A moment-matching robust collaborative optimization method

Robust collaborative optimization (RCO) is a widely used approach to design multidisciplinary system under uncertainty. In most of the existing RCO frameworks, the mean of the state variable is considered as auxiliary design variable and the implicit uncertainty propagation method is employed for estimating their uncertainties (interval or standard deviation), which are then used to calculate uncertainties in the ending performances. However, as repeated calculation of the global sensitivity equations (GSE) is demanded during the optimization process of the existing approaches, it is typically very cumbersome or even impossible to obtain GSE for many practical engineering problems due to the non-smoothness and discontinuity of the black-box-type analysis models. To address this issue, a new RCO method is proposed in this paper, in which the standard deviation of the state variable is introduced as auxiliary design variable in addition to the mean. Accordingly, interdisciplinary compatibility constraint on the standard deviation of state variable is added to enhance the design compatibility between various disciplines. The effectiveness of the proposed method is demonstrated through two mathematical examples. The results generated by the conventional robust all-in-one (RAIO) approach are used as benchmarks for comparison. Our study shows that the optimal solutions produced by the proposed RCO method are highly close to those of RAIO while exhibiting good interdisciplinary compatibility.     

基于FORM的齿轮传动多学科优化设计

通常多学科设计优化是一种确定性设计方法,未考虑不确定性因素的影响。为降低多学科设计优化过程中不确定性因素对系统性能的影响,将一次可靠性方法与协同优化方法相结合,应用到多学科设计优化中。建立基于一次可靠性方法的协同优化的数学模型,并阐述其求解流程,该方法可用于多学科设计优化领域的可靠性设计问题。分别运用协同优化方法和基于一次可靠性方法的协同优化实现了减速器齿轮传动的多学科优化设计,在这两种方法的系统级优化中,引入松弛变量,将一致性等式约束转化为不等式约束,使算法易于收敛。优化结果表明基于一次可靠性方法的协同优化方法求得的最优解使得约束条件满足了可靠性要求,提高了系统的可靠性,具有实际工程意义。     

MULTIDISCIPLINARY ROBUST OPTIMIZATION DESIGN

Because uncertainty factors inevitably exist under multidisciplinary design environment, a hierarchical multidisciplinary robust optimization design based on response surface is proposed. The method constructs optimization model of subsystem level and system level to coordinate the coupling among subsystems, and also the response surface based on the artificial neural network is introduced to provide information for system level optimization tool to maintain the independence of subsystems, i.e. to realize multidisciplinary parallel design. The application case of electrical packaging demonstrates that reasonable robust optimum solution can be yielded and it is a potential and efficient multi-disciplinary robust optimization approach.     

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.     

ROBUST DESIGN OF A TWO DEGREE FREEDOM SYSTEM DUE TO THE PARAMETER UNCERTAINTY

A method based on the robust design optimization is presented to handle the structural uncertainty problems. The variations caused in dynamic performance can be expressed by the mean response and the standard deviation of the performance. The robust optimization approach, based on a multi-objective and non-deterministic method, attempts to both optimize the mean performance and minimize the variance of the performance simultaneously. The best possible design optimization is chosen by a trade-off decision. An example of robust design of a two degree freedom system is used to effectively illustrate the application in dynamics. The mass and stiffness uncertainty in the main system as well as the uncertainty of the mass, stiffness and damping in the absorber are considered all together in order to minimize the displacement response of the main system within a wide band of excitation frequencies. The robust optimization results show a significant improvement in performance compared with the conventional solution recommended from vibration textbooks. It is indicated that robust design methods have great potential for application in structural dynamics to deal with uncertainty problems.     

Robust optimization of the billet for isothermal local loading transitional region of a Ti-alloy rib-web component based on dual-response surface method

Billet optimization can greatly improve the forming quality of the transitional region in the isothermal local loading forming (ILLF) of large-scale Ti-alloy rib-web components. However, the final quality of the transitional region may be deteriorated by uncontrollable factors, such as the manufacturing tolerance of the preforming billet, fluctuation of the stroke length, and friction factor. Thus, a dual-response surface method (RSM)-based robust optimization of the billet was proposed to address the uncontrollable factors in transitional region of the ILLF. Given that the die underfilling and folding defect are two key factors that influence the forming quality of the transitional region, minimizing the mean and standard deviation of the die underfilling rate and avoiding folding defect were defined as the objective function and constraint condition in robust optimization. Then, the cross array design was constructed, a dual-RSM model was established for the mean and standard deviation of the die underfilling rate by considering the size parameters of the billet and uncontrollable factors. Subsequently, an optimum solution was derived to achieve the robust optimization of the billet. A case study on robust optimization was conducted. Good results were attained for improving the die filling and avoiding folding defect, suggesting that the robust optimization of the billet in the transitional region of the ILLF was efficient and reliable.     

