A mature mathematical technique called copula joint function is introduced in this paper, which is commonly used in the financial risk analysis to estimate uncertainty. The joint function is generalized to the n-dimen...A mature mathematical technique called copula joint function is introduced in this paper, which is commonly used in the financial risk analysis to estimate uncertainty. The joint function is generalized to the n-dimensional Frank’s copula. In addition, we adopt two attenuation models proposed by YU and Boore et al, respectively, and construct a two-dimensional copula joint probabilistic function as an example to illustrate the uncertainty treatment at low probability. The results show that copula joint function gives us a better prediction of peak ground motion than that resultant from the simple linear weight technique which is commonly used in the traditional logic-tree treatment of model uncertainties. In light of widespread application in the risk analysis from financial investment to insurance assessment, we believe that the copula-based technique will have a potential application in the seismic hazard analysis.展开更多
In this paper, we establish asymptotically optimal simultaneous confidence bands for the copula function based on the local linear kernel estimator proposed by Chen and Huang [1]. For this, we prove under smoothness c...In this paper, we establish asymptotically optimal simultaneous confidence bands for the copula function based on the local linear kernel estimator proposed by Chen and Huang [1]. For this, we prove under smoothness conditions on the derivatives of the copula a uniform in bandwidth law of the iterated logarithm for the maximal deviation of this estimator from its expectation. We also show that the bias term converges uniformly to zero with a precise rate. The performance of these bands is illustrated by a simulation study. An application based on pseudo-panel data is also provided for modeling the dependence structure of Senegalese households’ expense data in 2001 and 2006.展开更多
Drought,which restricts the sustainable development of agriculture,ecological health,and social economy,is affected by a variety of factors.It is widely accepted that a single variable cannot fully reflect the charact...Drought,which restricts the sustainable development of agriculture,ecological health,and social economy,is affected by a variety of factors.It is widely accepted that a single variable cannot fully reflect the characteristics of drought events.Studying precipitation,reference evapotranspiration(ET_(0)),and vegetation yield can derive information to help conserve water resources in grassland ecosystems in arid and semi-arid regions.In this study,the interactions of precipitation,ET_(0),and vegetation yield in Darhan Muminggan Joint Banner(DMJB),a desert steppe in Inner Mongolia Autonomous Region,China were explored using two-dimensional(2D)and three-dimensional(3D)joint distribution models.Three types of Copula functions were applied to quantitatively analyze the joint distribution probability of different combinations of precipitation,ET_(0),and vegetation yield.For the precipitation–ET_(0)dry–wet type,the 2D joint distribution probability with precipitation≤245.69 mm/a or ET_(0)≥959.20 mm/a in DMJB was approximately 0.60,while the joint distribution probability with precipitation≤245.69 mm/a and ET_(0)≥959.20 mm/a was approximately 0.20.Correspondingly,the joint return period that at least one of the two events(precipitation was dry or ET_(0)was wet)occurred was 2 a,and the co-occurrence return period that both events(precipitation was dry and ET_(0)was wet)occurred was 5 a.Under this condition,the interval between dry and wet events would be short,the water supply and demand were unbalanced,and the water demand of vegetation would not be met.In addition,when precipitation remained stable and ET_(0)increased,the 3D joint distribution probability that vegetation yield would decrease due to water shortage in the precipitation–ET_(0)dry–wet years could reach up to 0.60–0.70.In future work,irrigation activities and water allocation criteria need to be implemented to increase vegetation yield and the safety of water resources in the desert steppe of Inner Mongolia.展开更多
In the context of global warming,drought events occur frequently.In order to better understanding the process and mechanism of drought occurrence and evolution,scholars have dedicated much attention on drought propaga...In the context of global warming,drought events occur frequently.In order to better understanding the process and mechanism of drought occurrence and evolution,scholars have dedicated much attention on drought propagation,mainly focusing on drought propagation time and propagation probability.However,there are relatively few studies on the sensitivities of drought propagation to seasons and drought levels.Therefore,we took the Heihe River Basin(HRB)of Northwest China as the case study area to quantify the propagation time and propagation probability from meteorological drought to agricultural drought during the period of 1981–2020,and subsequently explore their sensitivities to seasons(irrigation and non-irrigation seasons)and drought levels.The correlation coefficient method and Copula-based interval conditional probability model were employed to determine the drought propagation time and propagation probability.The results determined the average drought propagation time as 8 months in the whole basin,which was reduced by 2 months(i.e.,6 months)on average during the irrigation season and prolonged by 2 months(i.e.,10 months)during the non-irrigation season.Propagation probability was sensitive to both seasons and drought levels,and the sensitivities had noticeable spatial differences in the whole basin.The propagation probability of agricultural drought at different levels generally increased with the meteorological drought levels for the upstream,midstream,and southern downstream regions of the HRB.Lesser agricultural droughts were more likely to be triggered during the irrigation season,while severer agricultural droughts were occurred mostly during the non-irrigation season.The research results are helpful to understand the characteristics of drought propagation and provide a scientific basis for the prevention and control of droughts.This study is of great significance for the rational planning of local water resources and maintaining good ecological environment in the HRB.展开更多
The joint probability distribution of wind speed and significant wave height in the Bohai Bay was investigated by comparing the Gurnbel logistic model, the Gumbel-Hougaard （GH） copula function, and the Clayton copul...The joint probability distribution of wind speed and significant wave height in the Bohai Bay was investigated by comparing the Gurnbel logistic model, the Gumbel-Hougaard （GH） copula function, and the Clayton copula function. Twenty years of wind data from 1989 to 2008 were collected from the European Centre for Medium-Range Weather Forecasts （ECMWF） database and the blended wind data of the Quick Scatterometer （QSCAT） satellite data set and re-analysis data from the United States National Centers for Environmental Prediction （NCEP）. Several typhoons were taken into account and merged with the background wind fields from the ECMWF or QSCAT/NCEP database. The 20-year data of significant wave height were calculated with the unstructured-grid version of the third-generation wind wave model Simulating WAves Nearshore （SWAN） under extreme wind process conditions. The Gumbel distribution was used for univariate and marginal distributions. The distribution parameters were estimated with the method of L-moments. Based on the marginal distributions, the joint probability distributions, the associated return periods, and the conditional probability distributions were obtained. The GH copula function was found to be optimal according to the ordinary least squares （OLS） test. The results show that wind waves are the prevailing type of wave in the Bohai Bay.展开更多
