Robust Collaborative Optimization Method Based on Dual-response Surface

A novel method for robust collaborative design of complex products based on dual-response surface (DRS-RCO) is proposed to solve multidisciplinary design optimization (MDO) problems under uncertainty. Collaborative optimization (CO) which decomposes the whole system into a double-level nonlinear optimization problem is widely Accepted as an efficient method to solve MDO problems. In order to improve the quality of complex product in design process, robust collaborative optimization (RCO) is developed to solve those problems under uncertain conditions. RCO does opfmiTation on the linear sum of mean and standard deviation of objective function and gets an optimal solution with high robustnmess. Response surfaces method is an important way to do approximation in robust design. DRS-RCO is an improved RCO method in which dual-response surface replaces system uncertainty analysis module of CO. The dual-response surface is the approximate model of mean and standard deviation of objective function respectively. In DRS-RCO, All the information of subsystems is included in dual-response surfaces. As an additional item, the standard deviation of objective function is added to the subsystem optimization. This item guarantee both the mean and standard deviation of this subsystem is reaching the minima at the same time. Finally, a test problem with two coupled subsystems is conducted to verify the feasibility and effectiveness of DRS-RCO.     

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。     

Design optimization using support vector regression

Polynomial regression (PR) and kriging are standard meta-model techniques used for approximate optimization (AO). Support vector regression (SVR) is a new meta-model technique with higher accuracy and a lower standard deviation than existing techniques. In this paper, we propose a sequential approximate optimization (SAO) method using SVR. Inherited latin hypercube design (ILHD) is used as the design of experiment (DOE), and the trust region algorithm is used as the model management technique, both adopted to increase efficiency in problem solving. We demonstrate the superior accuracy and efficiency of the proposed method by solving three mathematical problems and two engineering design problems. We also compare the proposed method with other meta-models such as kriging, radial basis function (RBF), and polynomial regression.     

Standard uncertainty evaluation of multivariate polynomial

The uncertainty propagation law helps to infer the uncertainty of unobservable variables from known or assumed relationship with observable variable. Currently only analytical linear approximation or Monte Carlo simulation methods is widely adopted. The former method is limited to weakly nonlinear systems while the latter does not provide any analytical expression that links the uncertainties of input to uncertainties of output quantities. This paper proposes procedures to evaluate the standard uncertainty of multivariate polynomial using basic algebraic manipulation and tabulated Mellin transform. Case studies are presented whereby the effectiveness and practicality of the proposed method is demonstrated. The proposed method can be readily automated using computer algebra systems, thus negating the need for practitioners to perform the actual complex computation. The work theoretically enriches and extends the validity of the analytic approach in the existing uncertainty evaluation framework, thus enabling the analytic evaluation of uncertainty for many nonlinear cases which was previously an impossible task.     

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.     

稳健优化设计中代理模型不确定性的研究

代理模型的应用解决了稳健设计中计算量大的难题,但由于代理模型与真实模型间存在误差(代理模型的不确定性),而传统的稳健设计忽视了这种不确定性,必然会带来一定的设计误差。因此,针对稳健设计提出了一种基于蒙特卡洛抽样的代理模型不确定性的量化方法,在传统仅考虑参数不确定性的基础上,额外计入代理模型的不确定性对设计的影响。将提出的方法应用于一个数学算例和一个火箭弹卷弧翼气动稳健优化设计,所得优化结果较传统的未考虑代理模型不确定的稳健设计更为精确、合理,证实了提出方法的有效性。     

Design of a vibrating MEMS gyroscope considering design variable uncertainties

Recently, several micro electro-mechanical systems (MEMS) such as a MEMS gyroscope have been developed by using micro manufacturing technologies. Micro scale products, however, usually have a relatively large manufacturing uncertainty compared to normal macro scale products. It is quite expensive to lower the variance of material properties as well as the geometric properties of a micro scale product. The material and geometric uncertainties caused by a micro manufacturing process inevitably lead to the uncertainty of the product performance. Therefore, to achieve a reliable design of a product, the performance uncertainty of the product, which is often expressed by the variance or the standard deviation, needs to be estimated in a reliable way. In this paper, the equations of motion of a MEMS gyroscope model are derived to analyze the system performance indices (sensitivity and bandwidth). The mean values of the design variables are determined from the requirements of product size, maximum vibration amplitude, and driving frequency. Then the standard deviation of some critical design variables is determined from the performance requirements. Finally, a statistical analysis procedure based on sample statistics is proposed to estimate the confidence interval of the performance index statistics.     

