Gaussian Process Regression Research Articles

State of health estimation for lithium-ion batteries with Bayesian optimized Gaussian process regression

The estimation of the state of health (SOH) of lithium-ion batteries is of great importance to ensure the safe and stable operation of a lithium-ion battery management system (BMS). Accurate estimation of SOH can effectively prevent unnecessary losses of lithium-ion batteries due to failures. Therefore, a Bayesian-optimized Gaussian process regression (BO-GPR) method is proposed for SOH estimation. Firstly, the ageing characteristics reflecting the SOH of the battery are extracted from the charge/discharge time and incremental capacity (IC) curve, and the correlation between the health characteristics and the SOH is analysed by means of grey correlation (GRA). On the other hand, a Bayesian optimization algorithm is used to automatically find the optimal hyperparameters of the GPR model and trained using the battery dataset to obtain the SOH estimating model. To validate the effectiveness of the method, the datasets provided by NASA and Oxford are used as experimental objects and compared with different data-driven models to verify the accuracy and reliability of the proposed model. The experimental results show that the method proposed in this paper has a high accuracy in the estimation of the SOH, with the maximum average estimation error being within 1%.

Selection of optimal spectral features for leaf chlorophyll content estimation

Leaf chlorophyll content (LCC) is crucial for monitoring the physiological processes of crops. Many studies have utilized spectral features to develop regression models for accurate LCC estimation, enabling the quantitative assessment and evaluation of crop growth status. The selection of optimal spectral features and regression algorithms significantly affects the precision of LCC estimation. In this study, we compared and analyzed the optimal spectral features for LCC estimation, as well as the consistency of machine learning methods across different crop types, phenology periods, and sensors. First, we extracted various spectral features, including the original spectral features (OS), first-order derivative spectral features (FDS), original continuum-removed spectra (CR) along with their four related derivative spectral features, principal component variables derived from different spectral features, and highly correlated spectral features with LCC. These extracted spectral features were then employed to construct the LCC models using six common regression algorithms on different datasets. Finally, we analyzed the optimal combination of spectral features and regression algorithms for accurate LCC estimation considering various dimensions, such as crop type, phenological period, and sensor used in observation conditions. The results demonstrate that the combinations of the principal component variables of continuum-removed derivative reflectance with the top 10 correlations with LCC (PCA_CRDR_R) combined with Gaussian process regression (GPR) can be considered as the optimal choice for estimating LCC under diverse observation conditions at a canopy scale, and its R2 can reach 0.62 for sugar beet LCC estimation; thus providing valuable theoretical guidance for selecting appropriate spectral features for LCC estimation.

Stacking BSRG-PLS: A physical and data-driven real-time stability safety analysis of arch dams during operation

Anti-sliding stability is the foundation for the normal operation of arch dams. In recent years, extreme weather has occurred frequently. It is important to grasp the anti-slide stability of arch dam (ASSAD) under complex load conditions in time. Currently, the ASSAD safety factor is primarily analyzed through the finite element method (FEM), which are time-consuming, labor-intensive, and lack timeliness. To address this, this paper proposes a real-time ASSAD analysis method during operation based on the Stacking BSRG-PLS model, which integrates a Bidirectional long short-term memory network, Residual neural network, Support vector machine, Gaussian process regression model and Partial Least Squares regression method. Firstly, based on the Stacking BSRG-PLS model and measured temperature combing with FEM, the transient temperature field of arch dam is established. Subsequently, a sample dataset containing the load data and the corresponding ASSAD safety factors calculated by FEM is constructed. Whereafter, using the Stacking BSRG-PLS model again, the real-time ASSAD safety factor is obtained based on the sample dataset. Case studies indicate that this method is effective and feasible, and has high analysis precision. It provides an effective way to quickly evaluate the ASSAD safety based on the measured data.

