In this paper we present an experimental investigation of the identification of crack location and size. By providing the first three natural frequencies through vibration measurements, curves of crack equivalent stiffness versus crack location are plotted, and the intersection of the three curves predicts the crack location and size. In the experiments, the cracked specimens were made using a wire-cut electrical discharge machine, and the cantilever beams were excited next to the free end by means of an impulse force hammer. In order to obtain the accurate natural frequencies from the transient signal measured, the method of zoom fast Fourier transform is adopted to improve frequency resolution. From experimental results, it is observed that the identification errors of crack location and size are less than 2% and 4%, respectively. The effectiveness of crack identification through vibration measurements is verified.

A new time-domain analysis method that uses second generation wavelet transform (SGWT) for weak fault feature extraction is proposed. To extrata incipient fault feature, a biorthogonal wavelet with the characteristics of impact is constructed by using SGWT. Processing detail signal of SGWT with a sliding window devised on the basis of rotating operation cycle, and extracting modulus maxi-mum from each window, fault features in time-domain are highlighted. To make fitrther analysis on the reason of the fault, wavelet package transform based on SGWT is used to process vibration data again. Calculating the energy of each frequency-band, the energy distribution features of die signal are at- tained. Then taking account of the fault features and the energy distribution, the reason of die fault is worked out. An early impact-rob fault caused by axis misalignment and rotor imbalance is successfully detected by using this method in an oil refinery.

小波变换是非平稳信号处理的有力工具，小波性质取决于它的基函数。在模态分析、机械监测诊断等领域,冲击响应信号十分普遍。一种单边衰减复指数型的Laplace小波基函数具有分析冲击响应信号的优势，采用Laplace小波相关滤波方法可提取振动信号中的冲击响应分量，成功地诊断出内燃机进气阀的磨损故障和识别出大型水轮机轴系的一阶固有频率。

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.