Traditional methods for early warning of dam displacements usually assume that residual displacements follow a normal distribution.This assumption deviates from the reality,thereby affecting the reliability of early w...Traditional methods for early warning of dam displacements usually assume that residual displacements follow a normal distribution.This assumption deviates from the reality,thereby affecting the reliability of early warning results and leading to misjudgments of dam displacement behavior.To solve this problem,this study proposed an early warning method using a non-normal distribution function.A new early warning index was developed using cumulative distribution function(CDF)values.The method of kernel density estimation was used to calculate the CDF values of residual displacements at a single point.The copula function was used to compute the CDF values of residual displacements at multiple points.Numerical results showed that,with residual displacements in a non-normal distribution,the early warning method proposed in this study accurately reflected the dam displacement behavior and effectively reduced the frequency of false alarms.This method is expected to aid in the safe operation of dams.展开更多
Multiple failuremodes and strength degradation are usually inherent in the gear transmission system,which brings new challenges for conducting fatigue reliability analysis and design.This paper proposes a novel dynami...Multiple failuremodes and strength degradation are usually inherent in the gear transmission system,which brings new challenges for conducting fatigue reliability analysis and design.This paper proposes a novel dynamic fatigue reliability analysis method for failure dependence and strength degradation based on the combination of theCopula function and Gamma process.Firstly,the dynamic simulation model of the gear transmission system is established to obtain the dynamic stress-time history.The Gamma process is then used to describe the strength degradation to establish the dynamic stress-strength interference model.The marginal distribution functions of tooth contact fatigue and dedendumbending fatigue are calculated respectively based on the dynamic interferencemodel.Finally,the joint distribution of the two failure modes can be obtained by the t-Copula function to characterize the failure dependence,and so the dynamic fatigue reliability considering failure dependence can be estimated.The effectiveness of the proposed method is illustrated with examples.The results reveal the temporal law of reliability and the effects of failure dependence on dynamic fatigue reliability.展开更多
7 kinds of probability distribution functions were used to fit extreme rainfall indexes R1d（ the maximum 1-d rainfall in the year） and R5d（ the maximum continuous 5-d rainfall in the year） at 18 observation statio...7 kinds of probability distribution functions were used to fit extreme rainfall indexes R1d（ the maximum 1-d rainfall in the year） and R5d（ the maximum continuous 5-d rainfall in the year） at 18 observation stations of Beijiang River basin,and linear moment method was used to estimate parameters. According to fitting goodness test,the best probability distribution function was determined. On this basis,spatial analysis of design values of R1d and R5d with 50-a and 100-a reappearance periods was conducted. Via further selection,GH Copula was taken as connection function,and R1d-R5d joint probability distribution in the basin was studied. The results showed that R1d or R5d probability with 50-a and 100-a reappearance periods was larger in Wengyuan and Qingyuan,while R1d and R5d co-occurrence probability with 50-a and 100-a reappearance periods was larger in central north region.展开更多
The GRACE satellite mission provides a new approach for monitoring,tracking,and assessing drought conditions by detecting changes in Earth's gravitational fields and inversing signals of terrestrial water storage ...The GRACE satellite mission provides a new approach for monitoring,tracking,and assessing drought conditions by detecting changes in Earth's gravitational fields and inversing signals of terrestrial water storage anomalies.Existing studies of terrestrial water storage anomalies related droughts paid rare attention to the behind atmospheric physical mechanisms,nor quantified the risk propagation patterns between terrestrial water storage deficits and hydrological or agricultural droughts.In this study,we first extract terrestrial water storage(TWS) droughts,hydrological droughts,and agricultural droughts by using multiple variables including TWS from the GRACE/GRACE-FO satellites,runoff and soil moisture from the ERA5-Land reanalysis dataset.We then identify key atmospheric and oceanic oscillation indices affecting water deficits by employing machine learning technologies.We characterize the joint distributions between drought duration and severity by using the Copula function and quantify the risk propagation of hydrological and agricultural droughts to TWS droughts.The results show that:(1) From 2002 to 2021,there is a significant decrasing trend of TWS in China;the WPIO group atmospheric circulation indices(sea surface temperature index within the Western Pacific and Indian Ocean) contributes the most to TWS.Specifically,the sea surface temperature anomalies within the NINO 3.4 region as well as the Western Pacific Warm Pool area index show significantly positive correlation relationships with TWS in southern China;(2) The northwestern China,the Yangtze River basin,and the downstream of the Pearl River basin are the hotspots of TWS droughts.Besides,the hotspots of hydrological droughts locate in northwestern China and the hotspots of agricultural droughts locate in South China and eastern Tibetan Plateau;(3) The elastic coefficients of hydrological droughts propagating to TWS droughts are higher than those of agricultural droughts,indicating that the TWS droughts are more sensitive to hydrological droughts than to agricultural droughts.展开更多
Wind speed dependences on different areas in a wind farm have influences on security and economic operation in power system.In order to simulate the correlation of wind speed series between different positions,this pa...Wind speed dependences on different areas in a wind farm have influences on security and economic operation in power system.In order to simulate the correlation of wind speed series between different positions,this paper applies Copula function and rank correlation matrix methods to measure the coherence of wind speed in a wind farm.The correlated wind sample space is established.According to active power output characteristics of wind turbines,the polymerization model in a wind farm can be achieved.Monte Carlo optimal power flow is applied to IEEE-30 and IEEE-300 bus systems based on the principle of energy saving dispatching.The study shows that the accuracy of outputs is improved,thus reducing the fluctuation ranges in unit generating costs and power flow in branches while considering wind speed polymerization.This approach provides a new method to improve the effectiveness of energy saving dispatching and system operation arrangement.Results have been tested to be effective.展开更多