Optimal process parameter determination in selective laser melting via machine learning-guided sequential quadratic programing

Selective Laser Melting (SLM) is a widely used additive manufacturing method with critical processing parameters such as Laser Power, Scanning Speed, Hatch Distance, and Laser Beam Diameter, which significantly impact process quality and mechanical properties of fabricated parts like Relative Density, Hardness, and Surface Roughness. This study investigates an effective approach to modeling the SLM process for predicting and optimizing processing parameters using a combination of Machine Learning (ML) and Sequential Quadratic Programing (SQP). The proposed method aims to predict the mechanical properties of SLM-produced AlSi10Mg parts using Machine Learning techniques and then transform the process into a constrained multiple-objective optimization model employing the SQP algorithm to determine optimal process parameters. Artificial Neural Networks (ANN), Gaussian Process Regression (GPR), and Support Vector Machine (SVM) algorithms are applied to establish correlations between process parameters and mechanical properties, represented as mathematical functions. A cost function is formulated using these functions and minimized using the SQP method. Statistical analysis is implemented to validate the influence of processing parameters on mechanical properties accordingly. The outcomes of the method are verified through additional experiments and analyses using Micro-CT scanning techniques. The results demonstrate that processing parameters have a significant impact on part properties across different scales, with Micro-CT scanning proving instrumental in validating mechanical properties. Overall, this study establishes that multiple objectives can be efficiently optimized through the integration of ML and SQP methods, complemented by a judicious number of experiments.

Decentralized Multi-Agent Search for Moving Targets Using Road Network Gaussian Process Regressions

Unmanned aerial vehicles (UAVs) can collaborate as teams to accomplish diverse mission objectives, such as target search and tracking. This paper introduces a method that leverages accumulated target-density information over the course of a UAV mission to adapt path-planning rewards, guiding UAVs toward areas with a higher likelihood of target presence. The target density is modeled using a Gaussian process, which is iteratively updated as the UAVs search the environment. Unlike conventional search algorithms that prioritize unexplored regions, this approach incentivizes revisiting target-rich areas. The target-density information is shared across UAVs using decentralized consensus filters, enabling cooperative path selection that balances the exploration of uncertain regions with the exploitation of known high-density areas. The framework presented in this paper provides an adaptive cooperative search method that can quickly develop an understanding of the region’s target-dense areas, helping UAVs refine their search. Through Monte Carlo simulations, we demonstrate this method in both a 2D grid region and road networks, showing up to a 26% improvement in target density estimates.

Predicting shear strength of corroded RC columns: A probabilistic model with enhanced Gaussian Process Regression

This study proposes a new probabilistic model for predicting the shear strength of corroded reinforced concrete (RC) columns. The probabilistic model addresses limitations of traditional methods by combining mechanical understanding with enhanced Gaussian Process Regression (GPR). A novel mean function for enhanced GPR is developed first based on the shear resistance mechanism of corroded RC columns. Then the hyper-parameters of both the mean function and kernel function for the enhanced GPR are optimized using the maximum likelihood estimation method. This leads to the establishment of the probabilistic model that is based on the enhanced GPR. Finally, the accuracy and effectiveness of the enhanced GPR probabilistic model are validated by comparing it with both traditional mechanical models and machine learning models. The results indicate that the proposed probabilistic model can not only describes the probabilistic characteristics for shear strength of corroded RC columns based on probability density functions, but also provides an efficient calibration method for traditional prediction models based on confidence intervals.

A machine-learned kinetic energy model for light weight metals and compounds of group III-V elements

Abstract We present a machine-learned (ML) model of kinetic energy for orbital-free density functional theory (OF-DFT) suitable for bulk light weight metals and compounds made of group III–V elements. The functional is machine-learned with Gaussian process regression (GPR) from data computed with Kohn-Sham DFT with plane wave bases and local pseudopotentials. The dataset includes multiple phases of unary, binary, and ternary compounds containing Li, Al, Mg, Si, As, Ga, Sb, Na, Sn, P, and In. A total of 433 materials were used for training, and 18 strained structures were used for each material. Averaged (over the unit cell) kinetic energy density is fitted as a function of averaged terms of the 4th order gradient expansion and the product of the density and effective potential. The kinetic energy predicted by the model allows reproducing energy-volume curves around equilibrium geometry with good accuracy. We show that the GPR model beats linear and polynomial regressions. We also find that unary compounds sample a wider region of the descriptor space than binary and ternary compounds, and it is therefore important to include them in the training set; a GPR model trained on a small number of unary compounds is able to extrapolate relatively well to binary and ternary compounds but not vice versa.

