To ensure the safety and reliability of an echelon-use lithium-ion battery (EULIB), the performance of a EULIB is accurately reflected. This paper presents a method of estimating the combined state of energy (SOE) and state of charge (SOC). First, aiming to improve the accuracy of the SOE and SOC estimation, a third-order resistor-capacitance equivalent model (TRCEM) of a EULIB is established. Second, long short-term memory (LSTM) is introduced to optimize the Ohmic internal resistance (OIR), actual energy (AE), and actual capacity (AC) parameters in real time to improve the accuracy of the model. Third, in the process of the SOE and SOC estimation, the observation noise equation and process noise equation are updated iteratively to make adaptive corrections and enhance the adaptive ability. Finally, an SOE and SOC estimation method based on LSTM optimization and an adaptive extended Kalman filter (AEKF) is established. In simulation experiments, when the capacity decays to 90%, 60% and 30% of the rated capacity, regardless of whether the initial value is consistent with the actual value, the values of the SOE and SOC estimation can track the actual value with strong adaptive ability, and the estimated error is less than 1.19%, indicating that the algorithm has a high level of accuracy. The method presented in this paper provides a new perspective for estimating the SOE and SOC of a EULIB.

Owing to the degradation of the performance of a retired battery and the unclear initial value of the state of charge (SOC), the estimation of the state of power (SOP) of an echelon-use battery is not accurate. An SOP estimation method based on an adaptive dual extended Kalman filter (ADEKF) is proposed. First, the second-order Thevenin equivalent model of the echelon-use battery is established. Second, the battery parameters are estimated by the ADEKF: (a) the SOC is estimated based on an adaptive extended Kalman filtering algorithm, that uses the process noise covariance $Q_k$ and observes the noise covariance $R_k$ , and (b) the ohmic internal resistance and actual capacity are estimated based on the aforementioned algorithm, that uses the process noise covariance $Q_{\theta ,k}$ and observes the noise covariance $R_{\theta ,k}$. Third, the working voltage and internal resistance are predicted using optimal estimation, and the SOP of the echelon-use battery is estimated. MATLAB simulation results show that, regardless of whether or not the initial value of the SOC is clear, the proposed algorithm can be adjusted to the adaptive algorithm, and if the estimation accuracy error of the echelon-use battery SOP is less than 4.8%, it has high accuracy. This paper provides a valuable reference for the prediction of the SOP of an echelon-use battery, and will be helpful for understanding the behavior of retired batteries for further discharge and use.

An echelon-use lithium-ion battery (EULB) refers to a powered lithium-ion battery used in electric vehicles when the battery capacity is attenuated to less than 80% and greater than 20%. Aiming at the degradation of the performance of the EULB and the unclear initial value of the state of energy (SOE), estimations of the state of power (SOP) of an EULB are not accurate. An SOP estimation method based on an adaptive dual unscented Kalman filter (ADUKF) is proposed. First, the second-order resistor-capacitance symmetry equivalent model (SRCSEM) of the EULB is established. Second, an unscented transformation (UT) is introduced and the battery parameters estimated by the ADUKF: (a) the SOE is estimated based on an adaptive unscented Kalman filtering (AUKF) algorithm, that uses the observation noise equation γ_k, R_k and the processes noise equation q_k, Q_k, and (b) the ohmic internal resistance (OIR) and actual capacity (AC) are estimated based on the aforementioned algorithm, which uses the observation noise equation γ_θ,k, R_θ,k and the process noise equation q_θ,k, Q_θ,k. Third, the working voltage and OIR are predicted using optimal estimation, and the SOP of the EULB is estimated. MATLAB simulation results show that EULB symmetry capacity decays to 80%, 60%, 40%, and 20% of rated capacity, the proposed algorithm is adaptive regardless of whether the initial SOE value is consistent with the actual value, and the estimation error of the EULB’s SOP is less than 3.28%, showing high accuracy. The results of this study can provide valuable reference for estimating EULB parameters, and help to understand the usage behavior of retired batteries.

Accurately predicting the remaining useful cycle life of a lithium-ion battery is essential for health management of battery systems. Aiming at the time-varying and nonlinear problems of lithium-ion batteries, a remaining useful cycle life estimation method based on Takagi-Sugeno fuzzy model is proposed, which not only reduces the amount of data calculation, but also reduces massive data and has high accuracy. First, collect the rate of change of working voltage in the charging process, and analyze the relationship between the position of voltage rate curve and the number of cycles. Second, in order to reduce the amount of historical data, the interval with obvious mapping relationship is selected, and the recursive least square method is used to fit the curve off-line, which reduces the amount of data calculation and is easy to achieve in battery management system engineering. And then, the Takagi-Sugeno fuzzy model is applied to establish the remaining useful cycle life method based on Takagi-Sugeno fuzzy model. Finally, battery management system application shows that the proposed method can achieve high prediction accuracy and also provides a new perspective for remaining useful cycle life prediction.

Owing to the degradation of an echelon-use lithium-ion battery (EULIB), the Ohmic internal resistance (OIR) and actual capacity (AE) have both changed greatly, and the state of energy (SOE) can more accurately represent the state of a EULIB than the state of charge (SOC) because of the working voltage. To improve the accuracy and adaptability of SOE estimation, in the paper, we study the energy state estimation of a EULIB. First, the four-order resistor–capacitance equivalent model of a EULIB is established, and an unscented transformation is introduced to further improve the estimation accuracy of the SOE. Second, a EULIB’s SOE is estimated based on adaptive unscented Kalman filter (AUKF), and the OIR and AE of a EULIB are estimated based on the AUKF. Third, a Takagi–Sugeno fuzzy model is introduced to optimize the OIR and AE of the EULIB, and the SOE estimation method is established based on an adaptive dual unscented Kalman filter (ADUKF). Through simulation experiments, verification, and comparison, energy decayed to 80%, 60%, and 40% of the rated energy, respectively, even with a large initial error; with the initial value of the SOE starting at 100%, 60%, or 20%, the estimated SOE can track the actual value. It can be seen that the method has a strong adaptive ability, and the estimation accuracy error is less than 1.0%, indicating that the algorithm has high accuracy. The method presented in this paper provides a new perspective for SOE estimation of EULIBs.

Accurate diagnosis of bearing faults is crucial for ensuring the safe and reliable operation of rotating machinery. To enhance the recognition accuracy of rolling bearings under nonlinear and non-stationary vibration conditions, this study proposes an integrated approach combining a multi-stage signal preprocessing strategy, termed EMDWS (Empirical Mode Decomposition with Wavelet denoising and SMOTE), with a hybrid deep learning architecture that integrates a Convolutional Neural Network (CNN) and a Transformer model, hereinafter referred to as CNT (CNN-Transformer). The method first applies empirical mode decomposition (EMD) in conjunction with wavelet denoising to enhance the representation of non-stationary fault features. Subsequently, the synthetic minority oversampling technique (SMOTE) is employed to address the issue of class imbalance in the dataset. A hybrid CNN-Transformer model is constructed by integrating convolutional neural networks and Transformer modules, enabling the extraction of both local and global signal characteristics. Furthermore, Bayesian optimization is applied to fine-tune the model’s hyperparameters, thereby enhancing both the efficiency and robustness of the model. Experimental results demonstrate that the proposed method achieves a high identification accuracy of 99.83%, indicating its effectiveness in distinguishing various bearing fault types.