基于粒子群优化和协同优化的多学科设计优化研究

协同优化是进行多学科设计优化的有效方法之一。本文将粒子群优化算法应用于协同优化,通过对系统级优化等式约束条件进行转换,克服了协同优化自身内部的计算缺陷,有效解决了当原始系统优化问题不满足Kuhn-Tucker条件时导致的计算困难,最后以数值计算和减速器设计为例进行了验证。结果表明本文提出的方法是有效的,同时也为将新型算法应用于多学科设计优化问题提供了参考。     

基于近似模型的两级集成系统协同优化方法

在两级集成系统协同优化(BLISCO)方法的基础上提出了一种基于近似模型的BLISCO方法,该方法在继承了BLISCO方法优点的同时,具有能够减少设计优化过程中仿真分析和计算次数、平滑设计空间数值噪声、加快收敛速度等优点。通过两个算例,针对子系统存在耦合和不存在耦合两种情况对所提出方法进行了测试,分析结果表明,采用基于近似模型的BLISCO方法可以快速、准确地获得最优解,且综合性能优于原BLICO方法和相关文献所提出的方法。     

基于双响应面模型的碰撞安全性稳健性优化设计

建立稳健的车体耐撞结构是提高汽车碰撞安全性的有效途径.传统的耐撞性优化设计,由于忽视制造工艺、材料特性和边界条件中存在的不确定因素,导致汽车碰撞安全性能不够稳健.近年来,稳健性设计得到广泛的关注,并在汽车工业中得到应用.将稳健性设计方法应用到汽车碰撞安全性设计中,以某轿车的前纵梁为研究对象,运用双响应面方法对其进行稳健性优化设计.采用拉丁超立方抽样(Latin hypercube sampling,LHS)方法和最小二乘方法创建碰撞响应的二阶多项式双响应面模型,将材料特性作为不确定性因素.稳健性优化后,对前纵梁碰撞性能的稳健性与优化前进行对比分析.分析结果表明,该稳健性设计方法精度较高;经稳健性优化后,前纵梁碰撞性能的稳健性获得了显著提高,且质量减少了3.32％.     

协同优化算法的改进

针对协同优化算法是多学科设计优化方法中应用最广、效果最好的MDO算法,但是在应用中存在计算困难的现状,分析了引起协同优化算法计算困难的原因,提出一种改良的协同优化算法——ICO多学科设计优化方法。改进学科一致性约束,增加系统级罚函数,采用快速启动方法,较好地克服了协同优化算法存在计算困难的缺点。标准算例试验结果表明,ICO多学科设计方法能够有效提高算法的稳定性、可靠性和计算效率。     

一种通用的机械大系统优化设计的协调模型

针对机械大系统设计的特点 ,并结合新兴的多学科设计优化技术 ,本文给出了一种协调优化模型 ,用 Kuhn-Tucker定理证明其能够保证求得原型问题的解 ,所附的算例也证明了该模型的正确性     

基于ISIGHT的曲柄连杆机构多学科优化

多学科优化方法(MDO)可以弥补传统优化的不足,有效解决复杂优化问题,提高工程项目的设计和优化效率.针对柴油机曲柄连杆机构多学科部件优化问题,综合考虑曲轴和连杆两部件,采用协同优化方法,建立了相应的多学科优化数学模型,并基于ISIGHT软件构建多学科优化平台,进行了曲柄连杆机构多学科综合优化计算.研究结果表明,采用多学...     

A Study for robustness of objective function and constraints in robust design optimization

Since randomness and uncertainties of design parameters are inherent, the robust design has gained an ever increasing importance in mechanical engineering. The robustness is assessed by the measure of performance variability around mean value, which is called as standard deviation. Hence, constraints in robust optimization problem can be approached as probability constraints in reliability based optimization. Then, the FOSM (first order second moment) method or the AFOSM (advanced first order second moment) method can be used to calculate the mean values and the standard deviations of functions describing constraints and object. Among two methods, AFOSM method has some advantage over FOSM method in evaluation of probability. Nevertheless, it is difficult to obtain the mean value and the standard deviation of objective function using AFOSM method, because it requires that the mean value of function is always positive. This paper presented a special technique to overcome this weakness of AFOSM method. The mean value and the standard deviation of objective function by the proposed method are reliable as shown in examples compared with results by FOSM method.     