Development of electromagnetic pollution maps utilizing Gaussian process spatial models

The rapid proliferation of wireless technologies in everyday environments demands the quick and precise estimation of electromagnetic field distribution. This distribution is commonly depicted through the electric field strength across various geographical areas. The objective of this research is to determine the most effective geospatial model for generating a national-level electric field strength map within the 30 MHz–6 GHz frequency range. To achieve this, we employed five different methodologies for constructing the electric field strength map. Four of these methodologies are based on Gaussian process regression, while the fifth utilizes the classical weighted-average method of the nearest neighbor. Our study focused on a country with a total area of 9251 km2, using a dataset comprising 3621 measurements. The findings reveal that Gaussian process spatial models, also known as Kriging models, generally outperform other methods when applied to spatial data. However, it was observed that, after excluding some outlier data points, the performance of the classical nearest neighbor models becomes comparable to that of the Gaussian process models. This indicates the potential for both approaches to be effective, depending on the data quality and the presence of outliers.

Data-driven predictions of retained austenite content and yield strength and elucidation of the sliding wear performance of carbide-free bainitic steels

Carbide-free bainitic (CFB) steels have drawn much attention due to their high strength and toughness. The present work aims to build machine learning (ML) based surrogate models to predict retained austenite (RA) content and yield strength (YS) of isothermal transformed CFB steels and study the sliding wear performance. The input data for ML prediction were related to compositions, heat treatment process, and phases. The Random Forest regression and Gaussian process regression were respectively selected to build the predictive models for RA content and YS. Result shows that the predicted RA content agrees well with the experimentally determined ones in steel with high stability of untransformed austenite. For YS prediction, the present surrogate model can predict YS of CFB steels even without additional microstructural information such as dislocation and effective substructure size. Steels with different YS and RA content were designed to study the sliding wear performance. Result shows that the dominant wear mechanism of the tested steels is abrasive wear and the weight loss is inversely proportional to hardness when the load and wear distance are constant. Increasing YS and RA content can increase the initial hardness and work hardening ability at the worn surface, thereby enhancing wear resistance.

Smart Grid Forecasting with MIMO Models: A Comparative Study of Machine Learning Techniques for Day-Ahead Residual Load Prediction

With the fast expansion of intermittent renewable energy sources in the upcoming smart grids, simple and accurate day-ahead systems for residual load forecasts are urgently needed. Machine learning strategies can facilitate towards drastic cost minimizations in terms of operating-reserves avoidance to compensate the mismatches between the actual and forecasted values. In this study, a multi-input/multi-output model is developed based on artificial neural networks to map the relationship between different predictor inputs, including time indices, weather variables, human activity parameters, and energy price indicators, and target outputs such as wind and photovoltaic generation. While the information flows in only one direction (from the predictor nodes through the hidden layers to the target node), benchmark training algorithms are employed and assessed under different case studies. The model is evaluated under both parametric and non-parametric formulations, namely neural networks and Gaussian process regression. Essential improvements are achieved by enhancing the number of embedded predictors, while superior performance is observed by using Bayesian regularization mechanisms. In terms of mean-error indices and determination coefficient, this opens the pathway towards minimization via Bayesian inference-based approaches in the presence of increased and highly stochastic renewable inputs.

Computationally efficient and error aware surrogate construction for numerical solutions of subsurface flow through porous media

