An Improved Unscented Particle Filter Method for Remaining Useful Life Prognostic of Lithium-ion Batteries With Li(NiMnCo)O₂ Cathode With Capacity Diving

Abstract

An improved method for the remaining useful life (RUL) prognostic of Lithium-ion batteries with Li(NiMnCo)O 2 cathode using improved unscented particle filter (UPF) is proposed with respect to capacity diving in later capacity degradation curve. Key points of this paper are: (1) An appropriate empirical model for the situation as the most contributive work, is put forward as an alternative to the widely used UPF models, and the prediction performance is respectively verified by least square fitting and the improved UPF; (2) Systematic noise in Gamma distribution is attempted in state space equations of the proposed method, so as to avoid potential shape shifting of the prediction curve after sampling the particles with Gaussian noise, for model parameters could get zero-crossed; (3) With training data preprocessed considering the capacity recovery phenomenon concisely, the residual error and root mean square error of fitting could get further reduced, as a supplement to traditional treatments like smoothing, thus relieving the sensitivity of datadriven methods to data by enhancing quality. Validations are implemented by applying the proposed method to the battery data by conducting cycle aging tests under different working conditions, where improved approximation and prediction performance can be obtained. INDEX TERMS Lithium-ion battery, remaining useful life, state of health, unscented particle filter, capacity diving phenomenon.

A Novel Remaining Useful Life Prediction Method for Capacity Diving Lithium-Ion Batteries

“…In the paper, two different model transitions are designed to describe the system well and are easy to build to meet the practice’s real-time and flexibility requirements. In the referenced literature, 31 , 35 , 38 , 40 the double exponential model is widely used in the RUL prediction of LIBs due to its fluency, smoothness, and simplicity. It is expressed as where k is the number of charge/discharge cycles, Q ( k ) is the battery capacity at the k th time, and a , b , c , and d are constants that vary with time ( a and b are related to the internal impedance of the battery, c an d are aging parameters 31 ).…”

“…In the paper, the proposed adaptive approach to determine the inflection point is to identify the 3σ interval criterion using the differential capacity curve. 40 Moreover, the current capacity is less than 90% of the initial capacity introduced as one of the conditions. However, it is worth noting that the inflection points found by the adaptation are not the same as the true capacity dive points shown in Figure 2 c,d.…”

“…This method determines the p , d , and q by competent observation. To avoid subjectivity, Akaike Information Criterion (AIC) , and Bayesian Information Criterion (BIC) , are introduced to determine the model order. The AIC and BIC values are calculated after an ARIMA model with different orders is constructed for a given time series in this paper.…”

“…In the paper, the proposed adaptive approach to determine the inflection point is to identify the 3σ interval criterion using the differential capacity curve . Moreover, the current capacity is less than 90% of the initial capacity introduced as one of the conditions.…”

“…In addition, the predictions of RUL are in a narrow probability distribution. PF has the ability to express the uncertainty of each cycle, − which in combination with SVR corrects for future errors, so that the hybrid approach plays a crucial role. However, the data preprocessing technique DWT is essential to make the SVR converge; without preprocessing, a large number of training attempts cannot produce a converged SVR.…”