Mixed Uncertainty Quantification And Robust Optimization Method Based On Probability Box

The uncertain parameters in aerospace structures and systems are of mixed types with many dimensions.The uncertainty quantification and robust optimization method are studied on the probability box framework of aleatory,epistemic and mixed uncertainties.This paper uses numerical examples and engineering cases to verify the effectiveness of the methods.Finally,the NASA multidisciplinary uncertainty quantification challenge problem is studied by using the methods of the uncertainty propagation,model calibration,global sensitivity analysis based on probability box,cross-layer dimension reduction,and robust optimization design are comprehensively applied.The main contents are as follows:(1)Uncertainty propagation is studied in this paper.The probability box is used to deal with the propagation of aleatory,epistemic and mixed uncertainties in the models.The effects of various types of uncertainty on the output are distinguished,and the output characteristics under the combined effects of aleatory,epistemic and mixed uncertainties are intuitively described.(2)With the prior information and sample data,the calibration of epistemic uncertain parameters is studied.The transitional Markov chain Monte Carlo(TMCMC)algorithm is used to obtain the samples of the posterior distributions of uncertain parameters,and then boundaries of the parameters are effectively reduced.The validity of parameter calibration based on TMCMC algorithm is verified with a numerical example.(3)Based on the mixed uncertainty propagation with probability box,the area change of the probability box is used as the sensitivity index to quantitatively determine the importance of the uncertain parameter.The pinching method is proposed for the global sensitivity analysis of the probability box,and the validity of the method is verified by a numerical example and the case of variable angle tow(VAT)laminate thermal buckling analysis.(4)On the basis of the global sensitivity analysis of the probability box,the simplification of the complex multi-dimensional models with mixed uncertainties is studied.With the eigen-decomposition of the gradient covariance matrix of the output variables,which is used to determine the basis vector of dimension reduction,the active subspace method is used to reduce the parameter dimensions of the models.Furthermore,a cross-layer dimension reduction method combining the global sensitivity analysis of the probability box and active subspace method is proposed to solve the simplification problem of complex multi-dimensional systems with mixed uncertainties.The effectiveness of the method is verified by a numerical example.(5)The basic theories and methods of deterministic optimization design and robust optimization design are summarized,and the differences between the input variables and the objective function of the two methods are compared.Taking a numerical example and aero engine turbine disk design as cases,the deterministic optimization and robust optimization are used to obtain the values of design parameters and objective function respectively,and the results of the robust optimization are compared by changing the weight ratio of mean and variance of the objective.