A generic physics-informed machine learning framework for battery remaining useful life prediction using small early-stage lifecycle data

Batteries, recognized as effective energy storage solutions, are considered the main facilitators of the world-wide transition towards clean and renewable energy sources. Among different types of batteries, lithium-ion (Li-ion) variants offer higher energy densities and relatively longer life spans when compared to other types. Nonetheless, a primary concern with these batteries is their lifetime. Batteries undergo various degradation mechanisms under storage and use, significantly impacting their lifespan. To this end, it is crucial to predict the degradation and lifetime of Li-ion batteries under given conditions.Researchers use three main methodologies to perform battery health diagnostics and to predict the lifetime of batteries. One approach revolves around using mechanistic, first-principle electrochemical models, also known as physics-based models. If equipped with proper thermodynamic theories, such models can show promising capabilities; however, holistic degradation prediction with these models is still challenging due to the computational complexities and the multitude of parameters that need to be fine-tuned in this approach. The other common strategy is to use empirical models to predict battery degradation. These models generally entail fewer parameters to be identified and are computationally less intensive to solve. Nonetheless, empirical models can suffer from the accuracy point-of-view as they are constrained to predict degradation trends introduced by certain degradation modes. Another common technique in battery life prediction is to utilize purely data-driven methods, such as machine learning (ML) algorithms, which also have shown promising results in the literature on rapid health predictions. However, these methods require large volumes of experimental data for training and testing ML models to ensure accuracy. In addition, data-driven methods are likely to extrapolate poorly to conditions beyond their training data and are indifferent towards the underlying degradation mechanisms. Recently, physics-informed machine learning (PI-ML) methods have garnered significant attention. They integrate physics-based or empirical models (developed based on physics) with a data-driven approach and allow one to train ML models on a smaller set of experimental data.To the best of the authors’ knowledge, the performance comparison between first-principle and empirical models when integrated within PI-ML remains unclear. Therefore, in this work, we aim to compare these two models when applied to prognostics (capacity forecasting and remaining useful life prediction) of a set of Li-ion batteries. To perform this study, we generate aging data for 40 Li-ion coin cells cycled under randomized conditions. Each cell undergoes a three-step charging stage followed by a two-step discharge stage. After obtaining the aging data, we will develop two PI-ML models, one equipped with a physics-based model and another with a set of empirical models. Both PI-ML models in this work will follow the sequential integration approach, where the training data for the final PI-ML model come from both experimental and computational data, the latter of which are obtained from the physics-based or empirical models. The parameters for the physics-based and empirical models are identified from another set of experimental data. Finally, the PI-ML models will be tested with experimental data obtained at different cycling conditions. The data flow for the sequential architecture of PI-ML is shown in the attached figure. This comparative study will help identify the performance of physics-based and empirical models when integrated into PI-ML. The main performance metric considered in this work is each model’s ability to extrapolate beyond the experimental training data set, hence aiding the final PI-ML model in generalizing to conditions not covered by its experimental training data set. Figure 1

Physics-informed machine learning framework for creep-fatigue life prediction of a Ni-based superalloy using ensemble learning

Data-driven intelligent method has shown superior performance in remaining useful life (RUL) prediction. However, the model training is difficult due to the limited degradation data. To address the challenges of small data set, a Sequence Adaptation Adversarial Network (SAAN) is proposed in this paper. SAAN could expand training data with auxiliary set by sequence domain adaption. We verify the proposed method with C-MAPSS dataset. By comparing with the literature methods, results show SAAN could significantly improve the accuracy of RUL prediction under small data set, and also keeps a competitive performance on sequence life prediction.

