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.     

基于信息熵理论中的含模糊参数的响应面法

利用信息熵理论中的概率熵与模糊熵之间的关系式，建立两类不同性质变量之间的转换关系，然后利用这种关系建立一种新型的含有模糊随机变量的响应面法，或根据不确定的信息量，用最大熵法直接建立近似的概率密度函数表达式，算例显示本文方法的可行性和有效性，最后指出，如果结合并行算法，可以从根本上解决响应面法计算效率不高的缺点，使响应面法可用于大型结构的可靠性分析。     

循环对称结构动态响应问题的可靠性分析

以提高复杂循环对称结构动态响应问题的可靠性分析精度为主要目的,运用三参数可靠性模型,对循环对称结构动态响应问题的概率有限元方法的基本理论及计算进行了研究。以结构的材料性能参数、几何参数等为随机变量,导出了求解循环对称结构的动态响应及动应力的数字特征及概率分布的计算表达式。在此基础上计算了在动载荷工作状态下的圆盘和齿轮的可靠度,并与Monte-Carlo法的计算结果进行了对比。结果表明文中的方法更加有效、简捷。     

随机参数智能桁架结构在随机力下的闭环控制动力响应分析

针对随机参数压电智能桁架结构研究了基于概率的结构闭环控制系统动力响应分析模型与方法。利用振型迭加法导出了结构的物理参数、外荷载幅值以及闭环系统控制力同时具有随机性时 ,结构动力响应随机变量的数字特征计算表达式。通过算例考察了智能结构物理参数、外荷载幅值以及控制力的随机性对结构闭环控制系统动力响应的影响 ,并获得了一些有意义的结论     

Reliability analysis using an enhanced response surface moment method

Moment methods, which are powerful and simple techniques for analyzing the reliability of a system, evaluate the statistical moments of a system response function and use information from the probability distribution in the analysis. The full factorial moment method (FFMM) performs reliability analysis by using a 3ⁿ full factorial design of experiments (DOE) and the Pearson system for random variables. To overcome the inefficiency of FFMM, the response surface moment method (RSMM) has been proposed, which is based on a response surface model (RSM) that is updated by adding cross product terms into the simple quadratic model. In this paper, we propose the enhanced RSMM (RSMM+) that modifies the procedure of selecting a cross product term in the RSMM and adds a process of judging whether the response surface model can be established before performing an additional experiment. We apply the proposed method to several examples and show that it gives better results in efficiency.     

基于概率模型检测的机电系统动态可靠性评价

为克服传统动态可靠性分析方法的不足,提出基于概率模型检测的机电系统动态可靠性评价方法。介绍了概率模型检测的概念及概率模型检测工具PRISM。用形式化建模语言描述系统单元的状态变迁过程,建立了机电系统的形式化模型。利用连续随机逻辑对机电系统可靠性评价指标进行形式化描述,建立了可靠性指标的规约表达式,借助概率模型检测工具自动解算可靠性指标,实现了基于概率模型检测的机电系统动态可靠性评价。所提方法建模过程简单,能有效提高机电系统动态可靠性分析的效率。     

Dynamic response analysis of closed-loop control system for random intelligent truss structure under random forces

Considering the randomness of structural damping, physical parameters of structural materials, geometric dimensions of active bars and passive bars, applied loads and control forces simultaneously, the problems of dynamic response analysis of closed-loop control system based on probability for the random intelligent truss structures are studied in this paper. The computational expressions of numerical characteristics of structural dynamic response of closed-loop control system are derived by means of the mode superposition method. Through the engineering examples, the influences of the randomness of them on structural dynamic response are inspected and some significant conclusions are obtained.     

某型飞机翼身连接接头可靠性分析

首先将标准有限元程序与改进的均值法相结合，对某型飞机翼身连接接头处的刚度可靠性进行分析，结果表明在所给载荷和允许应变的情况下，该接头结构在外载变异系数为0．15，弹性模量和剪切模量的变异系数分别为0．05时仍具有较高的可靠度。然后又将标准有限元分析程序与响应面法结合，在假设接头的响应极限状态方程为一不包括交叉项的二次多项式的基础上，利用有限元分析确定响应极限状态方程，通过迭代运算，保证响应极限状态方程在最有可能失效点处与接头结构真实的隐式极限状态方程有很好的近似程度。两种方法的计算结果具有较好的一致性。最后基于弹塑性应变分析，给出大过载情况下低周疲劳寿命可靠性分析结果，得到在给定寿命要求下结构可靠度随疲劳寿命变异系数变化的曲线，并给出在要求可靠度情况下安全寿命随疲劳寿命变异系数的变化曲线，为该型飞机的设计定型提供依据。     

