Research On Uncertainty-based Design Optimization Approach And Application With Active Subspace Dimension Reduction

With increasingly fierce competition in aerospace,flight vehicles are faced with higher requirements for the performance robustness and reliability.The design of flight vehicles usually involves multiple disciplines,multidimensional variables,and computational expensive simulation models,and also relates to many kinds of propagating uncertainties.How to achieve a robust and reliable system with optimum performace is an urgent issue to solve.Uncertainty-based Desgin Optimization(UBDO)approach handles the optimization design issue of complex system under uncertainty,which is recognized as an effective method to advance the system design quality.In this paper,the UBDO theory and its application in the system design of aerospace vehicles are systematically studied.Based on the research on the fundamental issues,including uncertainty dimension reduction,uncertainty propagation,extreme case analysis,and optimization under uncertainty(OUU),a complete set of UBDO methodology is established and applied in component-level and system-level problems,like reliability assessment of satellite separation process,earth observation satellite system design,and lunar exploration nanosat system design.1.The part of UBDO theoretical research is structured as follows.(1)With respect to the computational dimension bottleneck of UBDO,a dimension reduction approach based on Generalized Active Subspaces(GAS)is proposed to tackle the limitation of existing active subspaces.This GAS is suitable for both the Aleatory and the Epistemic uncertainty,and can be applicable to linear and nonlinear problems.Considering the hardly accurate solution of GAS,three approximate implementation methods are presented,i.e.Interval Eigenvalue Analysis(IEA),Empirical Distribution Function(EDF),and Taylor Expansion,which are verified by the test examples.(2)With respect to uncertainty propagation issue in complex systems,a propagation process including GAS dimension reduction and surrogate model is discussed for mixed uncertainty analysis,which does not nest the probabilistic analysis and just need an interval analysis based on active variable.The establishment of adaptive response surface in reduced subspace is presented and an adaptive interval response surface method(AIRSM)is given,which avoids the interval expansion issue and ensures the boundary estimation accuracy.An extended interval dynamic correlate analysis criterion is defined for mixed uncertainty cases,which achieves the qualitative assessment of AIRSM fitting accuracy.(3)With respect to the challenging inverse problem in UBDO,a reduced Bayesian Inference method is proposed for extreme case analysis.The formulation of input parameters for corresponding output response is derived based on the Bayesian posterior density and the solving process is also improved by enabling iteration in the prior reduced subspace.Compared with other quantification methods based on posterior distribution,this method exhibit more efficiency advantages and the computational complexity is largely simplified.(4)In order to improve the optimization precision of OUU,a density matching optimization approach based on objective distribution information is studied.Two optimization formulations of distribution matching based on objective low-order moments and cumulative density function are derived,which largely extend the applicable scope,suitable for mixed uncertainty and discrete/continuous cases.The general solving process based on GAS dimension reduction is given,which ensures the high integral points and high estimation samples.The dynamic penalty function and multiobjective optimization algorithm based on the constraint strength are mainly investigated to gain the reliable Pareto-optimal solusions.The precision and efficiency of the aforementioned approach are verified by several test examples.2.The part of UBDO application research is organized as follows.(1)As for the reliability assessment needs for small satellite separation,the component-level application of UBDO is studied.The uncertainty quantification of small satellite separation is necessary.The separation dynamics and the equation of motion are established by fully considering the compression spring devices,gravitational perturbations,and center of gravity(CG)offsets.Based on engineering experience,the propagation of structural and mechanical uncertainty is mainly investigated.The separation angular velocity and minimum relative distance can be analyized in the reduced subspace.The complete objective distribution function is approximated to provide an effective reliability and safety assessment of satellites owning different control abilities during separation,which is also demonstrated by ground separation tests.Moreover,the optimization design of satellite separation mechanism is conducted based on UBDO,which indicates the approach better digs the reliable potential design and reduces the system mass.(2)As for the system design of earth observation satellites,the system-level application of UBDO is studied.The function analysis and preliminary design are conducted for this kind of satellites.The discipline models of earth observation satellites are built for the conceptual design phase.Based on the GAS-AIRSM,the 23-dimensional uncertainty problem can efficiently propagate in a one-dimensional active subspace with good analysis accuracy.The single-objective and multi-objective uncertainty optimization are studied respectively.First,a density matching optimization incorporating aleatory uncertainy is given for the minimum mass;then,a multiobjective optimization considering satellites mass,satellite cost and observation accuracy is studied;lastly,the satellite overall design including mixed uncertainty is further investigated,which provides the optimal scheme satisfying the belief constraints.(3)As for the system design issue of lunar exploration nanosats,the system-level application of UBDO is studied.The discipline models of lunar exploration nanosats are built for the conceptual design phase.Combining special requirements of lunar exploration mission,the couplings among all the disciplines are analyzed.A one-dimensional active subspace in the conceptual design of micro-nanosats is further proved,along with the uncertainty analysis precision.The economic cost per unit data and satellite mass are regarded as the optimization targets,and the system reliability and imaging accuracy are indicated as constraints.The UBDO methodology in this paper is applied to achieve the multiobjective optimization of both aleatory and mixed uncertainty cases,which obtains more reliable and robust Pareto-optimal solutions compared with the deterministic optimization.To sum up,the major technological difficulties in the UBDO theory are systematically studied in this paper,which constitute a complete and feasible set of UBDO methodology,better overcoming the existing issues of UBDO,i.e.costly computation,limited analysis accuracy,and engineering application bottleneck.Moreover,this UBDO methodology is successfully applied in flight vehicle design of both component-level and system-level.The research achievements have favorable theoretical and application values,providing a beneficial foundation for the development of UBDO theory and the enhancement of flight vehicle design quality.