In Industry 4.0, the integration of artificial intelligence (AI) has transformed industrial operations, with predictive maintenance (PdM) emerging as a key application. As the core of PdM, remaining useful life (RUL) prediction enables a shift from reactive or preventive maintenance to proactive, data-driven strategies, helping to optimize scheduling, reduce downtime, and cut costs. Despite the high predictive accuracy of machine learning and deep learning models in RUL prediction, their inherent ‘black-box’ nature presents significant barriers to practical industrial adoption. These barriers include compromised trust in model outputs, difficulties in debugging and error tracing, challenges in meeting regulatory compliance requirements, and limited alignment with domain-specific expertise. Consequently, explainable AI (XAI) has become indispensable for addressing these issues and enabling wider deployment of RUL prediction systems in industrial settings. This paper presents a comprehensive survey of XAI for industrial RUL prediction. The survey begins by exploring the significance of RUL prediction, challenges of black-box models, the role of XAI, and its value in enhancing the reliability of RUL methods. Subsequently, it systematically synthesizes recent research advancements, categorizes XAI techniques into five types, and traces their technical evolution. It also develops a holistic evaluation framework encompassing approaches, properties, and metrics, supported by 11 functionally grounded quantitative indicators. Moreover, it establishes a comparative analysis system on eight typical public datasets to clarify their suitability for XAI integration and industrial applications, and puts forward future research directions that combine data, physics, large language models, and digital twins to bridge the gap between academic research and industrial deployment.

Aiming to improve the predictive ability of Walker model for fatigue life prediction and taking the turbine disc alloy GH4133 as the application example, this paper investigates a new approach for probabilistic fatigue life prediction when considering parameter uncertainty inherent in the life prediction model. Firstly, experimental data are used to update the model parameters using Bayes’ theorem, so as to obtain the posterior probability distribution functions of two parameters of the Walker model, as well to achieve the probabilistic life prediction model for turbine disc. During the updating process, Markov Chain Monte Carlo (MCMC) technique is used to generate samples of the given distribution and estimating the parameters distinctly. After that, the turbine disc life is predicted using the probabilistic Walker model based on Monte Carlo simulation technique. The experimental results indicate that: (1) after using the small sample test data obtained from turbine disc, parameter uncertainty of the Walker model can be quantified and the corresponding probabilistic model for fatigue life prediction can be established using Bayes’ theorem; (2) there exists obvious dispersion of life data for turbine disc when predicting fatigue life in practical engineering application.

Given the difficulty of developing physics-based degradation process models in practice, data-driven prognostics approaches are preferred in several industrial applications. Among data-driven approaches, one can distinguish between (i) degradation-based approaches that predict the future evolution of the equipment degradation and (ii) direct Remaining Useful Life (RUL) prediction approaches which directly predict the equipment RUL. In this work, we compare two direct RUL prediction approaches one based on Back Propagation-Artificial Neural Networks (BP-ANN) and the other one on Extreme Learning Machines (ELM). The two approaches are compared on data from turbofan engines. We consider different prognostic metrics such as RMSE, Accuracy Index, Steadiness Index, a-I metric and the time necessary to train and execute the model. The obtained results show that the ELM-based model is performing only slightly worse than the BP-ANN-based model in terms of accuracy and stability, but it requires a considerably shorter training time.

Remaining useful life (RUL) prediction is a key enabler for making optimal maintenance strategies. Data-driven approaches, especially employing neural networks (NNs) such as multi-layer perceptrons (MLPs) and convolutional neural networks (CNNs), have gained increasing attention in the field of RUL prediction. Most of the past research has mainly focused on minimizing the RUL prediction error by training NNs with back-propagation (BP), which in general requires an extensive computational effort. However, in practice, such BP-based NNs (BPNNs) may not be affordable in industrial contexts that normally seek to save cost by minimizing access to expensive computing infrastructures. Driven by this motivation, here, we propose: (1) to use a very fast learning scheme called extreme learning machine (ELM) for training two different kinds of feed-forward neural networks (FFNNs), namely a single-layer feed-forward neural network (SL-FFNN) and a Convolutional ELM (CELM); and (2) to optimize the architecture of those networks by applying evolutionary computation. More specifically, we employ a multi-objective optimization (MOO) technique to search for the best network architectures in terms of trade-off between RUL prediction error and number of trainable parameters, the latter being correlated with computational effort. In our experiments, we test our methods on a widely used benchmark dataset, the C-MAPSS, on which we search such trade-off solutions. Compared to other methods based on BPNNs, our methods outperform a MLP and show a similar level of performance to a CNN in terms of prediction error, while using a much smaller (up to two orders of magnitude) number of trainable parameters.

