Evidence for deterministic chaos as the origin of electrical tree breakdown structures in polymeric insulation

Abstract

Electrical discharges were measured during the propagation stage of electrical tree breakdown in an epoxy resin. An analysis of their number sequence provides strong evidence for the existence of an underlying deterministic chaotic mechanism. The fractal dimension of the tree and that of the reconstructed attractor and Lyapunov exponent were found to be related. The higher fractal dimension tree (${\mathit{d}}_{\mathit{t}}$\ensuremath{\sim}1.9) is associated with an attractor dimension ${\mathit{d}}_{\mathit{f}}$\ensuremath{\sim}3.1 and Lyapunov exponent \ensuremath{\lambda}\ensuremath{\sim}0.008 bit/s. The lower fractal dimension tree (${\mathit{d}}_{\mathit{t}}$\ensuremath{\sim}1.5) is associated with values of ${\mathit{d}}_{\mathit{f}}$\ensuremath{\sim}3.56 and \ensuremath{\lambda}\ensuremath{\sim}0.028 bit/s. No evidence for the presence of random stochastic processes, an essential ingredient of the dielectric breakdown model, has been found.