Research On Reliability Based Multidisciplinary Design Optimization With Mixed Uncertainties

With the continuous development of science technology and continuous improvement of human needs,the engineering product becomes more and more complex.And therefore,in the process of products design and development,more and more coupling disciplines are involved,and many types of uncertainty are also contained.For the purpose of meeting the requirements of reliability and meanwhile,taking full advantage of the interdisciplinary coupling cooperation mechanism to achieve the overall optimization of complex product,the reliability based multidisciplinary design optimization(RBMDO)becomes an important means of modern complex product design.The random,fuzzy and interval uncertainties are the most common uncertainty form in practical engineering.For a long time,most of RBMDO methods had only taken random uncertainty into account,while ignoring other uncertainties.However,in the complex product design that contains multiple disciplines,a variety of uncertainties usually exist simultaneously,and if the method which only considers random uncertainty is still used to design products,the products will not meet the requirements of reliability.Therefore,in the process of product design,the influence of all kinds of uncertainty should be considered to ensure that the design results will have sufficient reliability.In order to solve the problems that current RBMDO methods can only handle limited kinds of uncertainties and have high computation complexity,this work conducted a series of researches from single disciplinary to multidisciplinary,as well as from reliability analysis and reliability based design optimization.This work devotes itself to extend and perfect the theory of RBMDO under multiple uncertainties,and offers a technological support for the complex product design under multiple uncertainties.The main researches of this dissertation are as follows.(1)Research on the reliability analysis method under random-fuzzy-interval uncertainties.The current reliability analysis methods under random-fuzzy-interval uncertainties are still at the preliminary exploration stage,and the developed methods are only based on convex model.However,the convex model is only one modeling form of interval uncertainty,and there also exists the evidence variable modeling form.Therefore,in this paper,in order to solve the reliability analysis problem with random fuzzy and evidence variables,the unified reliability analysis model(URAM)under random-fuzzy-interval uncertainties is established based on the analysis of these three kinds of uncertainty quantification theory named probability theory,possibility theory and evidence theory.The URAM belongs to a three layers conditional failure form analysis model.Then,on the basis of URAM,first order reliability method(FORM)and α cut,the unified reliability analysis method,which is referred to as FORM-α-URA,is proposed for the reliability analysis under random-fuzzy-interval uncertainties.Finally the effectiveness of the method is verified by two engineering examples.(2)Research on the modeling of RBMDO with the consideration of random-fuzzy-interval uncertainties.In this chapter,the input mixed uncertainties and its propagation in the coupling multidisciplinary system are discussed.With the combination of probability,the possibility and evidence theory,reliability evaluation under the three kinds of uncertainties is analyzed.On the basis of above,the RBMDO model which is referred to as random fuzzy and interval multidisciplinary design optimization(RFIMDO)is established.Thereafter,this paper points out that the key portions which deeply influence the solve efficiency of RFIMDO are the deterministic multidisciplinary design optimization,the multidisciplinary analysis of reliability and the whole calculation process.(3)Research on the deterministic multidisciplinary collaborative design optimization algorithm.For the problem that collaborative optimization combined with linear approximations(CLA-CO)cannot always obtain a correct solution for optimization problems with nonconvex constraints,linear approximation filter(LAF)strategy is introduced,and the CLA-CO based on LAF strategy is proposed.In LAF strategy,whether conflict exists is first identified through transforming the identification problem into the existence problem of feasible region of linear programming;then,the conflicting linear approximations are coordinated by eliminating the larger violated linear approximations.Thereafter,the accumulative linear approximations are replaced by the minimum violated linear approximation as the system-level constraint.The CLA-CO based on LAF strategy can not only achieve the efficiency computation but also can successfully solve the optimization problems with nonconvex constraints.The effectiveness of the method is verified by examples.(4)Research on the multidisciplinary inverse reliability analysis method under random-fuzzy-interval uncertainties.For the condition of the simultaneous existence of random,fuzzy and interval uncertainties in the design of complex products,firstly,an interpolation-based sequential performance measure approach(IS-PMA)is proposed for single disciplinary.In the most probable point searching parts in IS-PMA,the part of fuzzy variables and the part of evidence variables are combined together,and they form a sequence solving way with the part of random variables,and the angle interpolation are also used to further improve the efficient.Then,combining IS-PMA,an interpolation-based sequential multidisciplinary performance measure approach(IS-MDPMA)is proposed to deal with the multidisciplinary inverse reliability analysis under random-fuzzy-interval uncertainties.In IS-MDPMA,the nested multidisciplinary probability analysis,multidisciplinary possibility analysis and multidisciplinary interval analysis are effectively decoupled to improve the efficiency of the multidisciplinary inverse reliability analysis and the ability to deal with mixed uncertainties.(5)Research on the method of multidisciplinary sequential optimization and mixed uncertainty evaluation.The calculation principle of the sequential optimization and mixed uncertainty analysis method(SOMUA)under random-interval uncertainties is analyzed in detail.On the basis of the calculation characteristics of SOMUA,the parallel ideas and approximate calculation are imported into SOMUA,and the SOMUA based on parallel computing(PCSOMUA)is proposed to improve the computational efficiency of SOMUA.Based on the above,for the coupling problem of RFIMDO total calculation process,the RFIMDO-PCSOMUA method is proposed.In RFIMDO-PCSOMUA,the RFIMDO is decoupled into a process in which the optimization and uncertainty analysis are executed sequentially,and the solution in each focal set are completed in parallel.Moreover,the CLA-CO based on LAF strategy and IS-MDPMA are integrated into RFIMDO-PCSOMUA.The proposed RFIMDO-PCSOMUA effectively improves the computation efficiency.The effectiveness of the proposed PCSOMUA and RFIMDO-PCSOMUA is verified by numerical and engineering examples.(6)The prototype system of multidisciplinary design optimization with mixed uncertainties is designed and developed,and it can be used to conduct the unified reliability analysis,multidisciplinary reliability analysis,deterministic multidisciplinary design optimization,reliability based multidisciplinary design optimization,and the verification of the proposed models and methods.