A method for capacity prediction of lithium-ion batteries under small sample conditions

The machine learning method, now widely used for predicting well performance from unconventional reservoirs in the industry, generally needs large data sets for model development and training. The large data sets, however, are not always available, especially for newly developed unconventional plays. The objective of this work is to develop an innovative machine learning method for predicting well performance in unconventional reservoirs with a relatively small data set. For a small training data set, the corresponding machine learning model can significantly suffer from so-called overfitting meaning that the model can match the training data but has poor predictivity. To overcome this, our new method averages predictions from multiple models that are developed with the same model input, but different initial guesses of model parameters that are unknowns in a machine learning algorithm and determined in the model training. The averaged results are used for the final model prediction. Unlike traditional ensemble learning methods, each prediction in the new method uses all the input data rather than its subset. We mathematically prove that the averaged prediction provides less model uncertainty and under certain conditions the optimum prediction. It is also demonstrated that the method practically minimizes the overfitting and gives relatively unique prediction. The usefulness of the method is further confirmed by its successful application to the data set collected from less than 100 wells in an unconventional reservoir. Sensitivity results with the trained machine learning model show that the model results are consistent with the domain knowledge regarding the production from the reservoir.

The remaining life prediction of turbine engine plays an indispensable role in engine health management, which is of great significance to ensure flight safety and improve maintenance efficiency. With the development of engine health management technology, the engine is terminated before failure or failure, which makes it difficult to collect enough data with failure information. In order to improve the prediction accuracy of engine remaining life with limited data samples, a joint algorithm based on genetic algorithm and support vector regression (GA-SVR) is proposed in this paper. Genetic algorithm (GA) is used to solve the hyperparametric optimization problem in support vector regression (SVR) model. Based on the C-MAPSS public data set provided by NASA, the data of 20 engines are randomly selected to construct a small sample data set to train the GA-SVR model, and compared with other existing algorithms. The experimental results show that the prediction error of GA-SVR model is smaller in the case of small samples, It is proved that the proposed model can accurately deal with the problem of turbine engine residual life prediction in the case of small samples.

High-quality internal experimental materials data are often “small data.” Using external datasets, e.g., data from the literature and other groups, to expand the “small data” to relatively “big data” is particularly important for improving the prediction accuracy of machine learning models. However, the most critical issue is how to use a small amount of internal reliable data to filter external data extracted from multiple sources and obtain optimal datasets with a distribution similar to that of internal data. This is called the multi-source materials data problem. This question was addressed by designing an active learning-based data screening (ALDS) model that is suitable for small material samples. This study used negative expansion materials as subjects. The results show that ALDS can be used to screen the external multi-source dataset and far exceeds traditional outlier filtering methods. The average mean absolute percentage error (MAPE) of the predictive key target property of the negative thermal expansion coefficient (NTEC) was reduced from 4.301 to 0.056. Furthermore, reverse design experiments were conducted on anti-perovskite manganese nitride (AMN), a type of negative thermal expansion material, to prove that the ALDS model can guide the reverse design on a small AMN dataset using the MAPE between ALDS prediction and the ground truth of samples’ three property indicators. This achieves high confidence levels with values of 0.203,0.126, and 0.115. This verifies that the ALDS proposed method improves the effect of ”materials small internal data” in guiding material design and property prediction.

