This paper is concerned with the minimizers of L 2 -subcritical constraint variational problems with spatially decaying nonlinearities in a bounded domain Ω of ℝ N ( N ≥ 1). We prove that the problem admits minimizers for any M > 0. Moreover, the limiting behavior of minimizers as M → ∞ is also analyzed rigorously.

The increasing quantity of PV installation has brought great challenges to the grid owing to power fluctuations. Hybrid energy storage systems have been an effective solution to smooth out PV output power variations. In order to reduce the required capacity and extend the lifetime of the hybrid energy storage system, a two-stage self-adaptive smoothing approach based on the artificial potential field is proposed to decompose and allocate power among the grid, battery, and supercapacitor dynamically. In the ramp rate control stage, an unsymmetric artificial potential field method is used to regulate the cutoff frequency of a low-pass filter, so as to limit the PV power ramp rate within the prescribed range and allocate the power between the grid and the hybrid energy storage system. In the HESS power distribution stage, a symmetric artificial potential field is adopted to distribute power between the battery and supercapacitor by regulating the cutoff frequency of another low-pass filter. The effectiveness of the proposed strategy is validated through a case study based on real-world PV data in Denmark. The results show that the proposed method outperforms to reduce the over-smoothing effect and battery degradation, which can reduce battery loss by up to 17% to 49% compared to existing smoothing approaches.

Electric vehicles (EVs) suffer from long charging time and inconvenient charging due to limited charging stations, which are the main causes of drivers’ range anxiety. Real-time and accurate driving range prediction can help drivers plan journeys, alleviate range anxiety, and promote EV development. However, predicting the EV driving range is challenging due to different weather, road conditions, driver habits, and limited available data. To address this issue, this article proposes a novel digital twin-based driving range prediction method. First, a one-year real-world EV dataset in Beijing is utilized. Detailed feature selection is conducted for the dataset, and six key features are extracted: battery SOC, consumed battery SOC, battery total voltage, battery maximum cell voltage, battery minimum cell voltage, and mileage already driven. Then, a random forest method is used to train the EV driving range prediction model using the features described earlier. Four prediction models with different adopted features are trained, respectively. Finally, the sliding window algorithm is proposed for the input of random forest to investigate its impact on prediction accuracy in the four prediction models, and different window sizes are evaluated. Results show that the sliding window algorithm can significantly improve the prediction model with only SOC as input, while it can deteriorate other models with more features. The most accurate model taking all six features as inputs provides 89.8% data that has an accuracy of over 80%, while data proportion of the prediction model without past energy consumption is only 31.8%.

To enhance the energy efficiency of electrified vehicles (EVs), developing effective energy management strategies (EMS) for hybrid storage systems is essential. Predictive EMS (PEMS) that foresee future vehicle speeds have demonstrated substantial potential in boosting EMS performance. However, traditional PEMS models, employing a sequential approach of speed prediction followed by energy allocation, are hampered by cumulative errors. These errors from the initial speed predss this issue, this paper introduces a novel solution: the trainable integrated preiction negatively impact the efficiency of subsequent energy management. To addrediction and energy management strategy (TIP-EMS). Contrasting with conventional sequential PEMS, TIP-EMS features a dual-branch, integrated neural network, which is fully trainable. This network processes driving status inputs via attention layers, with one branch dedicated to energy management objectives using a reinforcement learning (RL) algorithm, and the other to vehicle speed prediction. Both branches are trained simultaneously, but post-training, only the RL branch is activated for energy management. Implemented with a soft actor-critic RL algorithm, TIP-EMS is applied to a fuel cell EV for optimized energy management. The validation involved training TIP-EMS using 27 driving profiles, which developed its prediction and energy management capabilities, followed by tests in untrained scenarios. The results show that TIP-EMS surpasses conventional sequential PEMS by up to 4.2% in scenarios where prediction accuracies are comparable, highlighting the efficacy of the trainable integrated mechanism. In addition, TIP-EMS exhibits superior energy conservation compared to non-predictive RL strategies. Lastly,TIP-EMS exhibits robustness to adjustments in the weight given to the prediction objective, further confirming its practical applicability.

