考虑可靠性鲁棒的结构非概率优化设计方法研究

传统基于概率模型可靠性设计优化(Reliability-based design optimization, RBDO)通过制定结构性能的概率约束,使得设计结果符合可靠性要求。然而,在参数信息缺乏时,准确的参数概率密度函数难以获取,且在不确定性因素影响下可靠性的稳健性并未被考虑。在参数信息缺乏的情况下,本文中利用非概率凸模型去有效地度量参数的不确定性。根据非概率可靠性分析理论,将极限状态函数进行泰勒展开,利用非概率可靠性指标的灵敏度分析,建立非概率可靠性的鲁棒性指标。将非概率可靠性设计优化与非概率鲁棒性设计集成到统一的设计模型中,结合SORA(Sequential optimization and reliability assessment)方法和微型多目标遗传算法进行求解。最后,通过两个工程算例分析结果,表明所提优化模型的可行性。     

可重构制造系统多态可靠性建模与分析

针对利用传统方法建立多状态系统可靠性模型引起的组合爆炸问题,提出一种基于随机过程方法和改进的通用产生函数法(Universal generating function,UGF)的含中间缓冲区的可重构制造系统(Reconfigurable manufacturing system,RMS)多态可靠性建模方法。利用随机过程方法建立存在非相邻状态转移的可重构机床(Reconfigurable machine tool,RMT)的马尔科夫模型,求解机床各理论稳态概率;定义中间缓冲区状态,并通过分析中间缓冲区对机床可用度的影响,得到中间缓冲区可用度和机床各状态的实际稳态概率;结合RMS和RMT性能多态性的特点,对UGF进行改进。在此基础上,表示设备层和系统层的发生函数,建立多零件族可修RMS的多态可靠性模型,并对系统的各项性能指标进行分析。以双零件族四工序非串行缸盖机加工系统为例,验证该模型与分析方法的有效性。     

基于改进LHS模式的可靠性设计优化

在设计优化中,确定性优化由于没有考虑输入量的不确定性,其优化结果可能不可靠(不安全),因此基于可靠性的设计优化(reliability-based design optimization,RBDO)得到关注.然而可靠性设计优化计算量大,尤其对于高维问题.基于此,提出一种新方法--改进拉丁超立方体取样(Latin hyp...     

基于性能退化和通用发生函数的在轨空间机构系统多状态可靠性分析

在轨空间机构在服役期间,其性能参数往往会因为耗损性机理(如磨损)发生退化,是具有多性能参数输出的多状态系统。因此,基于"两态性"假设的传统可靠性分析方法并不能准确的分析在轨空间机构的多状态可靠性。针对此问题,提出了性能退化和通用生成函数(Universal generating function,UGF)相结合的系统多状态可靠性分析方法。建立了性能参数分布矢量模型,在此基础上利用UGF建立了多性能参数退化下的在轨空间机构系统多状态可靠性模型。分别给出了已知退化机理模型和未知退化机理模型两种情况下的状态概率计算方法,并提出了多性能参数退化下的系统可靠度分析方法。结合双轴驱动机构系统的实例分析,验证了所提方法的有效性,具有工程应用的指导意义。     

平面连杆机构运动可靠性等效正态设计法

通过运动学分析,建立了平面连杆机构运动的矩阵分析模型;利用可靠性分析中的极限状态函数将机构的运动输出与机构运动的设计精度联系起来,建立了平面连杆机构的运动可靠性模型;利用可靠性分析中的等效思想,解决了状态函数包含非正态随机变量时可靠性指标的计算问题,并给出了常见分布函数参数的等效计算公式;利用迭代方法解决了在非线性状态函数非正态随机变量下可靠性指标的高精度求解问题.算例表明,基于等效正态设计的迭代求解方法可以很好地处理各种不同分布的非线性问题,足以满足机构运动可靠性分析的需要.     

车辆转向机构运动精度的可靠性稳健优化设计

在车辆转向机构设计中,考虑了可控因素和噪声因素对运动精度的影响,将可靠性优化和稳健设计方法相结合,以转向机构运动精度为目标函数建立转向机构的可靠性稳健优化数学模型.把运动精度的可靠性灵敏度溶入可靠性优化设计模型之中,将可靠性稳健优化设计转化为满足可靠性要求的多目标优化问题.实例计算表明,考虑制造误差、运动副间隙等不确定因素的影响,可靠性稳健优化设计方法能有效保证转向机构的运动精度和可靠性.     

