The invention provides a 
weak signal detection method based on adaptive cascading power 
function type bistable random 
resonance, and belongs to the technical field of 
signal processing. For the purpose of extracting weak signals in the background of strong 
noise, the invention brings forward a power 
function type bistable random 
resonance system by compounding a power 
function type single-potential-well model with a 
Gaussian Potential model. According to the method based on the 
system, first of all, noised signals are preprocessed so as to satisfy small-parameter conditions of a heat insulation approximation theory, then according to known conditions, a search scope of power function type bistable 
system parameters is arranged, by taking average 
signal-to-
noise gain as a performance average index, values of the power function type bistable 
system parameters are optimized, and thus an optimal 
resonance effect is generated. The power function type bistable 
potential well model brought forward by the invention has the advantages of the power function type single-potential-well model and a conventional bistable model, thereby having general significance in actual application. Searching optimization is carried out on the 
system parameters by use of an adaptive searching optimization 
algorithm so that a poor 
resonance effect caused by poor selection of the 
system parameters is avoided.