An efficient approach to reliability-based design optimization within the enhanced sequential optimization and reliability assessment framework

Reliability based design optimization (RBDO) has been widely implemented in engineering practices for high safety and reliability. It is an important challenge to improve computational efficiency. Sequential optimization and reliability assessment (SORA) has made great efforts to improve computational efficiency by decoupling a RBDO problem into sequential deterministic optimization and reliability analysis as a single-loop method. In this paper, in order to further improve computational efficiency and extend the application of the current SORA method, an enhanced SORA (ESORA) is proposed by considering constant and varying variances of random design variables while keeping the sequential framework. Some mathematical examples and an engineering case are given to illustrate the proposed method and validate the efficiency.     

Reliability-based design optimization using convex approximations and sequential optimization and reliability assessment method

In this study, an effective method for reliability-based design optimization (RBDO) is proposed enhancing sequential optimization and reliability assessment (SORA) method by convex approximations. In SORA, reliability estimation and deterministic optimization are performed sequentially. The sensitivity and function value of probabilistic constraint at the most probable point (MPP) are obtained in the reliability analysis loop. In this study, the convex approximations for probabilistic constraint are constructed by utilizing the sensitivity and function value of the probabilistic constraint at the MPP. Hence, the proposed method requires much less function evaluations of probabilistic constraints in the deterministic optimization than the original SORA method. The efficiency and accuracy of the proposed method were verified through numerical examples.     

Multi-objective reliability-based optimization for design of trapezoidal labyrinth weirs

In the present research, the reliability-based design optimization (RBDO) of labyrinth weirs has been investigated. The optimization problem is formulated such that the optimal shape of trapezoidal labyrinth weir described by a number of variables is found by minimizing the volume of the trapezoidal labyrinth weir and maximizing the reliability index. The constraint conditions are the weir geometric shape and its different ratios. In order to achieve this purpose, a framework is presented whereby non-dominated sorting genetic algorithm (NSGA-II) is integrated with monte carlo simulation (MCS) method to solve the RBDO approach of trapezoidal labyrinth weirs. The proposed method is applied to UTE Dam labyrinth weir, and the results are compared with the real one. The results show the need for design based on reliability in the labyrinth weirs that propose using RBDO for weir design. The results showed that RBDO approach can achieve a more reliable design in addition to reducing the volume of the trapezoidal labyrinth weir. Finally, the sensitivity analysis of the parameters effective on the reliability index revealed that three design variables of weir width, total upstream head and discharge coefficient are the main parameters affecting weir RBDO solution.     

耦合系统考虑可靠性的多学科设计优化分解方法

为了减少基于可靠性的多学科设计优化的计算成本,提出了一种面向耦合多学科设计优化的分解方法。定义了函数计算成本矩阵来处理可靠性函数的随机性,给出了根据函数随机特征计算函数计算成本矩阵的方法,同时定义了耦合关系矩阵来处理函数之间的耦合性,给出了识别耦合变量集的算法;基于函数计算成本矩阵和耦合关系矩阵提供的信息,改进了整体计算成本等评价指标的度量方法;利用遗传算法进行分解,寻求整体计算成本最小的分解方案;通过电子封装的多学科设计优化算例对上述方法进行了验证,通过与两个已有分解方案的对比表明,该方法能够显著减少整体计算成本。该方法与传统方法相比具有两个优势：一方面可以识别和分解耦合变量,使其能够用于耦合系统的分解;另一方面可以将可靠性函数平均分解到各子任务中,以获得更少的整体计算成本。     

Improved moment-based quadrature rule and its application to reliability-based design optimization

A moment method known as the fourth moment method can perform reliability analysis without optimization using the first four statistical moments. Numerical integration is used to calculate the statistical moments, where a moment-based quadrature rule can be used for integration nodes and weights. However, the moment-based quadrature rule has to solve a system of linear equations that can be numerically unstable. Considering this point, an improved moment-based quadrature rule is proposed and is applied to reliability-based design optimization. Finally, the moment-based RBDO is applied to numerical examples with a variety of random variables and target reliability indexes. From the numerical results, the performance of the improved moment-based quadrature rule can be confirmed and several guidelines are given for the moment-based RBDO.     

