Free-piston engine linear generators (FPELGs) are an innovative linear power device that exhibits the distinctive dynamics of pistons and performance of free-piston engines. Furthermore, the single-cylinder/single-piston FPELG structure type has more advantages than other FPELG structure types, including a straightforward structure and ease of control. However, when coupled with various rebound devices, the operational characteristics and piston and engine performance of single-cylinder/single-piston FPELGs are quite different. Therefore, this paper aims to quantitatively compare the dynamics of the piston and engine performance of single-cylinder/single-piston FPELGs coupled with various types of rebound device. The results indicate that when the equivalent stiffness of the gas spring is greater than that of the mechanical spring, the operating frequency of the piston of the FPELG coupled with a gas spring will be higher than that when coupled with a mechanical spring. During the compression stroke, the piston velocity of a FPELG coupled with a mechanical spring changes linearly, while the piston velocity of a FPELG coupled with a gas spring changes nonlinearly. FPELGs coupled with gas springs have shorter compression and expansion durations compared to those coupled with mechanical springs. In addition, the indicated powers of FPELGs coupled with ideal gas springs and mechanical springs are 1.5 kW and 1.3 kW, respectively. However, due to leakage, the thermal efficiency of a FPELG coupled with an actual gas spring is reduced by approximately 2.5% compared with the FPELG coupled with the ideal gas spring. Furthermore, the operation frequency of the piston is positively correlated with the stiffness of the mechanical spring. In addition, as the stiffness of the mechanical spring increases, the combustion process of the engine becomes close to an isovolumetric process. The changes in piston dynamics and engine performance when increasing the initial gas pressure of the gas spring are similar to those when increasing the stiffness of the mechanical spring.

The battery management system (BMS) is crucial for the efficient operation of batteries, with state of health (SOH) prediction being one of its core functions. Accurate SOH prediction can optimize battery management, enhance utilization and range, and extend battery lifespan. This study proposes an SOH estimation model for lithium-ion batteries that integrates the Crested Porcupine Optimizer (CPO) for parameter optimization, Extreme Learning Machine (ELM) for prediction, and Adaptive Bandwidth Kernel Function Density Estimation (ABKDE) for uncertainty quantification, aiming to enhance the long-term reliability and sustainability of energy storage systems. Health factors (HFs) are extracted by analyzing the charging voltage curves and capacity increment curves of lithium-ion batteries, and their correlation with battery capacity is validated using Pearson and Spearman correlation coefficients. The ELM model is optimized using the CPO algorithm to fine-tune input weights (IWs) and biases (Bs), thereby enhancing prediction performance. Additionally, ABKDE-based probability density estimation is introduced to construct confidence intervals for uncertainty quantification, further improving prediction accuracy and stability. Experiments using the NASA battery aging dataset validate the proposed model. Comparative analysis with different models demonstrates that the CPO-ELM-ABKDE model achieves SOH estimation with a mean absolute error (MAE) and root-mean-square error (RMSE) within 0.65% and 1.08%, respectively, significantly outperforming other approaches.

A State of Health (SOH) estimation of lithium-ion batteries is a core function of battery management systems, directly affecting the safe operation, lifetime prediction, and economic efficiency of batteries. However, existing methods still face challenges in balancing feature robustness and model generalization ability; for instance, some studies rely on features whose physical correlation with SOH lacks strict verification, or the models struggle to simultaneously capture the temporal dynamics of health factors and nonlinear mapping relationships. To address this, this paper proposes an SOH estimation method based on incremental capacity (IC) curves and a Temporal Convolutional Network—Relevance Vector Machine (TCN-RVM) model, with core innovations reflected in two aspects. Firstly, five health factors are extracted from IC curves, and the strong correlation between these features and SOH is verified using both Pearson and Spearman coefficients, ensuring the physical rationality and statistical significance of feature selection. Secondly, the TCN-RVM model is constructed to achieve complementary advantages. The dilated causal convolution of TCN is used to extract temporal local features of health factors, addressing the insufficient capture of long-range dependencies in traditional models; meanwhile, the Bayesian inference framework of RVM is integrated to enhance the nonlinear mapping capability and small-sample generalization, avoiding the overfitting tendency of complex models. Experimental validation is conducted using the lithium-ion battery dataset from the University of Maryland. The results show that the mean absolute error of the SOH estimation using the proposed method does not exceed 0.72%, which is significantly superior to comparative models such as CNN-GRU, KELM, and SVM, demonstrating higher accuracy and reliability compared with other models.

