Remaining useful life prediction of lithium-ion batteries: Semimartingale approximation of fractional Poisson process

Lithium-ion battery capacity degrades over time due charging and discharging. As a result, the capacity exhibits large jumps, that have long-range dependence and stochastic components. In this study we propose a method for estimation of remaining useful life of lithium-ion batteries by using fractional Poisson process with adaptive jump intensity modification. We derived a Molchan-Golosov-type integral transform which changes fractional Brownian motion of arbitrary Hurst index into the fractional Brownian motion of index H. Numerical simulations are performed for the fractional Poisson process with the Molchan-Golosov kernel. Poisson random walk is initiated by the integral term of the Riemann-Liouville fractional formula. A semimartingale approximation technique is devised to demonstrate the existence and uniqueness of the solution. In order to obtain the iterative model, the stochastic differential equation is discretized by using the Maruyama function. To solve the iterative prediction model, the distribution convergence and Fokker-Planck equation are utilized. As a result, we obtained the probability density function of the reliability function. Estimation of parameters in the solution is achieved by using the martingale function. The accuracy of the proposed remaining useful life prediction model is verified by using the NASA battery dataset for comparative models.