A diagnostic method based on vibration and acoustic signals is presented in order to resolve the problem of extraction and separation for the compound signals in an equipment room. The minimum mutually information gradient descent method is applied based on blind separation algorithm, and the algorithm performance is improved through the revision of fourth-order cumulative estimating value. When the quantity of fault sources is unkown, or more than the quantity of sensors, the most remarkable characteristics are extracted according to the independence relation between the information sources. The simultation product is proved that improved algorithm is reliable because the estimation error is reduced. In the diagnosis example, the acoustic signals are firstly separated in an equipment room to determine the major failure sources. And then vibration signals collected from these fault sources are processed based on non-linear blind separation model. The fault feathers are extracted including misalign, meshing failure and wearing fault from compressor of the heat pump. Finally, the fault types are recognized according to the separated signal features from vibration and accoustic signals. And the vibration and accoustic diagnosis method is established for multi-units in the big space based on blind source separation algorithm.