Hybrid Wavelet–Transformer–XGBoost Framework Optimized via Chaotic Billiards for Accurate Lithium-ion Battery Remaining Useful Life Prediction in Electric Vehicles

In the context of predicting the remaining useful life (RUL) of rolling bearings, many models often encounter challenges in identifying the starting point of the degradation stage, and the accuracy of predictions is not high. Accordingly, this paper proposes a technique that utilizes particle swarm optimization (PSO) in combination with the fusing of a one-dimensional convolutional neural network (CNN) and a multihead self-attention (MHSA) bidirectional long short-term memory (BiLSTM) network called PSO-CNN-BiLSTM-MHSA. Initially, the original signals undergo correlation signal processing to calculate the features, such as standard deviation, variance, and kurtosis, to help identify the beginning location of the rolling bearing degradation stage. A new dataset is constructed with similar degradation trend features. Subsequently, the particle swarm optimization (PSO) algorithm is employed to find the optimal values of important hyperparameters in the model. Then, a convolutional neural network (CNN) is utilized to extract the deterioration features of rolling bearings in order to predict their remaining lifespan. The degradation features are inputted into the BiLSTM-MHSA network to facilitate the learning process and estimate the remaining lifespan of rolling bearings. Finally, the degradation features are converted to the remaining usable life (RUL) via the fully connected layer. The XJTU-SY rolling bearing accelerated life experimental dataset was used to verify the effectiveness of the proposed method by k-fold cross-validation. After comparing our model to the CNN-LSTM network model and other models, we found that our model can achieve reductions in mean absolute error (MAE), root mean square error (RMSE), and mean absolute percentage error (MAPE) of 9.27%, 6.76%, and 2.35%, respectively. Therefore, the experimental results demonstrate the model’s accuracy in forecasting remaining lifetime and support its ability to forecast breakdowns.

For extrapolation, climate change and other meteorological analysis, a study of past and current weather events is a prerequisite. NASA (National Aeronautics and Space Administration) has been able to develop a model capable of predicting various weather data for any location on the Earth, including locations lacking weather stations, weather satellite coverage, and other weather measuring instruments. This paper evaluates the prediction accuracy of the NASA temperature data with respect to NiMet (Nigerian Meteorological Agency) ground truth measurement, using Akwa Ibom Airport as a case study. Exploratory data analysis (descriptive and diagnostic analyses) of temperature retrieved from NiMet and NASA was performed to give a clear path to follow for predictive and prescriptive analyses. Using 2783days of weather data retrieved from NiMet as ground truth, the accuracy of NASA predictions with the corresponding resolution was calculated. Mean absolute error (MAE) of 2.184°C and root mean square error (RMSE) of 2.579°C, with a coefficient of determination (R2) of 0.710 for maximum temperature, then MAE of 0.876°C, RMSE of 1.225°C with a coefficient of determination (R2) of 0.620 for minimum temperature was discovered. There is a good correlation between the two datasets; hence, a model can be developed to generate more accurate predictions, using the NASA data as input. Predictive and prescriptive analyses were performed by employing five prediction algorithms: decision tree regression, XGBoost regression and MLP (multilayer perceptron) with LBFGS (limited-memory Broyden-Fletcher-Goldfarb-Shanno) optimizer, MLP with SGD (stochastic gradient) optimizer and MLP with Adam optimizer. The MLP LBFGS algorithm performed best, by significantly reducing the MAE by 35.35% and RMSE by 31.06% for maximum temperature, accordingly, MAE by 10.05% and RMSE by 8.00% for minimum temperature. Results obtained show that given sufficient data, plugging NASA predictions as input to an LBFGS-MLP model gives more accurate temperature predictions for the study area.

Accurately predicting the Remaining Useful Life (RUL) of lithium-ion batteries is the key to the battery health management system. However, problems of unstable model output and extensive calculation limit the prediction accuracy. This article proposes a Particle Swarm Optimization Random Forest (PSO-RF) prediction method to improve the RUL prediction accuracy. First, the battery capacity extracted from the lithium-ion battery data set of the National Aeronautics and Space Administration (NASA) and the University of Maryland Center for Advanced Life Cycle Engineering (CALCE) is set as the battery life health factor. Then, a PSO-RF prediction model is established based on the optimal parameters for the number of trees and the number of random features to split by the PSO algorithm. Finally, the experiment is verified on the NASA and CALCE data sets. The experiment results indicate that the method predicts RUL with Mean Absolute Error (MAE) less than 2%, Root Mean Square Error (RMSE) less than 3%, and goodness of fit greater than 94%. This method solves the problem of parameter selection in the RF algorithm.

