Electrochemical systems are useful and popular class system that is under rapid development recently. To conduct investigations on these electrochemical systems, one needs accurate measurement in order to investigate the physical phenomenon in the system and to benchmark their performance. However, due to the complexity of typical electrochemical systems, extracting useful information from the respective experiments is often non-trivial. Situations such as non-identifiable parameters, lacking of a priori knowledge to the system often occur, which hinder the recovery of meaningful physical information from the experimental data. In this thesis, statistical techniques are applied to study two commonly used electrochemical experiments, the electrical conductivity relaxation (ECR) experimen...[ Read more ]

Electrochemical systems are useful and popular class system that is under rapid development recently. To conduct investigations on these electrochemical systems, one needs accurate measurement in order to investigate the physical phenomenon in the system and to benchmark their performance. However, due to the complexity of typical electrochemical systems, extracting useful information from the respective experiments is often non-trivial. Situations such as non-identifiable parameters, lacking of a priori knowledge to the system often occur, which hinder the recovery of meaningful physical information from the experimental data. In this thesis, statistical techniques are applied to study two commonly used electrochemical experiments, the electrical conductivity relaxation (ECR) experiment and the electrochemical impedance spectroscopy (EIS). In the first part of this thesis, we utilize an asymptotic statistical method to assess the quality of the parameters estimation in ECR for different sample geometries. We also highlight the importance of considering higher order nonlinearities when determining the confidence region and assessing the identifiability of the estimates. In the second part of this thesis, the application of distribution of relaxation time (DRT) for the EIS is discussed. Particularly, we utilize a novel discretization basis, the radial basis functions (RBFs), in order to improve the estimation quality of the DRT. Moreover, we extended our study on the regularized regression method for deconvolving the DRT by describing it in a Bayesian perspective. Such perspective allows the estimation of the maximum a posteriori and predictive interval, which help to understand the statistical performance when estimating the DRT.