The non-stationary signal is classified into the abrupt singular signal and the gradual singular signal. Because the fault of closed-loop control system is difficult to detect the initial moment when the fault happened, and often there is a more serious consequences once the fault was detected. A new method is proposed which can predict whether the fault happened through the trend signal of a dynamic system. The trend signal was got by the wavelet transform of the detected signal. In order to verify the effectiveness of the method, the leak fault was installed in the process control water tank experiment system, and the signal of liquid level and flow was collected. The gradual leak fault was found through the trend signal in low frequency which was got by the wavelet multi-scale resolution, so the practicability of the proposed method was proved.