考虑材料参数不确定性结构动力学稳健性拓扑优化设计

本文在考虑材料参数不确定性的条件下,对连续体结构动力学稳健性拓扑优化设计进行研究.在使结构的第一阶固有频率最大化的同时,显著减小其对材料性能不确定性的影响.基于非概率凸集模型,将材料参数的不确定性用有界区间变量表示;建立了能够抑制频率改变的结构动力学拓扑优化模型,用单层优化策略求解稳健性优化设计问题.通过对材料参数的导数分析,获得了在材料性能不确定情形下结构第一阶固有频率的二阶泰勒展开式,并推导出了频率对拓扑变量的一阶灵敏度显性表达式.基于变密度法,开展了结构动力学稳健性拓扑优化设计,并与确定性优化结果进行对比,验证了用本文方法获得的结构第一阶固有频率稳健性更高,受材料参数不确定性扰动影响更小,展示了考虑材料参数不确定性的重要性.     

Integrated multi-objective robust optimization and sensitivity analysis with irreducible and reducible interval uncertainty

Uncertainty considered in robust optimization is usually treated as irreducible since it is not reduced during an optimization procedure. In contrast, uncertainty considered in sensitivity analysis is treated as partially or fully reducible in order to quantify the effect of input uncertainty on the outputs of the system. Considering this, and the usual existence of both reducible and irreducible uncertainty, an approach that can perform robust optimization and sensitivity analysis simultaneously is of much interest. This article presents such an integrated optimization model that can be used for both robust optimization and sensitivity analysis for problems that have irreducible and reducible interval uncertainty, multiple objective functions and mixed continuous-discrete design variables. The proposed model is demonstrated by two engineering examples with differing complexity to demonstrate its applicability.     

Robust design with imprecise random variables and its application in hydrokinetic turbine optimization

In robust design, uncertainty is commonly modelled with precise probability distributions. In reality, the distribution types and distribution parameters may not always be available owing to limited data. This research develops a robust design methodology to accommodate the mixture of both precise and imprecise random variables. By incorporating the Taguchi quality loss function and the minimax regret criterion, the methodology mitigates the effects of not only uncertain parameters but also uncertainties in the models of the uncertain parameters. Hydrokinetic turbine systems are a relatively new alternative energy technology, and both precise and imprecise random variables exist in the design of such systems. The developed methodology is applied to the robust design optimization of a hydrokinetic turbine system. The results demonstrate the effectiveness of the proposed methodology.     

Adaptive gradient-assisted robust design optimization under interval uncertainty

Robust optimization techniques attempt to find a solution that is both optimum and relatively insensitive to input uncertainty. In general, these techniques are computationally more expensive than their deterministic counterparts. In this article two new robust optimization methods are presented. The first method is called gradient-assisted robust optimization (GARO). In GARO, a robust optimization problem is first converted to a deterministic one by using a gradient-based approximation technique. After solving this deterministic problem, the solution robustness and the accuracy of the approximation are checked. If the accuracy meets a threshold, a robust optimum solution is found; otherwise, the approximation is adaptively modified until the threshold is met and a solution, if it exists, is obtained. The second method is a faster version of GARO called quasi-concave gradient-assisted robust optimization (QC-GARO). QC-GARO is for problems with quasi-concave objective and constraint functions. The difference between GARO and QC-GARO is in the way that they check the approximation accuracy. Both GARO and QC-GARO methods are applied to a set of six engineering design test problems and the results are compared with a few related previous methods. It was found that, compared to the methods considered, GARO could solve all test problems but with a higher computational effort compared to QC-GARO. However, QC-GARO was computationally much faster when it was able to solve the problems.     

