小波分解重构截齿载荷谱的幅值关联性与分形特征

摘要

FFT technique is used to study the characteristics of load spectrum of the cutter pick on cutting coal and rock.Then,two kinds of wavelets,Db4 and Sym5 are applied to decompose and reconstruct the load spectrum and extract features of high-frequency and low-frequency components of the spectrum.Finally,fractal theory is used to calculate the box dimension in different layers of load spectrum after wavelet transform.Experimental results show that there is a steady-state value on the amplitude of load spectrum and it fluctuates mainly from 0 to 5 Hz.In addition,the fitting-curve of the load spectrum in different reconstruction layers based on Db4 and Sym5 are obtained.To be specific,the difference of maximum and average value in the fourth layer between the fitting curve and original load spectrum are 0.17％ and 0.12％ respectively.Furthermore,the low-frequency reconstructed load spectrum satisfied the distribution of original load spectrum,so it can be used as an efficient method to calculate the average value of the load.The decomposition and reconstruction precision can be measured based on the relationship between the low-frequency box dimension in previous layer and the low and high-frequency box dimension in the next layer.%为了研究截齿截割煤岩载荷谱的特性,采用FFT分析载荷谱频谱特性,利用Db4和Sym5两种小波基对载荷谱分解与重构,提取分解与重构后载荷谱各层高、低频幅值均值,基于分形理论计算2种小波基重构载荷谱各层的盒维数.结果表明:载荷谱的幅值存在稳态值,幅值主要集中在0～5Hz;获得了Db4和Sym5两种小波基下重构各层载荷谱幅值均值拟合曲线,其中第4层幅值均值拟合曲线的最大值与原载荷谱的分别相差0.17％和0.12％,在全域范围内,Db4与Sym5各层低频重构载荷谱更趋近于原载荷谱均值变化规律,可作为一种计算载荷均值的有效方法.通过前一层低频与后一层的高频和低频部分的盒维数线性叠加数学关系以及盒维数叠加误差,可判断小波分解重构的精度.