A high thrust force bi-double-sided permanent magnet linear synchronous motor used in gantry-type five-axis machining center is designed and its performance was tested in this article. This motor is the subproject of Chinese National Science and Technology Major Project named as “development of domestic large thrust linear motor used in high-speed gantry-type five-axis machining center project” jointly participated by enterprises and universities. According to the requirement of the application environment and motor performance parameters, the linear motor’s basic dimensions, form of windings, and magnet arrangement are preliminarily specified through theoretical analysis and calculation. To verify the correctness of the result of the calculation, the finite element model of the motor is established. The static and dynamic characteristics of the motor are studied and analyzed through the finite element method, and the initial scheme is revised. The prototype of the motor is manufactured based on the final revised structure parameters, and the performance of the motor is fully tested using the evaluation platform for direct-drive motor component. Experimental test results meet the design requirements and show the effectiveness of design method and process.

A (FPE-LG) is a new type of vehicle waste heat recovery device based on an organic Rankine cycle. It is expected to achieve the reuse of vehicle internal combustion engine waste heat and improve the comprehensive utilization rate of energy. To enable the FPE-LG to recover exhaust gas to a greater extent in practical applications, based on the FPE-LG coupling gas storage tank test platform, the gas is discharged from the expander cylinder. This paper analyzes the influence of differences to the tank volume, intake pressure, intake duration time, expansion duration time and exhaust duration time on piston motion characteristics and gas storage and release time during the cycle, and verifies the feasibility of gas working as a recycling medium. The results showed that the energy storage of lithium batteries increases with the increase of intake pressure, and the energy stored in lithium batteries during gas release is higher than that during gas storage; the intake duration time, expansion duration time and exhaust duration time have little effect on the storage of lithium battery energy during the cycle. When the intake pressure is 0.5 MPa, the volume of the gas tank is 30 L, and the intake duration time, expansion duration time and exhaust duration time are 50 ms, 80 ms and 30 ms, respectively, the maximum actual stroke of the piston can reach 89.592 mm.

Accurate estimation of SOC for lithium-ion batteries is a very important job in battery management systems, but under complex dynamic operating conditions, model misalignment often happens, and filtering algorithms usually do not make enough use of historical data, so the estimation accuracy is lowered. This paper puts forward a lithium-ion battery SOC estimation method that is based on weighted multi-innovation unscented Kalman filtering (WMIUKF); a hybrid parameter identification strategy that combines FFRLS and PSO is introduced to supply initial values for the global optimization of the model and to track dynamic drifts. To deal with the problems that the unscented Kalman Filter (UKF) does not make effective use of historical information and lacks an adaptive correction mechanism, multi-innovation theory and exponentially decaying weighting factors are incorporated into it; then, by fusing current and historical multi-step prediction residuals, a weighted freshness matrix can be constructed, and through this the method, we can improve the utilization efficiency of historical data and the system’s ability to resist interference. The performance of the proposed algorithm was validated through comparative experiments under various typical dynamic operating conditions, as well as at different temperatures (0 °C–45 °C) and discharge rates (0.5 C–2 C). The results indicate that the PSO-FFRLS hybrid parameter identification effectively improves model accuracy; compared to the UKF, MIUKF, and PSO-MIUKF algorithms, the WMIUKF achieved optimal SOC tracking under all types of dynamic operating conditions, with a root mean square error (RMSE) of no more than 0.58%. Even under extreme temperatures and high-rate discharge conditions, the error remained stable at a low level, demonstrating good environmental adaptability and robustness.