一种考虑概率分布的鲁棒优化模型

文章以随机规划中的机会约束思想为指导,根据随机参数的概率分布情况,提出了两种鲁棒性条件约束,并在此基础上建立了一种新的鲁棒优化模型,使模型的可行解控制在一定的鲁棒性指标的范围内。该模型不但可处理约束两端同时含有随机参数的情况,还可以方便地推广到非线性模型中。仿真实例说明了模型的有效性。     

输入力矩受限情况下漂浮基空间机械臂的鲁棒自适应混合控制

讨论了在空间机械臂关节控制输入力矩幅值受限且系统存在不确定参数的复杂情况下,载体位置与姿态均不受控的漂浮基空间机械臂系统的智能控制问题。结合系统动量守恒关系进行系统运动学、动力学分析,并借助增广变量法,将获得的系统动力学方程表示为一组适当选择的(组合)惯性参数的线性函数。以此为基础,针对关节控制输入力矩受限且空间机械臂末端爪手所持载荷的参数不确定的情况,设计了一种鲁棒自适应混合控制方法。所提出的控制方法通过运用连续可导递增函数,有效地限制了关节控制输入力矩的幅值;且通过对不确定的系统参数进行鲁棒自适应调节,有效地克服了不确定性对控制精度的影响;更重要的是,无论不确定参数的估计值是否超出给定的误差范围,提出的控制方法都能保证系统的稳定,体现了控制系统的强鲁棒性。仿真运算结果证实了该方法的有效性。     

价格不确定供应链的多目标运作鲁棒模型

建立了由一个制造商和一个供应商构成的多产品、多阶段供应链在原材料和最终产品的市场价格均不确定情况下运作的鲁棒模型.采用区间不确定性描述价格的不确定性.供应链的运作模型为一个多目标规划问题,满足诸如供应链协调运作、所有供应链成员的目标利润尽可能最大、对应于不确定供求价格的决策的鲁棒性等多个相互冲突的目标.数值算例的结果表明,一定范围内的市场价格波动不改变供应链的运作策略,仅对其运作性能产生一定影响,即所提出的模型是鲁棒的.     

DESIGN OPTIMIZATION FOR ROBUSTNESS USING QUADRATURE FACTORIAL MODELS

Abstract

This paper describes a robust optimization methodology for designs involving either complex simulations or actual experiments. The methodology adopts a new objective function that consists of the Expected Performance (EP) and the weighted Deviation Index (DI). The proposed Quadrature Factorial Model estimates the expected performance and the standard deviation of a design. This scheme greatly reduces the number of experiments and provides superior results for systems with significant interaction effects and nonlinear variations. The proposed methodology is applied to the design of helical gears with minimum transmission error. The robust optimum shows a significant reduction of the expected transmission error compared with previous studies, while maintaining the insensitivity to manufacturing errors and load variation.     

Robust optimization of structures subjected to stochastic earthquake with limited information on system parameter uncertainty

The optimization of structures subjected to stochastic earthquake and characterized by uncertain parameters is usually posed in the form of non-linear programming with stochastic performance measures where the uncertain parameters are modelled as random variables. Such an approach, however, cannot be adopted in many real life situations when the limited information about uncertainty can be only modelled as of the uncertain but bounded (UBB) type. A robust optimization strategy for stochastic dynamic systems characterized by UBB parameters is proposed in the present study in the framework of the response surface method (RSM). In evaluating the stochastic constraints, repeated computations of the dynamic responses are avoided by applying an adaptive RSM based on the moving least squares method. Numerical results are presented to highlight the effectiveness of the proposed procedure. The effect of parameter uncertainty is also studied by comparing the results obtained from the proposed optimization approach with the conventional stochastic optimization results.     

柔性结构系统不确定性的μ分析

提出了一种柔性结构系统不确定性的结构奇异值（μ）分析方法,分析了结构系统的高频未建模动态,将其作为名义模型的加型因子或加乘性因子不确定性,并从模态空间的参数摄动出发,推导了系统的参数不确定模型。采用结构奇异值（μ）分析方法对结构系统及其控制器进行鲁棒稳定性和鲁棒性能分析。给出的算例表明,本文的柔性结构不确定性模型的构造方法及控制系统的μ分析方法是有效的。     

基于鲁棒模型参考控制器的智能结构振动主动控制研究

针对压电智能结构建模的不确定性和干扰,设计一种新的鲁棒模型参考控制律来抑制其振动,该控制器包括状态反馈控制器和用来补偿不确定影响的鲁棒补偿器。通过Ｌｙａｐｕｎｏｖ方法确定补偿项并证明该闭环系统的稳定性。分别在单模态和多模态下,分析三种不同补偿函数对系统的影响,指出运用ｔａｎｈ或ｅｒｆ函数可有效避免ｓｇｎ函数补偿出现的抖振现象。仿真和实验结果表明该方法具有很好的控制效果和鲁棒性。