On the basis of each gear's failure correlation, the reliability Copula model of a wind turbine gearbox is established and a 1.5 MW wind turbine gearbox is taken as the research object. Firstly, based on the dynam...On the basis of each gear's failure correlation, the reliability Copula model of a wind turbine gearbox is established and a 1.5 MW wind turbine gearbox is taken as the research object. Firstly, based on the dynamic reliability model of mechanical parts, each gear's life distribution function of a wind turbine gearbox is obtained.The life distribution function can be used as the marginal distributions of the system's joint distribution. Secondly,Copula function is introduced to describe the failure correlation between parts, and the appropriate Copula function is selected according to the shape characters of Copula probability density function. Finally, the wind turbine gearbox system is divided into three parts according to the failure correlation of each gear. The Sklar theorem and the thought of step by step analysis are used to obtain the reliability Copula model for a wind turbine gearbox based on failure correlation.展开更多
The drivers of vacant taxis tend to cruise the road network searching new passengers,which leads to additional traffic congestion,air pollution and other problems.This study introduces a Copula-based joint model to an...The drivers of vacant taxis tend to cruise the road network searching new passengers,which leads to additional traffic congestion,air pollution and other problems.This study introduces a Copula-based joint model to analyse destination selection and route choice behaviour in the customer-search process.A multinomial logit model is used to analyse the destination selection behaviour,and a path size logit model is used to explore the routes choice behaviour.Accordingly,the joint model applied Copula function is then established to analyse the correlation between these two behaviours.The destination customer generation rate,destination distance,route customer generation rate,path travel time,cumulative intersection delay,path size and route length are selected as explanatory variables.The taxis trajectory data were collected by global positioning system in Xidan District of Beijing City from September 2014 to February 2015.Using the log-likelihood,Bayesian information criterion as evaluation indexes to measure the fitting result,the joint model applied Copula function has the highest goodness-of-fit.The effect of explanatory variables on customer search behaviour is discussed based on the parameter estimation results.The results of this study are helpful to understand the customer-search behaviour of taxi drivers to reduce operating costs and improve the efficiency of the taxi operation system.展开更多
The Gaussian Copula Probability Density Function （PDF） plays an important role in the fields of finance, hydrological modeling, biomedical study, and texture retrieval. However, the existing schemes for evaluating t...The Gaussian Copula Probability Density Function （PDF） plays an important role in the fields of finance, hydrological modeling, biomedical study, and texture retrieval. However, the existing schemes for evaluating the Gaussian Copula PDF are all computationally-demanding and generally the most time-consuming part in the corresponding applications. In this paper, we propose an FPGA-based design to accelerate the computation of the Gaussian Copula PDF. Specifically, the evaluation of the Gaussian Copula PDF is mapped into a fully-pipelined FPGA dataflow engine by using three optimization steps： transforming the calculation pattern, eliminating constant computations from hardware logic, and extending calculations to multiple pipelines. In the experiments on 10 typical large-scale data sets, our FPGA-based solution shows a maximum of 1870 times speedup over a well-tuned single- core CPU-based solution, and 610 times speedup over a well-optimized parallel quad-core CPU-based solution when processing two-dimensional data.展开更多
This paper introduces a Monte Carlo scenario generation method based on copula theory for the stochastic optimal power flow （STOPF） problem with wind power. By using copula theory, the scenarios are simulated from m...This paper introduces a Monte Carlo scenario generation method based on copula theory for the stochastic optimal power flow （STOPF） problem with wind power. By using copula theory, the scenarios are simulated from multivariable joint distribution but only from their dependency matrix. Hence, the scenarios generated by proposed method can contain flail statistical information of multivariate. Here, the details of simu- lating scenarios for multi-wind-farm are explained with four steps： determine margin of one wind farm, fit the copulas, choose optimal copulas and simulate scenarios by Mote Carlo. Moreover, the producing process of scenarios is demonstrated by two adjacent actual wind farms in China. With the scenarios, the STOPF is con- verted into the same amount deterministic sub OPF models which can be solved by available technology per- fectly. Results using copula theory are compared against results from history samples based on two designs： IEEE 30-bus and IEEE 118-bus systems. The comparison results prove the accuracy of the proposed methodology.展开更多
This paper discusses the correlation structure between London Interbank Offered Rates （LIBOR） by using the copula function. We start from one simplified model of A. Brace, D. Gatarek, and M. Musiela （1997） and fin...This paper discusses the correlation structure between London Interbank Offered Rates （LIBOR） by using the copula function. We start from one simplified model of A. Brace, D. Gatarek, and M. Musiela （1997） and find out that the copula function between two LIBOR rates can be expressed as a sum of an infinite series, where the main term is a distribution function with Gaussian copula. Partial differential equation method is used for deriving the copula expansion. Numerical results show that the copula of the LIBOR rates and Gaussian copula are very close in the central region and differ in the tail, and the Gaussian copula approximation to the copula function between the LIBOR rates provides satisfying results in the normal situation.展开更多
With the increase of economic environment uncertainty,it is of great importance to study the linkage and spillover effects of economic policy uncertainty among countries.Especially,this article selects eight countries...With the increase of economic environment uncertainty,it is of great importance to study the linkage and spillover effects of economic policy uncertainty among countries.Especially,this article selects eight countries along the Belt and Road as the core countries(China,Korea,Croatia,India,Russia,Greece,Pakistan,and Singapore)and four countries(Germany,France,Japan,and UK)as the peripheral countries,and then copula technique and mixed-frequency global vector autoregressive model are employed to analyze the correlation and the spillover effect of the economic policy uncertainty(EPU)for the twelve selected countries,respectively.The proposed empirical findings show clearly that the EPU correlation among the eight core Belt and Road countries is stronger and the spillover effect of the core countries to the peripheral countries is statistically significant.As a result,for harmonious and win-win development,the Belt and Road countries should pay a close attention to the EPU,because the stability of the EPU promotes greatly the economy development.展开更多
