Improved Maximum Entropy Method And Its Application In Reliability Analysis Of Underwater Vehicle

In the design of engineering structure,it is necessary to predict the real response of the structure according to its mechanical model to verify whether the performance index of the structure meets the design requirements.In the procedure of design,processing,manufacturing and service of engineering structures,uncertainties,such as materials and loads,often affect the actual bearing capacity of the structures,which may deviate from the performance requirements.Therefore,accurate analysis and quantification of the influence of input uncertainties on structural response is of great guiding significance for evaluating structural reliability.To consider uncertainties in practical engineering and evaluate the reliability of structures accurately,the reliability analysis method based on probability theory and mathematical statistics has become an important means in analyzing and quantifying the impact of uncertainties on the safety of structures.Among many reliability analysis methods,the maximum entropy method(MEM)is an effective moment method to study uncertainty propagation and to solve structural reliability.By using this method,the approximate expression of probability density of the performance function can be obtained only from statistical moment information,without obtaining design point and calculating derivative of the performance function.Consequently,it has attracted wide attention in theoretical research and engineering application in recent years.In this dissertation,an improved scheme of MEM via integer moments(IM-MEM)and MEM via fractional moments(FM-MEM)is proposed to aim at some difficult problems in the theory of MEM.based on the nonlinear transformation of performance function in structural reliability analysis.Main works of this dissertation are:1.Aiming at the traditional IM-MEM,an improved technique based on nonlinear transformation function is proposed.The performance function is transformed nonlinearly by the monotone incremental function,to fit the exponential polynomial expansion of the probability density function(PDF)estimated by MEM.The range of transformed performance function is changed from infinite interval to bounded interval,which improves the accuracy of numerical integration considerably.The improved method is implemented by using three typical nonlinear transformation functions,including arctangent function,logistic sigmoid function and hyperbolic tangent function.It is demonstrated by examples that the prediction accuracy of the failure probability obtained by the proposed improved method based on the nonlinear transformation is higher than that of the traditional IM-MEM considering the first four-order moments.At the same time,the problem that the traditional IM-MEM fails to converge in the reliability analysis for some performance functions with non-normal input variables is solved.2.The technique of nonlinear transformation of performance function is extended to the improvement of the FM-MEM.Because cumulative distribution function is in the range of[0.1].it is considered as the nonlinear transformation function to satisfy the requirements of the FM-MEM.Thus,the FM-MEM can be used for the performance functions defined on any interval.Three kinds of cumulative distribution functions are given as the nonlinear transformation,including Cauchy distribution function,Logistic distribution function and Gumbel distribution function.Several typical examples are tested to illustrate the advantage of the proposed method in terms of accuracy compared with the original method,when only four terms are in the expression of the estimated PDF.3.Considering the problem that it is difficult for the traditional MEM to evaluate the error of the result,a zero-entropy transformation criterion is established to assess the accuracy of the PDF estimated by MEM,and the optimal modulation parameter of the nonlinear transformation in the improved MEM is realized.The change of information entropy of the transformed performance function after the nonlinear transformation is theoretically deduced from the probability conservation equation.It is found that when the selected nonlinear transformation function is the true cumulative distribution function of the original performance function,the entropy value of the transformed performance function is zero.According to the change characteristics of the entropy value,an estimation criterion of the accuracy of the failure probability prediction is established,based on zero-entropy distribution in the interval of[0,1].The fractional moment function is used to calculate the error,and the concrete realization method of the criterion is given.This zero-entropy criterion can not only be applied to the improved MEM based on nonlinear transformation,but also to any other method of probability density estimation to evaluate the output error.4.The proposed improved MEM based on nonlinear transformation is applied to the probabilistic modeling of the dynamic response and reliability analysis of the underwater vehicle structure,and the influence of the nonlinearity of the connection of the underwater vehicle structure on the statistical characteristics of the dynamic response is obtained.Considering the spatial and temporal uncertainties of the distribution of the hydrodynamic external loads and the nonlinear characteristics of the connecting structures,the probability density functions of the maximum internal force,the moment of the maximum internal force and the position of the maximum internal force of the underwater vehicle structure are solved by using the improved MEM based on the nonlinear transformation.The influence of the nonlinear parameters of the connection on the dynamic response of the structure is discussed.