Determining the joint probability distribution of correlated non-normal geotechnical parameters based on incomplete statistical data is a challenging problem.This paper proposes a Gaussian copula-based method for mode...Determining the joint probability distribution of correlated non-normal geotechnical parameters based on incomplete statistical data is a challenging problem.This paper proposes a Gaussian copula-based method for modelling the joint probability distribution of bivariate uncertain data.First,the concepts of Pearson and Kendall correlation coefficients are presented,and the copula theory is briefly introduced.Thereafter,a Pearson method and a Kendall method are developed to determine the copula parameter underlying Gaussian copula.Second,these two methods are compared in computational efficiency,applicability,and capability of fitting data.Finally,four load-test datasets of load-displacement curves of piles are used to illustrate the proposed method.The results indicate that the proposed Gaussian copula-based method can not only characterize the correlation between geotechnical parameters,but also construct the joint probability distribution function of correlated non-normal geotechnical parameters in a more general way.It can serve as a general tool to construct the joint probability distribution of correlated geotechnical parameters based on incomplete data.The Gaussian copula using the Kendall method is superior to that using the Pearson method,which should be recommended for modelling and simulating the joint probability distribution of correlated geotechnical parameters.There exists a strong negative correlation between the two parameters underlying load-displacement curves.Neglecting such correlation will not capture the scatter in the measured load-displacement curves.These results substantially extend the application of the copula theory to multivariate simulation in geotechnical engineering.展开更多
As an important tool for the description and analysis of hydrological processes,the watershed hydrological model has been increasingly applied to watershed hydrological simulations and water resource management.Howeve...As an important tool for the description and analysis of hydrological processes,the watershed hydrological model has been increasingly applied to watershed hydrological simulations and water resource management.However,in most cases,model parameters are only determined in a calibration scheme which fits the modeled data to observations,thus significant uncertainties exist in the model parameters.How to quantitatively evaluate the uncertainties in model parameters and the resulting uncertainty impacts on model simulations has always been a question which has attracted much attention.In this study,two methods based on the bootstrap method(specifically,the model-based bootstrap and block bootstrap)are used to analyze the parameter uncertainties in the case of the SWAT(Soil and Water Assessment Tool)model applied to a hydrological simulation of the Dongliao River Watershed.Then,the uncertainty ranges of five sensitivity parameters are obtained.The calculated variation coefficients and the variable parameter contributions show that,among the five parameters,ESCO and CN2 have relatively high uncertainties:the variation coefficients and contribution rates are 23.98 and 70%,14.43 and 18%,respectively.The three remaining parameters have relatively low uncertainties.We compare the two uncertainty ranges of parameters acquired by the two bootstrap methods,and find that the uncertainty ranges of parameters acquired by the block bootstrap are narrower than those acquired by the model-based bootstrap.Further analysis of the effects of parameter uncertainties on the model simulation reveals that the parameter uncertainties have great impacts on results of the model simulation,and in the model calibration stage 60%70%of runoff observations were within the corresponding 95%confidence interval.The uncertainty in the model simulation during the flood season(i.e.the wet period)is relatively higher than that during the dry season.展开更多
基金supported by the National Basic Research Program of China ("973" Program) (Grant No. 2011CB013506)the National Natural Science Foundation of China (Grant Nos. 51028901 and 50839004)
文摘Determining the joint probability distribution of correlated non-normal geotechnical parameters based on incomplete statistical data is a challenging problem.This paper proposes a Gaussian copula-based method for modelling the joint probability distribution of bivariate uncertain data.First,the concepts of Pearson and Kendall correlation coefficients are presented,and the copula theory is briefly introduced.Thereafter,a Pearson method and a Kendall method are developed to determine the copula parameter underlying Gaussian copula.Second,these two methods are compared in computational efficiency,applicability,and capability of fitting data.Finally,four load-test datasets of load-displacement curves of piles are used to illustrate the proposed method.The results indicate that the proposed Gaussian copula-based method can not only characterize the correlation between geotechnical parameters,but also construct the joint probability distribution function of correlated non-normal geotechnical parameters in a more general way.It can serve as a general tool to construct the joint probability distribution of correlated geotechnical parameters based on incomplete data.The Gaussian copula using the Kendall method is superior to that using the Pearson method,which should be recommended for modelling and simulating the joint probability distribution of correlated geotechnical parameters.There exists a strong negative correlation between the two parameters underlying load-displacement curves.Neglecting such correlation will not capture the scatter in the measured load-displacement curves.These results substantially extend the application of the copula theory to multivariate simulation in geotechnical engineering.
基金supported by the Major Science and Technology Program for Water Pollution and Treatment of China(Grant No.2012ZX07201-001)
文摘As an important tool for the description and analysis of hydrological processes,the watershed hydrological model has been increasingly applied to watershed hydrological simulations and water resource management.However,in most cases,model parameters are only determined in a calibration scheme which fits the modeled data to observations,thus significant uncertainties exist in the model parameters.How to quantitatively evaluate the uncertainties in model parameters and the resulting uncertainty impacts on model simulations has always been a question which has attracted much attention.In this study,two methods based on the bootstrap method(specifically,the model-based bootstrap and block bootstrap)are used to analyze the parameter uncertainties in the case of the SWAT(Soil and Water Assessment Tool)model applied to a hydrological simulation of the Dongliao River Watershed.Then,the uncertainty ranges of five sensitivity parameters are obtained.The calculated variation coefficients and the variable parameter contributions show that,among the five parameters,ESCO and CN2 have relatively high uncertainties:the variation coefficients and contribution rates are 23.98 and 70%,14.43 and 18%,respectively.The three remaining parameters have relatively low uncertainties.We compare the two uncertainty ranges of parameters acquired by the two bootstrap methods,and find that the uncertainty ranges of parameters acquired by the block bootstrap are narrower than those acquired by the model-based bootstrap.Further analysis of the effects of parameter uncertainties on the model simulation reveals that the parameter uncertainties have great impacts on results of the model simulation,and in the model calibration stage 60%70%of runoff observations were within the corresponding 95%confidence interval.The uncertainty in the model simulation during the flood season(i.e.the wet period)is relatively higher than that during the dry season.