一种新的多学科系统不确定性分析方法——协同不确定性分析法

多学科设计优化中的不确定性对整个工程系统的设计过程具有非常重要的影响。对现存的不确定性定义进行比较和分类。详细描述多学科系统中的不确定性及其传播过程。在已有不确定性分析方法的基础上,提出一种新的多学科不确定性分析方法——协同不确定性分析法。该方法的基本思想是利用泰勒近似估算耦合变量和系统输出的方差,经过二次优化获得系统的稳健最优解,并对其具体计算过程进行详细描述。算例结果表明,协同不确定性分析法不仅是可行的,而且具有很高的精度,是分析多学科系统中不确定性的有效方法。     

Multidisciplinary design optimization of vehicle instrument panel based on multi-objective genetic algorithm

Typical multidisciplinary design optimization(MDO) has gradually been proposed to balance performances of lightweight, noise, vibration and harshness(NVH) and safety for instrument panel(IP) structure in the automotive development. Nevertheless, plastic constitutive relation of Polypropylene(PP) under different strain rates, has not been taken into consideration in current reliability-based and collaborative IP MDO design. In this paper, based on tensile test under different strain rates, the constitutive relation of Polypropylene material is studied. Impact simulation tests for head and knee bolster are carried out to meet the regulation of FMVSS 201 and FMVSS 208, respectively. NVH analysis is performed to obtain mainly the natural frequencies and corresponding mode shapes, while the crashworthiness analysis is employed to examine the crash behavior of IP structure. With the consideration of lightweight, NVH, head and knee bolster impact performance, design of experiment(DOE), response surface model(RSM), and collaborative optimization(CO) are applied to realize the determined and reliability-based optimizations, respectively. Furthermore, based on multi-objective genetic algorithm(MOGA), the optimal Pareto sets are completed to solve the multi-objective optimization(MOO) problem. The proposed research ensures the smoothness of Pareto set, enhances the ability of engineers to make a comprehensive decision about multi-objectives and choose the optimal design, and improves the quality and efficiency of MDO.     

A response surface based hierarchical approach to multidisciplinary robust optimization design

A multidisciplinary robust optimization design framework, concurrent subsystem robust design optimization, is proposed to obtain robust optimum solution in the large-scaled and coupled system. In this framework, response surfaces in the form of artificial neural networks provide information pertaining to system performance characteristics, and individual subsystems engage in performing robust optimization design in parallel while communicating with the system level. This optimization approach incorporates uncertainty analysis and generates a global robust optimum solution in an iterative fashion. Two applications are considered, and the results demonstrate that the approach yields a reasonable robust optimum solution, and it is a potential and efficient multidisciplinary robust optimization approach .     

Multidisciplinary design optimization of a structurally nonlinear aircraft wing via parametric modeling

In this study, the optimization of an aircraft wing design was conducted using multidisciplinary design optimization (MDO), which integrates aerodynamic and structural analysis in considering nonlinear structural behavior. Automation is an absolute necessity to make the MDO framework practical for actual engineering optimization problems. The objective of this research was to develop a fully automated MDO framework in which the entire process is automated through a parametric-modeling approach. The computational fluid dynamics (CFD) grid was generated automatically from parametric modeling using CATIA and Gridgen, followed by automatic flow analysis using FLUENT. The computational structure mechanics (CSM) grid was generated automatically by the parametric methods of CATIA and MSC/Patran. The structure was analyzed by ABAQUS considering the deformation nonlinearity, and the aerodynamic load was transferred from the CFD grid to the CSM grid using the volume spline method. The response surface method was applied for optimization, which helped achieve the global optimum. The developed MDO framework was applied to a wing optimization problem in which the objective was wing weight and the constraints were the lift-drag ratio, wing deflection, and structural stress level. The aspect ratio, taper ratio, quarter-chord sweep angle, skin thickness, and spar flange area were the design variables. The optimization design result demonstrated a successful application of the fully automatic MDO framework.     

用遗传算法提高协同优化方法的可靠性

分析了协同优化方法可靠性不好的根源。提出了用遗传算法来替代系统级优化问题中的基于梯度的优化算法的策略。实例表明所提出的策略是可行有效的。     

稳健优化的表述、不确定分析与求解策略

首先通过对优化问题的表述,说明稳健优化与传统确定性优化的区别。稳健优化需进行不确定性分析,为此对目标的均值和方差同时进行优化。然后分析和比较了蒙特卡罗法、基于敏感度法、解析法、基于代理模型法等不确定性分析方法的特点,其中着重介绍了基于代理模型的不确定性分析方法。最后讨论了2类求解稳健优化问题的策略：加权法和多目标遗传算法。     

断开式转向梯形机构的稳健优化设计模型

为解决传统优化设计方法中存在的最优解的函数值波动过大且容易违反约束的问题,将稳健设计运用于汽车断开式转向梯形机构的优化设计中.首先分别分析了稳健设计和转向机构的数学模型;其次在目标函数与约束中同时考虑运动副间隙的影响,建立了稳健优化设计模型.实例分析表明,与传统的优化方法相比较,该模型不仅可以得到较小的误差还具有较高的...