Two-Dimensional Coupled Flutter Method Based on Genetic Hybrid Algorithm
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摘要: 对于传统的二维二自由度耦合颤振分步分析解法，创新性地将颤振分析转变为关于求解系统振动频率的非线性方程组问题.基于数值分析理论，引入如拟牛顿法等超线性收敛的数值迭代解法，研究了该类方法在数值迭代时的局部收敛性、初始值依赖性等问题.为规避上述风险发生在颤振分析中，将具有全局搜索优势的遗传算法应用于二维二自由度耦合颤振分析，结合最优算法L-M算法进行局部收敛修正，提出了基于遗传混合算法的分析方法.算例分析结果表明：在各个检测风速节点处，两种方法下的系统振动圆频率和系统牵连阻尼比计算误差都低于0.1‰，结果几乎一致；所建立的新分析方法思路清晰，求得颤振临界风速与传统方法完全一致，说明新的计算流程可行且计算结果准确；与传统方法相比，基于遗传混合算法的颤振方法每步求解过程无需初值的自选取，具有无条件收敛的优点.Abstract: Based on the traditional systematic analysis method of 2d2DOF (two dimensional two degree of freedom), flutter analysis was transformed into a solution to the nonlinear equations of system vibration frequency, innovatively. Several numerical iterative methods for superlinear convergence, such as the quasi-Newton method, were introduced on the basis of numerical analysis theory. Then, the local convergence and initial value dependency of these methods in numerical iteration were studied. To avoid the above-mentioned risks in the flutter analysis, the genetic hybrid algorithm, which has advantages in global searching, was combined with the optimal algorithm "L-M" for local convergence correction, and introduced into the 2d2DOF flutter analysis; a new analysis method was subsequently proposed. The sample numerical analysis showed that in each detected wind node, the calculation errors of the system vibration circle frequency and the system-implicated damping ratio under the two methods were lower than 0.1 per thousand, and the results were almost the same. Thus, the new method is effective, and the corresponding calculation result of the critical wind velocity is consistent with the traditional method; this shows that the new calculation procedure is feasible and the calculation results are accurate. Compared with the traditional method, the proposed method has the advantages of unconditional convergence, wherein initial values do not require artificial selection in each step of the solving process.
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图 2 初值不在局部收敛域中的牛顿迭代法结果
Figure 2. Results of the Newton iteration method with initial value not in the local convergence domain
图 3 初值在局部收敛域中的牛顿迭代法结果
Figure 3. Results of the Newton iteration method with initial value in the local convergence domain
表 1 桥梁断面颤振分析结果对比
Table 1. Comparison results of the bridge flutter analysis
分析方法 颤振风速/(m·s-1) 颤振频率 传统不动点迭代法 74.9 1.288 1 本文遗传混合算法 74.9 1.288 1 
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