An Uncertainty Analysis and Reliability-Based Multidisciplinary Design Optimization Method Using Fourth-Moment Saddlepoint Approximation

In uncertainty analysis and reliability-based multidisciplinary design and optimization(RBMDO)of engineering structures,the saddlepoint approximation(SA)method can be utilized to enhance the accuracy and efficiency of reliability evaluation.However,the random variables involved in SA should be easy to handle.Additionally,the corresponding saddlepoint equation should not be complicated.Both of them limit the application of SA for engineering problems.The moment method can construct an approximate cumulative distribution function of the performance function based on the first few statistical moments.However,the traditional moment matching method is not very accurate generally.In order to take advantage of the SA method and the moment matching method to enhance the efficiency of design and optimization,a fourth-moment saddlepoint approximation(FMSA)method is introduced into RBMDO.In FMSA,the approximate cumulative generating functions are constructed based on the first four moments of the limit state function.The probability density function and cumulative distribution function are estimated based on this approximate cumulative generating function.Furthermore,the FMSA method is introduced and combined into RBMDO within the framework of sequence optimization and reliability assessment,which is based on the performance measure approach strategy.Two engineering examples are introduced to verify the effectiveness of proposed method.

An Efficient Method for Reliability-based Multidisciplinary Design Optimization

Design for modem engineering system is becoming multidisciplinary and incorporates practical uncertainties; therefore, it is necessary to synthesize reliability analysis and the multidisciplinary design optimization （MDO） techniques for the design of complex engineering system. An advanced first order second moment method-based concurrent subspace optimization approach is proposed based on the comparison and analysis of the existing multidisciplinary optimization techniques and the reliability analysis methods. It is seen through a canard configuration optimization for a three-surface transport that the proposed method is computationally efficient and practical with the least modification to the current deterministic optimization process.

EFFICIENT METHOD FOR MULTIDISCIPLINARY DESIGN OPTIMIZATION BY CONSIDERING UNCERTAINTY

A new reliability-based multidisciplinary design optimization （RBMDO） framework is proposed by combining the single-loop-based reliability analysis （SLBRA） method with multidisciplinary feasible （MDF） method. The Kriging approximate model with updating is introduced to reduce the computational cost of MDF caused by the complex structure. The computational efficiency is remarkably improved as the lack of iterative process during reliability analysis. Special attention is paid to a turbine blade design optimization by adopting the proposed method. Results show that the method is much more efficient than the commonly used double-loop based RBMDO method. It is feasible and efficient to apply the method to the engineering design.

RELIABILITY-BASED DESIGN OF COMPOSITES UNDER THE MIXED UNCERTAINTIES AND THE OPTIMIZATION ALGORITHM

This paper proposed a reliability design model for composite materials under the mixture of random and interval variables. Together with the inverse reliability analysis technique, the sequential single-loop optimization method is applied to the reliability-based design of composites. In the sequential single-loop optimization, the optimization and the reliability analysis are decoupled to improve the computational efficiency. As shown in examples, the minimum weight problems under the constraint of structural reliability are solved for laminated composites. The Particle Swarm Optimization （PSO） algorithm is utilized to search for the optimal solutions. The design results indicate that, under the mixture of random and interval variables, the method that combines the sequential single-loop optimization and the PSO algorithm can deal effectively with the reliability-based design of composites.

Optimization design of piles subjected to horizontal loads based on reliability theory

Based on reliability theory,a general method for the optimization design of piles subjected to horizontal loads is presented.This method takes into consideration various uncertainties caused by pile installation,variability of geotechnical materials from one location to another,and so on.It also deals with behavior and side constraints specified by standard specifications for piles.To more accurately solve the optimization design model,the first order reliability method is employed.The results from the numerical example indicate that the target reliability index has significant influence on design parameters.In addition,the optimization weight increases with the target reliability index.Especially when the target reliability index is relatively large,the target reliability index has significant influence on design weight of piles.