Extreme surges and rainfall represent major driving factors for compound flooding in estuary regions along the Chinese coast.The combined effect of extreme surges and rainfall(that is,compound floods)might lead to gre...Extreme surges and rainfall represent major driving factors for compound flooding in estuary regions along the Chinese coast.The combined effect of extreme surges and rainfall(that is,compound floods)might lead to greater impacts than if the drivers occurred in isolation.Hence,understanding the frequency and severity of compound flooding is important for improving flood hazard assessment and compound flood resilience in coastal cities.In this study,we examined the dependence between extreme surges and corresponding rainfall events in 26 catchments along the Chinese coastline during typhoon and non-typhoon seasons using copula functions,to identify where the two drivers more often occur together and the implication for flood management in these locations.We found that the interaction between flood drivers is statistically significant in 10catchments located around Hainan Island(south)and Shanghai,where surge peaks occur mainly during the typhoon season and around the Bohai Sea(north),where surge peaks occur mainly during the non-typhoon season.We further applied the copula-based framework to model the dependence between surge peaks and associated rainfall and estimate their joint and conditional probability in two specific locations—Hainan Island and the Bohai Sea,where the correlation between flood drivers is statistically significant.We observed that in Hainan Island where most of the surge peaks occur during the typhoon season,extreme rainfall events during the typhoon season are generally more intense compared to annual maxima rainfall.In contrast,around the Bohai Sea where surge peaks occur mainly outside the typhoon season,rainfall is less intense than annual maxima rainfall.These results show that the interaction between extreme surges and rainfall can provide valuable insight when designing coastal and urban infrastructure,especially in highly populated urban areas prone to both coastal and pluvial flooding,such as many Chinese coastal cities.展开更多
With several attractive properties, rotary lip seals are widely used in aircraft utility system, and their reliability estimation has drawn more and more attention. This work proposes a reliability estimation approach...With several attractive properties, rotary lip seals are widely used in aircraft utility system, and their reliability estimation has drawn more and more attention. This work proposes a reliability estimation approach based on time-varying dependence analysis. The dependence between the two performance indicators of rotary lip seals, namely leakage rate and friction torque, is modeled by time-varying copula function with polynomial to denote the time-varying parameters, and an efficient copula selection approach is utilized to select the optimal copula function. Parameter estimation is carried out based on a Bayesian method and the reliability during the whole lifetime is calculated based on a Monte Carlo method. Degradation test for rotary lip seal is conducted and the proposed model is validated by test data. The optimal copula function and optimal order of polynomial are determined based on test data. Results show that this model is effective in estimating the reliability of rotary lip seals and can achieve a better goodness of fit.展开更多
Based on the framework of [7], we discuss pricing bilateral counterparty risk of CDS, where each individual default intensity is modeled by a shifted CIR process with jump （3CIR＋＋）, and the correlation between the...Based on the framework of [7], we discuss pricing bilateral counterparty risk of CDS, where each individual default intensity is modeled by a shifted CIR process with jump （3CIR＋＋）, and the correlation between the default times is modeled by a copula function. We present a semi-analytical formula for pricing bilateral counterparty risk of CDS, which is more convenient to compute through calculating multiple numerical integration or using Monte-Carlo simulation without simulating default times. Moreover, we obtain simpler formulae under FGM copulas, Bernstein copulas and CA＇B copulas, which can be applied for speeding up the computation and reducing the pricing error. Numerical results under FGM copulas and CA＇B copulas show that our method performs better both in computation speed and accuracy.展开更多
In the context of climate change,coastal cities are at increased risk of extreme precipitation and sea level rise,and their interaction will aggravate coastal floods.Understanding the potential change of compound floo...In the context of climate change,coastal cities are at increased risk of extreme precipitation and sea level rise,and their interaction will aggravate coastal floods.Understanding the potential change of compound floods is valuable for flood risk reduction.In this study,an integrated approach coupling the hydrological model and copulabased design of precipitation and storm tides was proposed to assess the compound flood risk in a coastal city—Haikou,China.The copula model,most-likely weight function,and varying parameter distribution were used to obtain the combined design values of precipitation and storm tides under the nonstationary scenario,which were applied to the boundary conditions of the 1D-2D hydrological model.Subsequently,the change of the bivariate return periods,design values,and compound flood risks of precipitation and storm tides were investigated.The results show that the bivariate return period of precipitation and storm tides was reduced by an average of 34%under the nonstationary scenario.The maximum inundation areas and volumes were increased by an average of 31.1%and 45.9%respectively in comparison with the stationary scenario.Furthermore,we identified that the compound effects of precipitation and storm tides would have a greater influence on the flood risk when the bivariate return period is more than 50 years,and the peak time lag had a significant influence on the compound flood risk.The proposed framework is effective in the evaluation and prediction of flood risk in coastal cities,and the results provide some guidance for urban disaster prevention and mitigation.展开更多
基金Project of Institute of Crustal Dynamics, China Earthquake Administration (ZDJ2007-1)One Hundred Individual Program of Chinese Academy of Sciences (99M2009M02) National Natural Science Foundation of China (40574022)
文摘A mature mathematical technique called copula joint function is introduced in this paper, which is commonly used in the financial risk analysis to estimate uncertainty. The joint function is generalized to the n-dimensional Frank’s copula. In addition, we adopt two attenuation models proposed by YU and Boore et al, respectively, and construct a two-dimensional copula joint probabilistic function as an example to illustrate the uncertainty treatment at low probability. The results show that copula joint function gives us a better prediction of peak ground motion than that resultant from the simple linear weight technique which is commonly used in the traditional logic-tree treatment of model uncertainties. In light of widespread application in the risk analysis from financial investment to insurance assessment, we believe that the copula-based technique will have a potential application in the seismic hazard analysis.