In order to predict the remaining useful life (RUL) of rolling bearings in complex environmental conditions, a bearing RUL prediction method based on fractal dimension and one-dimensional convolutional neural network (1D-CNN) is proposed. This method uses fractal dimension to characterize the degeneration process of the rolling bearing and combines the features of time domain, frequency domain, wavelet packet domain, and entropy domain. Fractal dimension provides an analytical method for characterizing the complexity of vibration signals. The features extracted from different feature domains can complement each other’s advantages, reveal the degradation state of the bearing more comprehensively and achieve better performance. Then, the percentage of the remaining life of the bearing is used as the degradation tracking index of the rolling bearing. Based on the idea of stratified sampling, the training samples and test samples are constructed, and then a 6-layer CNN is constructed to train the model. Finally, three commonly used data sets of full-life bearings are used to verify the model, namely, IEEE prognostics and health management 2012 Data Challenge, IMS dataset, and XJTU-SY dataset. The experimental results show that, on the three experimental datasets, compared to the long short-term memory network (LSTM) and the extreme learning machine (ELM) methods, the prediction effect of the RUL of the bearing based on the fractal dimension and 1D-CNN proposed in our paper is better. Its mean absolute error and root mean square error (RMSE) and mean absolute percentage error (MAPE) have been reduced, and the correlation index ( R2), adjusted_ R2, and relative accuracy (RA) have been improved, which can predict the RUL of the bearing more accurately.

In this study, we address the challenge of predicting the Social Cohesion Index in Jakarta through a comprehensive analysis of machine learning models. Finding the most accurate and effective predictive model for this crucial urban evaluation task is the primary goal of our research. We use a variety of machine learning algorithms, comparing their performance using metrics like Mean Absolute Error (MAE), Root Mean Square Error (RMSE), Mean Absolute Percentage Error (MAPE), and computational cost. These algorithms include Gradient Boosted Decision Trees (GBDT), Polynomial Regression, Random Forest, Support Vector Machine (SVM), and Multi-Layer Perceptron (MLP). It should be noted that GBDT stands out as a top performer, regularly displaying outstanding accuracy with a competitive MAE of 0.692, RMSE of 0.887, and MAPE of 25.59%. The computational efficiency of GBDT is also impressive, with predictions taking only 0.05 seconds. These results underscore the potential of GBDT as a practical and precise tool for real-time assessments of social cohesion in large urban environments like Jakarta. The findings offer a data-driven way to guide policy decisions and community development activities, with important implications for urban planning and governance. Overall, this research emphasizes the promise of GBDT in boosting social cohesion evaluation approaches and increases our understanding of the application of machine learning in addressing complex urban difficulties.

Remaining useful life (RUL) prediction is critical for ensuring the reliability and safety of industrial equipment. In recent years, Transformer-based models have been widely employed in RUL prediction tasks for rolling bearings, owing to their superior capability in capturing global features. However, Transformers exhibit limitations in extracting local temporal features, making it challenging to fully model the degradation process. To address this issue, this paper proposes a parallel hybrid prediction approach based on Transformer and Long Short-Term Memory (LSTM) networks. The proposed method begins by applying Empirical Mode Decomposition (EMD) to the raw vibration signals of rolling bearings, decomposing them into a series of Intrinsic Mode Functions (IMFs), from which statistical features are extracted. These features are then normalized and used to construct the input dataset for the model. In the model architecture, the LSTM network is employed to capture local temporal dependencies, while the Transformer module is utilized to model long-range relationships for RUL prediction. The performance of the proposed method is evaluated using mean absolute error (MAE) and root mean square error (RMSE). Experimental validation is conducted on the PHM2012 dataset, along with generalization experiments on the XJTU-SY dataset. The results demonstrate that the proposed Transformer–LSTM approach achieves high prediction accuracy and strong generalization performance, outperforming conventional methods such as LSTM and GRU.

