a. Linear Approximation for Degradation Though we have found an exact implicit solution for this problem, implicit solutions can be computationally inefficient, particularly for optimization processes. Obtaining an explicit solution for complex problems can significantly reduce optimization time and provide valuable physical insights. Thus, we perform a first-order linearized approximation for the voltage shift to simplify the calculations. After linearization for the voltage shift, we apply the approximation of the half cell described in Eq. 8, generating an explicit expression for effect of degradation on the response. This approach combines computational efficiency with a high degree of accuracy.