基于幅谱分割的粒子群最优模态分解研究与应用

Optimization modal analysis with PSO based on spectrum segmentation

提出了一种利用粒子群最优化技术的模态分解方法。其中多个模态的参数组成粒子属性集,粒子按照粒子群算法不断迭代获得全局最佳粒子。引入模态聚类的思路来估计出各个模态参数的上下限范围,从而给出粒子属性值的上下界,大幅度减少粒子群算法的搜索空间。首先把频响函数的幅谱曲线看成是局部波峰的集合,引入聚类分割思路构造聚类距离函数,使用k-means算法把频响函数频谱自动聚类成多个单模态类,然后运用单模态分解算法估计出每个模态类的模态参数的上下限范围,这种上下限范围就是粒子属性值的上下界。另外还采用了混合变异粒子群算法来提高最优化搜索的效率。从仿真信号的大量实验研究结果看,与经典的正交多项式拟合算法相比,该算法的噪声抵抗能力更强、更稳定。把算法应用到轻轨锚固螺杆振动检测中表明,该算法能够提取出精确的模态参数,算法在实际工程中表现出很好的稳定性和抗干扰性。

An optimization modal analysis algorithm using particle swarm optimization is brought out in this paper. The modal parameters of a vibration signal are elements of particle, and at the end the best particle will be found based on PSO algorithm. There are two key problems to be solved. The first problem is how to estimate the initial modal parameters of the vibration signal, and the second problem is how to prevent the local optimization particle. This paper introduces the idea of clustering the spectrum to various estimates of the modal parameters of the maximum and minimum levels, thus the upper and lower bounds of the particle attribute value are given, and the search space of the particle swarm algorithm is reduced. At first, the spectral curve is looked upon as a set of small local peaks, the clustering distance function is constructed, and the k-means algorithm is used to automatically cluster the vibration signal spectrum into single-mode categories. Then a single-mode decomposition algorithm is used to estimate the modal parameters. This paper also uses a hybrid variant particle swarm algorithm to avoid falling into local optimization, and to improve the efficiency and accuracy. Considering a large amount of experimental results of simulation signals, the algorithm in this paper features stronger noise resistance and is more stable, compared with classic orthogonal polynomial fitting algorithm. Applied to the screw anchor of certain light rail, the algorithm in this paper can extract precise model parameters and has good stability.