风力机齿轮箱布局的多目标可靠性优化设计

针对风力机齿轮箱布局设计中存在的问题,采用多目标可靠性优化设计方法,以风力机齿轮箱的箱体体积和齿轮体积最小化为设计目标,建立了风力机齿轮箱布局的多目标可靠性优化设计模型,分析比较了3种常见传动方案对风力机齿轮箱布局的影响,以某型号1.5 MW风力机齿轮箱为例进行了优化分析。研究结果表明,采用该设计方法得到的齿轮箱箱体体积和齿轮体积加权和值比以齿轮体积为目标的单目标设计方法更低。同时,分析结果表明,提高输入转速可大大降低齿轮箱成本。     

机械零件的稳健可靠性优化设计

提出一种可以提高机械零件可靠性和稳健性的优化设计方法.用凸集模型描述零件设计中存在的不确定性,采用物理规划方法构造不确定性参数的不满意度函数,通过极小化不满意度函数最差值实现目标函数的稳健性,通过灵敏度分析实现约束函数的稳健性.建立了基于物理规划和灵敏度分析的稳健可靠性优化模型,这种模型是一种嵌套的优化模型,采用分层方法对其求解.通过气门弹簧优化设计实例说明了该方法的有效性和合理性.     

多目标模糊优化方法及其在可靠性设计中的应用

在基于模糊机会约束规划理论基础上,对多目标模糊优化方进行研究,通过模糊模拟求解模糊目标函数的理想极大值和极小值,建立了多目标优化问题的模糊机会约束规划模型,并给出了基于模糊模拟的遗传算法求解方法.通过对一个无约束处理的常规双目标模糊可靠性优化问题实例求解,验证了多目标模糊模拟遗传算法的有效性,并指出该算法的优点在于能较好处理多目标优化问题的分目标量纲不同及其函数值之间差距较大的情况.     

液压系统可靠性模糊设计与评价方法

液压系统的可靠性是保证设备整机工作可靠的关键因素,液压系统可靠性模糊设计比常规可靠性设计更科学更合理.以工程机械典型液压系统为例,基于模糊数学理论和方法,分析了常规可靠性设计的不足,提出了液压系统可靠性模糊设计的思想和方法,运用模糊理论对液压系统进行描述并计算出系统的模糊可靠度,给出了系统模糊可靠度预测与分配的方法,建立了系统可靠性的模糊评价模型.     

凸轮机构的遗传优化设计

针对标准遗传算法在解最优化问题时存在早熟收敛和后期收敛缓慢的现象，提出了一种基于小生境技术的改进遗传算法，然后结合凸轮机构的优化6设计原理，建立凸轮机构的遗传优化设计模型，并给出其应用实例和优化结果。     

牙嵌离合器的可靠性遗传优化设计

将标准遗传算法用于最优化问题时存在早熟收敛和后期收敛速度缓慢的现象。这里扼要分析了遗传算法的运行机制,提出了一种基于小生镜技术的改进遗传算法,根据牙嵌离合器的可靠性设计原理,建立了遗传优化的模型,并给出了应用改进的遗传算法进行优化设计的实例和计算结果。     

螺旋弹簧可靠性多目标优化设计

考虑可靠性等约束条件,以螺旋弹簧重量最轻、刚度误差最小为优化设计目标,建立多目标优化设计数学模型,用理想点法对模型进行求解,得到满足所有约束条件的最优解.该方法有效而实用,对求解同类零件优化设计问题具有普遍意义.     

大型行星齿轮系统可靠性设计的多目标优化

大型行星齿轮传动系统工况复杂,安全性能要求高,常规的设计方法因过于注重安全性,设计的结果偏于保守,技术经济指标不佳.以行星齿轮传动系统为对象,提出了大型机构可靠性设计的多目标优化模型,即以齿轮的关键参数——齿数、齿宽、模数为设计变量,充分考虑工程设计的约束性、多解性等特征,建立数学模型,进行可靠性分析计算,并在MATLAB优化工具箱里采用积极集策略进行多目标优化.将得到的结果与传统设计方案结果相比较,为大型行星齿轮系统的优化设计提供新思路.     

