对近两年我国及日本在机械监测诊断领域内小波技术的研究与应用进行了回顾，简述了小波技术的理论研究及其在旋转机械、往复机械、齿轮、轴承、建筑结构、疲劳损伤等方面的应用中所取得的可喜进展和特点。指出应根据小波函数的性质有针对性地应用，以取得更好的效果。

为了克服在无先验知识的情况下，人为选择时域无量纲指标作为故障敏感特征的盲目性，提出了一种基于特征评估和径向基函数（RBF）神经网络的机械故障诊断模型。该模型分别采用小波包和经验模式分解方法对原始振动信号进行分解，分别提取原始信号和各分解信号的时域无量纲指标组成联合特征，然后对联合特征进行评估，计算评估因子，并根据评估因子的大小选取敏感特征作为RBF神经网络的输入，实现对机器不同状态的自动识别。实验结果和工程应用表明，这种集成了小波包、经验模式分解、特征评估方法和RBF神经网络的机械故障诊断模型能够精细地获取故障信息，从大量的故障特征中筛选出敏感特征，因而减小了网络规模，提高了分类准确率，具有很强的鲁棒性。

机械设备由于故障而诱发的信号往往具有奇异性（Singularity），正确识别奇异性对设备监测诊断十分重要。采用高斯函数的一阶、二阶导数构成复数Hermitian小波进行奇异性识别，具有两个优点：其一是由于Hermitian小波的Fourier变换是实数，对信号进行变换时不会有相位的改变；其二是与Morlet小波相比较，Hermitian小波的实部和虚部振荡次数少，可用较少的数据点对信号进行卷积，从而不会损坏信号的奇异性。本文提出了基于Hermitian小波变换的时间-尺度幅图和相图的信号奇异性识别方法，在大型空气压缩机的齿轮箱撞击摩擦故障诊断中取得了成功的应用。

提出了任意尺度Daubechies小波一维二维单元构造方法以及小波有限元自适应提升算法，采用小波尺度函数作为插值函数，利用小波多分辨分析了具有变尺度逐层逼近函数的特性，获得了嵌套递进的多尺度有限元逼近空间。

The two-dimensional wavelet nite element (WFE) is constructed, in which the scaling functions of Daubechies wavelets are adopted as trial functions. In order to overcome the integral di:culty caused by lack of the explicit Daubechies scaling function expression, a new and e:cient integral method for stiffness and load matrices is presented. Then the bending characters of a thin plate are studied based on WFE. Numerical tests indicate that the WFE is highly accurate and effective. For engineering application, the internal temperature distribution of office paper used in office machines such as printers and copiers is analyzed by WFE. The results show that WFE has desirable calculation precision while dealing with singularity problems

提出了二维近似熵的概念，并用于表征轴心轨迹的复杂性，定量地评价了回转机械的运行状态。该方法具有计算所需数据短、抗噪及抗野点能力强、对确定性信号和随机信号都适用等特点。应用二维近似熵，对某机组关键轴瓦的轴心轨迹进行了复杂性度量，研究结果表明，二维近似熵在表征轴心轨迹的时间模式复杂性方面具有很强的能力，从而为机械设备状态监测与故障诊断提供了一种行之有效的新方法。

为了解决机电设备早期故障难以正确识别的问题，有效地提高分类的准确率，提出了一种基于提升小波包变换和集成支持矢量机的早期故障智能诊断新方法。首先，该方法采用提升策略构造基于冲击故障信号特征的双正交小波，借助提升小波包变换提取信号的敏感频带特征，从而通过对敏感频带中的小波包系数进行包络解调分析检测出故障特征频率。其次，通过距离评估技术从原始信号和小波包系数的统计特征中选取最优特征集。最后，将最优特征输入到集成支持矢量机中，实现对不同故障类型的识别。将该方法应用于滚动轴承的早期故障诊断中，测试结果表明，同常规的小波包变换相比，该方法能够有效地提取故障特征；同时，该方法具有比单一支持矢量机更好的分类性能，故障诊断准确率高。

The model-based forward and inverse problems in the diagnosis of structural crack location and size by using the finite element method of a B-spline wavelet on the interval (FEM BSWI) were studied. First the crack and uncracked elements of BSWI were built to solve the forward problem. The first three frequencies influencing functions of normalized crack location and size are approximated by means of surface-fitting techniques. Then the first three measured natural frequencies are employed as inputs of the functions. The intersection of the three frequencies contour lines predicted the normalized crack location and size. Both the numerical and experimental studies verified the validity of the BSWI elements in solving crack singular problems with high performance.

Vibration signals acquired from a gearbox usually are complex, and it is difficult to detect the symptoms of an inherent fault in a gearbox. In this paper, an adaptive redundant lifting scheme for the fault diagnosis of gearboxes is developed. It adopts data-based optimisation algorithm to lock on to the dominant structure of the signal, and well reveal the transient components of the vibration signal in time domain. Both lifting scheme and adaptive redundant lifting scheme are applied to analyse the experimental signal from a gearbox with wear fault and the practical vibration signal from a large air compressor. The results confirm that adaptive redundant lifting scheme is quite effective in extracting impulse and modulation feature components from the complex background.

针对强噪声背景下机械信号故障特征的提取问题,构造了一种提取该类信号时域特征的冗余第2代小波方法。该方法通过对初始预测算子和更新算子插值补0，来获得不同分解层上的预测算子和更新算子。冗余第2代小波不需要剖分运算,直接利用构造的算子对逼近信号进行对称预测和更新，可使逼近信号和细节信号的数据点数保持不变，并根据每层细节信号的噪声特点选取降噪阈值门限。实验和工程振动信号分析表明，冗余第2代小波的降噪效果优于其他类型的小波方法，较理想地提取出了滚动轴承内圈剥落和汽轮发电机组高压缸蒸汽激振的时域故障特征。