Algorithm 1: Constrained parameter estimation algorithm (CPEA)

The inputs include the following: monitored cobalt ion concentration, monitored pH $c_{{\mathrm{Co}}^{2+},i}^{\left(j\right)},j=1,\dots ,5,i=1,\dots ,n_{\mathrm{Co},j}, {\mathrm{pH}}_l,l=1,\dots ,n_{\mathrm{pH}}$ initial concentration vector $c_0^{\left(j\right)}$ initial mixed potential $E_0$ weight coefficient ${\lambda }_{\mathrm{pH}}$ Npop (the population size of the PSO algorithm), and MaxIters (the maximum number of iterations).

Output: Cobalt–hydrogen electrochemical competition model parameters $p^{\left(1\right)}$

Steps: (1)Use the PSO algorithm to solve Equation (59) for ${\beta }_1,{\alpha }_2,{\alpha }_3,z$ (2)Calculate $p^{\left(1,2\right)}$ according to Equation (58) (3)Calculate $p^{\left(1\right)}$ according to Equation (51)