Physics-based models for permeability prediction are essential for ensuring physically consistent reservoir characterization, yet they often fail to capture the full complexity of real geological systems. This study applies an explainable physics-informed machine learning (PIML) framework for discrepancy modeling to a legacy well dataset from a carbonate formation in southern Iraq. The dataset, originally comprising more than 2,400 samples from 10 wells, was heavily contaminated with incorrectly imputed or interpolated core permeability values. Through a rigorous zonation-based cleaning process, 1,130 high-quality samples were retained for modeling. A baseline physics model, built using well log–derived porosity and a porosity–permeability transform, was combined with a machine learning (ML) discrepancy model trained on three physics-informed features: neutron porosity (NPHI), the gamma ray/ bulk density (GR/RHOB) ratio, and depth. Three ML algorithms, Random Forest, XGBoost, and CatBoost, were evaluated, with five-fold cross-validation employed to ensure robustness. The discrepancy model effectively captured systematic biases in the physical model's predictions. When integrated into the boosted-ML frameworks, it delivered substantially higher permeability prediction performance, reducing root mean squared error (RMSE) by 56% and improving the adjusted coefficient of determination (adjusted R2) from −0.27 to 0.76 compared to the original physical model. These results demonstrate the strong potential of discrepancy-based ML-enhancement methodologies for improving permeability prediction in legacy well datasets. Explainable AI analysis using Shapley additive explanations (SHAP) to determine feature influence identified measured depth as the most influential predictor. Compaction effects not captured by the original physical model, GR/RHOB and NPHI also exerted substantial influence on the PIML permeability predictions. These findings not only improve permeability prediction performance but also reveal missing physics in the baseline model, enabling targeted refinement of physical relationships. This work highlights the feasibility and value of applying discrepancy-based PIML to noisy, incomplete legacy datasets, bridging the gap between empirical ML corrections and physically consistent modeling.

Haemodynamic profiling: when AI tells us what we already know.

The performance of heavy duty gas turbines is closely related to the material capability of the components of the 1st turbine stages. In modern gas turbines single crystal (SX) and directionally solidified (DS) nickel superalloys are applied which, compared to their conventionally cast (CC) version, hold a higher cyclic life and a significantly improved creep rupture strength. SX and DS nickel superalloys feature a significant directionally dependence of material properties. To fully exploit the material capability, the anisotropy needs to be accounted for in both, the constitutive and the lifing model. In this context, the paper addresses a cyclic life prediction procedure for DS materials with transverse isotropic material symmetry. Thereby, the well-known local approaches to fatigue life prediction of isotropic materials under uniaxial loading are extended towards materials with transverse isotropic properties under multiaxial load conditions. As part of the proposed methodology, a Hill type function is utilized for describing the anisotropic failure behavior. The coefficients of the Hill surface are determined from the actual multiaxial loading, the material symmetry and the anisotropic fatigue strength of the material. In the paper we first characterize the anisotropy of DS superalloys. We then present the general mathematical framework of the proposed lifing procedure. Later we discuss a validation of the cyclic life model by comparing measured and predicted fatigue lives of test specimens. Finally, the proposed method is applied to the cyclic life prediction of a gas turbine blade.

The performance of heavy duty gas turbines is closely related to the material capability of the components of the first turbine stage. In modern gas turbines single crystal (SX) and directionally solidified (DS) nickel superalloys are applied, which, compared with their conventionally cast version, hold a higher cyclic life and a significantly improved creep rupture strength. SX and DS nickel superalloys feature a significant directional dependence of the material properties. To fully exploit the material capability, the anisotropy needs to be accounted for in both the constitutive and lifing model. In this context, the paper addresses a cyclic life prediction procedure for DS materials with transverse isotropic material symmetry. Thereby, the well-known local approaches to fatigue life prediction of isotropic materials under uniaxial loading are extended toward materials with transverse isotropic properties under multiaxial load conditions. As part of the proposed methodology, a Hill type function is utilized for describing the anisotropic failure behavior. The coefficients of the Hill surface are determined from the actual multiaxial loading, material symmetry, and anisotropic fatigue strength of the material. In this paper we first characterize the anisotropy of DS superalloys. We then present the general mathematical framework of the proposed lifing procedure. Later we discuss a validation of the cyclic life model by comparing the measured and predicted fatigue lives of the test specimens. Finally, the proposed method is applied to the cyclic life prediction of a gas turbine blade.