Structural Interval Analysis And Optimization Design Based On Function Decomposition Method

Most engineering structures involve some uncertain or imprecise parameters such as geometric dimensions,material properties(e.g.,yield strength,Young's modulus,and Poisson's ratio),and external effects(e.g.,wind gusts,earthquakes,and other dynamic loads).Uncertainty in these inputs will lead to uncertainty in the structural response as well.If the deterministic values of input parameters are utilized in the structural analysis,the high precision and reliability of the structures cannot be guaranteed.Therefore,for more reliable performance and to meet the stringent design requirements of real structures,the uncertainties of the input parameters should be considered in the analysis.In the presence of parameter uncertainties,probabilistic methods,fuzzy methods,and interval analysis are often used to quantify the uncertainties associated with structures.Among them,interval analysis has gradually become an important complement to probabilistic methods because it only requires the range of values or interval bounds of uncertain parameters without the probability distribution function or fuzzy membership information within the ranges.This paper aims at the uncertainty analysis of structural systems containing interval parameters.Based on the interval algorithm,the research is carried out step by step from static structure to dynamic system,from structural optimization to multidisciplinary design optimization,and is dedicated to expanding and improving the theory of interval analysis and interval optimization analysis,providing technical support for complex structure design under consideration of interval uncertainties.The detail research contents of this paper are as follows:(1)For the static structure containing multiple uncertain parameters,univariate and bivariate-function decomposition methods are proposed for predicting the range of values of static responses.Firstly,based on the higher-order Taylor series expansion,the univariate and bivariate-function decomposition expressions are constructed,where includes the higher-order terms of Taylor expansion that have a significant influence on the precision.Then,the original static response function is decomposed into the sum of several one-and two-dimensional functions by using the function decomposition expression.Finally,the interval bounds of the static structure can be obtained by substituting the ends and midpoints of the interval parameters into these low-dimensional functions.The results show that the proposed method does not require solving sensitivity information that may not be available in real engineering,and is suitable for dealing with large uncertainty static problems compared to the Taylor expansion methods.(2)For the dynamic structure containing multiple uncertain parameters in engineering,a decomposition Chebyshev analysis method is developed for solving the upper and lower bounds of the dynamic response.Firstly,the surrogate model of the original dynamic response is built based on the bivariate-function decomposition method and Chebyshev polynomials,and thus the high-dimensional dynamic function is transformed into the sum of explicit one-and two-dimensional functions.Then,the maximum and minimum values of each uncertain parameter acquired from the sensitivity information are substituted into the approximate model to achieve the dynamic response interval in the whole uncertainty domain.The results show that the proposed method can effectively reduce the computational cost compared to the Chebyshev interval method.Meanwhile,the accuracy of the dynamic response bounds can be significantly improved by searching the optimal value of the interval parameters with the gradient information without increasing the calculation sample.(3)For the optimization problem of engineering structures containing many uncertain parameters,an efficient interval uncertainty optimization method based on adaptive strategy is put forward.Firstly,based on the bivariate-function decomposition expression,combined with the subinterval method and adaptive strategy,an adaptive bivariate-function decomposition method is developed and applied to evaluate the interval range of uncertain objective functions and constraints.Then,using interval order relation and reliability-based possibility degree of interval,the uncertainty optimization model is converted into a two-objective deterministic optimization model,which is further processed by the linear weighting and penalty function method to obtain a single-objective unconstrained optimization model.Finally,the lightning attachment procedure optimization is selected as an external optimizer to iteratively search for the optimal solution.The results show that the presented method can preserve better convergence properties at a lower cost while ensuring that the uncertain constraints are satisfied.(4)For the problem that interval uncertainties exist in objective function and constraints of the multidisciplinary optimization,a structural multidisciplinary interval optimization method based on improved adaptive function decomposition is established.The proposed method converts the interval multidisciplinary optimization model into a single-objective unconstrained multidisciplinary optimization model by the transformation methods.The solution of the transformed optimization model involves multiple layers of optimization loops,in which outer layer,middle layer,and inner layer are deterministic cycle,interval analysis,and multidisciplinary design respectively.Firstly,according to the cross term criterion,an improved adaptive bivariate-function decomposition method is proposed for interval analysis of the middle layer.The merit is that the interval analysis of the middle layer can be separated from multidisciplinary optimization,allowing interval analysis to form a loop with the outer optimization.Then,the multidisciplinary system is decoupled using the individual disciplinary feasible method in the inner layer analysis.Finally,the deterministic optimization of the outer layer is performed through the lightning attachment procedure optimization.The results show that the proposed method is instructive for addressing the multidisciplinary interval optimization problem of the structure.