The use of the L-curve method in the inversion of diffusion battery data

Regularisation techniques are often employed to find a unique solutions to the diffusion battery data inversion problem. This involves minimising a function of the form A + λB, where A measures the fit to the data and B measures the smoothness of the solution. The quality of the solution is critically dependent on the choice of λ. If A is plotted against B for all λ values then a curve with a characteristic L-shape is obtained and the solution at the corner has an optimum balance of fit and smoothness. We demonstrate the usefulness of the L-curve method in this application and show that it provides a good means of choosing λ. It has the particular advantage that solutions are independent of error estimates. We also show that the solutions obtained are superior to those obtained by Twomey's non-linear inversion algorithm.