Multi-objective reliability optimization design of high-speed heavy-duty gears based on APCK-SORA model

For high-speed heavy-duty gears in operation is prone to high tooth surface temperature rise and thus produce tooth surface gluing leading to transmission failure and other adverse effects,but in the gear optimization design and little consideration of thermal transmission errors and thermal resonance and other factors,while the conventional multi-objective optimization design methods are difficult to achieve the optimum of each objective.Based on this,the paper proposes a gear multi-objective reliability optimisation design method based on the APCK-SORA model.The PC-Kriging model and the adaptive k-means clustering method are combined to construct an adaptive reliability analysis method(APCK for short),which is then integrated with the SORA optimisation algorithm.The objective function is the lightweight of gear pair,the maximum overlap degree and the maximum anti-glue strength;the basic parameters of the gear and the sensitivity parameters affecting the thermal deformation and thermal resonance of the gear are used as design variables;the amount of thermal deformation and thermal resonance,as well as the contact strength of the tooth face and the bending strength of the tooth root are used as constraints;the optimisation results show that:the mass of the gear is reduced by 0.13kg,the degree of overlap is increased by 0.016 and the coefficient of safety against galling Compared with other methods,the proposed method is more efficient than the other methods in meeting the multi-objective reliability design requirements of lightweighting,ensuring smoothness and anti-galling capability of high-speed heavy-duty gears.

Global Optimization Method Using SLE and Adaptive RBF Based on Fuzzy Clustering

High fidelity analysis models,which are beneficial to improving the design quality,have been more and more widely utilized in the modern engineering design optimization problems.However,the high fidelity analysis models are so computationally expensive that the time required in design optimization is usually unacceptable.In order to improve the efficiency of optimization involving high fidelity analysis models,the optimization efficiency can be upgraded through applying surrogates to approximate the computationally expensive models,which can greately reduce the computation time.An efficient heuristic global optimization method using adaptive radial basis function（RBF） based on fuzzy clustering（ARFC） is proposed.In this method,a novel algorithm of maximin Latin hypercube design using successive local enumeration（SLE） is employed to obtain sample points with good performance in both space-filling and projective uniformity properties,which does a great deal of good to metamodels accuracy.RBF method is adopted for constructing the metamodels,and with the increasing the number of sample points the approximation accuracy of RBF is gradually enhanced.The fuzzy c-means clustering method is applied to identify the reduced attractive regions in the original design space.The numerical benchmark examples are used for validating the performance of ARFC.The results demonstrates that for most application examples the global optima are effectively obtained and comparison with adaptive response surface method（ARSM） proves that the proposed method can intuitively capture promising design regions and can efficiently identify the global or near-global design optimum.This method improves the efficiency and global convergence of the optimization problems,and gives a new optimization strategy for engineering design optimization problems involving computationally expensive models.

Reliability-based concurrent subspace optimization method

To avoid the high computational cost and much modification in the process of applying traditional reliability-based design optimization method, a new reliability-based concurrent subspace optimization approach is proposed based on the comparison and analysis of the existing multidisciplinary optimization techniques and reliability assessment methods. It is shown through a canard configuration optimization for a three-surface transport that the proposed method is computationally efficient and practical with the least modification to the current deterministic optimization process.

System reliability-based robust design of deep foundation pit considering multiple failure modes

Recently,reliability-based design is a universal method to quantify negative influence of uncertainty in geotechnical engineering.However,for deep foundation pit,evaluating the system safety of retaining structures and finding cost-effective design points are main challenges.To address this,this study proposes a novel system reliability-based robust design method for retaining system of deep foundation pit and illustrated this method via a simplified case history in Suzhou,China.The proposed method included two parts:system reliability model and robust design method.Back Propagation Neural Network(BPNN)is used to fit limit state functions and conduct efficient reliability analysis.The common source random variable(CSRV)model are used to evaluate correlation between failure modes and determine the system reliability.Furthermore,based on the system reliability model,a robust design method is developed.This method aims to find cost-effective design points.To solve this problem,the third generation non-dominated genetic algorithm(NSGA-III)is adopted.The efficiency and accuracy of whole computations are improved by involving BPNN models and NSGA-III algorithm.The proposed method has a good performance in locating the balanced design point between safety and construction cost.Moreover,the proposed method can provide design points with reasonable stiffness distribution.

