four representative sites along the NSR for extreme value analysis.The average conditional exceedance rate(ACER)method and the Gumbel method are employed to estimate extreme wind speed and air temperature at these sites.Comparative analysis reveals that the ACER method provides higher accuracy and lower uncertainty in estimations.The predicted extreme wind speed for a 100-year return period is 30.36 m/s,with a minimum temperature of-56.66°C,varying across the four sites.Furthermore,the study presents extreme values corresponding to each return period,providing temperature extremes as a basis for guiding steel thickness specifications.These findings provide valuable reference for designing polar vessels and offshore structures,contributing to enhanced engineering standards for Arctic conditions.展开更多
The fish cage design requires accurate predictions of long-term extreme loads and responses.Compared with the time-consuming full long-term analysis method integrating all the probability distribution of the short-ter...The fish cage design requires accurate predictions of long-term extreme loads and responses.Compared with the time-consuming full long-term analysis method integrating all the probability distribution of the short-term extremes,the environmental contour method gains much attention in predicting the long-term extreme values due to the less computational effort.This paper investigates the long-term extreme response of a fish cage using the environmental contour method.The fish cage is numerically simulated based on the lumped-mass method and the curved beam theory.Based on the one-dimensional(1D)and two-dimensional(2D)environmental contour,the extreme responses,including the surge and heave motions,mooring force,and vertical bending of the floater,are predicted for different return periods and compared with the full long-term analysis results.Results indicate that the 1D method greatly underestimates the extreme values.The 2D environmental contour method with a higher percentile level,namely90%,provides reasonable estimations and seems to be suitable for the long-term value analysis.Sensitivity studies show that the mooring arrangement and the bending stiffness have great effects on the bending moment and the mooring force and the mooring line pre-tension has minor effects on the fish cage response.展开更多
Heavy rains and floods are long considered critical societal concerns due to adverse effects on society,environment,and economies.The best appropriate identification for rainfall distribution is equally of significant...Heavy rains and floods are long considered critical societal concerns due to adverse effects on society,environment,and economies.The best appropriate identification for rainfall distribution is equally of significant concern to society and planners due to its application in the hydrological and water resources management sectors,and agricultural planning.Two methods for extreme values theory namely the annual maximum(AM)series method and the peaksover-threshold(POT)method are generally employed for extreme values analyses.This study therefore compared the results of both methods for ARC2 daily rainfall data at Bamako-Senou station for the period 1991-2021.Five(05)commonly used distribution functions,namely the Normal,Log-Normal(LN),Gumbel type I,Gamma and Pearson type 3(P3)distributions were used to fit the AM data.The method of moments(MOM)and the method of maximum likelihood estimation(MLE)were employed for parameters estimation in AM analyses.The generalized Pareto(GP)distribution was also used to fit the peaks over threshold(POT)method.The results indicated that the P3 distribution gave better result than other distributions when parameters were estimated with the MLE.The LN distribution was also best fit distribution to AM series when parameters were estimated with the MOM.The P3 distribution gave higher quantile estimates than other distributions.The POT method gave better results for quantiles estimation than the AM series.It is recommended that further study should include various truncation levels and tests for the choice of an optimal threshold in the POT method.展开更多
Sticky Brownian motions can be viewed as time-changed semimartingale reflecting Brownian motions,which find applications in many areas including queueing theory and mathematical finance.In this paper,we focus on stati...Sticky Brownian motions can be viewed as time-changed semimartingale reflecting Brownian motions,which find applications in many areas including queueing theory and mathematical finance.In this paper,we focus on stationary distributions for sticky Brownian motions.Main results obtained here include tail asymptotic properties in the marginal distributions and joint distributions.The kernel method,copula concept and extreme value theory are the main tools used in our analysis.展开更多
基金National Natural Science Foundation of China for Innovative Research Groups Under Grant No. 50321803 National Natural Science Foundation of China for Young Scholars Under Grant No. 10402030
文摘A new approach to evaluate the extreme value distribution （EVD） of the response and reliability of general multi-DOF nonlinear stochastic structures is proposed. The approach is based on the recently developed probability density evolution method, which enables the instantaneous probability density functions of the stochastic responses to be captured. In the proposed method, a virtual stochastic process is first constructed to satisfy the condition that the extreme value of the response equals the value of the constructed process at a certain instant of time. The probability density evolution method is then applied to evaluate the instantaneous probability density function of the response, yielding the EVD. The reliability is therefore available through a simple integration over the safe domain. A numerical algorithm is developed using the Number Theoretical Method to select the discretized representative points. Further, a hyper-ball is imposed to sieve the points from the preceding point set in the hypercube. In the numerical examples, the EVD of random variables is evaluated and compared with the analytical solution. A frame structure is analyzed to capture the EVD of the response and the dynamic reliability. The investigations indicate that the proposed approach provides reasonable accuracy and efficiency.
