岩土工程可靠度分析和设计中,合理地选取随机场参数和相关函数,并准确地描述土性参数空间变异性十分困难。基于贝叶斯理论,本文提出了一套量化砂土有效内摩擦角空间变异性的方法。该方法根据先验信息和静力触探试验锥尖阻力数据,确定砂...岩土工程可靠度分析和设计中,合理地选取随机场参数和相关函数,并准确地描述土性参数空间变异性十分困难。基于贝叶斯理论,本文提出了一套量化砂土有效内摩擦角空间变异性的方法。该方法根据先验信息和静力触探试验锥尖阻力数据,确定砂土有效内摩擦角的随机场参数和相关函数。该方法合理地考虑了砂土有效内摩擦角与锥尖阻力间经验回归方程的不确定性。采用马尔科夫链蒙特卡洛模拟(Markov Chain Monte Carlo Simulation,MCMCS)获取服从后验分布的随机场参数样本。利用MCMCS样本构建随机场参数的Gaussian Copula函数求解后验分布。估计备选相关函数的概率,选择概率最大的为最可能的相关函数。最后,采用美国德州农工大学国家岩土工程砂土试验场的CPT数据算例验证了文中所提方法的有效性。结果表明:文中所提方法可以正确、合理地利用间接测量的锥尖阻力数据确定砂土有效内摩擦角的随机场参数和相关函数,准确量化其空间变异性。对于美国德州农工大学国家岩土工程砂土试验场的砂土有效内摩擦角,建议选用二阶自回归函数作为其最可能的相关函数。展开更多
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
应用椭圆copulas描述干旱多变量间的相依性结构。采用Pearson'sγn、Spearman'sρn、Kendall'sτn、秩相关图、Chi-plot和K-plot度量2变量相依性;根据极大似然法估计3维copulas的参数,并以AIC、BIC和RMSE进行copulas拟合效...应用椭圆copulas描述干旱多变量间的相依性结构。采用Pearson'sγn、Spearman'sρn、Kendall'sτn、秩相关图、Chi-plot和K-plot度量2变量相依性;根据极大似然法估计3维copulas的参数,并以AIC、BIC和RMSE进行copulas拟合效果评价;运用基于Rosenblatt变换的Bootstrap法进行Gaussian copula和Student t copula的拟合度检验;选择Gaussiancopula描述干旱历时D、烈度S、和峰值P的联合概率分布,探讨渭河流域干旱重现期的空间分布规律。研究表明:①3维Gaussian copula和Student t copula均适合用来描述干旱多变量联合概率分布,且前者拟合效果优于后者;②渭河流域发生较长时期持续干旱的频率高、重现期短,应加强干旱预报与管理。展开更多
A novel multi-dimensional scenario forecast approach which can capture the dynamic temporal-spatial interdependence relation among the outputs of multiple wind farms is proposed.In the proposed approach,support vector...A novel multi-dimensional scenario forecast approach which can capture the dynamic temporal-spatial interdependence relation among the outputs of multiple wind farms is proposed.In the proposed approach,support vector machine(SVM)is applied for the spot forecast of wind power generation.The probability density function(PDF)of the SVM forecast error is predicted by sparse Bayesian learning(SBL),and the spot forecast result is corrected according to the error expectation obtained.The copula function is estimated using a Gaussian copula-based dynamic conditional correlation matrix regression(DCCMR)model to describe the correlation among the errors.And the multidimensional scenario is generated with respect to the estimated marginal distributions and the copula function.Test results on three adjacent wind farms illustrate the effectiveness of the proposed approach.展开更多
Rapid estimation of post-earthquake building damage and loss is very important in urgent response efforts.The current approach leaves much room for improvement in estimating ground motion and correctly incorporating t...Rapid estimation of post-earthquake building damage and loss is very important in urgent response efforts.The current approach leaves much room for improvement in estimating ground motion and correctly incorporating the uncertainty and spatial correlation of the loss.This study proposed a new approach for rapidly estimating post-earthquake building loss with reasonable accuracy.The proposed method interpolates ground motion based on the observed ground motion using the Ground Motion Prediction Equation(GMPE)as the weight.It samples the building seismic loss quantile considering the spatial loss correlation that is expressed by Gaussian copula,and kriging is applied to reduce the dimension of direct sampling for estimation speed.The proposed approach was validated using three historical earthquake events in Japan with actual loss reports,and was then applied to predict the building loss amount for the March 2022 Fukushima Mw7.3 earthquake.The proposed method has high potential in future emergency efforts such as search,rescue,and evacuation planning.展开更多
Wind farms usually cluster in areas with abundant wind resources.Therefore,spatial dependence of wind speeds among nearby wind farms should be taken into account when modeling a power system with large-scale wind powe...Wind farms usually cluster in areas with abundant wind resources.Therefore,spatial dependence of wind speeds among nearby wind farms should be taken into account when modeling a power system with large-scale wind power penetration.This paper proposes a novel non-parametric copula method,multivariate Gaussian kernel copula(MGKC),to describe the dependence structure of wind speeds among multiple wind farms.Wind speed scenarios considering the dependence among different wind farms are sampled from the MGKC by the quasi-Monte Carlo(QMC)method,so as to solve the stochastic economic dispatch(SED)problem,for which an improved meanvariance(MV)model is established,which targets at minimizing the expectation and risk of fuel cost simultaneously.In this model,confidence interval is applied in the wind speed to obtain more practical dispatch solutions by excluding extreme scenarios,for which the quantile-copula is proposed to construct the confidence interval constraint.Simulation studies are carried out on a modified IEEE 30-bus power system with wind farms integrated in two areas,and the results prove the superiority of the MGKC in formulating the dependence among different wind farms and the superiority of the improved MV model based on quantilecopula in determining a better dispatch solution.展开更多
文摘岩土工程可靠度分析和设计中,合理地选取随机场参数和相关函数,并准确地描述土性参数空间变异性十分困难。基于贝叶斯理论,本文提出了一套量化砂土有效内摩擦角空间变异性的方法。该方法根据先验信息和静力触探试验锥尖阻力数据,确定砂土有效内摩擦角的随机场参数和相关函数。该方法合理地考虑了砂土有效内摩擦角与锥尖阻力间经验回归方程的不确定性。采用马尔科夫链蒙特卡洛模拟(Markov Chain Monte Carlo Simulation,MCMCS)获取服从后验分布的随机场参数样本。利用MCMCS样本构建随机场参数的Gaussian Copula函数求解后验分布。估计备选相关函数的概率,选择概率最大的为最可能的相关函数。最后,采用美国德州农工大学国家岩土工程砂土试验场的CPT数据算例验证了文中所提方法的有效性。结果表明:文中所提方法可以正确、合理地利用间接测量的锥尖阻力数据确定砂土有效内摩擦角的随机场参数和相关函数,准确量化其空间变异性。对于美国德州农工大学国家岩土工程砂土试验场的砂土有效内摩擦角,建议选用二阶自回归函数作为其最可能的相关函数。
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.
