Reliability-based Design Optimization And The Applications In Electronic Product Structural Design

Traditional structural design optimization is generally based on determistic system parameters and optimization models,and solved by employing determistic optimization algorithms.However,there exist many uncertainties in practical engineering problems,including geometric dimensions,material properties,and loads etc.The combined effects of these uncertain factors can lead to large variations,and even failure in the structural properties.Reliability-based design optimization(RBDO)can fully take into account the impact of these uncertainties on the constraints in the optimization process;therefore,it can make the result satisfying the requirements of reliability.RBDO plays an important role in practical safety design of structures and products.However,RBDO still in the developing stage,and some key issues need to be resolved,in terms of the effective solution for the nested optimization,the mathematical modeling for complex problems,and the applications for actual product designs.This dissertation conducts a systematical research for RBDO,and aims at contributing some useful researches and trials in terms of decoupling algorithms,mathematical models,and engineering applications.Firstly,a decoupling strategy of incremental shifting vector is developed for conventional RBDO problem,and this part is the basis of the whole dissertation.Secondly,several mathematical models are formulated and the conresponding algorithms are proposed when practical RBDO problems involving some complex problems.Thirdly,these proposed methods are applied in solving some practical engineering problems for electronic product structural designs.As a result,the following studies are carried out in this dissertation:(1)This dissertation proposes a decoupling algorithm for the conventional RBDO problems with high performance in terms of efficiency and convergence,which provides an effective tool for reliability design of many complex structures.The algorithm proceeds by performing a shifting vector calculation and then solving a deterministic design optimization in each step,and eventually converges to the optimal solution.An incremental shifting vector(ISV)strategy is proposed to ensure stable convergence in the iteration process.In each step,the shifting vector preserves the information from the previous step,and only an adjustment is made for it through a shifting vector increment.A computation method is given for the shifting vector increment,avoiding solving an optimization problem during the reliability analysis and thus greatly reducing the computational cost of the iteration process.Six numerical examples and a application of smart watch design are presented to validate the effectiveness of the proposed method.(2)When RBDO involving multidisciplinary analysis,an important problem will emerge,namely reliability-based multidisciplinary design optimization(RBMDO).In order to enhance the efficiency and convergence of the overall solving process,a new algorithm of RBMDO is proposed.Firstly,to decouple the multidisciplinary analysis through employing the individual disciplinary feasible approach,the RBMDO is converted into a conventional form of RBDO.Secondly,the ISV strategy is adopted to decouple the nested optimization of RBDO to a sequential iteration process composed of the design optimization and reliability analysis,by which the efficiency is improved significantly.Finally,the proposed RBMDO method is applied to two actual product designs:an aerial camera and a car pad.For these applications,two corresponding RBMDO models are created,with each containing several finite element models(FEMs)and relatively strong coupling relationship between the involved disciplines.The computational results demonstrate the effectiveness of proposed method.(3)In the process of long-term use,the uncertainty of an engineering structure often presents time-variant or dynamic characteristics due to the influence of stochastic loads and material performance degradations.In such situation,the structural design optimization will involve an important problem of time-variant RBDO(TRBDO).In this paper,a decoupling approach is proposed to convert the nested optimization in TRBDO into a sequence iterative process composed of the time-variant reliability analysis,constraint discretization,and design optimization.In each iteration step,the time-variant reliability analysis method based on stochastic process discretization is firstly used to calculate the time-variant reliability of constraints;secondly,through introducing the concept of the target reliability index of discretized time period and proposing the corresponding algorithm,each time-variant constraint is discretized into a series of time-invariant constraints to formulate a conventional reliability-based design optimization problem.The validity and practicality of the decoupling approach are validated by two numerical examples and a design problem for the chassis of a self-balancing vehicle.(4)The conventional RBDO generally describes uncertain variables using random distributions,while some crucial distribution parameters in practical engineering problems can only be given intervals rather than precise values due to the limited information.Then,an important probability-interval hybrid uncertainty problem emerged.For uncertain problems in which interval variables are included in probability distribution functions of the random parameters,this dissertation establishes a hybrid reliability optimization design model and the corresponding efficient decoupling algorithm,which aims to provide an effective computational tool for reliability design of many complex structures.The reliability of an inner constraint is an interval since the interval distribution parameters are involved;this paper thus establishes the probability constraint using the lower bound of the reliability degree which ensures a safety design of the structure.An approximate reliability analysis method is given to avoid the time-consuming multivariable optimization of the inner hybrid reliability analysis.By using an ISV technique,the nested optimization problem involved in RBDO is converted into an efficient sequential iterative process of the deterministic design optimization and the hybrid reliability analysis.Three numerical examples are presented to verify the proposed method,which include one simple problem with explicit expression and an application of smart pad design.(5)For the problem of evidence-theory-based reliability design optimization(EBDO),this dissertation presents a decoupling approach which provides an effective tool for the reliability design of some complex structures with epistemic uncertainty.The method converts the original nested optimization into a sequential iterative process including design optimization and reliability analysis.In each iteration step,through the uniformity approach,the original EBDO is firstly transformed to a conventional RBDO and an optimal solution is obtained by solving it.At the solution,the first-order approximate reliability analysis method is then used to perform the evidence-theory-based reliability analysis for each constraint.In addition,the RBDO solving and the evidence-theory-based reliability analysis are carried out alternately until reaching the convergence.Finally,2 numerical examples and an application of augment reality glass design show the effectiveness of the proposed method.