自适应多小波混合构造方法及在故障诊断中应用

摘要

Vanishing moments and approximation orders of basis functions are both the important properties in the wavelet theory.The traditional adaptive multiwavelet construction methods can only reform either vanishing moments or approaching orders.Meanwhile,their time-frequency characteristics and waveform differences among the new multiple basis functions are quite small to lead to difficulties of efficiently adaptive extraction and identification of complex dynamic faults.Thus,the adaptive multiwavelet hybrid construction method combined with the two-scale similarity transformation and the lifting transformation was proposed.Using linear and nonlinear combinations of multi-scaling wavelet functions to extend the construction space,the multi-scaling functions with higher approximation orders and the multi-wavelet functions covered with multiple vanishing moments were obtained to enhance the regularity,smoothness,capability of signal approaching and local positioning,and to improve the signal analysis accuracy.It provided adaptive basis functions with super properties and a diagnosis method for weak and compound fault features extraction and identification.For the optimal selection of adaptive basis functions,the improved local fault field spectral entropy minimization rules were proposed to classify typical shaft systems,gear and rolling bearing faults and to simplify fault-classifying modes.The engineering applications showed that the method can effectively identify bearing weak inner-race damages under complex background noise,and successfully diagnose impact and rubbing compound faults with multiple features from thrust splints of gearbox in air-compressors.%小波理论中基函数的逼近阶和消失矩特性都是信号处理中非常重要的性质。传统自适应多小波构造方法仅能对逼近阶或消失矩单一特性进行改造，并且所生成的多个基函数时频特征和波形差异较小，难以有效实现复杂动态故障的自适应提取与识别。为此，提出基于两尺度相似变换和提升方法相结合的自适应多小波混合构造框架，对原有多尺度函数和多小波函数进行线性与非线性组合，扩大多小波改造空间，获得具有高阶逼近阶的多尺度函数和消失矩涵盖多阶次的多小波函数，增强多小波正则性、光滑性、信号逼近能力和局部定位能力，并提高信号分析精度，为复杂动态信号中微弱和复合故障特征提取与识别提供优良性质的自适应基函数及诊断方法；为按需优选自适应基函数，提出改进局部故障域谱熵最小化原则的自适应基函数优选方法，实现轴系、齿轮和轴承故障的分门别类优选，简化故障分类模式。工程实例表明该方法可以有效识别复杂背景噪声干扰下的轴承内圈微弱损伤，并成功诊断出空气分离压缩机组齿轮箱止推夹板碰撞与摩擦的多特征复合故障。