文摘In this paper, we establish asymptotically optimal simultaneous confidence bands for the copula function based on the local linear kernel estimator proposed by Chen and Huang [1]. For this, we prove under smoothness conditions on the derivatives of the copula a uniform in bandwidth law of the iterated logarithm for the maximal deviation of this estimator from its expectation. We also show that the bias term converges uniformly to zero with a precise rate. The performance of these bands is illustrated by a simulation study. An application based on pseudo-panel data is also provided for modeling the dependence structure of Senegalese households’ expense data in 2001 and 2006.
基金This research was supported by the Natural Science Foundation of Inner Mongolia Autonomous Region,China(2022QN04003)the Central Government to Guide Local Scientific and Technological Development(2021ZY0031).
文摘Drought,which restricts the sustainable development of agriculture,ecological health,and social economy,is affected by a variety of factors.It is widely accepted that a single variable cannot fully reflect the characteristics of drought events.Studying precipitation,reference evapotranspiration(ET_(0)),and vegetation yield can derive information to help conserve water resources in grassland ecosystems in arid and semi-arid regions.In this study,the interactions of precipitation,ET_(0),and vegetation yield in Darhan Muminggan Joint Banner(DMJB),a desert steppe in Inner Mongolia Autonomous Region,China were explored using two-dimensional(2D)and three-dimensional(3D)joint distribution models.Three types of Copula functions were applied to quantitatively analyze the joint distribution probability of different combinations of precipitation,ET_(0),and vegetation yield.For the precipitation–ET_(0)dry–wet type,the 2D joint distribution probability with precipitation≤245.69 mm/a or ET_(0)≥959.20 mm/a in DMJB was approximately 0.60,while the joint distribution probability with precipitation≤245.69 mm/a and ET_(0)≥959.20 mm/a was approximately 0.20.Correspondingly,the joint return period that at least one of the two events(precipitation was dry or ET_(0)was wet)occurred was 2 a,and the co-occurrence return period that both events(precipitation was dry and ET_(0)was wet)occurred was 5 a.Under this condition,the interval between dry and wet events would be short,the water supply and demand were unbalanced,and the water demand of vegetation would not be met.In addition,when precipitation remained stable and ET_(0)increased,the 3D joint distribution probability that vegetation yield would decrease due to water shortage in the precipitation–ET_(0)dry–wet years could reach up to 0.60–0.70.In future work,irrigation activities and water allocation criteria need to be implemented to increase vegetation yield and the safety of water resources in the desert steppe of Inner Mongolia.
基金supported by the National Natural Science Foundation of China (41101038)the Belt and Road Special Foundation of the State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering (2021nkms03)
文摘In the context of global warming,drought events occur frequently.In order to better understanding the process and mechanism of drought occurrence and evolution,scholars have dedicated much attention on drought propagation,mainly focusing on drought propagation time and propagation probability.However,there are relatively few studies on the sensitivities of drought propagation to seasons and drought levels.Therefore,we took the Heihe River Basin(HRB)of Northwest China as the case study area to quantify the propagation time and propagation probability from meteorological drought to agricultural drought during the period of 1981–2020,and subsequently explore their sensitivities to seasons(irrigation and non-irrigation seasons)and drought levels.The correlation coefficient method and Copula-based interval conditional probability model were employed to determine the drought propagation time and propagation probability.The results determined the average drought propagation time as 8 months in the whole basin,which was reduced by 2 months(i.e.,6 months)on average during the irrigation season and prolonged by 2 months(i.e.,10 months)during the non-irrigation season.Propagation probability was sensitive to both seasons and drought levels,and the sensitivities had noticeable spatial differences in the whole basin.The propagation probability of agricultural drought at different levels generally increased with the meteorological drought levels for the upstream,midstream,and southern downstream regions of the HRB.Lesser agricultural droughts were more likely to be triggered during the irrigation season,while severer agricultural droughts were occurred mostly during the non-irrigation season.The research results are helpful to understand the characteristics of drought propagation and provide a scientific basis for the prevention and control of droughts.This study is of great significance for the rational planning of local water resources and maintaining good ecological environment in the HRB.
基金supported by the Science Fund for Creative Research Groups of the National Natural ScienceFoundation of China (Grant No. 51021004)the National High Technology Research and DevelopmentProgram of China (863 Program, Grants No. 2012AA112509 and 2012AA051702)
文摘The joint probability distribution of wind speed and significant wave height in the Bohai Bay was investigated by comparing the Gurnbel logistic model, the Gumbel-Hougaard （GH） copula function, and the Clayton copula function. Twenty years of wind data from 1989 to 2008 were collected from the European Centre for Medium-Range Weather Forecasts （ECMWF） database and the blended wind data of the Quick Scatterometer （QSCAT） satellite data set and re-analysis data from the United States National Centers for Environmental Prediction （NCEP）. Several typhoons were taken into account and merged with the background wind fields from the ECMWF or QSCAT/NCEP database. The 20-year data of significant wave height were calculated with the unstructured-grid version of the third-generation wind wave model Simulating WAves Nearshore （SWAN） under extreme wind process conditions. The Gumbel distribution was used for univariate and marginal distributions. The distribution parameters were estimated with the method of L-moments. Based on the marginal distributions, the joint probability distributions, the associated return periods, and the conditional probability distributions were obtained. The GH copula function was found to be optimal according to the ordinary least squares （OLS） test. The results show that wind waves are the prevailing type of wave in the Bohai Bay.