高温构件蠕变损伤的概率计算及概率损伤图

由于材料性质以及操作条件的随机性 ,高温构件的蠕变损伤也同样具有随机性。文中根据概率计算的基本原理和高温构件蠕变损伤确定性解 ,得到蠕变损伤的概率方程。探讨各参数的分布规律 ,利用K S检验方法 ,对高温材料数据进行全面的检验 ,包括高温材料的蠕变系数和指数、损伤系数和指数 ;同时 ,对操作温度以及高温构件的蠕变损伤进行检验 ,认为这些参数分别符合正态或对数正态分布。在全面考虑各参数的随机性和相关性基础上 ,最终获得高温构件的概率蠕变损伤解。为了表达它们之间的关系 ,以期最终达到高温构件寿命预测和可靠性评估的目的 ,考虑两个参数 ,确定性时间t和随机性的炉管损伤值D。将它们之间的关系表述成为t—D—f(D)图 ,形成高温构件的概率损伤图 ,清晰地勾画出不同时间D值的概率分布关系 ,为高温构件的可靠性分析和概率寿命预测提供基础     

并联机构敏感性分析和多目标优化设计方法

为了解决并联机构全局性能指标高计算成本引起的敏感性分析和多目标优化设计困难,提出了一种结合多项式响应面模型、基于方差的敏感性分析方法和智能优化算法的高效计算方法。首先,确定并联机构的目标函数和设计参数,增加节点密度以提高目标函数的计算精度,基于拉丁超立方体抽样方法和最小二乘多项式拟合技术建立全局目标函数与设计参数之间的响应面解析映射模型,并结合基于方差的Sobol’敏感性分析方法得到对目标函数有重要影响的设计参数。然后,结合敏感性分析结果简化设计参数并建立并联机构的多目标优化设计模型,包括目标函数、约束函数和设计参数,结合响应面模型与智能优化算法开展并联机构多目标优化设计。最后,考虑规则工作空间体积、运动学性能和动力学性能指标为目标函数,以DELTA并联机构为例实现了本文提出的方法。优化前后的结果对比证明了算法的有效性。     

PROBABILISTIC METHODOLOGY OF LOW CYCLE FATIGUE ANALYSIS

The cyclic stress-strain responses (CSSR), Neuber's rule (NR) and cyclic strain-life relation(CSLR) are treated as probabilistic curves in local stress and strain method of low cycle fatigue analy-sis. The randomness of loading and the theory of fatigue damage accumulation (TOFDA) are consid-ered. The probabilistic analysis of local stress, local strain and fatigue life are constructed based on thefirst-order Taylor's series expansions. Through this method proposed fatigue reliability analysis can beaccomplished.     

Reliability-based design optimization of slider air bearings

This paper presents a design methodology for determining configurations of slider air bearings considering the randomness of the air-bearing surface (ABS) geometry by using the iSIGHT. A reliability-based design optimization (RBDO) problem is formulated to minimize the variations in the mean values of the flying heights from a target value while satisfying the desired probabilistic constraints keeping the pitch and roll angles within a suitable range. The reliability analysis is employed to estimate how the fabrication tolerances of individual slider parameters affect the final flying attitude tolerances. The proposed approach first solves the deterministic optimization problem. Then, beginning with this solution, the RBDO is continued with the reliability constraints affected by the random variables. Reliability constraints overriding the constraints of the deterministic optimization attempt to drive the design to a reliability solution with minimum increase in the objective. The simulation results of the RBDO are listed in comparison with the values of the initial design and the results of the deterministic optimization, respectively. To show the effectiveness of the proposed approach, the reliability analyses are simply carried out by using the mean value first-order second-moment (MVFO) method. The Monte Carlo simulation of the RBDO’s results is also performed to estimate the efficiency of the proposed approach. Those results are demonstrated to satisfy all the desired probabilistic constraints, where the target reliability level for constraints is defined as 0.8.     

Dynamics in the small for nonlinear oscillation systems in precision theory problems

Specific problems of computational reasoning for the precision of dynamic systems are considered under the assumptions that primary errors take place during the manufacture and assembly of individual system units. The method of logical possibility trees is used to estimate the precision parameters; this method yields the most compact form of probabilistic computations for such problems. An example demonstrating the main points of this method is given.     