Predicting the remaining useful life (RUL) is a pivotal step in ensuring the reliability of lithium-ion batteries (LIBs). In order to enhance the precision and stability of battery RUL prediction, this study introduces an innovative hybrid deep learning model that seamlessly integrates convolutional neural network (CNN) and gated recurrent unit (GRU) architectures. Our primary goal is to significantly improve the accuracy of RUL predictions for LIBs. Our model excels in its predictive capabilities by skillfully extracting intricate features from a diverse array of data sources, including voltage (V), current (I), temperature (T), and capacity. Within this novel architectural design, parallel CNN layers are meticulously crafted to process each input feature individually. This approach enables the extraction of highly pertinent information from multi-channel charging profiles. We subjected our model to rigorous evaluations across three distinct scenarios to validate its effectiveness. When compared to LSTM, GRU, and CNN-LSTM models, our CNN-GRU model showcases a remarkable reduction in root mean square error, mean square error, mean absolute error, and mean absolute percentage error. These results affirm the superior predictive capabilities of our CNN-GRU model, which effectively harnesses the strengths of both CNNs and GRU networks to achieve superior prediction accuracy. This study draws upon NASA data to underscore the outstanding predictive performance of the CNN-GRU model in estimating the RUL of LIBs.

This research aims to use a vibration monitoring system along with machine learning techniques to predict the downtime and Remaining Useful Life (RUL) of three-phase induction motors in the manufacturing sector. The study obtains measurement data from accelerometer sensors that collect various parameters related to motor performance. The research includes a data preprocessing stage to handle missing data, select predictor attributes, and remove duplicates. Supervised learning algorithms are applied, including Decision Tree (DT), Naive Bayes (NB), Random Forest (RF), and Artificial Neural Network (ANN). The results show that DT and NB models have the best performance in downtime classification, achieving 100% accuracy, recall, precision and F1 values. In terms of predicting Remaining Useful Life (RUL), the RF model outperforms the base model and ANN, showing better results in Root Mean Square Error (RMSE), Mean Absolute Error (MAE), Mean Absolute Percentage Error (MAPE), and correlation coefficient.

This study extends previous research on Remaining Useful Life (RUL) prediction for agricultural vehicles by utilizing an enriched dataset to overcome earlier limitations in forecasting RUL for electric and hydraulic system components. Influential features have been identified through Pearson correlation and Random Forest feature importance analysis. Discrete Wavelet Transform (DWT) has been applied to extract additional approximation and detail coefficients, enhancing the feature set. Prediction algorithms—LSTM, FCNN, and SVM—have been evaluated using Mean Absolute Error (MAE), Mean Absolute Percentage Error (MAPE), Root Mean Squared Error (RMSE), and Coefficient of Determination (R²) metrics. Results indicate that LSTM models demonstrate superior performance, particularly those incorporating DWT- extracted features and geospatial factors such as weather and terrain conditions. The findings suggest that the developed RUL prediction models can be integrated into future Internet of Things (IoT) systems for remote monitoring and predictive maintenance of agricultural machinery.

The rolling bearing remaining useful life (RUL) prediction is a hot topic issue in the field of rail transportation. The existing RUL prediction methods for rolling bearing have problems such as unreasonable division of rolling bearing degradation stages and incomplete extraction of degradation features by feature selection indicators. In order to solve these problems, an entire life-cycle rolling bearing RUL prediction method using new degradation feature evaluation indicators is proposed. Firstly, the degradation feature evaluation indicator is designed to evaluate the stability of the degradation feature. Then, the combination of stability evaluation indicator and correlation evaluation indicator is used as the basis for feature selection. Secondly, the Gaussian Mixture Model (GMM) method is fused with the Support Vector Machine (SVM) to divide the bearing entire life-cycle into three stages: normal stage, early degradation stage, and degradation stage. Finally, the Long Short-Term Memory (LSTM) network model is trained separately to predict the rolling bearing RUL for different rolling bearing degradation stages. The effectiveness of the proposed prediction method based on different degradation stages of rolling bearing in predicting the RUL of rolling bearing is verified through PRONOSTIA bearing dataset. The comparison with existing methods shows that this approach demonstrates superior accuracy and predictive performance. For example, the Mean Square Error (MSE) evaluation metric has decreased by 60%. The Root Mean Square Error (RMSE) evaluation metric has decreased by 36.5%. The Mean Absolute Error (MAE) evaluation metric has decreased by 48.6%. The Mean Absolute Percentage Error (MAPE) evaluation metric has decreased by 36.9%.

As the main cause of asphalt pavement distress, rutting severely affects pavement safety. Establishing an accurate rutting prediction model is crucial for asphalt pavement maintenance, pavement structure design, and pavement repair. This study explores five machine learning methods, namely Support Vector Regression (SVR), Artificial Neural Network (ANN), Gradient Boosting Decision Tree (GBDT), Random Forest (RF), and Extra Trees, to predict the development of rutting depth using data from RIOHTRack. The model’s performance is measured by comparing the performance evaluation indicators of different models, such as the coefficient of determination, root mean square error, mean absolute error, and mean absolute percentage error. The results demonstrate that integrated learning techniques such as RF, GBDT, and Extra Trees works best with R2 = 0.9761, 0.9833, and 0.9747. Moreover, the GBFT model can capture the trend of the measured rutting progression curve better than the mechanistic-empirical (M-E) model. The analysis of feature importance reveals that, in addition to external factors such as temperature and axle load, the aggregate of the asphalt concrete layer and air void crucially affect rutting. The higher the base strength, the smaller the rutting depth. The proposed model is highly straightforward and serves as an accessible analysis tool for engineers in practice.