基金supported by the National Natural Science Foundation of China(Grant No.52109156)the Science and Technology Project of the Jiangxi Provincial Education Department(Grant No.GJJ190970).
文摘Traditional methods for early warning of dam displacements usually assume that residual displacements follow a normal distribution.This assumption deviates from the reality,thereby affecting the reliability of early warning results and leading to misjudgments of dam displacement behavior.To solve this problem,this study proposed an early warning method using a non-normal distribution function.A new early warning index was developed using cumulative distribution function(CDF)values.The method of kernel density estimation was used to calculate the CDF values of residual displacements at a single point.The copula function was used to compute the CDF values of residual displacements at multiple points.Numerical results showed that,with residual displacements in a non-normal distribution,the early warning method proposed in this study accurately reflected the dam displacement behavior and effectively reduced the frequency of false alarms.This method is expected to aid in the safe operation of dams.
基金the National Natural Science Foundation of China under Contract No.51875073the Scientific Research Project of Education Department of Liaoning Province under Contract No.JDL2019005+1 种基金the Dalian Science and Technology Innovation Fund Plan under Contract No.2019J11CY017the Innovation Team Support Plan of Liaoning Higher Education under Contract No.LT2016010.
文摘Multiple failuremodes and strength degradation are usually inherent in the gear transmission system,which brings new challenges for conducting fatigue reliability analysis and design.This paper proposes a novel dynamic fatigue reliability analysis method for failure dependence and strength degradation based on the combination of theCopula function and Gamma process.Firstly,the dynamic simulation model of the gear transmission system is established to obtain the dynamic stress-time history.The Gamma process is then used to describe the strength degradation to establish the dynamic stress-strength interference model.The marginal distribution functions of tooth contact fatigue and dedendumbending fatigue are calculated respectively based on the dynamic interferencemodel.Finally,the joint distribution of the two failure modes can be obtained by the t-Copula function to characterize the failure dependence,and so the dynamic fatigue reliability considering failure dependence can be estimated.The effectiveness of the proposed method is illustrated with examples.The results reveal the temporal law of reliability and the effects of failure dependence on dynamic fatigue reliability.
基金Supported by the National Natural Science Fund of China(41571091)Youth Fund of Humanistic and Social Sciences of the Ministry of Education of PRC in 2017(17YJCZH114)the "13~(th) Five-year" Planning Item of Guangdong Philosophy and Social Sciences(GD16CGL10)
文摘7 kinds of probability distribution functions were used to fit extreme rainfall indexes R1d（ the maximum 1-d rainfall in the year） and R5d（ the maximum continuous 5-d rainfall in the year） at 18 observation stations of Beijiang River basin,and linear moment method was used to estimate parameters. According to fitting goodness test,the best probability distribution function was determined. On this basis,spatial analysis of design values of R1d and R5d with 50-a and 100-a reappearance periods was conducted. Via further selection,GH Copula was taken as connection function,and R1d-R5d joint probability distribution in the basin was studied. The results showed that R1d or R5d probability with 50-a and 100-a reappearance periods was larger in Wengyuan and Qingyuan,while R1d and R5d co-occurrence probability with 50-a and 100-a reappearance periods was larger in central north region.
基金supported by the National Natural Science Foundation of China (Grant No.52209020)the Natural Science Foundation of Hubei Province (Grant No.2023AFB722)。
文摘The GRACE satellite mission provides a new approach for monitoring,tracking,and assessing drought conditions by detecting changes in Earth's gravitational fields and inversing signals of terrestrial water storage anomalies.Existing studies of terrestrial water storage anomalies related droughts paid rare attention to the behind atmospheric physical mechanisms,nor quantified the risk propagation patterns between terrestrial water storage deficits and hydrological or agricultural droughts.In this study,we first extract terrestrial water storage(TWS) droughts,hydrological droughts,and agricultural droughts by using multiple variables including TWS from the GRACE/GRACE-FO satellites,runoff and soil moisture from the ERA5-Land reanalysis dataset.We then identify key atmospheric and oceanic oscillation indices affecting water deficits by employing machine learning technologies.We characterize the joint distributions between drought duration and severity by using the Copula function and quantify the risk propagation of hydrological and agricultural droughts to TWS droughts.The results show that:(1) From 2002 to 2021,there is a significant decrasing trend of TWS in China;the WPIO group atmospheric circulation indices(sea surface temperature index within the Western Pacific and Indian Ocean) contributes the most to TWS.Specifically,the sea surface temperature anomalies within the NINO 3.4 region as well as the Western Pacific Warm Pool area index show significantly positive correlation relationships with TWS in southern China;(2) The northwestern China,the Yangtze River basin,and the downstream of the Pearl River basin are the hotspots of TWS droughts.Besides,the hotspots of hydrological droughts locate in northwestern China and the hotspots of agricultural droughts locate in South China and eastern Tibetan Plateau;(3) The elastic coefficients of hydrological droughts propagating to TWS droughts are higher than those of agricultural droughts,indicating that the TWS droughts are more sensitive to hydrological droughts than to agricultural droughts.
文摘Wind speed dependences on different areas in a wind farm have influences on security and economic operation in power system.In order to simulate the correlation of wind speed series between different positions,this paper applies Copula function and rank correlation matrix methods to measure the coherence of wind speed in a wind farm.The correlated wind sample space is established.According to active power output characteristics of wind turbines,the polymerization model in a wind farm can be achieved.Monte Carlo optimal power flow is applied to IEEE-30 and IEEE-300 bus systems based on the principle of energy saving dispatching.The study shows that the accuracy of outputs is improved,thus reducing the fluctuation ranges in unit generating costs and power flow in branches while considering wind speed polymerization.This approach provides a new method to improve the effectiveness of energy saving dispatching and system operation arrangement.Results have been tested to be effective.
