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There is a considerable noise in the measured signal of pressure and flow of a running pipeline due to friction drag and medium diffusion, which poses an obstacle to the quick detection and precise classification of pipeline leakage, especially to the acquiring of weak incipient fault. This paper offers an incipient fault detection method based on nonlinear manifold learning algorithm, which treats the negative pressure wave signal as transient signal and reduces noise of original signal by using multi-scale wavelet transform. The method also learns original fault signal and extracts the intrinsic manifold features of data by using a nonlinear dimensionality reduction algorithm based on Laplacian Eigenmaps. With this method, the identification efficiency of optimal fault characteristics is noticeably improved, and the advantage of this method has been proved by simulation experiments.