摘要
稳健优化设计作为一种提高产品质量降低产品成本的有效方法,已逐渐引起国内外学者的重视。存在于实际工程问题中的不确定因素影响了产品质量的稳定性,从而影响了产品的竞争力。尤其是在一些复杂装备中,如风电设备、盾构、飞机,如果由于不确定因素估计不足而导致质量稳定性较差,则不仅仅会发生经济损失,甚至可能引发一系列的社会问题。因此,在设计阶段就必须考虑工程问题中的不确定因素,使得在不增加成本的前提下能够有效提高产品质量稳定性。当现有稳健优化设计理论与方法应用于工程问题时,出现了理论适用性小、计算复杂性高的问题。针对上述问题,在国内外稳健设计研究的基础上,本文对稳健优化设计理论和方法做了进一步的研究和探讨,主要内容如下：
1)针对不确定因素数据信息不完整的工程问题,提出了基于区间分析的非概率稳健优化设计方法。该方法秉承了非概率稳健设计的思想,给出了具有区间型参数的稳健优化模型,并从数学规划层面将该模型转换为能实现稳健性的确定性形式。该方法不需要考虑设计变量以及设计参数的分布类型,也不要求函数连续、可导等,对工程优化问题的数学模型要求不高,适用面广；更易于工程设计人员表达对目标稳健性和约束稳健性的偏好信息。
2)针对同时存在随机型不确定变量和区间型不确定变量的工程问题,建立了能够实现目标稳健性和约束稳健性的概率-非概率混合稳健优化数学模型。该模型分析了混合变量下性能函数的稳健性问题,并给出含有混合变量的稳健模型建立准则,为合理精确描述混合不确定变量提供了一种有效的方案。
3)针对非线性程度较高而没有显式数学模型的工程问题,提出了基于子空间多项式响应面的稳健优化设计方法。该方法综合考虑了拟合精度和计算效率,通过合理划分设计变量空间,在局部子空间内能够以较小样本点实现较高的拟合精度,即利用了多项式响应面函数构造简单的优点,又解决了传统多项式响应面对高阶非线性问题拟合精度不够的缺点,节省了稳健设计在非线性较高工程问题应用中的计算成本。
4)风电增速箱特殊的工作环境和对可靠性极高的要求,使得不确定因素对风电增速箱各性能指标的影响不容忽视。基于前述设计理论与方法,对风电增速箱进行了稳健优化设计。通过定量分析不确定因素对风电增速箱可靠性等性能的影响,确保了风电增速箱的优化设计方案能够满足性能稳健性的要求。
Robust design optimization method, as an effective way to improve product quality and reduce cost, has been paid more attention. The uncertainties existed in practical engineering problem affect the quality stability, so does the product competency. Especially in the complex equipment system, such as wind power system, tunnel shield or plane, if the uncertainties are not considered, then not only economic loss occurs and may even trigger a series of social problems. Therefore, the uncertainties have to be considered in the design stage. However, Existing robust design optimization methods have some limitations, such as small application field and high computational costs. Based on the existent work in literatures the dissertation further develops the robust design theory. The main content of this paper include the following aspects:
1) For the problem without sufficient data information on the uncertainties, a novel robust design optimization method using interval analysis is suggested. The original formulation is replaced with the deterministic form at the level of mathematical programming, carried the principle of non-probabilistic method. The method has the advantages that it has less requirements on uncertainty and mathematical, and it is capable of expressing the preference information of the decision maker, resulting in wide suitability.
2) For the problem involved with both random and interval uncertain variables, a hybrid probabilistic and non-probabilistic model is suggested for the objective robustness and constraint robustness. The performance robustness is analyzed under mix-uncertainties, and the criterion to build robust model is given. The model provides a new choice for describing the uncertainties accuratedly.
3) For the practical engineer robust design problem without explicit mathematical model, a novel robust design optimization method using subspace response surfacing method is suggested. This method is proposed by the rational division of the original response surface approximation space, with the consideration of precision and efficiency. The computational cost is saved due to less sample points for the same fitting precision.
4) Aiming at both special working environments and highly reliability requirements of gearbox for wind turbine, the robust design optimization method of gearbox is researched systematically considering the uncertainties based on the proposed robust design theory and methods, in which the transmission system with mathematical model and the supporting system without engineering model are conducted. The robust solution obtained by proposed method ensures optimal design scheme to meet the requirements of various constraints and decreases the sensitivity of the objective to uncertainties, through quantitative analysis of the uncertainty effect to the performance of gearbox.
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