基金the National Natural Science Foundation of China(No.51265025)
文摘On the basis of each gear's failure correlation, the reliability Copula model of a wind turbine gearbox is established and a 1.5 MW wind turbine gearbox is taken as the research object. Firstly, based on the dynamic reliability model of mechanical parts, each gear's life distribution function of a wind turbine gearbox is obtained.The life distribution function can be used as the marginal distributions of the system's joint distribution. Secondly,Copula function is introduced to describe the failure correlation between parts, and the appropriate Copula function is selected according to the shape characters of Copula probability density function. Finally, the wind turbine gearbox system is divided into three parts according to the failure correlation of each gear. The Sklar theorem and the thought of step by step analysis are used to obtain the reliability Copula model for a wind turbine gearbox based on failure correlation.
基金funded in part by the National Natural Science Foundation of China (Grant No.52172310)Humanities and Social Sciences Foundation of the Ministry of Education (Grant No.21YJCZH147)+1 种基金Innovation-Driven Project of Central South Univer-sity (Grant No.2020CX041)Fundamental Research Funds for the Central Universities (Grant No.300102341507).
文摘The drivers of vacant taxis tend to cruise the road network searching new passengers,which leads to additional traffic congestion,air pollution and other problems.This study introduces a Copula-based joint model to analyse destination selection and route choice behaviour in the customer-search process.A multinomial logit model is used to analyse the destination selection behaviour,and a path size logit model is used to explore the routes choice behaviour.Accordingly,the joint model applied Copula function is then established to analyse the correlation between these two behaviours.The destination customer generation rate,destination distance,route customer generation rate,path travel time,cumulative intersection delay,path size and route length are selected as explanatory variables.The taxis trajectory data were collected by global positioning system in Xidan District of Beijing City from September 2014 to February 2015.Using the log-likelihood,Bayesian information criterion as evaluation indexes to measure the fitting result,the joint model applied Copula function has the highest goodness-of-fit.The effect of explanatory variables on customer search behaviour is discussed based on the parameter estimation results.The results of this study are helpful to understand the customer-search behaviour of taxi drivers to reduce operating costs and improve the efficiency of the taxi operation system.
基金supported in part by the National Natural Science Foundation of China (Nos. 61303003,41374113,and 41375102)the National High-Tech Research and Development (863) Program of China (Nos. 2011AA01A203 and 2013AA01A208)the National Key Basic Research and Development (973) Program of China (No. 2014CB347800)
文摘The Gaussian Copula Probability Density Function （PDF） plays an important role in the fields of finance, hydrological modeling, biomedical study, and texture retrieval. However, the existing schemes for evaluating the Gaussian Copula PDF are all computationally-demanding and generally the most time-consuming part in the corresponding applications. In this paper, we propose an FPGA-based design to accelerate the computation of the Gaussian Copula PDF. Specifically, the evaluation of the Gaussian Copula PDF is mapped into a fully-pipelined FPGA dataflow engine by using three optimization steps： transforming the calculation pattern, eliminating constant computations from hardware logic, and extending calculations to multiple pipelines. In the experiments on 10 typical large-scale data sets, our FPGA-based solution shows a maximum of 1870 times speedup over a well-tuned single- core CPU-based solution, and 610 times speedup over a well-optimized parallel quad-core CPU-based solution when processing two-dimensional data.
基金supported by National Natural Science Foundation of China(Grant No.51277034,51377027)
文摘This paper introduces a Monte Carlo scenario generation method based on copula theory for the stochastic optimal power flow （STOPF） problem with wind power. By using copula theory, the scenarios are simulated from multivariable joint distribution but only from their dependency matrix. Hence, the scenarios generated by proposed method can contain flail statistical information of multivariate. Here, the details of simu- lating scenarios for multi-wind-farm are explained with four steps： determine margin of one wind farm, fit the copulas, choose optimal copulas and simulate scenarios by Mote Carlo. Moreover, the producing process of scenarios is demonstrated by two adjacent actual wind farms in China. With the scenarios, the STOPF is con- verted into the same amount deterministic sub OPF models which can be solved by available technology per- fectly. Results using copula theory are compared against results from history samples based on two designs： IEEE 30-bus and IEEE 118-bus systems. The comparison results prove the accuracy of the proposed methodology.
基金The authors thank the referees for their valuable comments. Yang＇s research was partly supported by the Key Program of National Natural Science Foundation of China （Grant No. 11131002） and the National Natural Science Foundation of China （Grants No. 11271033）. Zheng＇s research was supported by the Ng-Jhit-Cheong Foundation.
文摘This paper discusses the correlation structure between London Interbank Offered Rates （LIBOR） by using the copula function. We start from one simplified model of A. Brace, D. Gatarek, and M. Musiela （1997） and find out that the copula function between two LIBOR rates can be expressed as a sum of an infinite series, where the main term is a distribution function with Gaussian copula. Partial differential equation method is used for deriving the copula expansion. Numerical results show that the copula of the LIBOR rates and Gaussian copula are very close in the central region and differ in the tail, and the Gaussian copula approximation to the copula function between the LIBOR rates provides satisfying results in the normal situation.
