| Estimation of statistical moments of structural response is one of the main contents for stochastic analysis of engineering structure.The balance between accuracy and efficiency remains a challenge.Dimension-reduction method(DRM)is mainly focused in this paper.And then Shift-Multiplicative DRM(SMDRM)and Hybrid Approximation based point estimation method(PEM)is proposed,as well as SMDRM based fractional moment maximum entropy.The practicality of proposed methods are verified with an engineering example.Firstly,the theory of invariance of the DRMs in algebra operation is derived.And the difference obviously existed in statistical moment estimation for different forms of approximations.The invariance based on exponential operation proves that it’s more reasonable to approximate the origin function by DRMs.Based on the invariance theorem of translation transformation,the shift constant is introduced into the traditional product approximation and a new PEM is proposed.Combined with the orthogonal experiment strategy in sample grids selection and cubic spline interpolation,the constant is determined though parameter optimization.The proposed method greatly develops the precision of the traditional univariate approximation while keeps high efficiency,and has good robustness for the response function with either additive nature or multiplicative nature.Then,in order to reduce the influence of the cross terms of random variables,three kinds of PEMs based on HHDMR、improved HHDMR and rational HHDMR are proposed.A more effective method to acquire the hybrid coefficient γ is proposed.Then the multiplicative of components in the HHDMR and rational HHDMR are replaced by SMDRM respectively,and the precision is quite improved.After the comprehensive comparison among various PEMs,the suggestion of the application of PEMs is given:The SMDRM or HHDMR is better for efficiency while improved rational hybrid HDMR is better for accuracy.Next,combined with the maximum entropy(ME)of fractional moment and SMDRM,a new moment based reliability analysis method is developed.The probability density function(PDF)fitted by the proposed method is more accurate than traditional ME,especially for the tail probabilities.Finally,the stochastic analysis for a RC frame building is carried by proposed PEM.The finite element model is established in ANSYS,then the rule of structure internal force and deformation under the seismic response is studied by statistical moment.Combined with the theory equivalent extreme-value event,the reliability analysis is carried out for the RC building.And the analysis result is in line with engineering reality.It can provide theoretical support for engineering design. |
