EMD包络线拟合算法改进及在泡沫尺寸趋势提取中的应用

Improvement of EMD Envelope Extraction and Its Application in the Tendency Distillation of Bubble Size

包络线拟合是EMD算法中的关键步骤,针对现有三次样条插值(CSI)法拟合包络线存在插值点冗余、端点发散、拟合松散等问题,提出了改进的EMD包络线提取算法。将插值点由传统的极值点改为特殊点,并对特殊点分段处理,删除冗余点;利用加权最小二乘多项式拟合对边界的特殊点进行三次拟合,求出端点值作为边界处的插值点抑制端点效应;用带约束的保形三次埃尔米特插值法替代三次样条插值方法,保证每个插值子区间的单调性使得拟合更紧密。定义包络线与信号的方差和以及曲线长度协同作为评判标准,判定所提算法拟合效果良好,在浮选泡沫尺寸趋势提取中的应用也验证了其有效性。

The process of envelope extraction is a key step of the EMD method. For the problems of the redundancy of interpolation points,the end divergence,and the loose fitting in the exsiting cubic spline interpolation method,an improved envelope extraction method for EMD is presented. Firstly,the traditional extreme point was replaced by the special points as interpolation points. In order to remove the excess extreme points,the special points are segmented.Then the cubic fitting is performed to the special points on the edge using the weighted least squares method to calculate the value of the end to restrain the end effect. Finally,to replace the cubic spline interpolation method with the cubic Hermite interpolation method with constraints to keep the monotonicity in each interval for the sake of tight fitting. Along to the defined judging standard of sum of the variance between the signal and the fitting envelope and the length of the fitting envelope,the improved method can achieve better fitting effect. The application in the tendency distillation of bubble size reveals a better fitting effect as well.