基金supported by the National Natural Science Foundation of China under Grant Nos. 71631004,72033008the Humanity and Social Science Foundation of Ministry of Education of China under Grant No.18YJA790101
文摘With the increase of economic environment uncertainty,it is of great importance to study the linkage and spillover effects of economic policy uncertainty among countries.Especially,this article selects eight countries along the Belt and Road as the core countries(China,Korea,Croatia,India,Russia,Greece,Pakistan,and Singapore)and four countries(Germany,France,Japan,and UK)as the peripheral countries,and then copula technique and mixed-frequency global vector autoregressive model are employed to analyze the correlation and the spillover effect of the economic policy uncertainty(EPU)for the twelve selected countries,respectively.The proposed empirical findings show clearly that the EPU correlation among the eight core Belt and Road countries is stronger and the spillover effect of the core countries to the peripheral countries is statistically significant.As a result,for harmonious and win-win development,the Belt and Road countries should pay a close attention to the EPU,because the stability of the EPU promotes greatly the economy development.
基金sponsored by the Major Program of National Social Science Foundation of China(Grant No.18ZDA105)the National Natural Science Foundation of China(Grant No.41971199)+1 种基金Jinkai Tan is thankful for financial support from the China Postdoctoral Science Foundation(Grant No.2021M693584)Hanqing Xu is thankful for financial support from the program of China Scholarships Council(Grant No.202006140040)。
文摘Extreme surges and rainfall represent major driving factors for compound flooding in estuary regions along the Chinese coast.The combined effect of extreme surges and rainfall(that is,compound floods)might lead to greater impacts than if the drivers occurred in isolation.Hence,understanding the frequency and severity of compound flooding is important for improving flood hazard assessment and compound flood resilience in coastal cities.In this study,we examined the dependence between extreme surges and corresponding rainfall events in 26 catchments along the Chinese coastline during typhoon and non-typhoon seasons using copula functions,to identify where the two drivers more often occur together and the implication for flood management in these locations.We found that the interaction between flood drivers is statistically significant in 10catchments located around Hainan Island(south)and Shanghai,where surge peaks occur mainly during the typhoon season and around the Bohai Sea(north),where surge peaks occur mainly during the non-typhoon season.We further applied the copula-based framework to model the dependence between surge peaks and associated rainfall and estimate their joint and conditional probability in two specific locations—Hainan Island and the Bohai Sea,where the correlation between flood drivers is statistically significant.We observed that in Hainan Island where most of the surge peaks occur during the typhoon season,extreme rainfall events during the typhoon season are generally more intense compared to annual maxima rainfall.In contrast,around the Bohai Sea where surge peaks occur mainly outside the typhoon season,rainfall is less intense than annual maxima rainfall.These results show that the interaction between extreme surges and rainfall can provide valuable insight when designing coastal and urban infrastructure,especially in highly populated urban areas prone to both coastal and pluvial flooding,such as many Chinese coastal cities.
基金co-supported by the National Natural Science Foundation of China (51875015,51620105010,51675019)Natural Science Foundation of Beijing Municipality(L171003)。
文摘With several attractive properties, rotary lip seals are widely used in aircraft utility system, and their reliability estimation has drawn more and more attention. This work proposes a reliability estimation approach based on time-varying dependence analysis. The dependence between the two performance indicators of rotary lip seals, namely leakage rate and friction torque, is modeled by time-varying copula function with polynomial to denote the time-varying parameters, and an efficient copula selection approach is utilized to select the optimal copula function. Parameter estimation is carried out based on a Bayesian method and the reliability during the whole lifetime is calculated based on a Monte Carlo method. Degradation test for rotary lip seal is conducted and the proposed model is validated by test data. The optimal copula function and optimal order of polynomial are determined based on test data. Results show that this model is effective in estimating the reliability of rotary lip seals and can achieve a better goodness of fit.
基金supported by the National Natural Science Foundation of China(Grants No.11671021,11271033)National Social Science Fund of China(Grant No.16ZDA052)
文摘Based on the framework of [7], we discuss pricing bilateral counterparty risk of CDS, where each individual default intensity is modeled by a shifted CIR process with jump （3CIR＋＋）, and the correlation between the default times is modeled by a copula function. We present a semi-analytical formula for pricing bilateral counterparty risk of CDS, which is more convenient to compute through calculating multiple numerical integration or using Monte-Carlo simulation without simulating default times. Moreover, we obtain simpler formulae under FGM copulas, Bernstein copulas and CA＇B copulas, which can be applied for speeding up the computation and reducing the pricing error. Numerical results under FGM copulas and CA＇B copulas show that our method performs better both in computation speed and accuracy.
基金supported by the National Natural Science Foundation of China (Grant Numbers 52109040, 51739009)China Postdoctoral Science Foundation (Grant Number 2021M702950)+1 种基金Scientific and Technological Projects of Henan Province (Grant Number 222102320025)Key Scientific Research Project in Colleges and Universities of Henan Province of China (Grant Number 22B570003)
文摘In the context of climate change,coastal cities are at increased risk of extreme precipitation and sea level rise,and their interaction will aggravate coastal floods.Understanding the potential change of compound floods is valuable for flood risk reduction.In this study,an integrated approach coupling the hydrological model and copulabased design of precipitation and storm tides was proposed to assess the compound flood risk in a coastal city—Haikou,China.The copula model,most-likely weight function,and varying parameter distribution were used to obtain the combined design values of precipitation and storm tides under the nonstationary scenario,which were applied to the boundary conditions of the 1D-2D hydrological model.Subsequently,the change of the bivariate return periods,design values,and compound flood risks of precipitation and storm tides were investigated.The results show that the bivariate return period of precipitation and storm tides was reduced by an average of 34%under the nonstationary scenario.The maximum inundation areas and volumes were increased by an average of 31.1%and 45.9%respectively in comparison with the stationary scenario.Furthermore,we identified that the compound effects of precipitation and storm tides would have a greater influence on the flood risk when the bivariate return period is more than 50 years,and the peak time lag had a significant influence on the compound flood risk.The proposed framework is effective in the evaluation and prediction of flood risk in coastal cities,and the results provide some guidance for urban disaster prevention and mitigation.
