Interval Uncertain Optimazation Method For Multi-component Structural With The Same Components

Interval uncertain optimization usually transforms interval model into numerical model to solve the optimization problems,the converted numerical model is essentially a nesting optimization model with low efficiency.In the field of civil engineering,architectural structures are generally multi-component structures with the same components,and the calculation of interval uncertainty optimization for such structures is huge.Moreover,the method is not applicable for multi-component structures with the same components when considering the uncertainties of design variables and related parameters.Since the values of design variables are not unique in one case,which can’t meet the numerical calculation requirements.Therefore,interval uncertain optimization method for multi-component structures with the same components is introduced in this paper,which makes interval uncertainty optimization better applied to engineering structure optimization.(1)Through comparative analysis of four small calculation examples,the difference and connection between interval computation and numerical computation is pointed out,and then the essential reason of interval expansion is given.According to the difference and relation between interval computation and numerical computation,the interval calculation method based on numerical conversion is proposed,and the method is applied to interval Taylor expansion,then the interval calculation method based on second order interval Taylor expansion is proposed.The analysis results of a six-bar truss demonstrate that,compared with the original Taylor expansion method,the error is decreased from 0.047-0.08 to 0.001-0.005,and the calculation accuracy is significantly improved.(2)The nesting genetic algorithm is used to solve the mathematical transformation model of interval uncertainty optimization.Aiming at the shortcomings of nesting genetic algorithm,such as poor stability and low computational efficiency,the GA is improved from four aspects: the processing of constraints,the construction of fitness function,crossover operator and mutation operator.And the analysis results of a numerical example proves that the improved nesting genetic algorithm has good stability and convergence speed.(3)A interval uncertain optimization method of multi-component structure with the same components is proposed,the method directly establishes the interval uncertainty optimization model,and then the objective function and constraint are transformed into upper and lower bound functions represented by ideal design variables and parameters by the interval second-order Taylor expansion formula based on numerical transformation,which ensuring that the values of each interval design variable and interval parameter are unique under one possibility.Finally,it is transformed into a deterministic optimization problem and solved by genetic algorithm.The analysis results of a 10-bar truss demonstrate that,for small uncertainty problems,the method’s optimization result is consistent with the nesting optimization method,which proves that the method can effectively avoid interval expansion and interval reduction with a high computational accuracy.Moreover,the iteration time of the genetic algorithm is only about 1/30 of that of the nesting optimization method,which proves that the calculation amount of this method is small.