压力容器受低周疲劳裂纹萌生寿命的可靠性分析

由于压力容器构件的不确定因素,造成了构件局部应力应变响应和疲劳寿命具有随机性。通过将循环迟滞回线,应变寿命曲线表示为概率曲线,并考虑累积损伤的随机性,反映了构件的不确定性。使用Taylor多项式计算局部应力应变的均值和方差,并求出构件疲劳萌生寿命的均值和方差。计算了一定可靠性下的疲劳萌生寿命,得出在一定使用寿命时,结构的可靠度曲线。算例表明,它在疲劳寿命的可靠性估计中的应用及其工程意义。     

利用响应面方法的汽轮机叶片振动可靠性分析

考虑随机因素的影响,确定汽轮机叶片固有振动静、动频率的统计特性,建立叶片避开共振时的功能函数.以汽轮机扭叶片为研究对象,在考虑几何因素、安装因素、材料因素和转速随机性的同时,将确定性有限元法、响应面方法和Monte-Carlo模拟法相结合对叶片进行振动可靠性分析.在对扭叶片复杂叶型进行有限元参数化建模和试验设计基础上,分别采用多项式响应面法和神经网络响应面法构建了扭叶片静、动频率与随机变量之间的近似关系式,并代替有限元模型,同时结合Monte-Carlo模拟技术得到静频、动频的统计特性和累积分布函数.针对叶片危险振型,在合理确定功能函数的基础上对其进行了振动可靠性分析,并以Latin Hypercube样本Monte-Carlo 模拟法计算结果作为相对精确解,对两种不同响应面法进行了对比.     

随机参数刚架结构的平稳随机位移响应动力可靠性分析

研究物理参数具有随机性的刚架结构的平稳随机位移响应动力可靠性的计算方法。考虑结构的物理参数具有随机性，从结构随机响应的频域表达式出发，利用求解随机变量数字特征的代数综合法和矩法，导出随机参数刚架结构在平稳随机激励下的位移及速度响应均方值的数字特征，再由动力可靠性的Poisson公式导出结构动力可靠度的计算公式。通过算例就各参数的随机性对结构动力可靠度的影响进行分析，验证本文方法的可行性。     

响应面法与遗传算法相结合的注塑工艺优化

应用田口方法进行试验设计,应用计算机辅助工程技术对注塑成形过程进行了分析,建立了注塑成形工艺参数与翘曲度关系的代理模型——响应面模型,对模型进行了验证研究,将响应面法与遗传算法相结合进行了注塑工艺参数优化。结果表明,响应面模型是准确可靠的,将响应面法和遗传算法相结合,可有效提高运算速度和优化效率。     

Robust design of railway vehicle suspension using a process capability index

Robust design for the primary suspension of a railway vehicle was performed according to the optimization of 10 dynamic responses representing driving safety and ride comfort, in which response surface models (RSMs) from the design of experiments (DOEs) were applied. To evaluate the probabilistic feasibility of robustness, an intensive computational process is mandatory. In the present study, the authors utilized the first-order Taylor series expansion to reduce the computational burden associated with a probabilistic feasibility evaluation, thus easily obtaining both an individual mean and variance of constraints. To overcome the difficulty of optimizing the mean and probabilistic variances for the 10 dynamic responses, a process capability index (C_pk) was introduced, which shows the mean value and scattering of the product quality to a certain extent and normalizes the objective functions irrespective of varying dimensions. Consequently, the robust design to optimize the 10 dynamic responses minimized the C_pk subjected to the constraint of C_pk ≥ 2, which satisfied 6σ. The proposed method improved the C_pk that violated the constraints obtained by the RSMs from DOEs and minimized the variance of the C_pk.     

A contribution on the optimization strategies based on moving least squares approximation for sheet metal forming design

Computer-aided procedures to design and optimize forming processes are, nowadays, crucial research topics since industrial interest in costs and times reduction is always increasing. Many researchers have faced this research challenge with various approaches. Response surface methods (RSM) are probably the most known approaches since they proved their effectiveness in the recent years. With a peculiar attention to sheet metal forming process design, RSM should offer the possibility to reduce the number of numerical simulations which in many cases means to reduce design times and complexity. Actually, the number of direct problems (FEM simulations) to be solved in order to reach good function approximations by RSM is a key aspect of their application in sheet metal forming operations design. In this way, the possibility to build response surfaces basing on moving least squares approximations (MLS) by utilizing a moving and zooming region of interest can be considered a very attractive methodology. In this paper, MLS is utilized to solve two optimization problems for sheet metal forming processes. The influence on the optimization results was analyzed basing on MLS peculiarities. The idea is to utilize these peculiarities and make the MLS approximation as flexible as possible in order to reduce the computational effort of an optimization strategy. An innovative optimization method is proposed and the results show it is possible to strongly reduce the computational effort of sheet metal forming processes optimization. In particular, the advantages, in terms of computational effort reduction, with respect to classical RSM approaches have been demonstrated and quantified.     

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.