基于组合赋权法的小波阈值降噪综合评价指标研究  

Investigation on Comprehensive Evaluation Index of Wavelet Threshold Denoising Based on Combination Weighting Method

作　　者：熊春宝[1] 庞红星 Xiong Chunbao;Pang Hongxing(School of Civil Engineering,Tianjin University,Tianjin 300072,China)

机构地区：[1]天津大学建筑工程学院,天津300072

出　　处：《天津大学学报（自然科学与工程技术版）》2022年第12期1300-1308,共9页Journal of Tianjin University：Science and Technology

基　　金：国家自然科学基金资助项目(61971037).

摘　　要：均方根误差、信噪比、相关系数、平滑度等传统小波降噪效果评价指标适用于纯净信号已知的情况,而在实际应用中监测所得信号的纯净状态一般是未知的.为解决传统评价指标的局限性问题,提出一种基于组合赋权法的综合评价指标.该指标首先是在理论分析和实例验证的基础上,从增减性与物理意义角度确定了指标分量为均方根误差和平滑度;然后利用阈值极大法对两个指标进行归一化;最后采用熵权法与变异系数法对均方根误差和平滑度的归一化值进行相应的权重计算并线性组合相加.综合评价指标的极小值对应的分解尺度与小波基函数即为最优小波参数.通过对3种不同信噪比(5 dB、12.5 dB、20 dB)的仿真信号进行分析,结果表明,该综合指标均成功识别到最优的分解尺度和小波基函数,降噪效果达到最佳.与其他综合指标相比,该指标的准确性和普适性更好.另外,将该指标应用到GNSS监测信号中也是可行的,具有一定的工程价值.The traditional wavelet denoising effect evaluation indexes,such as the root mean square error,signal-to-noise ratio(SNR),correlation coefficient,and smoothness,are suitable for known pure signals.However,the pure state of a monitored signal is often unknown in practical applications.To solve the limitations of traditional evaluation indexes,a comprehensive evaluation index based on the combination weighting method is proposed in this study.First,on the basis of theoretical analysis and case verification,the index component was determined as the root mean square error and smoothness from the perspectives of increase-decrease characteristics and physical meaning.Then,the threshold maximum method was used to normalize the two indicators.Finally,the entropy weight method and variation coefficient method were applied to calculate the corresponding weights of the normalized values of root mean square error and smoothness,and the linear combination was added.The decomposition scale and wavelet basis function corresponding to the minimum value of the comprehensive evaluation index were the optimal wavelet parameters.The analysis of three SNR(5,12.5,and 20 dB)simulation signals shows that the optimal decomposition scale and wavelet basis function are identified,and the noise reduction effect is optimal.Compared with other comprehensive indicators,the accuracy and universality of the index are better.In addition,this index can be applied to GNSS monitoring signals,which has certain engineering value.

关 键 词：小波阈值降噪 综合评价指标 熵权法 变异系数法 组合赋权 

分 类 号：P228[天文地球—大地测量学与测量工程]