中文说明：使用拉亚普诺夫指数的公式，添加噪声处理，计算晶粒的生长，入门级别程序,自写曲率计算函数 ,BP神经网络用于函数拟合与模式识别，分析了该信号的时域、频域、倒谱，循环谱等。
English Description：
Use La Jaap Andrianof index formula and add noise to deal with, the calculation of grain growth, entry-level program, since the writing of curvature calculation function and BP neural network for function approximation and pattern recognition and analysis of the signal in time domain and frequency domain, cepstrum, the cyclic spectrum.