带ESO的ANFTSMC控制PMSM的新型MPTC无传感器控制策略

针对电动汽车中永磁同步电机传统控制策略对电机控制性能差的问题,提出了一种新型的自适应非奇异快速终端滑模模型预测转矩控制策略.设计了新型自适应指数趋近率,用性质更佳的双曲正切函数tanh()替换传统的切换函数sgn(),并构造了带ESO扰动观测的新型ANFTSMC作为系统转速控制器,消弱了抖振,提高了系统鲁棒性.为实现调速系统的无传感器控制,构造了基于tanh(Fal)的ESO转速观测器.与传统基于Fal函数的ESO相比,观测误差较小,观测精度较高.同时,针对预测转矩控制策略,提出了新型的目标函数构造方法,避免了权重系数的设计,并对传统电压矢量选择方法进行了改进与优化,减少了算法的计算量,结合所设计的新型控制器可有效提高系统的快速性,增加算法的实用性.     

基于设计验算点拟合的响应面法可靠性分析

对于复杂机械结构的可靠性分析，通常需要形式简单的功能函数来定义结构失效，响应面法是结构可靠性分析中最常用的近似功能函数形式，传统近似过程在以基本随机变量均值点为中心开展拟合实验，对于大多数可靠性问题可以得到满足工程需要的结构可靠度。针对核电设备等精度要求较高的结构可靠性问题，文中提出基于设计验算点拟合的响应面近似功能函数，并采用矩法计算结构可靠度，仿真结果表明，基于设计验算点拟合的响应面更接近真实失效曲面，结构可靠度精度明显提高。     

区间模型非概率可靠性指标的仿射算法

针对标准区间运算易引发误差爆炸,导致计算结果丧失实用价值的缺陷,文中将不确定性变量的仿射型及仿射运算引入区间模型非概率可靠性指标的计算中.利用仿射型表示变量的不确定性,由仿射运算计算出结构的响应区间(功能函数的上下界),并由响应区间与其许用区间获得非概率可靠性指标.仿射运算的规则具有优化意义,不会引发误差爆炸.以仿射运算求取区间模型非概率可靠性指标,其计算精度远高于区间运算.     

基于Kriging模型的调心滚子轴承优化设计

为了提高调心滚子轴承的综合性能,对其结构参数进行分析和优化设计.首先,建立满足精度要求的轴承单个滚子静力学模型.然后,选取接触角、滚子半径、滚子长度和滚子轮廓半径作为设计变量,以接触应力最小、切应力最小和质量最小为目标函数,考虑几何结构的约束,采用最优空间填充设计(OSF)进行试验设计.基于试验设计的结果,采用Kriging模型建立目标函数的响应面优化模型,并通过自适应细化和手动细化两种方法来提高模型的精度.最后利用多目标遗传算法(MOGA)得到最佳优化结果,并通过设计变量对目标函数的影响分析和目标函数对设计变量的局部敏感度分析来验证优化结果的可靠性.结果 表明:优化结果可靠且优化后模型的接触应力、切应力和质量分别降低了15.17％、32.13％和0.47％.     

Reliability-based design optimization via high order response surface method

To reduce the computational effort of reliability-based design optimization (RBDO), the response surface method (RSM) has been widely used to evaluate reliability constraints. We propose an efficient methodology for solving RBDO problems based on an improved high order response surface method (HORSM) that takes advantage of an efficient sampling method, Hermite polynomials and uncertainty contribution concept to construct a high order response surface function with cross terms for reliability analysis. The sampling method generates supporting points from Gauss-Hermite quadrature points, which can be used to approximate response surface function without cross terms, to identify the highest order of each random variable and to determine the significant variables connected with point estimate method. The cross terms between two significant random variables are added to the response surface function to improve the approximation accuracy. Integrating the nested strategy, the improved HORSM is explored in solving RBDO problems. Additionally, a sampling based reliability sensitivity analysis method is employed to reduce the computational effort further when design variables are distributional parameters of input random variables. The proposed methodology is applied on two test problems to validate its accuracy and efficiency. The proposed methodology is more efficient than first order reliability method based RBDO and Monte Carlo simulation based RBDO, and enables the use of RBDO as a practical design tool.     

