The faults initiated in operation (i.e. incipient fault) with the obscure symptoms and weak features, are always contaminated by a large amount of background noise. Hence, fault diagnosis and prognosis of incipient faults have been the difficulty and focus of the research field. The paper studied the principle of inner product transform of dynamic signals and basis functions, proposed several construction methods of adaptive multiwavelet basis functions,and improved several multiwavelet denoising methods with neighborhood and local threshold. The typical engineering cases of the equipment of heavy oil catalytic cracking, the continuous casting and rolling mills, the air compressor, the electric locomotive and the transmission device of satellite comunication on ship were studied, and the results showed the effectiveness of enhancement of weak dynamic signals and features extraction of compound faults.