Eco-driving plays an increasingly important role in intelligent transportation systems, where the vehicle-following economy and safety are receiving increasing attention in recent years. In this context, this article proposes a novel deep deterministic policy gradient (DDPG)-based driving control strategy for connected electric vehicles (CEVs) under vehicle-following scenarios. Three original contributions make this article distinctive from existing studies. First, a multi-objective optimization problem including driving safety, passenger comfort, and the driving economy for the following vehicle is established, in which the battery capacity degradation cost is first considered in the vehicle-following problem. Second, a DDPG-based driving control strategy is proposed where a penalty is introduced into the multi-objective optimization reward function to accelerate the convergence process. Third, the coupling relationship of the three objectives is carefully studied. Different weighting factors are tested and analyzed to balance the three objectives. Detailed discussion and comparison under different driving cycles validate the superiority of the proposed method, e.g., a 16–31% reduction of battery capacity degradation cost with better safety and comfort, compared with existing vehicle-following strategies. This work makes a potential contribution to the artificial intelligence application of intelligent transportation systems.

The control of a battery thermal management system (BTMS) is essential for the thermal safety, energy efficiency, and durability of electric vehicles (EVs) in hot weather. To address the battery cooling optimization problem, this paper utilizes dynamic programming (DP) to develop an online rule-based control strategy. Firstly, an electrical-thermal-aging model of the $\rm LiFePO_4$ battery pack is established. A control-oriented onboard BTMS model is proposed and verified under different speed profiles and temperatures. Then in the DP framework, a cost function consisting of battery aging cost and cooling-induced electricity cost is minimized to obtain the optimal compressor power. By exacting three rules "fast cooling, slow cooling, and temperature-maintaining" from the DP result, a near-optimal rule-based cooling strategy, which uses as much regenerative energy as possible to cool the battery pack, is proposed for online execution. Simulation results show that the proposed online strategy can dramatically improve the driving economy and reduce battery degradation under diverse operation conditions, achieving less than a 3% difference in battery loss compared to the offline DP. Recommendations regarding battery cooling under different real-world cases are finally provided.

The microstructures and magnetic properties of Co28Fe28Ni19Si13B12 high-entropy amorphous toroidal cores are investigated by X-ray diffractometer (XRD), transmission electron microscopy (TEM), MATS -2010 SD/MATS2010SA soft magnetic DC (AC) tester, WK6500B LCR bridge and precision LCZ tester. The results indicate that the alloy combines high curie temperature (Tc) and excellent soft magnetic properties. After heat treatment, the Co7Fe3 phase first precipitates in the alloy, and then follows the lamellar precipitate as Fe -B and Ni -Si phase. At elevated temperatures, the Co7Fe3 phase is transformed into the (Ni, Fe) phase with a precipitation of the Co2B phase. Compared to normal annealing (NA), the ordered rearrangement of domains induced by the magnetic field during heat treatment simplifies the domain structure and significantly improves the magnetic properties. Following stepwise longitudinal magnetic field annealing (NA+LFA), rectangular hysteresis loops are formed through domain movement, enhancing saturation induction (Bs) and remanence ratio, while reducing coercivity (Hc) and permeability. Conducting stepwise transverse magnetic field annealing (NA+TFA) increases permeability, maintains constant magnetic conductivity, reduces losses, and the ability to resist external direct current (DC) field interference is greatly enhanced.

Model predictive control is a real-time energy management method for hybrid energy storage systems, whose performance is closely related to the prediction horizon. However, a longer prediction horizon also means a higher computation burden and more predictive uncertainties. This paper proposed a predictive energy management strategy with an optimized prediction horizon for the hybrid energy storage system of electric vehicles. Firstly, the receding horizon optimization problem is formulated to minimize the battery degradation cost and traction electricity cost for the electric vehicle operation. Then, the optimal control sequence is solved to obtain the power allocation between the battery and the supercapacitor. Furthermore, the effect of different horizons on the optimization results is analyzed under diverse operating conditions, determining the optimal horizon to balance the system costs and computation burden. Compared with the short horizon, the optimal horizon can achieve 5.2% $\sim$ 8.5% performance improvement with the acceptable computation time approaching 1 s.