基于响应面法的血管支架拉伸、扭转性能优化及考虑加工精度影响的强度可靠性分析

为分析设计变量对血管支架拉伸性能、扭转性能的精准影响,进行血管支架拉伸性能、扭转性能优化,考虑加工精度的影响,进行血管支架的强度可靠性分析。方法:取血管支架支撑筋宽度、支撑筋长度、连接筋宽度和支架厚度为设计变量,应用斯皮尔曼等级相关系数法分析设计变量对血管支架拉伸刚度、扭转刚度等响应变量的精准影响;采用响应面方法进行以拉伸刚度、扭转刚度为目标进行血管支架的优化设计;对优化后的血管支架,考虑加工精度所致设计变量的随机性,利用六西格玛工具分析应力的概率分布。结果:对于血管支架拉伸刚度,支撑筋宽度和连接筋宽度灵敏度系数大,且均为正值;对于血管支架扭转刚度,支撑筋宽度灵敏度系数较大,且为负值;优化后的血管支架相比原始血管支架,拉伸刚度降低了11.5%;扭转刚度减小了50.6%;考虑加工精度所致设计变量的随机性进行可靠性分析,在可靠度为99.8%时,虽然血管支架的拉伸刚度和扭转刚度最大值高于优化值,但血管支架的最大应力满足强度条件。结论:支撑筋宽度对血管支架的拉伸性能影响最大,连接筋宽度次之,支撑筋长度和支架厚度影响较小;支撑筋宽度对血管支架的扭转性能影响最大,连接筋宽度、支撑筋长度和支架厚度影响较小;随机因素加工精度对血管支架优化目标有一定的影响,但优化结果仍是可靠的。本文提供了一种血管支架优化的思路:首先是进行基于目标的优化,然后考虑随机因素的影响进行基于概率的强度可靠性分析。

基于Kriging模型与FORM的钢板组合梁桥结构优化设计

考虑材料参数的不确定性以及设计变量多重约束条件的影响,提出了基于可靠性分析的钢板组合梁桥结构优化设计方法。首先,利用拉丁超立方试验设计(Latin hypercube design,LHD)构建试验组合方案,并通过有限元分析获取试验设计组合下的最大挠度响应值。基于获取的训练样本,构建能够表征结构最大挠度值与随机输入之间映射关系的Kriging代理模型。基于建立的代理模型,以钢结构截面积最小化为目标函数,建立符合规范要求与可靠度约束的优化数学模型,并采用一阶可靠性方法(first order reliability method,FORM),实现设计变量优化。通过比较具有相同设计变量上限,但下限分别为初始值的80%和70%两种优化设计方案,评估了两者在相同阈值以及不同阈值下设计变量的优化结果。最后对方案二在阈值为17 mm下的优化结果进行极限状态验算。结果表明:两个优化设计方案在阈值为17 mm下的优化结果更具合理性,并且方案二在同一阈值下具有更高的优化程度。随着阈值增加,优化程度增加,且腹板高度在较大阈值下对结果影响更大,而翼缘宽度在较小阈值下影响更大。

Sequential ensemble optimization based on general surrogate model prediction variance and its application on engine acceleration schedule design

The Efficient Global Optimization(EGO)algorithm has been widely used in the numerical design optimization of engineering systems.However,the need for an uncertainty estimator limits the selection of a surrogate model.In this paper,a Sequential Ensemble Optimization(SEO)algorithm based on the ensemble model is proposed.In the proposed algorithm,there is no limitation on the selection of an individual surrogate model.Specifically,the SEO is built based on the EGO by extending the EGO algorithm so that it can be used in combination with the ensemble model.Also,a new uncertainty estimator for any surrogate model named the General Uncertainty Estimator(GUE)is proposed.The performance of the proposed SEO algorithm is verified by the simulations using ten well-known mathematical functions with varying dimensions.The results show that the proposed SEO algorithm performs better than the traditional EGO algorithm in terms of both the final optimization results and the convergence rate.Further,the proposed algorithm is applied to the global optimization control for turbo-fan engine acceleration schedule design.