具有状态约束的电液伺服系统模型参考鲁棒自适应控制

针对电液伺服系统中的模型不确定性和状态约束问题,设计了一种模型参考鲁棒自适应控制(MRRAC)方法。将电液伺服系统的近似模型作为模型预测控制(MPC)的设计对象,在设计过程中考虑状态约束,并生成受约束的状态期望,作为后续伺服控制方法的参考指令。为了克服液压系统中的模型不确定性,基于反步法设计了鲁棒自适应控制器(RAC),实现了兼顾模型不确定性和状态约束的伺服控制。基于Lyapunov稳定性理论证明了所设计控制策略的闭环渐近稳定性,且系统所有信号均有界。仿真结果表明,控制器对于系统模型不确定性具有较强的鲁棒性,且可实现对指定状态的有效约束,充分验证了该控制策略的有效性。     

基于灵敏度的电磁结构形状优化方法研究

研究基于灵敏度的电磁结构形状优化设计方法。针对以往用磁位作为状态变量不方便的情况，文中直接采用磁通密度为状态变量。在用直接法求解矢量磁位灵敏度方程的基础上，给出适合形状优化的磁通密度灵敏度分析的两种方法——半解析法和局部差分法。前者在磁通密度灵敏度计算中对形函数导数采用了差分近似，后者用一阶近似方法得到设计变量扰动后的矢量磁位和磁通密度，然后用差分法计算磁通密度灵敏度。两种方法简单且计算效率高，精度能够满足要求。优化问题求解采用序列线性规划算法。应用本文方法对电磁铁和同步电机磁极进行形状优化，取得了满意的结果。     

基于近似模型的铣削工艺参数可靠性设计优化

针对现有铣削工艺参数优化方法未考虑设计参数不确定性,导致优化结果难以满足实际产品性能要求的问题,引入近似模型对铣削工艺参数进行可靠性设计优化。以铣削加工表面粗糙度为目标函数,以最大铣削力小于给定值的可靠度作为约束,综合考虑铣削加工过程中铣削速度和每齿进给量的变动,建立了铣削工艺参数可靠性优化模型,并分别采用Kriging近似和径向基函数近似对铣削表面粗糙度、铣削力与设计变量之间的隐式关系进行近似替代,最后采用Monte Carlo仿真-序列近似规划对模型进行了寻优求解,通过试验对可靠性优化的结果进行了验证。结果表明,该方法可有效地降低铣削加工表面粗糙度,并且可保证加工过程中最大铣削力的可靠度要求。     

Uncertainty evaluation for determining linezolid in injectable solution by UV spectrophotometry

The aim of this work was to identify the main sources of uncertainty, quantify the standard deviation of each source of uncertainty, and calculated combined and expended uncertainties for the determination of linezolid in injectable dosage forms by UV spectrophotometry. The contributions of precision, linearity and weight of linezolid reference standard are the most significant, contributing with about 77% of the overall uncertainty. The uncertainties on the absorbances (sample and standard), volumetric flasks and volumetric pipettes have virtually no influence on the overall uncertainty. The estimated uncertainty of the spectrophotometric method for determination of linezolid was adequate for the scope of the method.     

不确定信息条件下Job-shop调度的混合智能算法

目前大多数生产调度的研究往往聚焦于经典调度问题的优化算法而忽略了车间中大量存在的不确定性，因而难以应用于实际车间调度。采用随机变量来描述真实车间中存在的一些不确定信息，在基于不确定规划理论的基础上建立了相应的不确定性调度模型，并研究了解决此类问题的混合智能算法。开发了混合智能优化原型系统，并结合仿真工具对该调度模型和混合智能算法进行了验证。     

[学科发展]随机不确定性下的可靠性设计优化研究进展

Reliability-based design optimizationhas gained much attention due to the ability of considering the various uncertainty informations. Since reliability-based design optimization played a significant role in the improvement of product reliability and other performances in the full life cycle, it is one of the most popular research topics in the field of engineering design. The state-of-the-art achievements and contributions in the field of the reliability-based design optimization as well as the time-dependent reliability-based design optimization under aleatory uncertainties were reviewed from the perspectives of analytical strategies and surrogate models. Moreover, the existing problems and challenges were discussed, and some research directions in future were concluded.     

