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This paper first discusses the principles of how to identify whether a time series has chaotic characteristics, and explores a method of finding out the embedding dimension of a time series. Then Grassberger-Procaccia (G-P) algorithm is adopted to calculate correlative dimension. After the validity of G-P algorithm is confirmed using several traditional strange attractors, it is applied to calculate the fractal dimension of some vibration signals of an automotive transmission. This article presents how to apply chaos and fractal theories to diagnose the wearing of ball bearings in automotive transmissions based on the analysis of the transmission acceleration vibration signals. The results show that the vibration signals of automotive transmissions have fractal nature. There are certain correlations between a bearing's condition and the fractal dimension of its vibration signal.