Abstract: Singularity dectection theory and method based on wavelet transform were presented in this paper. Based on the analysis of the characteristics of the connecting rod and its relative bearing the failure signals were multi-scale decomposed by wavlet tranform of spline function. Singularity exponents called Lip exponents representing the failure serious degree were computed respectively. The result demonstrated the effective and practical value of wavelet transform applied in the failure dignosis of reciprocating machinery.