Multidisciplinary wing design optimization considering global sensitivity and uncertainty of approximation models

In recent years, high-fidelity analysis tools, such as computational fluid dynamics and finite element method, have been widely used in multidisciplinary design optimization (MDO) to enhance the accuracy of design results. However, complex MDO problems have many design variables and require long computation times. Global sensitivity analysis (GSA) is proposed to assuage the complexity of design problems by reducing dimensionality where variables that have low impact on the objective function are neglected. This avoids wasting computational effort and time on low-priority variables. Additionally, uncertainty introduced by the fidelity of the analysis tools is considered in design optimization to increase the reliability of design results. Reliability-based design optimization (RBDO) and possibility-based design optimization (PBDO) methods are proposed to handle uncertainty in design optimization. In this paper, the extended Fourier amplitude sensitivity test was used for GSA, whereas a collaborative optimization-based framework with RBDO and PBDO was used to consider uncertainty introduced by approximation models. The proposed method was applied to an aero-structural design optimization of an aircraft wing to demonstrate the feasibility and efficiency of the developed method. The objective function was to maximize the lift-to-drag ratio. The proposed process reduced calculation efforts by reducing the number of design variables and achieved the target probability of failure when it considered uncertainty. Moreover, this work evaluated previous research in RBDO with MDO for the wing design by comparing it with the PBDO result.     

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.     

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.     

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.     

Reliable Space Pursuing for Reliability-based Design Optimization with Black-box Performance Functions

Reliability-based design optimization (RBDO) is intrinsically a double-loop procedure since it involves an overall optimization and an iterative reliability assessment at each search point. Due to the double-loop procedure, the computational expense of RBDO is normally very high. Current RBDO research focuses on problems with explicitly expressed performance functions and readily available gradients. This paper addresses a more challenging type of RBDO problem in which the performance functions are computation intensive. These computation intensive functions are often considered as a "black-box" and their gradients are not available or not reliable. On the basis of the reliable design space (RDS) concept proposed earlier by the authors, this paper proposes a Reliable Space Pursuing (RSP) approach, in which RDS is first identified and then gradually refined while optimization is performed. It fundamentally avoids the nested optimization and probabilistic assessment loop. Three well known RBDO problems from the literature are used for testing and demonstrating the effectiveness of the proposed RSP method.     

非独立区间变量和随机变量下的单步可靠性计算方法

随机变量和非独立区间变量往往共存,两种变量共存不仅导致出现双层优化问题,而且会降低可靠性的计算效率。为解决双层优化问题和提高可靠性计算效率,基于椭球模型描述的非独立区间变量,利用高维模型表示方法（HDMR）解耦随机变量和非独立区间变量,转换双层优化问题为简单的单步求解问题,基于提出的采样方法,利用二次多项式近似HDMR展式,将隐式的单步求解问题转化为显式问题,提出了一种混合型单步可靠性计算方法。算例结果表明,所提出的单步可靠性计算方法具有较高的计算效率和精度;该方法仅需少量的极限状态函数调用次数,即可获得较高精度的计算结果。     

基于通用生成函数的混流制造系统脆弱性评价方法

为了解决基于状态熵的脆弱性评价方法在面对多状态系统组合爆炸问题时的困难,提出了一种基于通用生成函数的混流制造系统脆弱性量化评价方法。首先,分析求解各制造单元的状态及其概率,得到制造单元的通用生成函数,定义并计算各单元的脆性熵,建立制造单元的脆弱性分析模型;其次,根据混流制造系统结构特征和通用生成函数的串并联构造算子,得到系统通用生成函数,定义其脆性熵,基于脆性熵建立混流制造系统的脆弱性评价模型;最后,以某典型的混流制造系统为例,利用所提出的脆弱性评价方法,评估其脆弱性,并与基于状态熵的评价方法进行对比,结果表明该方法可显著提高脆弱性评价的效率。     

Enhanced sequential optimization and reliability assessment for reliability-based design optimization

Reliability-based design optimization (RBDO) has been receiving increasing attention for achieving high safety and reliability in engineering design. Sequential optimization and reliability assessment (SORA), as one of the efficient single-loop methods, decouples an RBDO problem into sequential deterministic optimization and reliability analysis. An enhanced SORA (ESORA) method is proposed with the aim of further improving the computational efficiency for RBDO, considering both cases of constant and varying variances of random design inputs while keeping the single-loop framework. Vehicle side impact example is used to test and compare the efficiency of the proposed method with existing approaches.