文摘应用椭圆copulas描述干旱多变量间的相依性结构。采用Pearson'sγn、Spearman'sρn、Kendall'sτn、秩相关图、Chi-plot和K-plot度量2变量相依性;根据极大似然法估计3维copulas的参数,并以AIC、BIC和RMSE进行copulas拟合效果评价;运用基于Rosenblatt变换的Bootstrap法进行Gaussian copula和Student t copula的拟合度检验;选择Gaussiancopula描述干旱历时D、烈度S、和峰值P的联合概率分布,探讨渭河流域干旱重现期的空间分布规律。研究表明:①3维Gaussian copula和Student t copula均适合用来描述干旱多变量联合概率分布,且前者拟合效果优于后者;②渭河流域发生较长时期持续干旱的频率高、重现期短,应加强干旱预报与管理。
基金This work is supported by National Natural Science Foundation of China(No.51007047,No.51077087)Shandong Provincial Natural Science Foundation of China(No.20100131120039)National High Technology Research and Development Program of China(863 Program)(No.2011AA05A101).
文摘A novel multi-dimensional scenario forecast approach which can capture the dynamic temporal-spatial interdependence relation among the outputs of multiple wind farms is proposed.In the proposed approach,support vector machine(SVM)is applied for the spot forecast of wind power generation.The probability density function(PDF)of the SVM forecast error is predicted by sparse Bayesian learning(SBL),and the spot forecast result is corrected according to the error expectation obtained.The copula function is estimated using a Gaussian copula-based dynamic conditional correlation matrix regression(DCCMR)model to describe the correlation among the errors.And the multidimensional scenario is generated with respect to the estimated marginal distributions and the copula function.Test results on three adjacent wind farms illustrate the effectiveness of the proposed approach.
基金supported by the Scientific Research Fund of the Institute of Engineering Mechanics,China Earthquake Administration(Grant No.2021B09)the National Natural Science Foundation of China(Grant No.51978634)。
文摘Rapid estimation of post-earthquake building damage and loss is very important in urgent response efforts.The current approach leaves much room for improvement in estimating ground motion and correctly incorporating the uncertainty and spatial correlation of the loss.This study proposed a new approach for rapidly estimating post-earthquake building loss with reasonable accuracy.The proposed method interpolates ground motion based on the observed ground motion using the Ground Motion Prediction Equation(GMPE)as the weight.It samples the building seismic loss quantile considering the spatial loss correlation that is expressed by Gaussian copula,and kriging is applied to reduce the dimension of direct sampling for estimation speed.The proposed approach was validated using three historical earthquake events in Japan with actual loss reports,and was then applied to predict the building loss amount for the March 2022 Fukushima Mw7.3 earthquake.The proposed method has high potential in future emergency efforts such as search,rescue,and evacuation planning.
基金This research is supported by the Key-Area Research and Development Program of Guangdong Province(No.2020B010166004)the Fundamental Research Funds for the Central Universities,SCUT(No.2018ZD06).
文摘Wind farms usually cluster in areas with abundant wind resources.Therefore,spatial dependence of wind speeds among nearby wind farms should be taken into account when modeling a power system with large-scale wind power penetration.This paper proposes a novel non-parametric copula method,multivariate Gaussian kernel copula(MGKC),to describe the dependence structure of wind speeds among multiple wind farms.Wind speed scenarios considering the dependence among different wind farms are sampled from the MGKC by the quasi-Monte Carlo(QMC)method,so as to solve the stochastic economic dispatch(SED)problem,for which an improved meanvariance(MV)model is established,which targets at minimizing the expectation and risk of fuel cost simultaneously.In this model,confidence interval is applied in the wind speed to obtain more practical dispatch solutions by excluding extreme scenarios,for which the quantile-copula is proposed to construct the confidence interval constraint.Simulation studies are carried out on a modified IEEE 30-bus power system with wind farms integrated in two areas,and the results prove the superiority of the MGKC in formulating the dependence among different wind farms and the superiority of the improved MV model based on quantilecopula in determining a better dispatch solution.
