Synergy of ( $${\text{H}}_{2}$$ H 2 , $${\text{H}}_{\infty }$$ H ∞ ) norms for nonlinear optimal PEMFC dynamic MIMO model reduction using a novel EAO approach

In this paper, a new nature-inspired Artificial Ecosystem Optimization (AEO) methodology is presented for reducing the complexity of nonlinear PEMFC SR-12 500 W system. From the point view of this system, the hydrogen and oxygen pressures $$P_{H2} = 60\,{\text{atm}}$$ P H 2 = 60 atm , $$P_{O2} = 30 \,{\text{atm}}$$ P O 2 = 30 atm as two inputs, the cell voltage and current as two outputs.By implementation of identification technique, the state space model of PEMFC stack is generated using nlarx modelling procedures where the obtained model is reduced their order by AEO method. The AEO mimics the energy flow behaviour between living organisms in a natural ecosystem, including production, consumption, and decomposition.This algorithm minimize the synergy ( $${\text{H}}_{2} ,{\text{H}}_{\infty }$$ H 2 , H ∞ ) norm of error between full PEMFC model and reduced order model. The obtained results are compared with the other optimization algorithms such as MRFO,SSA,ALO and GWO, and they are confirmed that the approximate model obtained by proposed algorithm has faster convergence and better approximation performance in synergy ( $${\text{H}}_{2} ,{\text{H}}_{\infty }$$ H 2 , H ∞ ) norm than those obtained by comparative algorithms in addition, it is proven to be accurate and reliable to investigate the PEMFC optimum global reduced order model which preserved the main behaviour of original PEMFC SR-12 500 W model.