Structural probabilistic analysis quantifies the effect of input random variables, such as material proper- ties, geometrical parameters and loading conditions, on the structural responses. The point estimate method (...Structural probabilistic analysis quantifies the effect of input random variables, such as material proper- ties, geometrical parameters and loading conditions, on the structural responses. The point estimate method (PEM) is a direct and easy-used way to perform the structural probabilistic analysis in practice. In this paper, a novel and efficient point estimate method is proposed for computing the first four statistical moments of structural response which is a function of input random variables. The method adopts Nataf transformation to replace Rosenblatt transformation in conventional point estimate method. Because of the nature of engineering problems and limited statistical data, the joint probability density function (PDF) of all input random variables is hard to acquire, but it must be known in Rosenblatt transformation. A more common case is that the marginal PDF of each random variable and the correlation matrix are available, which just satisfy the service condition of Nataf transformation. Hence the Nataf transformation based point estimate method is particularly suitable for engineering applications. The comparison between the proposed method and the conventional point estimate method shows that (1) they are equivalent when all random variables are mutually independent; (2) if the marginal PDFs and the correlation matrix are known, the conventional PEM cannot be applicable, but the proposed method can give a rational approximation. Finally, the procedure is demonstrated in detail through a simple illustration.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the National Natural Science Foundation of China (Grant No. 10572117)Program for New Century Excellent Talents in University (Grant No. NCET-05-0868)+1 种基金Aviation Science Foundation (Grant No. 2007ZA53012)Hi-Tech Research and Development Program of China (Grant No. 2007AA04Z401)
文摘Structural probabilistic analysis quantifies the effect of input random variables, such as material proper- ties, geometrical parameters and loading conditions, on the structural responses. The point estimate method (PEM) is a direct and easy-used way to perform the structural probabilistic analysis in practice. In this paper, a novel and efficient point estimate method is proposed for computing the first four statistical moments of structural response which is a function of input random variables. The method adopts Nataf transformation to replace Rosenblatt transformation in conventional point estimate method. Because of the nature of engineering problems and limited statistical data, the joint probability density function (PDF) of all input random variables is hard to acquire, but it must be known in Rosenblatt transformation. A more common case is that the marginal PDF of each random variable and the correlation matrix are available, which just satisfy the service condition of Nataf transformation. Hence the Nataf transformation based point estimate method is particularly suitable for engineering applications. The comparison between the proposed method and the conventional point estimate method shows that (1) they are equivalent when all random variables are mutually independent; (2) if the marginal PDFs and the correlation matrix are known, the conventional PEM cannot be applicable, but the proposed method can give a rational approximation. Finally, the procedure is demonstrated in detail through a simple illustration.
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.
