A new tree structure code for equivalent circuit and evolutionary estimation of parameters

To optimize the parameters of electrical elements contained in an equivalent circuit for electrochemical impedance spectroscopy, we proposed a simple, intuitive and universal tree structure code (TSC) to encode an arbitrary complex circuit, then designed a genetic algorithm for parameter optimization (GAPO) to work with the TSC and estimate the parameter values of electrical elements. The GAPO uses a novel crossover operator that performs by the non-convex linear combination of multiple parents and sets up a crossover subspace to enhance the global search. We first examined the effects of some key control parameters in the GAPO on the optimization process by selecting a relatively complex equivalent circuit to generate simulated data and comparing the parameters obtained by GAPO with the original values. Secondly, to examine the effectiveness and robustness of GAPO, we chose a set of simulated data generated by a relatively simple circuit, three sets of real impedance data on modified gold electrodes and a set of real impedance data on the anode of lithium-ion battery to run the GAPO and compared their calculated results with those obtained by complex nonlinear least square method (CNLS) supported by LEVM software. Finally, we compared the effects of five representative weighting strategies on the GAPO based on a set of simulated data generated by a relatively complicated circuit but with up to 10% Gaussian noise and the set of real impedance data on the anode of lithium-ion battery. All of these experimental results show that the GAPO works more quickly, efficiently and stably than CNLS when optimizing the element parameters. We also found that appropriate weighting strategies can help reduce the effects of experimental errors on GAPO, but the effects really depend on the nature of the specific impedance data.