Battery cooling is crucial for electric vehicles' thermal safety, energy consumption, and battery life in hot climatic conditions. For electric vehicles with battery/supercapacitor hybrid energy storage system, battery cooling is deeply coupled with load power split from the electrical-thermal-aging perspective, leading to challenging thermal and energy management issues. This paper proposes a hierarchical multi-horizon model predictive control (MH-MPC) method to optimize battery cooling and energy management simultaneously. First, the electrical-thermal-aging coupling relationship between battery cooling and energy management is systematically analyzed. Then, by decoupling a centralized MH-MPC, an upper-level MH-MPC is designed to optimize the battery capacity loss cost and battery cooling cost by generating optimal compressor power, then a lower-level MH-MPC tends to minimize the battery capacity loss cost by allocating the total load power demand. The prediction horizon and sampling time are determined. Numerical results show that, compared with the centralized method, the proposed hierarchical method provides a lower battery capacity loss for long-term driving with only about 20% computation burden. Compared with standalone energy management without battery cooling, the total cost can be reduced by 12%-16% under long-term driving. Compared with optimizing energy management with Bangbang cooling, the battery degradation and total costs can be reduced by 15%-52% under short-term driving without deteriorating long-term performance.

The crystallized behavior, microstructure and magnetic properties of Co 28 Fe 28 Ni 19 Si 13 B 8 Cu 1 Nb 1 Mo 2 highentropy metallic glass are studied by DSC, XRD, TEM and VSM. The results show that two crystallization peaks occur with a difference of approximately 129 - 149 K, but the activation energy is different. The activation energy of the first peak is 175.3 kJ/mol and the second is that of 460.1 kJ/mol. After annealing, the Co 7 Fe 3 phase first precipitates with a feature of three-dimensional growth. When the annealing temperature is higher than the second crystallization temperature, the phases such as (Fe,Ni,Mo) 23 B 6 , Co 3 Mo 2 Si, Co 4 B, Fe 3 Mo precipitate sequentially, meanwhile Cu accumulates into small clusters to provide heterogeneous nucleation centers for the crystalline phase in the early stage of crystallization. Finally, the Hc increase with temperature, and the Ms first increasing and then decreasing with the maximum value of 93.11 emu/g at 893 K.

Although the advancements in marine engines diagnosis technologies and systems, estimating faults combinations at the entire operating envelope is challenging. This study aims at first investigating the path logarithmic signatures (logS) method for information extraction and dimensions reduction from the in-cylinder pressure signals, and secondly, proposing the most effective data-driven hybrid approach employing logS as input to artificial neural networks (ANN) regression to estimate the severity of critical faults in marine engines. A large four-stroke marine diesel engine is considered and in-cylinder pressures are generated using a validated physics-based digital twin by simulating scenarios with four faults combinations of varying severity in the entire operating envelope. A parametric study is performed to quantify the logS number impact on the ANN regression models accuracy and training time. Four data pre-processing approaches, which consider elementary or high variance logS, without or with the use of Principal Components Analysis (PCA), are also comparatively assessed. The results demonstrate that the approach involving the use of eight elementary logS, Principal Components Analysis (PCA), standardisation and an ANN regression model comprising two hidden layers with ten neurons each is the most effective, as it exhibits the lowest values on both the root mean square and the standard error 95% confidence interval. This is the first study on logS application for marine engines faults severity estimation, and as such it impacts the development of future data-driven diagnostics methods.

Driving style can significantly affect the energy consumption, battery lifespan, and driving economy of electric vehicles. In this context, this paper proposes a novel driving style-aware energy management strategy for electric vehicles with battery/supercapacitor hybrid energy storage systems based on deep reinforcement learning. Firstly, a semi-supervised support vector machine-based driving style recognition method is presented to recognize the driving style, where twenty features are extracted from limited labeled velocity/acceleration data and then reduced to six dimensions by locally linear embedding. The six dimension features are used to obtain accurate recognition results. Then a proximal policy optimization-based energy management strategy is proposed with the driving style as an additional input state, to optimize the power allocation and minimize the battery capacity loss cost. Extensive results illustrate the effectiveness of the proposed methods, e.g., the proposed driving style recognition method can recognize the real-time driving style with an accuracy of over 95%. Taking the recognized style as input, the proposed driving style-aware energy management strategy can reduce the battery capacity loss cost by 3.30–4.19% and 1.77–8.15%, compared with no driving style and incorrect driving style input energy management methods, respectively.

