Condensation technique of degree of freedom is first proposed to improve the computational efficiency of meshfree method with Galerkin weak form for elastic dy- namic analysis. In the present method, scattered nodes w...Condensation technique of degree of freedom is first proposed to improve the computational efficiency of meshfree method with Galerkin weak form for elastic dy- namic analysis. In the present method, scattered nodes with- out connectivity are divided into several subsets by cells with arbitrary shape. Local discrete equation is established over each cell by using moving Kriging interpolation, in which the nodes that located in the cell are used for approxima- tion. Then local discrete equations can be simplified by con- densation of degree of freedom, which transfers equations of inner nodes to equations of boundary nodes based on cells. The global dynamic system equations are obtained by as- sembling all local discrete equations and are solved by using the standard implicit Newmark＇s time integration scheme. In the scheme of present method, the calculation of each cell is carried out by meshfree method, and local search is imple- mented in interpolation. Numerical examples show that the present method has high computational efficiency and good accuracy in solving elastic dynamic problems.展开更多
Determining soilewater characteristic curve(SWCC) at a site is an essential step for implementing unsaturated soil mechanics in geotechnical engineering practice, which can be measured directly through various in-situ...Determining soilewater characteristic curve(SWCC) at a site is an essential step for implementing unsaturated soil mechanics in geotechnical engineering practice, which can be measured directly through various in-situ and/or laboratory tests. Such direct measurements are, however, costly and timeconsuming due to high standards for equipment and procedural control and limits in testing apparatus. As a result, only a limited number of data points(e.g., volumetric water content vs. matric suction)on SWCC at some values of matric suction are obtained in practice. How to use a limited number of data points to estimate the site-specific SWCC and to quantify the uncertainty(or degrees-of-belief) in the estimated SWCC remains a challenging task. This paper proposes a Bayesian approach to determine a site-specific SWCC based on a limited number of test data and prior knowledge(e.g., engineering experience and judgment). The proposed Bayesian approach quantifies the degrees-of-belief on the estimated SWCC according to site-specific test data and prior knowledge, and simultaneously selects a suitable SWCC model from a number of candidates based on the probability logic. To address computational issues involved in Bayesian analyses, Markov Chain Monte Carlo Simulation(MCMCS), specifically Metropolis-Hastings(M-H) algorithm, is used to solve the posterior distribution of SWCC model parameters, and Gaussian copula is applied to evaluating model evidence based on MCMCS samples for selecting the most probable SWCC model from a pool of candidates. This removes one key limitation of the M-H algorithm, making it feasible in Bayesian model selection problems. The proposed approach is illustrated using real data in Unsaturated Soil Database(UNSODA) developed by U.S. Department of Agriculture. It is shown that the proposed approach properly estimates the SWCC based on a limited number of site-specific test data and prior knowledge, and reflects the degrees-of-belief on the estimated SWCC in a rational and quantitative manner.展开更多
Some attributes are uncertain for evaluation work because of incomplete or limited information and knowledge.It leads to uncertainty in evaluation results.To that end,an evaluation method,uncertainty entropy-based exp...Some attributes are uncertain for evaluation work because of incomplete or limited information and knowledge.It leads to uncertainty in evaluation results.To that end,an evaluation method,uncertainty entropy-based exploratory evaluation(UEEE),is proposed to guide the evaluation activities,which can iteratively and gradually reduce uncertainty in evaluation results.Uncertainty entropy(UE)is proposed to measure the extent of uncertainty.First,the belief degree distributions are assumed to characterize the uncertainty in attributes.Then the belief degree distribution of the evaluation result can be calculated by using uncertainty theory.The obtained result is then checked based on UE to see if it could meet the requirements of decision-making.If its uncertainty level is high,more information needs to be introduced to reduce uncertainty.An algorithm based on the UE is proposed to find which attribute can mostly affect the uncertainty in results.Thus,efforts can be invested in key attribute(s),and the evaluation results can be updated accordingly.This update should be repeated until the evaluation result meets the requirements.Finally,as a case study,the effectiveness of ballistic missiles with uncertain attributes is evaluated by UEEE.The evaluation results show that the target is believed to be destroyed.展开更多
为减少海上交通事故的发生,在建立沿海水域(Coastal Water Area,CWA)交通安全评估因素三层次结构的基础上,针对事故统计数据的不确定性,尝试采用证据推理(Evidential Reasoning,ER)方法进行CWA交通安全评估,并运用案例证实该方法的可行...为减少海上交通事故的发生,在建立沿海水域(Coastal Water Area,CWA)交通安全评估因素三层次结构的基础上,针对事故统计数据的不确定性,尝试采用证据推理(Evidential Reasoning,ER)方法进行CWA交通安全评估,并运用案例证实该方法的可行性.评估结果可以为海事安全管理工作决策提供参考依据.展开更多
基金supported by the National Natural Science Founda-tion of China(11272118)Open Found of State Key Laboratory of Explosion Science and Technology(KFJJ12-5M)
文摘Condensation technique of degree of freedom is first proposed to improve the computational efficiency of meshfree method with Galerkin weak form for elastic dy- namic analysis. In the present method, scattered nodes with- out connectivity are divided into several subsets by cells with arbitrary shape. Local discrete equation is established over each cell by using moving Kriging interpolation, in which the nodes that located in the cell are used for approxima- tion. Then local discrete equations can be simplified by con- densation of degree of freedom, which transfers equations of inner nodes to equations of boundary nodes based on cells. The global dynamic system equations are obtained by as- sembling all local discrete equations and are solved by using the standard implicit Newmark＇s time integration scheme. In the scheme of present method, the calculation of each cell is carried out by meshfree method, and local search is imple- mented in interpolation. Numerical examples show that the present method has high computational efficiency and good accuracy in solving elastic dynamic problems.