随机与区间不确定下基于近似灵敏度的序列

为解决复杂系统多学科可靠性设计优化过程中由于存在多源不确定性和多层嵌套而导致的计算效率低的问题,将近似灵敏度技术与两级集成系统综合策略(Bi-level integrated system synthesis,BLISS)和功能测度法集成,提出一种能同时处理随机和区间不确定性的序列化多学科可靠性设计优化方法。基于概率论和凸模型对混合不确定性进行量化,提出一种随机和区间不确定性下的混合可靠性评价指标,并基于功能测度法建立多学科可靠性设计优化模型。采用近似灵敏度信息替代实际灵敏度值,将近似灵敏度技术同时嵌入多级多学科设计优化策略和多学科可靠性分析方法中,避免每轮循环都进行全局灵敏度信息的分析与迭代,提高了计算效率。基于序列化思想同时将四层嵌套的多学科可靠性设计优化循环和三层嵌套的多学科可靠性分析过程进行解耦,形成一个单循环顺序执行的多学科可靠性设计优化过程,避免了每轮循环对整个可靠性分析模型进行迭代分析的过程,减少灵敏度分析和多学科分析次数。以汽车侧撞工程设计为例,验证了该法具有同时处理随机和区间不确定性的能力,并且计算效率较传统方法分别提高了10.98%和23.63%,表明该法具有一定工程实用价值。     

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.     

基于AHP-NSGA-Ⅲ的车辆悬架预瞄最优控制研究

针对车辆主动悬架线性二次最优控制存在的权值系数确定问题,提出了一种结合主客观性能评价的权值系数选择方法---层次分析-三代遗传算法。利用层次分析法确定变量范围,以6个主动控制悬架性能指标为目标函数,利用三代遗传算法进行多目标优化并以控制力作为限制条件筛选出最优解。以半车模型为例,结合前轮预瞄信息与卡尔曼估计器估计的状态变量,设计预瞄最优控制器,并采用虚拟激励法直接在频域范围内进行求解。仿真结果表明,所提出的控制策略可改善车辆的乘坐舒适性。     

Improved design of constrained model predictive tracking control for batch processes against unknown uncertainties

In this paper, an improved constrained tracking control design is proposed for batch processes under uncertainties. A new process model that facilitates process state and tracking error augmentation with further additional tuning is first proposed. Then a subsequent controller design is formulated using robust stable constrained MPC optimization. Unlike conventional robust model predictive control (MPC), the proposed method enables the controller design to bear more degrees of tuning so that improved tracking control can be acquired, which is very important since uncertainties exist inevitably in practice and cause model/plant mismatches. An injection molding process is introduced to illustrate the effectiveness of the proposed MPC approach in comparison with conventional robust MPC.     

A fuzzy rule for job dispatching in a wafer fabrication factory—a simulation study

Job scheduling in wafer fabrication factories is subject to many sources of uncertainty or randomness. To consider the uncertainty and improve the scheduling performance in a wafer fabrication factory, this paper proposes an innovative fuzzy rule that solves the problem of slack overlapping in a non-subjective way. The fuzzy rule considers the uncertainty in the remaining cycle time and is aimed at the simultaneous optimization of the average cycle time and cycle time standard deviation. Few existing publications discuss this issue. A systematic procedure has also been established to optimize the value of the adjustable parameter in the fuzzy rule. On the other hand, a novel fuzzy back propagation network approach is also proposed in this paper to estimate the remaining cycle time accurately. The performance of the proposed methodology is evaluated with a series of production simulation experiments.     

Uncertainty analysis of deep drawing using surrogate model based probabilistic method

Deep drawing is an important manufacturing process in industry. In order to obtain high-quality products produced by deep drawing, the set of design variables used in forming operation is designed through deterministic optimization. However, in real forming process, the design variables show variability and randomness which will affect the product quality. These uncertainties are an inherent characteristic of nature and cannot be avoided. This paper focuses on uncertainty analysis of deep drawing with the consideration of uncertainties in material parameters and friction. An uncertainty analysis approach which combines the finite element method (FEM) simulation, surrogate modeling, and Monte Carlo simulation (MCS) is presented in this work. The constructed surrogate models are validated and compared by cross validation and error measures. Then Monte Carlos Simulation is conducted by the use of the constructed surrogate model. The surrogate model based probabilistic method used in this paper is an approach with high-efficiency and sufficient accuracy for uncertainty analysis in deep drawing.