基于可校正强化搜索遗传算法的光学系统自动设计

阻尼最小二乘法(DLS)与遗传算法(GA)均适用于光学系统自动设计,前者搜索效率高但极易陷入局部极值陷阱,后者光学结构参数空间全局搜索能力强但局部搜索能力弱。针对上述问题,提出一种可校正强化搜索GA(CRSGA)。该算法在GA基础上进行了两方面的改进:首先,在GA交叉算子后,引入DLS增强局部搜索能力;其次,引入校正策略,即在下轮迭代前按比例回滚进化后评价函数值变差的个体以校正进化结果。选取双高斯(DG)、反远摄(RT)和有限共轭距成像(FCDI)这3种典型光学系统设计实验以验证CRSGA的有效性,CRSGA优化效果优于DLS、GA,且依次优于商业光学设计软件Zemax阻尼最小二乘法约8.92%、12.19%和9.39%,特别是优化结果分别达到Zemax HAMMER算法的99.98%、94.33%和88.45%。实验结果表明,所提算法对光学系统优化效果良好,可用于光学系统自动设计工作。

电动缸举升机构伺服性能的亚全局并行优化设计

针对电动缸举升伺服机构的非线性环节对武器站伺服性能的影响,基于应用背景开展了伺服性能优化方法的研究。针对可设计非线性环节中的增益波动、间隙宽度、不平衡力矩和摩擦力矩进行了作用机理分析;基于机构布局和控制器参数建立了运动学、动力学和控制策略的数学模型、设计约束和目标优化函数;提出了亚全局并行优化方法,对可设计非线性环节进行了基于内点法的多目标优化,解决了局部串行优化的局部最优问题;对基于PI控制器+DOB观测器的复合控制策略进行了单独设计,解决了机械惯量参数、控制器参数和观测器名义模型不匹配的问题。经验证,亚全局并行优化方法的优化结果在整体上更佳,且更加贴合工程实际。

装备可用性建模与优化设计方法研究

针对目前行业内缺少关于装备可用性建模与优化设计方法方面的研究成果这一问题,提出一种装备可用性建模与优化设计方法。通过可靠性、测试性、维修性和保障性信息提取,获得装备可用性设计方案的关键设计指标;建立面向多任务的装备可用性模型,并基于该模型完成装备在不同任务工作模式下的优化分析;确定装备可用性设计方案优选的多个决策属性,建立基于多属性决策的装备可用性设计方案优选模型,并基于该模型优选出装备可用性设计方案;通过案例分析验证所提方法的合理性和有效性,为装备可用性优化设计工作提供依据。

A Comparison of Deterministic, Reliability-Based Topology Optimization under Uncertainties

Reliability and optimization are two key elements for structural design. The reliability~ based topology optimization （RBTO） is a powerful and promising methodology for finding the optimum topologies with the uncertainties being explicitly considered, typically manifested by the use of reliability constraints. Generally, a direct integration of reliability concept and topol- ogy optimization may lead to computational difficulties. In view of this fact, three methodologies have been presented in this study, including the double-loop approach （the performance measure approach, PMA） and the decoupled approaches （the so-called Hybrid method and the sequential optimization and reliability assessment, SORA）. For reliability analysis, the stochastic response surface method （SRSM） was applied, combining with the design of experiments generated by the sparse grid method, which has been proven as an effective and special discretization technique. The methodologies were investigated with three numerical examples considering the uncertainties including material properties and external loads. The optimal topologies obtained using the de- terministic, RBTOs were compared with one another; and useful conclusions regarding validity, accuracy and efficiency were drawn.

