自适应粒子群优化算法在混沌系统参数估计中的应用

A Modified Particle Swarm Optimizer for Parameter Estimation of Chaotic System

惯性权重w的变化会影响粒子群优化算法的搜索能力,本文针对基本粒子群算法不能适应复杂的非线性优化搜索过程的问题,在其基础上提出了一种动态改变惯性权的自适应粒子群算法。该自适应算法引入了h来衡量算法的进化速度,引入s来衡量算法的粒子聚集度,并将其作为函数w的变量,使w与算法的运行状态相关,从而使算法具有动态自适应性。最后,本文引入了两个经典的测试函数对该PSO算法进行测试,结果表明该算法明显优于基本PSO算法。

This paper first constructs an appropriate fitness function and transforms the problem of parameter estimation for a chaotic system to that of parameter optimization. Then, on the premise of ensuring the global search capability of particle swarm optimization algorithm （PSO）, we adopt a kind of improved particle swarm algorithm which can dynamically change the inertia weight and test this PSO algorithm by using the test function. The test result illustrates that this improved algorithm is obviously superior to the basic PSO algorithm. Finally, we introduce the improved PSO algorithm into parameter estimation for a chaotic system and make a numerical simulation by taking the representative Lorenz chaotic system as example. The actual result indicates that this kind of improved algorithm can effectively estimate the parameter for a chaotic system and has a good adaptability and high convergence. Even under the condition of signal superposition noise, it still has robustness.