CAJ | 학술논문

小波变换被称为“数学显微镜”，它对机械信号的多尺度分析在机械设备状态监测和故障诊断领域发挥着重要的作用。然而传统二进小波变换在工程应用中存在一些显著的不足，如平移敏感性、小波尺度能量泄漏、固定的二进“频率-尺度”划分网格等。尤其是后者使得经典小波变换对处于二进网格过渡带的特征分析中产生不可避免的“盲区”。基于此，提出一种基于过完备小波紧框架的新式“时间-尺度”分析方法-衍生增强离散解析小波分析框架。该小波分析框架基于双树复小波变换进行构造，通过合理地选择双树复小波基函数，并将之应用于增广树形迭代滤波器组中生成近似解析小波包变换，通过对近似解析小波包变换的分析结果进行子空间重排和小波包尺度空间交叉结合，构造伪二进小波包隐框架。在多尺度分解的意义下，所提出的衍生增强离散解析小波分析框架(近似解析小波框架和伪二进小波包隐框架)很好地改进了经典小波存在时频表达能力方面的限制，有效地移动了小波尺度的中心频率，实现了自顶向下、多中心连续细化的“频率-尺度”分析网格。将之应用于的带钢精轧机的微弱故障特征提取中，验证了所提出方法对于经典小波分析方法的优越性。
소파변환피칭위“수학현미경”，타대궤계신호적다척도분석재궤계설비상태감측화고장진단영역발휘착중요적작용。연이전통이진소파변환재공정응용중존재일사현저적불족，여평이민감성、소파척도능량설루、고정적이진“빈솔-척도”화분망격등。우기시후자사득경전소파변환대처우이진망격과도대적특정분석중산생불가피면적“맹구”。기우차，제출일충기우과완비소파긴광가적신식“시간-척도”분석방법-연생증강리산해석소파분석광가。해소파분석광가기우쌍수복소파변환진행구조，통과합리지선택쌍수복소파기함수，병장지응용우증엄수형질대려파기조중생성근사해석소파포변환，통과대근사해석소파포변환적분석결과진행자공간중배화소파포척도공간교차결합，구조위이진소파포은광가。재다척도분해적의의하，소제출적연생증강리산해석소파분석광가(근사해석소파광가화위이진소파포은광가)흔호지개진료경전소파존재시빈표체능력방면적한제，유효지이동료소파척도적중심빈솔，실현료자정향하、다중심련속세화적“빈솔-척도”분석망격。장지응용우적대강정알궤적미약고장특정제취중，험증료소제출방법대우경전소파분석방법적우월성。
As the celebrated “mathematical scope”, the multi-resolution analyzing capacity of wavelet transform (WT) plays an important role in condition monitoring and fault diagnosis of mechanical equipment. However, it has proven that the effectiveness of WT is hampered by several negative factors, such as shift-sensitiveness, significant energy leakage, and the fixed dyadic“frequency-sale” paving. Especially, the dyadic “frequency-sale” paving creates inevitable deficiency in identifying mechanical signatures located in transition areas of adjacent wavelet scales. A novel “time-sale” analysis methodology, named as derived ensemble analytic framelet (DEAF), based on overcomplete wavelet tight frame, is proposed. The DEAF is developed based on the existing dual tree complex wavelet transform (DTCWT). The DEAF starts from a selected DTCWT basis, and combines it with a hybrid augmented tree-structured filter-bank, which results in quasi analytic wavelet packet decomposition (QAWPD). With the results of QAWPT, an ensemble wavelet packet generating strategy is applied such that an unprecedented implicit wavelet packet tight frame (IWPTF) containing pseudo dyadic wavelet packets is obtained. With the combination of QAWPD and IWPTF, the proposed DEAF can be derived which possesses the“frequency-sale”paving characterized by continued time-frequency refinement of analysis centers. The proposed technique is applied to the mechanical signature analysis of an engineering application to validate its superiority compared with the existing methods.