文摘The bootstrap method is one of the new ways of studying statistical math which this article uses but is a major tool for studying and evaluating the values of parameters in probability distribution.Our research is concerned overview of the theory of infinite distribution functions.The tool to deal with the problems raised in the paper is the mathematical methods of random analysis(theory of random process and multivariate statistics).In this article,we introduce the new function to find out the bias and standard error with jackknife method for Generalized Extreme Value distributions.
基金supported by the National Natural Science Foundation of China(Grant No.52201379)the Fundamental Research Funds for the Central Universities(Grant No.WUT:3120622898)+2 种基金State Key Laboratory of Structural Analysis,Optimization and CAE Software for Industrial Equipment,Dalian University of Technology(Grant No.GZ 231088)Shanghai Key Laboratory of Naval Architecture Engineering(Grant No.SE202305)funded by European Research Council project under the European Union’s Horizon 2020 research and innovation program(Grant No.TRUST CoG 2019864724).
文摘Due to global warming and diminishing ice cover in Arctic regions,the northern sea route(NSR)has attracted increasing attention in recent years.Extreme cold temperatures and high wind speeds in Arctic regions present substantial risks to vessels operating along the NSR.Consequently,analyzing extreme temperature and wind speed values along the NSR is essential for ensuring maritime operational safety in the region.This study analyzes wind and temperature data spanning 40 years,from 1981 to 2020,at four representative sites along the NSR for extreme value analysis.The average conditional exceedance rate(ACER)method and the Gumbel method are employed to estimate extreme wind speed and air temperature at these sites.Comparative analysis reveals that the ACER method provides higher accuracy and lower uncertainty in estimations.The predicted extreme wind speed for a 100-year return period is 30.36 m/s,with a minimum temperature of-56.66°C,varying across the four sites.Furthermore,the study presents extreme values corresponding to each return period,providing temperature extremes as a basis for guiding steel thickness specifications.These findings provide valuable reference for designing polar vessels and offshore structures,contributing to enhanced engineering standards for Arctic conditions.
基金financially supported by the China Postdoctoral Science Foundation(Grant No.2019M661024]the Open Foundation of State Key Laboratory of Coastal and Offshore Engineering(Grant No.LP1901)。
文摘The fish cage design requires accurate predictions of long-term extreme loads and responses.Compared with the time-consuming full long-term analysis method integrating all the probability distribution of the short-term extremes,the environmental contour method gains much attention in predicting the long-term extreme values due to the less computational effort.This paper investigates the long-term extreme response of a fish cage using the environmental contour method.The fish cage is numerically simulated based on the lumped-mass method and the curved beam theory.Based on the one-dimensional(1D)and two-dimensional(2D)environmental contour,the extreme responses,including the surge and heave motions,mooring force,and vertical bending of the floater,are predicted for different return periods and compared with the full long-term analysis results.Results indicate that the 1D method greatly underestimates the extreme values.The 2D environmental contour method with a higher percentile level,namely90%,provides reasonable estimations and seems to be suitable for the long-term value analysis.Sensitivity studies show that the mooring arrangement and the bending stiffness have great effects on the bending moment and the mooring force and the mooring line pre-tension has minor effects on the fish cage response.
文摘Heavy rains and floods are long considered critical societal concerns due to adverse effects on society,environment,and economies.The best appropriate identification for rainfall distribution is equally of significant concern to society and planners due to its application in the hydrological and water resources management sectors,and agricultural planning.Two methods for extreme values theory namely the annual maximum(AM)series method and the peaksover-threshold(POT)method are generally employed for extreme values analyses.This study therefore compared the results of both methods for ARC2 daily rainfall data at Bamako-Senou station for the period 1991-2021.Five(05)commonly used distribution functions,namely the Normal,Log-Normal(LN),Gumbel type I,Gamma and Pearson type 3(P3)distributions were used to fit the AM data.The method of moments(MOM)and the method of maximum likelihood estimation(MLE)were employed for parameters estimation in AM analyses.The generalized Pareto(GP)distribution was also used to fit the peaks over threshold(POT)method.The results indicated that the P3 distribution gave better result than other distributions when parameters were estimated with the MLE.The LN distribution was also best fit distribution to AM series when parameters were estimated with the MOM.The P3 distribution gave higher quantile estimates than other distributions.The POT method gave better results for quantiles estimation than the AM series.It is recommended that further study should include various truncation levels and tests for the choice of an optimal threshold in the POT method.
基金supported by the Shandong Provincial Natural Science Foundation of China(Grtant No.ZR2019MA035)the Natural Sciences and Engineering Research Council(NSERC)of Canadasupported by the China Scholarship Council(Grant No.201708370006)。
文摘Sticky Brownian motions can be viewed as time-changed semimartingale reflecting Brownian motions,which find applications in many areas including queueing theory and mathematical finance.In this paper,we focus on stationary distributions for sticky Brownian motions.Main results obtained here include tail asymptotic properties in the marginal distributions and joint distributions.The kernel method,copula concept and extreme value theory are the main tools used in our analysis.