基金supported by the National Key Research and Development Program of China(Project No.2016YFC0800208)the National Natural Science Foundation of China(Project Nos.51329901,51528901,51579190,51779189)
文摘Determining soilewater characteristic curve(SWCC) at a site is an essential step for implementing unsaturated soil mechanics in geotechnical engineering practice, which can be measured directly through various in-situ and/or laboratory tests. Such direct measurements are, however, costly and timeconsuming due to high standards for equipment and procedural control and limits in testing apparatus. As a result, only a limited number of data points(e.g., volumetric water content vs. matric suction)on SWCC at some values of matric suction are obtained in practice. How to use a limited number of data points to estimate the site-specific SWCC and to quantify the uncertainty(or degrees-of-belief) in the estimated SWCC remains a challenging task. This paper proposes a Bayesian approach to determine a site-specific SWCC based on a limited number of test data and prior knowledge(e.g., engineering experience and judgment). The proposed Bayesian approach quantifies the degrees-of-belief on the estimated SWCC according to site-specific test data and prior knowledge, and simultaneously selects a suitable SWCC model from a number of candidates based on the probability logic. To address computational issues involved in Bayesian analyses, Markov Chain Monte Carlo Simulation(MCMCS), specifically Metropolis-Hastings(M-H) algorithm, is used to solve the posterior distribution of SWCC model parameters, and Gaussian copula is applied to evaluating model evidence based on MCMCS samples for selecting the most probable SWCC model from a pool of candidates. This removes one key limitation of the M-H algorithm, making it feasible in Bayesian model selection problems. The proposed approach is illustrated using real data in Unsaturated Soil Database(UNSODA) developed by U.S. Department of Agriculture. It is shown that the proposed approach properly estimates the SWCC based on a limited number of site-specific test data and prior knowledge, and reflects the degrees-of-belief on the estimated SWCC in a rational and quantitative manner.
基金the National Natural Science Foundation of China(61872378).
文摘Some attributes are uncertain for evaluation work because of incomplete or limited information and knowledge.It leads to uncertainty in evaluation results.To that end,an evaluation method,uncertainty entropy-based exploratory evaluation(UEEE),is proposed to guide the evaluation activities,which can iteratively and gradually reduce uncertainty in evaluation results.Uncertainty entropy(UE)is proposed to measure the extent of uncertainty.First,the belief degree distributions are assumed to characterize the uncertainty in attributes.Then the belief degree distribution of the evaluation result can be calculated by using uncertainty theory.The obtained result is then checked based on UE to see if it could meet the requirements of decision-making.If its uncertainty level is high,more information needs to be introduced to reduce uncertainty.An algorithm based on the UE is proposed to find which attribute can mostly affect the uncertainty in results.Thus,efforts can be invested in key attribute(s),and the evaluation results can be updated accordingly.This update should be repeated until the evaluation result meets the requirements.Finally,as a case study,the effectiveness of ballistic missiles with uncertain attributes is evaluated by UEEE.The evaluation results show that the target is believed to be destroyed.
文摘为减少海上交通事故的发生,在建立沿海水域(Coastal Water Area,CWA)交通安全评估因素三层次结构的基础上,针对事故统计数据的不确定性,尝试采用证据推理(Evidential Reasoning,ER)方法进行CWA交通安全评估,并运用案例证实该方法的可行性.评估结果可以为海事安全管理工作决策提供参考依据.