A Polynomial Chaos Expansion Trust Region Method for Robust Optimization

Robust optimization is an approach for the design of a mechanical structure which takes into account the uncertainties of the design variables.It requires at each iteration the evaluation of some robust measures of the objective function and the constraints.In a previous work,the authors have proposed a method which efficiently generates a design of experiments with respect to the design variable uncertainties to compute the robust measures using the polynomial chaos expansion.This paper extends the proposed method to the case of the robust optimization.The generated design of experiments is used to build a surrogate model for the robust measures over a certain trust region.This leads to a trust region optimization method which only requires one evaluation of the design of experiments per iteration(single loop method).Unlike other single loop methods which are only based on a first order approximation of robust measure of the constraints and which does not handle a robust measure for the objective function,the proposed method can handle any approximation order and any choice for the robust measures.Some numerical experiments based on finite element functions are performed to show the efficiency of the method.

轿车自动化生产线中吊具的可靠性分析及优化

随着汽车工业的迅猛发展,提高汽车流水线的生产效率变得至关重要。吊具作为生产线上起重运输工具应用广泛,对于生产汽车生产线吊具的可靠性研究尤其重要。文中对轿车自动化生产线中地板吊具可靠性进行分析,并对吊具结构进行相应的优化设计。通过调整吊装运载下部总成钣金件的方案以及优化前后的结构进行有限元分析,优化后的梁在承受相同载荷情况下变形能力得到了大幅改善,为实现安全高效汽车流水线提供了可靠理论依据。

涡轮盘疲劳寿命可靠性设计仿真及优化策略

涡轮盘是航空发动机主要部件之一,一旦发生破坏性故障将导致严重的后果。在充分考虑影响涡轮盘高低周复合疲劳寿命因素不确定性基础上,以MATLAB为平台,设计了涡轮盘高低周复合疲劳寿命可靠性优化设计的联合仿真平台。利用寿命函数和寿命可靠性分析极限状态函数中的共性需求,提出了在优化迭代的过程中自适应构建寿命函数Kriging模型和寿命可靠性极限状态面Kriging模型时共用训练样本点的策略。同时,提出了一种构建寿命函数Kriging模型的学习函数。使用所搭建的疲劳寿命可靠性优化设计平台,完成了某型涡轮盘盘心、榫槽以及涡轮盘系统高低周复合疲劳寿命的可靠性优化设计。结果表明,最优设计方案的局部最大应力显著降低,均值寿命大幅提高,并满足可靠性约束。

基于围岩变形失效的隧道结构可靠度设计方法

为科学地处理隧道工程中由于材料属性和复杂地质环境等带来的不确定性,使支护设计更加安全合理,基于可靠度理论,提出一种实用隧道可靠度设计计算方法.首先,基于可靠度指标的几何意义,结合Nataf变换和Cholesky分解等考虑参数相关性与非负性,建立约束在原始空间的最优化模型;其次,利用数值软件内嵌的优化函数在不需人为计算偏导数的情况下直接获得设计点;然后,引入重要抽样方法,在设计点处计算失效概率,形成兼顾收敛性和精度的实用可靠度计算方法;再次,通过高度非线性的数值算例和非圆坑道算例验证该方法的有效性和适应性;最后,基于围岩变形失效功能函数,采用本文方法进行隧道支护抗力设计计算.算例分析结果表明:本文方法能够以较小代价获取设计点,最终结果和蒙特卡洛法结果相对误差小于1.0%,并且能够结合含交叉项响应面函数处理无解析功能函数的非圆坑道可靠度问题;本文方法能够获取准确的支护抗力设计值,与蒙特卡洛法结果相对误差小于0.5%;内摩擦角的敏感性比黏聚力和变形模量的大.