The uncertainty quantification of flows around a cylinder is studied by the non-intrusive polynomial chaos method. Based on the validation with benchmark results, discussions are mainly focused on the statistic proper...The uncertainty quantification of flows around a cylinder is studied by the non-intrusive polynomial chaos method. Based on the validation with benchmark results, discussions are mainly focused on the statistic properties of the peak lift and drag coefficients and base pressure drop over the cylinder with the uncertainties of viscosity coefficient and inflow boundary velocity. As for the numerical results of flows around a cylinder, influence of the inflow boundary velocity uncertainty is larger than that of viscosity. The results indeed demonstrate that a five-order degree of polynomial chaos expansion is enough to represent the solution of flow in this study.展开更多
The proof system, based on resolution method, has become quite popular in automatic theorem proving, because this method is simple to implement. At present many kinds of extensions for resolution method are known： Re...The proof system, based on resolution method, has become quite popular in automatic theorem proving, because this method is simple to implement. At present many kinds of extensions for resolution method are known： Resolution with restricted number of variables in disjuncts, resolution over Linear Equations, Cutting planes, etc. For Classical, Intuitionistic and Minimal （Johansson＇s） propositional logics, the authors introduce the family of resolution systems with full substitution rule （SRC, SRI and SRM） and with e-restricted substitution rule （SeRC, SeRf and SeRM）, where the number of substituted formula connectives is bounded by . The authors show that for each of mentioned logic the SR-type system （in tree form） is polynomially equivalent to Frege systems by size, but for every ~＇ 〉 0, Se＋lR-type has exponential speed-up over the SeR-type （in tree form）.展开更多
Dependence among random input variables affects importantly the results of probabilistic load flow(PLF),system economic operation,and system security.To solve this problem,the main objectiveness of the paper is to ana...Dependence among random input variables affects importantly the results of probabilistic load flow(PLF),system economic operation,and system security.To solve this problem,the main objectiveness of the paper is to analyze the performance of several schemes for simulating correlated variables combined with the point estimate method(PEM).Unlike the existing works that considering one single scheme combined with Monte Carlo simulation(MCS) or PEM,by neglecting the correlation among random input variables,four schemes were presented for disposing the dependence of correlated random variables,including Nataf transformation /polynomial normal transformation(PINT) combined with orthogonal transformation(OT) / elementary transformation(ET).Combining with the 2m+1 approach of PEM,a space transformation-based formulation was proposed and adopted for solving the PLF.The proposed approach is applied in the modified IEEE 30-bus system while considering correlated wind generations and load demands.Numerical results show the effectiveness of the proposed approach compared with those obtained from the MCS.Results also show that the scheme of combining Nataf transformation and ET with PEM provides the best performance.展开更多
基金Supported by the National Natural Science Foundation of China under Grant No 11371069the Young Foundation of Institute of Applied Physics and Computational Mathematics under Grant No ZYSZ1518-13the Science Foundation of China Academy of Engineering Physics under Grant No 2013A0101004
文摘The uncertainty quantification of flows around a cylinder is studied by the non-intrusive polynomial chaos method. Based on the validation with benchmark results, discussions are mainly focused on the statistic properties of the peak lift and drag coefficients and base pressure drop over the cylinder with the uncertainties of viscosity coefficient and inflow boundary velocity. As for the numerical results of flows around a cylinder, influence of the inflow boundary velocity uncertainty is larger than that of viscosity. The results indeed demonstrate that a five-order degree of polynomial chaos expansion is enough to represent the solution of flow in this study.
文摘The proof system, based on resolution method, has become quite popular in automatic theorem proving, because this method is simple to implement. At present many kinds of extensions for resolution method are known： Resolution with restricted number of variables in disjuncts, resolution over Linear Equations, Cutting planes, etc. For Classical, Intuitionistic and Minimal （Johansson＇s） propositional logics, the authors introduce the family of resolution systems with full substitution rule （SRC, SRI and SRM） and with e-restricted substitution rule （SeRC, SeRf and SeRM）, where the number of substituted formula connectives is bounded by . The authors show that for each of mentioned logic the SR-type system （in tree form） is polynomially equivalent to Frege systems by size, but for every ~＇ 〉 0, Se＋lR-type has exponential speed-up over the SeR-type （in tree form）.
基金National Science Foundation of China(No.61533010)the Science and Technology Commission of Shanghai Municipality,China(No.14ZR1415300)
文摘Dependence among random input variables affects importantly the results of probabilistic load flow(PLF),system economic operation,and system security.To solve this problem,the main objectiveness of the paper is to analyze the performance of several schemes for simulating correlated variables combined with the point estimate method(PEM).Unlike the existing works that considering one single scheme combined with Monte Carlo simulation(MCS) or PEM,by neglecting the correlation among random input variables,four schemes were presented for disposing the dependence of correlated random variables,including Nataf transformation /polynomial normal transformation(PINT) combined with orthogonal transformation(OT) / elementary transformation(ET).Combining with the 2m+1 approach of PEM,a space transformation-based formulation was proposed and adopted for solving the PLF.The proposed approach is applied in the modified IEEE 30-bus system while considering correlated wind generations and load demands.Numerical results show the effectiveness of the proposed approach compared with those obtained from the MCS.Results also show that the scheme of combining Nataf transformation and ET with PEM provides the best performance.