Accurate prediction of the remaining useful life (RUL) of lithium-ion batteries (LIBs) is crucial for enhancing the safety, reliability, and efficiency of battery-powered applications like electric vehicles and energy storage systems. This review analyzed over 200 peer-reviewed studies and categorized RUL prediction methods into three major approaches: physics-based, data-driven, and hybrid models. Hybrid models, which combine physical insights with data-driven methods, are the most widely used due to their adaptability, accuracy, and interpretability. Data-driven models, such as long short-term memory and convolutional neural networks, excel in capturing complex, nonlinear relationships but require large datasets and high computational power. While physics-based models offer high accuracy, they are less commonly employed due to their complexity and extensive parameter tuning requirements. Despite their benefits, hybrid models face challenges, including increased computational complexity and integration difficulties. This review also highlights key datasets and evaluation metrics used in LIB RUL prediction. The NASA dataset is the most frequently used, appearing in 30.8% of the papers, followed by the CALCE dataset. Root mean square error is the most common evaluation metric, used in 29.6% of the studies, followed by mean absolute error and mean absolute percentage error, which are essential for assessing prediction accuracy. Through comparative analysis, this review identified key challenges and outlined future research directions, including the need for lightweight hybrid models, standardized benchmarking datasets, and uncertainty-aware evaluation frameworks to support real-time, robust battery management systems. In conclusion, the future of LIB RUL prediction lies in the integration of advanced hybrid models, improved datasets, and uncertainty-aware performance metrics, with a focus on refining data-driven approaches for handling real-time, multi-sensor data.

Remaining useful life (RUL) serves as a pivotal metric for quantifying lithium-ion batteries’ state of health (SOH) in electric vehicles and plays a crucial role in ensuring their safety and reliability. In order to achieve accurate and reliable RUL prediction, a novel RUL prediction method which employs a back propagation (BP) neural network based on the Harris Hawks optimization (HHO) algorithm is proposed. This method optimizes the BP parameters using the improved HHO algorithm. At first, the circle chaotic mapping method is utilized to solve the problem of the initial value. Considering the problem of local convergence, Gaussian mutation is introduced to improve the search ability of the algorithm. Subsequently, two key health factors are selected as input features for the model, including the constant-current charging isovoltage rise time and constant-current discharging isovoltage drop time. The model is validated using aging data from commercial lithium iron phosphate (LiFePO4) batteries. Finally, the model is thoroughly verified under an aging test. Experimental validation using training sets comprising 50%, 60%, and 70% of the cycle data demonstrates superior predictive performance, with mean absolute error (MAE) values below 0.012, root mean square error (RMSE) values below 0.017 and mean absolute percentage error (MAPE) within 0.95%. The results indicate that the model significantly improves prediction accuracy, robustness and searchability.

Proton exchange membrane fuel cell (PEMFC) is considered as one of the most promising green energy devices. Although fruitful results can be available for the remaining useful life (RUL) prediction of PEMFC, stochastic uncertainties have never been considered. To tackle this problem, a hybrid method is proposed in this paper. Wiener process with temporal uncertainty and individual uncertainty is adopted to model the degradation of the state of health (SOH), which is then estimated from monitoring voltage with measurement noise using the unscented Kalman filter (UKF), where unknown filtering and model parameters are jointly identified by expectation-maximization (EM) algorithm and Rauch-Tung-Striebel (RTS) smoother. Finally, gated recurrent unit (GRU) network is employed to realize the RUL prediction with the prediction uncertainty quantified by the Bayesian variational inference technology. The proposed method is verified on the experimental data. Results indicate that smaller mean absolute percentage error (MAPE), root mean square error (RMSE), and mean absolute error (MAE) values can be obtained compared with other methods. When 60% data are used for prediction, the proposed method can achieve a RUL prediction accuracy with 1.63% and 2.17% relative errors under static and dynamic conditions, respectively, which illustrates the feasibility and superiority of the proposed method.

Remaining useful life prediction of PEMFC based on long short-term memory recurrent neural networks