In this paper,an efficient interval analysis method called dimension-reduction interval analysis(DRIA)method is proposed to calculate the bounds of response functions with interval variables,which provides a kind of s...In this paper,an efficient interval analysis method called dimension-reduction interval analysis(DRIA)method is proposed to calculate the bounds of response functions with interval variables,which provides a kind of solution method for uncertainty analysis problems of complex structures and systems.First,multi-dimensional function is transformed into multiple one-dimensional functions by extending dimension reduction method to the interval analysis problem.Second,all the one-dimensional functions are transformed to standard quadratic form by second order Taylor expansion method.As a result,the multi-dimensional function is approximately represented by the functions that each interval variable occurs once,and interval power arithmetic can be used to efficiently calculate the bounds of response functions in restricted overestimation.Finally,three numerical examples and an engineering application are investigated to demonstrate the validity of the proposed method.展开更多
In this paper,an uncertainty propagation analysis method is developed based on an extended sparse grid technique and maximum entropy principle,aiming at improving the solving accuracy of the high-order moments and hen...In this paper,an uncertainty propagation analysis method is developed based on an extended sparse grid technique and maximum entropy principle,aiming at improving the solving accuracy of the high-order moments and hence the fitting accuracy of the probability density function(PDF)of the system response.The proposed method incorporates the extended Gauss integration into the uncertainty propagation analysis.Moreover,assisted by the Rosenblatt transformation,the various types of extended integration points are transformed into the extended Gauss-Hermite integration points,which makes the method suitable for any type of continuous distribution.Subsequently,within the sparse grid numerical integration framework,the statistical moments of the system response are obtained based on the transformed points.Furthermore,based on the maximum entropy principle,the obtained first four-order statistical moments are used to fit the PDF of the system response.Finally,three numerical examples are investigated to demonstrate the effectiveness of the proposed method,which includes two mathematical problems with explicit expressions and an engineering application with a black-box model.展开更多
文摘In this paper,an efficient interval analysis method called dimension-reduction interval analysis(DRIA)method is proposed to calculate the bounds of response functions with interval variables,which provides a kind of solution method for uncertainty analysis problems of complex structures and systems.First,multi-dimensional function is transformed into multiple one-dimensional functions by extending dimension reduction method to the interval analysis problem.Second,all the one-dimensional functions are transformed to standard quadratic form by second order Taylor expansion method.As a result,the multi-dimensional function is approximately represented by the functions that each interval variable occurs once,and interval power arithmetic can be used to efficiently calculate the bounds of response functions in restricted overestimation.Finally,three numerical examples and an engineering application are investigated to demonstrate the validity of the proposed method.
基金the National Science Fund for Distinguished Young Scholars(Grant No.51725502)the major program of the National Natural Science Foundation of China(Grant No.51490662)the National Key Research and Development Project of China(Grant No.2016YFD0701105).
文摘In this paper,an uncertainty propagation analysis method is developed based on an extended sparse grid technique and maximum entropy principle,aiming at improving the solving accuracy of the high-order moments and hence the fitting accuracy of the probability density function(PDF)of the system response.The proposed method incorporates the extended Gauss integration into the uncertainty propagation analysis.Moreover,assisted by the Rosenblatt transformation,the various types of extended integration points are transformed into the extended Gauss-Hermite integration points,which makes the method suitable for any type of continuous distribution.Subsequently,within the sparse grid numerical integration framework,the statistical moments of the system response are obtained based on the transformed points.Furthermore,based on the maximum entropy principle,the obtained first four-order statistical moments are used to fit the PDF of the system response.Finally,three numerical examples are investigated to demonstrate the effectiveness of the proposed method,which includes two mathematical problems with explicit expressions and an engineering application with a black-box model.
