Caisson breakwaters are mainly constructed in deep waters to protect an area against waves.These breakwaters are con-ventionally designed based on the concept of the safety factor.However,the wave loads and resistance...Caisson breakwaters are mainly constructed in deep waters to protect an area against waves.These breakwaters are con-ventionally designed based on the concept of the safety factor.However,the wave loads and resistance of structures have epistemic or aleatory uncertainties.Furthermore,sliding failure is one of the most important failure modes of caisson breakwaters.In most previous studies,for assessment purposes,uncertainties,such as wave and wave period variation,were ignored.Therefore,in this study,Bayesian reliability analysis is implemented to assess the failure probability of the sliding of Tombak port breakwater in the Persian Gulf.The mean and standard deviations were taken as random variables to consider dismissed uncertainties.For this purpose,the frst-order reliability method(FORM)and the frst principal curvature cor-rection in FORM are used to calculate the reliability index.The performances of these methods are verifed by importance sampling through Monte Carlo simulation(MCS).In addition,the reliability index sensitivities of each random variable are calculated to evaluate the importance of diferent random variables while calculating the caisson sliding.The results show that the reliability index is most sensitive to the coefcients of friction,wave height,and caisson weight(or concrete density).The sensitivity of the failure probability of each of the random variables and their uncertainties are calculated by the derivative method.Finally,the Bayesian regression is implemented to predict the statistical properties of breakwater sliding with non-informative priors,which are compared to Goda’s formulation,used in breakwater design standards.The analysis shows that the model posterior for the sliding of a caisson breakwater has a mean and standard deviation of 0.039 and 0.022,respectively.A normal quantile analysis and residual analysis are also performed to evaluate the correctness of the model responses.展开更多
Weintroduce a general class of orbital-free density functionals(OF-DFT)decomposed into a local part in coordinate space and a local part in reciprocal space.As a demonstration of principle,we choose for the former the...Weintroduce a general class of orbital-free density functionals(OF-DFT)decomposed into a local part in coordinate space and a local part in reciprocal space.As a demonstration of principle,we choose for the former the Thomas-Fermi-von Weizsäcker(TFW)kinetic energy density functional(KEDF)and for the latter a form derived from the Lindhard function,but with the two system-dependent adjustable parameters.These parameters are machine-learned from Kohn-Sham data using Bayesian linear regression with a kernel method,which employs moments of the Fourier components of the electronic density as the descriptor.Through a number of representative cases,we demonstrate that our machine-learned model provides more than an order-of-magnitude improvement in the accuracy of the frozen-phonon energies compared to theTFWKEDF,with negligible increase in the computational cost.Overall,this work opens an avenue for the construction of accurate KEDFs for OF-DFT.展开更多
文摘Caisson breakwaters are mainly constructed in deep waters to protect an area against waves.These breakwaters are con-ventionally designed based on the concept of the safety factor.However,the wave loads and resistance of structures have epistemic or aleatory uncertainties.Furthermore,sliding failure is one of the most important failure modes of caisson breakwaters.In most previous studies,for assessment purposes,uncertainties,such as wave and wave period variation,were ignored.Therefore,in this study,Bayesian reliability analysis is implemented to assess the failure probability of the sliding of Tombak port breakwater in the Persian Gulf.The mean and standard deviations were taken as random variables to consider dismissed uncertainties.For this purpose,the frst-order reliability method(FORM)and the frst principal curvature cor-rection in FORM are used to calculate the reliability index.The performances of these methods are verifed by importance sampling through Monte Carlo simulation(MCS).In addition,the reliability index sensitivities of each random variable are calculated to evaluate the importance of diferent random variables while calculating the caisson sliding.The results show that the reliability index is most sensitive to the coefcients of friction,wave height,and caisson weight(or concrete density).The sensitivity of the failure probability of each of the random variables and their uncertainties are calculated by the derivative method.Finally,the Bayesian regression is implemented to predict the statistical properties of breakwater sliding with non-informative priors,which are compared to Goda’s formulation,used in breakwater design standards.The analysis shows that the model posterior for the sliding of a caisson breakwater has a mean and standard deviation of 0.039 and 0.022,respectively.A normal quantile analysis and residual analysis are also performed to evaluate the correctness of the model responses.
基金the support of the Quantum Science and Engineering Center(QSEC)at George Mason UniversityP.S.gratefully acknowledges funding from the U.S.Department of Energy,Office of Science,under Grant No.DE-SC0023445+1 种基金T.O.acknowledges support provided by the George Mason University Provost Dissertation Completion GrantM.E.has been partially supported by the Simons Foundation.
文摘Weintroduce a general class of orbital-free density functionals(OF-DFT)decomposed into a local part in coordinate space and a local part in reciprocal space.As a demonstration of principle,we choose for the former the Thomas-Fermi-von Weizsäcker(TFW)kinetic energy density functional(KEDF)and for the latter a form derived from the Lindhard function,but with the two system-dependent adjustable parameters.These parameters are machine-learned from Kohn-Sham data using Bayesian linear regression with a kernel method,which employs moments of the Fourier components of the electronic density as the descriptor.Through a number of representative cases,we demonstrate that our machine-learned model provides more than an order-of-magnitude improvement in the accuracy of the frozen-phonon energies compared to theTFWKEDF,with negligible increase in the computational cost.Overall,this work opens an avenue for the construction of accurate KEDFs for OF-DFT.
