In this paper, a Levy reptile search algorithm (LRSA) is proposed to improve the global search capability and convergence speed of reptile search algorithm which has advantages in solving single‐modal, multi‐modal and composite problems. Firstly, circle chaotic mapping is introduced to make the initial distribution of population more uniform and diversified. Secondly, Levy flight strategy is employed in the global search, which can improve the accuracy and convergence speed. In order to test and verify the optimization performance of the LRSA, 12 benchmark functions are tested and compared with four other intelligent optimization algorithms. It can be seen that LRSA is effective and advantageous in average convergence speed. In addition, the proposed LRSA is applied to a fractional order model identification of lithium battery with a very small error (less than 2%). The experimental results show that the LRSA can effectively estimate the parameters of the fractional order model and aid to state of charge and state of health estimation.

This paper studies the parameter estimation of fractional order equivalent circuit model of lithium-ion batteries. Since intelligent optimization algorithms can achieve parameters with high accuracy by transforming the parameter estimation into optimization problem, coyote optimization algorithm is taken in this paper by modifying two key steps so as to improve the accuracy and convergence speed. Firstly, tent chaotic map is introduced to avoid falling into local optimum and enhance population diversity. Secondly, dual strategy learning is employed to improve the searching ability, accuracy and convergence speed. Non-parametric statistical significance is tested by 6 benchmark functions with the comparison of other 5 optimization algorithms. Furthermore, the proposed algorithm is applied to identify the fractional order model of the Samsung ICR18650 (2600 mAh) and compared with conventional coyote optimization algorithm and particle swarm algorithm, which declared the excellence in identification accuracy.