Research On Efficient Decoupling And Local Approximation Of Reliability-based Design Optimization

Reliability-based design optimization(RBDO)has gradually become an indispensable technology in the design of complex mechanical products,whose application is further enhanced by the rapid development of computer simulation.Because of the high computational cost in function evaluation,developing accurate and efficient methods for reliability analysis and design optimization is necessary.Many researches have been proposed,including the reconstruction of RBDO model、approximation of multiple integra、itegration of reliability analysis and design optimization and metamodel-based methods.However,there are still some shortcomings in existing methods,such as:the optimal shifting vector is difficult to calculate for nonlinear problems;inactive probabilistic constraint is difficult to remove;the modeling efficiency is low for problem with multiple probabilistic constraints;lacking efficient integration strategy for tradtional analytic approximation method and metamodel-based method;low fidelity information is difficult to utilize and variable fidelity model is difficult to construct.To solve these problems,further researches are carried out in this dissertation to constitute the theory system using efficient decoupling and local approximation.Details are as follows:(1)A moving shifting vector method with the effectiveness assessment of probabilistic constraints is proposed.According to reliability index at the current design and target reliability,a novel probabilistic constraint handling scheme is developped to check the effectiveness of probabilistic constraints.Then a decoupling strategy based on moving shifting vector is proposed to avoid the low efficiency caused by unparallel contours of performance function.(2)A local Kriging approximation method with variable radius for multi-constraint problem is proposed.Local sampling region around the current design is constructed for each probabilistic constraint according to the target reliability and the nonlinearity.Samples located on the constraint boundary and the points with high uncertainty are selected in this region to update the Kriging model and local sampling radius.To further enhance the uniformity of samples,a new sequential sampling criterion LEFF is developped.(3)A local Kriging approximation method using MPP for RBDO is proposed.Using Kriging approximation to calculate the most probable point,then MPP is selected as the local sequential sampling center to update the Kriging approximation.To avoid the the function evaluation for inactive probabilistic constraints,a novel effectiveness-checking method for Kriging-based RBDO is proposed.To further improve the efficiency in failue probability calculation,Importance Sampling method using MPP as sampling center is ulitized.(4)A VF-SLP framework using least squares hybrid scaling for RBDO is proposed.Using the high fidelity function value and gradient value at all evaluated points around the current design,the weight coefficient of additive scaling method and multiplicative scaling method is calculated by solving a least square problem.Then the weight coefficient is used to tune the low fidelity model to replace the implicit performance function.A novel method which considers the target reliability and the influence domain at the current design is developed to determine the design space in every sub-optimization problem in SLP.Integrating the scaling method and sequential linear programming strategy,a new VF-SLP framework is developped to improve the efficiency of VF-based RBDO.(5)Based on the researches in this paper,the modeling error handling scheme in RBDO、the metamodel-based variable fidelity method and the solution strategy for high dimensionality reliability problem are prospected.