Deep reinforcement learning has emerged as a promising candidate for online optimal energy management of multi-energy storage vehicles. However, how to ensure the adaptability and optimality of the reinforcement learning agent under realistic driving conditions is still the main bottleneck. To enable the reinforcement learning agent to efficiently learn the optimal power allocation strategies under diverse driving conditions, this paper proposes an incentive learning-based energy management strategy for battery-supercapacitor electric vehicles to minimize the battery capacity loss cost and power loss cost. First, an incentive reward function based on supercapacitor state-of-charge and vehicle acceleration is proposed for proximal policy optimization-based energy management strategy, which can stimulate the agent to learn for optimal power allocation policy under high load power conditions quickly. Second, a random sampling-based velocity transfer probability surface is constructed for pre-training to guarantee strategy optimality under unfamiliar driving cycles. Third, the generalized advantage estimation and layer normalization of neural networks are incorporated to improve the learning convergence. Results show that the proposed method can reduce the above costs by 5.8%–13.8% and 11.7%–38.8% compared with existing deep reinforcement learning methods under the pre-training driving cycle and test driving cycles, respectively, which yields closer results to offline dynamic programming.

For multi-energy storage vehicles, the performance of online predictive energy management strategies largely relies on the length and effective utilization of predictive information. In this context, this paper proposes a novel velocity prediction method for the full driving cycle of electric vehicles based on the spatial–temporal commuting data, then the predicted velocity is applied to predictive energy management in electric vehicles with battery/supercapacitor hybrid energy storage system. Firstly, an one-year real-world commuting data set is collected on a Chinese arterial road with 10 intersections, 225 records are classified into 79 categories. Then, a real-time two-stage full driving cycle prediction method is proposed, where a medium-term prediction based on a long–short term memory (LSTM) network and a long-term prediction generated by a spatial–temporal interpolation method (STIM) are spliced for each category. The most probable category, i.e., the executed LSTM and STIM can be updated in real-time. Finally, a multi-horizon model predictive control method (MH-MPC) is established to leverage the predicted velocity for optimal power distribution. Compared with the conventional short-sighted MPC, the MH-MPC can reduce 4.2% battery degradation cost in a statistics form with real-time computation requirements satisfied.

This paper focuses on the adaptive event-triggered cooperative tracking control problem for multiple high-speed trains (MHSTs) system. A new adaptive cooperative tracking control protocol is presented based on the multi-agent system (MAS) concept and the event-triggered control theory. Firstly, to build a refined train dynamical model, the uncertain nonlinear resistances are approximated by a fuzzy logic system. Moreover, a distributed sliding-mode estimator is used to estimate the states of the leader train to obtain the system errors to perform the subsequent backstepping control design. In the event-triggered mechanism, the controller updates are triggered only when the measurement error exceeds a specified threshold, which can reduce the waste of computation resources and the overuse of actuators. It is demonstrated that all signals in the MHSTs system are ultimately bounded. Finally, a simulation example is provided to validate the effectiveness of the proposed event-triggered control methods.

Driving intention and speed prediction are essential factors in the energy management of plug-in hybrid electric vehicles (PHEVs). This paper proposes an improved energy management strategy for the subject vehicle by speed prediction fused with driving intention and LIDAR data in a vehicle-following scenario. A driving intention recognition model is developed based on the gated recurrent unit (GRU), which takes the vehicle speed, throttle opening, and brake pedal force of the subject vehicle as input. Then integrating the LIDAR point cloud data and driving intention result of the subject vehicle to achieve more accurate speed prediction, where joint probabilistic data association and interacting multiple models methods are used to process LIDAR data. The more accurate speed prediction is then applied to design a prediction-informed adaptive equivalent consumption minimization strategy (PIA-ECMS) for real-time energy management optimization. Experimental results demonstrate the recognition accuracy of up to 88%, indicating that the driver’s driving intention can be identified effectively. The speed prediction has an error margin of no more than 5.9 km/h. Compared with existing adaptive ECMS without speed prediction, the proposed PIA-ECMS can enhance fuel economy by 1.3–2.7% while achieving better SOC charge sustainability.

