【作者】 王璐；

【导师】 宋述芳；

【作者基本信息】 西北工业大学 ， 飞行器设计， 2018， 硕士

【摘要】 传统工程结构的优化设计是基于确定性的结构参数和优化模型的,并借助经典优化算法进行优化模型的求解,没有考虑设计变量和其他输入变量的不确定性,因此有可能造成结构设计的失败。而稳健优化设计既能保证优化解满足可靠性约束条件,又能使目标值对扰动不敏感,具有重要的实际工程意义。本文在已有的研究基础上,围绕稳健优化设计及与其密切相关的代理模型、全局灵敏度分析等方面进行了研究,主要的工作和创新点如下:1.在经典的GMDH神经网络算法基础上,通过改进神经元筛选准则及各层神经元的耦合方式,提出了改进的GMDH神经网络算法,它不仅保持了原算法自组织建立最佳网络结构的优点,还能减少所需样本量、提高计算结果的精度。此外,借鉴切割点的思想提出了Cut-GMDH神经网络算法,能够进一步地减少计算GMDH神经网络系数的时间。2.将GMDH神经网络算法与HDMR相结合,提出了GMDH-HDMR方法用于高效高精度地求解基于方差的全局灵敏度指标,并用数值算例和工程算例验证了该方法的精度和效率,扩展了对变量分布形式的适用性。3.提出一种新的基于概率加权矩的全局灵敏度测度,提供了两种求解方法(双循环重复样本数值模拟法和双循环单组样本数值模拟法)的详细步骤,该指标与传统的基于方差的全局灵敏度指标相比需要的样本点更少,对样本中的异常值不敏感,部分情况还能够反映函数系数的正负号对输出响应的影响。4.针对稳健优化设计中的主要问题,包括稳健度量,目标函数的处理及数学模型的建立以及求解策略进行了研究。提出了确定性优化解是否满足稳健要求的判断准则;对于线性加权法将多目标问题转换为单目标问题利用超平面法确定最优权重系数;提出了基于最大熵的新的稳健度量及实施方法;最后给出了稳健优化设计单循环求解策略。5.将全局灵敏度分析方法、代理模型方法与稳健优化设计相结合,提出了基于代理模型的稳健优化设计,首先利用全局灵敏度分析对优化模型的输入变量进行筛选,以有效降低模型的维度;然后利用代理模型显式化目标函数或约束条件的具体表达式;最后利用遗传算法进行稳健优化设计的全局寻优。更多还原

【Abstract】 Traditional optimization design of project structure is based on deterministic structure parameters and optimization model which is solved by classical optimal algorithms.It does not take the uncertainty of design variables and other inputs into consideration,which is likely to lead to the failure of structure design.However,robust optimization design not only ensures the optimal solution can satisfy probability constraints but also makes the objective value insensitive to fluctuation,thus showing very important engineering meaning.Based on the existing researches,robust optimization design,metalmodel and global sensitivity analysis are detailedly investigated in this paper.The main work and innovative points are summarized as follows:1.The modified GMDH neural network algorithm is presented,which is based on the classical GMDH neural network algorithm.The new method improves the selection criteria of neurons as well as the coupling mode of these neurons in each layer.It maintains the advantages of traditional method in constructing the optimal network structure.Meanwhile,it reduces the required samples and increases the precision of model.Besides,inspired by cut-point theory,Cut-GMDH algorithm is proposed.2.HDMR expansion is combined with GMDH-NN algorithm,and proposed GMDHHDMR method can solve the variance-based global sensitivity indices more precisely and efficienctly.In addition,the new method extends the application to variables’ distribution and its precision and efficiency were proved by numerical examples and engineering examples.3.A new global sensitivity measure which is based on probability weighted moments is proposed.Then two numerical methods are introduced to estimate the proposed measure,i.e.,the double-loop-repeated-set numerical estimation and the double-loopsingle-set numerical estimation.The new measure needs quite less sample points and is insensitive to outliers when comparing with traditional variance-based global sensitivity indices.What’s more,it can reflect the influence of function coefficients in some situation.4.The main issues of robust optimization design are studied,containing robustness assessment,objective function handling,mathematical models and solution strategies.Firstly,a criterion which judges the deterministic solution whether satisfies robustness or not is offered.The multi-objective optimization problem is transformed into the single-objective optimization problem by weighted sum method,whose weights are decided by hyperplane method.Maximum entropy,a new robustness assessment,and its application ways are introduced.Finally,the single loop solution strategy of robust optimization is provided.5.Robust optimization design is combined with global sensitivity analysis and metamodel.To begin with,in order to reduce the model dimension,input variables can be selected by global sensitivity indices.Then,metamodelling can give the explicit expression of objective function or constraints.In the end,genetic algorithm can help search the global optimal solution in the robust optimization design.更多还原