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。

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。

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 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

Based on two-dimensional tensor product B-spline wavelet on the interval (BSWI), a class of C0 type plate elements is constructed to solve plane elastomechanics and moderately thick plate problems. Instead of traditional polynomial interpolation, the scaling functions of two-dimensional tensor product BSWI are employed to form the shape functions and construct BSWI elements. Unlike the process of direct wavelets adding in the previous work, the elemental displacement field represented by the coefficients of wavelets expansions is transformed into edges and internal modes via the constructed transformation matrix in this paper. The method combines the versatility of the conventional finite element method (FEM) with the accuracy of B-spline functions approximation and various basis functions for structural analysis. Some numerical examples are studied to demonstrate the proposed method and the numerical results presented are in good agreement with the closed-form or traditional FEM solutions