Abstract: The power generation process of proton exchange membrane fuel cell（PEMFC）is complex to describe,this paper,considering the fractional order characteristics of PEMFC system,proposes an optimization based fractional order time domain subspace identification method,and establishes a fractional order state space model of PEMFC. The fractional differential theory is combined with subspace identification method,and Poisson filter is used to filter the input and output data. The weight matrix is introduced to improve the accuracy of identification. Then,a mutation reverse learning adaptive monarch butterfly optimization algorithm（ALMBO）is proposed for the identification of fractional order and other parameters. The mutation reverse learning strategy is introduced into the transfer operator,and the adaptive weight is integrated to improve the optimization accuracy and prevent falling into the local optimal solution. Finally,the simulation results verify the effectiveness of the algorithm,and the identification model can accurately describe the dynamic process of PEMFC.