The crystallization behavior and magnetic properties of Co-based alloy are investigated by DSC, XRD, TEM, VSM, and impedance analyzer. The results indicate that the non-isothermal crystallization of Co50Fe25Nb15B10 alloy has a significant glass transition with a supercooled liquid region of about 80 K. When the heat treatment is above crystallization temperature, some phases appear successively as the Co2B and (Co, Fe)21Nb2B6, and with the increase of annealing temperature, the values of coercivity Hc and saturation magnetic induction strength Bs increase correspondingly. After measuring the impedance effect of the Co-based alloy, it is found that the in-crease in impedance value is attributed to the decrease in magnetic anisotropy performance of the alloy, and the impedance curves of both amorphous and nanocrystalline alloys show a similar single peak trend. However, the crystallization phases after annealing form with a large size that hind the magnetization process resulting in a significant decrease of (& UDelta;Z/Z)max value.

The concept of the Internet-of-Batteries (IoB) has recently emerged and offers great potential for the control and optimization of battery utilization in electric vehicles (EV). This concept, which combines aspects of the Internet-of-Things (IoT) with the latest advancements in battery technology and cloud computing, can provide a wealth of new information about battery health and performance. This information can be used to improve battery management in a number of ways, including continuous battery prognosis and improved battery and vehicle management. In this paper, we reviewed in detail the basic structure of IoB, based on many existing studies. We also explored the potential benefits of this new approach, such as continuous battery prognosis and improved battery and vehicle management. Implementing the IoB in EVs is not without challenges, as the IoB faces a number of challenges, including the security of battery data, cross-platform functionality, and the technical complexities of applying IoB on a large scale. However, the potential benefits of the IoB are significant and with continued research and development, it has the ability to revolutionize the EV industry. The purpose of this review paper is to provide a comprehensive overview of the IoB, discussing its potential benefits and challenges. The paper also provides a roadmap for the future development of IoB, highlighting the key areas that need to be addressed to fully realize the potential of this technology.

State/temperature monitoring is one of the key requirements of battery management systems that facilitates efficient and intelligent management to ensure the safe operation of batteries in electrified transportation. This paper proposes an online end-to-end state monitoring method based on transferred multi-task learning. Measurement data is directly used for sharing information generation with the convolutional neural network. Then, the multiple task-specific layers are added for state/temperature monitoring. The transfer learning strategy is designed to improve accuracy further under various application scenarios. Experiments under different working profiles, temperatures, and aging conditions are conducted to evaluate the method, which covers the wide usage ranges in electric vehicles. Comparisons with several benchmarks illustrate the superiority of the proposed method with better accuracy and computational efficiency. The monitoring results under extremely current working profiles and variable internal and external conditions are evaluated. Results show that the mean absolute error and root mean square error of state of charge and state of energy estimation are less than 2.31% and 3.31%, respectively. The above errors in the prediction of future temperature five steps ahead are less than 0.89 °C and 1.29 °C, respectively. The framework is also suitable for monitoring second-life batteries retired from electric vehicles. This paper illustrates the potential application of data-driven multi-state monitoring throughout the entire battery life.

The crystallization kinetics, phase formation and magnetic properties of (FeCoNiMn0.25Al0.25)75Si13B12 high-entropy metallic glass are investigated by thermal analysis, electron microscopic imaging, X-ray and magnetic tests. The results indicate that the alloy combines good glass forming ability and thermal stability. After heat treatment, the alloy precipitates with a feature of three-dimensional growth, while the α-Fe,Co phase first precipitates, and following the lamellar eutectic precipitate as Fe-B and Co2Si. This ultra-fine α-Fe,Co at low temperatures and the solid solution of non-ferromagnetic elements in the α-Fe,Co at high temperatures decrease the saturation magnetization of the alloy. In addition, the change from antiferromagnetic to ferromagnetic of Mn is confirmed through first-principles density functional theory calculations.