机械系统可靠性的多目标模糊优化设计

本文应用模糊集理论,探讨了多目标模糊优化的数学模型及春求解方法,并将其应用到机械系统可靠性的多目标优化设计中。     

Practical reliability-based design of gear pairs

Techniques from perturbation method and reliability-based design theory are employed to present the practical and effective method for the reliability-based design of gear pairs. The theoretical formulae of reliability-based design of gear pairs are obtained. The corresponding program can be used to obtain the reliability-based design parameters of gear pairs accurately and quickly.     

改进的粒子群算法在可靠性优化设计中的应用

针对粒子群优化算法在处理约束问题时产生的不可行解,引用基于多级罚函数的约束处理方法。为了改进罚函数粒子群算法易早熟、后期收敛慢、易陷入局部最优解的缺点,提出了动态改变惩罚系数的改进粒子群算法。应用于几个经典的测试函数,都在较少的迭代次数内得到了高精度的优化解,验证了算法的有效性。以某一机械零部件的可靠性优化为例,建立了基于改进粒子群算法的可靠性优化设计模型。结果表明:该方法能快速有效地解决可靠性优化设计问题,计算结果明显优于常规的多级罚函数法。     

Enhanced Morris for the extraction of significant parameters in high-dimensional design optimization

The traditional Morris method cannot ensure the consistent extraction of significant parameters because its random sampling strategy often leads to an improper coverage of the input space, especially when the number of sample points is small. To overcome the drawbacks, we developed an improved sampling strategy to enhance the performance of Morris method based on Latin hypercube sampling (LHS) with the idea of Central composite design (CCD) and a fluctuant step to generate a more uniform points set. A comparison on the results of a numerical example obtained by the enhanced Morris, the traditional methods and CCS-Morris demonstrated that the former had a much better performance. The application of the enhanced Morris method in the high-dimensional optimization of a compressor shell with 15 design parameters aimed at increasing its natural frequencies and keeping its mass relatively light demonstrates that the method is effective and applicable in engineering design.

     

封闭行星齿轮传动系统的稳健可靠性优化设计

利用稳健可靠性优化设计方法建立了封闭行星齿轮传动的数学模型,包括设计变量、目标函数和约束条件的建立。最后运用遗传算法求得封闭行星齿轮的稳健可靠解,并对其结果进行了分析。     

考虑磨损与变形的谐波齿轮精度可靠性分析与优化设计

针对谐波齿轮减速器中存在的磨损和变形因素导致减速器传动精度低、可靠性差等问题,建立考虑磨损与变形的谐波齿轮减速器传动误差模型,并进行精度可靠性分析与优化设计。通过分析传动误差的影响因素建立了传动误差模型;基于磨损经验模型和试验数据,应用贝叶斯修正方法建立动态磨损模型,同时根据试验数据和高斯过程回归建立柔轮变形模型;综合获得的传动误差模型、磨损模型和柔轮变形模型建立谐波齿轮精度可靠性模型,并应用基于拉丁超立方抽样的Kriging代理模型和蒙特卡洛法求解某谐波齿轮减速器传动精度可靠度。最后采用序列二次规划法对谐波齿轮减速器进行优化设计。优化结果表明,在工况参数(输出端负载17.5 N·m,输入端转速100 r/min)下,优化后的谐波齿轮减速器在工作时间3 000 h处的可靠度达到99.02%,相比未优化前提升7.85%,而成本却只增加1.70%。     

基于霍普菲尔神经网络的螺栓联接可靠性优化设计

机械强度的可靠性设计是机械设计的重要内容,在可靠性设计中,材料强度和载荷等均视为服从某种分布的随机变量.求解螺栓联接可靠性优化问题,可以采用霍普菲尔(Hopfield)神经网络优化方法.