Structural Reliability Analysis Based On Improved Maximum Entropy Method

Due to the widespread uncertainty in actual engineering,structural reliability analysis becomes particularly important in the study of engineering structures.Scholars at home and abroad have continuously developed many structural reliability analysis methods,such as sampling simulation method,moment method,agent model method,etc.Different types of analytical methods have their own scope of application when performing structural reliability analysis.With the development of science and technology,society has put forward new requirements for all aspects of the structure,and the reliability analysis of the structure has become more stringent accordingly:how to analyze more accurate structural reliability results with limited information and ensure the efficiency of calculation is the common goal of researchers.In order to perform structural reliability analysis more effectively,an improved maximum entropy method is proposed as the basis for structural reliability analysis in this paper,and then a new converted mixed volume formula is proposed to calculate the statistical moments required for the maximum entropy method.In addition,the traditional Sobol sequence is used to calculate the statistical moments,and the Vine Copula structure is used to describe the complex correlation between variables,and a reliability analysis method is developed to effectively solve the complex correlation between variables.In this paper,the traditional maximum entropy method based on fractional moment is improved,and then combined with the converted mixed cabature formula for structural reliability analysis.Combine the traditional fractional moment with the Laplace transform to a fractional exponential moment.By combining the third-order spherical and seventh-order radial integration rules,a new mixed cabature formula that takes into account both computational efficiency and precision is produced for calculating the statistical moments required for the improved maximum entropy method.In order to avoid insufficient calculation accuracy caused by the small number of integration points in the mixed cabature formula,the integration points are rotated to improve the utilization of the integration point information.For the rotation angle,the two-step strategy is used to determine.First,the relative error of the estimated standard deviation of the random variable and its exact value is used as the criterion for the first step of angle selection.When the number of rotation angles selected in the first step is greater than 1,proceed to the second step of selection,and determine the final rotation angle based on the Kullback-Leibler divergence between the edge probability density function of the reconstructed variable in standard normal space and the standard normal probability density function.Combined with the mixed volume integral points after rotation,the maximum entropy method based on the fractional exponential moment can efficiently and accurately reconstruct the probability density function of the limit state function.In this paper,a new calculation method is proposed for structural reliability analysis under the condition of complex correlation between external load variables.First of all,the correlation between the external load variables is described by using the Vane Copula structure and decomposed in the form of D-Vine.After obtaining the joint probability density function of a random variable with complex correlation using Vine Copula,sampling is performed using the Sobol sequence and the obtained joint probability density function is used to convert the variables to the relevant original space.Using Sobol sequence sampling can effectively use fewer sample points and improve computational efficiency.Finally,the statistical moments required for the improved maximum entropy method are calculated using the sampling points of the converted Sobol sequence,and combined with the maximum entropy method based on the fractional exponential moment.This method can quickly and accurately obtain the probability density function and the transcendent probability function of the desired response by considering the complex correlation between the external load variables.