基于遗传算法的改进谐波平衡算法

针对标准谐波平衡算法存在迭代收敛慢,计算量大的问题,采用遗传算法所具有的隐含并行性、全局解空间搜索特性,以及其优化过程不受限制性条件约束的优点,提出了引入遗传算法加速其收敛过程的改进谐波平衡算法。通过将遗传算法的随机自适应优化过程与标准谐波平衡算法的迭代运算过程相结合,简化了标准谐波平衡算法迭代计算的过程,提高标准谐波平衡算法的收敛速度和计算精度。并采用该算法对Duffing-VanDerPol方程的进行了求解,得到了该方程的近似解析解,通过与Runge-Kutta法所得数值解相比较,两者的一致性较好,表明了该算法的有效性。

Improved harmonic-balance algorithms based on the genetic algorithms

As the slow of iterative convergence and large amount of calculation quantity in general harmonic balance algorithm （GHBA）, an improved harmonic-balance algorithm which is based on the genetic algorithms’ implicit parallelism, overall superior solution and problem model independence for speeding up the convergence of iteration procedure is proposed. This method combines genetic algorithms’ stochastic self-adaptive optimization process and GHBA’s iterative process, it makes GHBA’s iterative calculation process is simplified and GHBA’s iterative convergence speed and calculation precision are improved. By using Duffing-Van Der Pol equations as example, approximate analytic solutions is obtained with this algorithm, acquired the better consistent with numerical value solution by using Runge-Kutta methods, which indicates that this algorithm is valid.