Limiting the injection rate to restrict the pressure below a threshold at a critical location can be an important goal of simulations that model the subsurface pressure between injection and extraction wells. The pressure is approximated by the solution of Darcy’s partial differential equation for a given permeability field. The subsurface permeability is modeled as a random field since it is known only up to statistical properties. This induces uncertainty in the computed pressure. Solving the partial differential equation for an ensemble of random permeability simulations enables estimating a probability distribution for the pressure at the critical location. These simulations are computationally expensive, and practitioners often need rapid online guidance for real-time pressure management. An ensemble of numerical partial differential equation solutions is used to construct a Gaussian process regression model that can quickly predict the pressure at the critical location as a function of the extraction rate and permeability realization. The Gaussian process surrogate analyzes the ensemble of numerical pressure solutions at the critical location as noisy observations of the true pressure solution, enabling robust inference using the conditional Gaussian process distribution.Our first novel contribution is to identify a sampling methodology for the random environment and matching kernel technology for which fitting the Gaussian process regression model scales as O(nlogn) instead of the typical O(n3) rate in the number of samples n used to fit the surrogate. The surrogate model allows almost instantaneous predictions for the pressure at the critical location as a function of the extraction rate and permeability realization. Our second contribution is a novel algorithm to calibrate the uncertainty in the surrogate model to the discrepancy between the true pressure solution of Darcy’s equation and the numerical solution. Although our method is derived for building a surrogate for the solution of Darcy’s equation with a random permeability field, the framework broadly applies to solutions of other partial differential equations with random coefficients.

Estimation of Urban Tree Chlorophyll Content and Leaf Area Index Using Sentinel-2 Images and 3D Radiative Transfer Model Inversion

Urban trees play an important role in mitigating effects of climate change and provide essential ecosystem services. However, the urban environment can stress trees, requiring the use of effective monitoring methods to assess their health and functionality. The objective of this study, which focused on four deciduous tree species in Rennes, France, was to evaluate the ability of hybrid inversion models to estimate leaf chlorophyll content (LCC), leaf area index (LAI), and canopy chlorophyll content (CCC) of urban trees using eight Sentinel-2 (S2) images acquired in 2021. Simulations were performed using the 3D radiative transfer model DART, and the hybrid inversion models were developed using machine-learning regression algorithms (random forest (RF) and gaussian process regression). Model performance was assessed using in situ measurements, and relations between satellite data and in situ measurements were investigated using spatial allocation (SA) methods at the pixel and tree scales. The influence of including environment features (EFs) as model inputs was also assessed. The results indicated that random forest models that included EFs and used the pixel-scale SA method were the most accurate with R2 values of 0.33, 0.29, and 0.46 for LCC, LAI, and CCC, respectively, with notable variability among species.

Machine Learning Model Trained with Finite Element Modeling Can Predict the Risk of Osteoarthritis: Data from the Osteoarthritis Initiative

Objective: Despite long simulation times, recently developed finite element analysis (FEA) models of knee joints have demonstrated their suitability for predicting individual risk of onset and progression of knee osteoarthritis. Therefore, the objective of this study was to assess the feasibility of machine learning (ML) to replicate outcomes obtained from FEA when simulating mechanical responses and predicting cartilage degeneration within the knee joint.Design: Two ML models based on the Gaussian Process Regression (GPR) algorithms were developed. The first model (GPR1) utilized age, weight, and anatomical joint dimensions as predictor variables to predict tissue mechanical responses and cartilage degeneration based on FEA data. The second model (GPR2) utilized age, weight, height, and gender to predict anatomical joint dimensions, which were then used as inputs in the GPR1 model. Finally, the GPR1 and combined GPR1+GPR2 models were used to investigate the importance of clinical imaging when making personalized predictions for knees from healthy subjects with no history of knee injuries.Results: In the GPR1 model, R2 of 0.9 was exceeded for most of the predicted mechanical parameters. The GPR2 model was able to predict knee shape with R2 of 0.67–0.9. Both GPR1 and combined GPR1+GPR2 models offered equally good performances (AUC = 0.73–0.74) in classifying patients at high risk for the onset and development of knee osteoarthritis.Conclusions: In the future, real-time and easy-to-use GPR models may provide a rapid technology to evaluate mechanical responses within the knee for researchers or clinicians who have no former knowledge of FEA.

Applications of fractal-type kernels in Gaussian process regression and support vector machine regression

Applications of fractal-type kernels in Gaussian process regression and support vector machine regression

Kernel-Based Versus Tree-Based Data-Driven Models: On Applying Suspended Sediment Load Estimation

River sediment load estimation poses a critical challenge for water engineers due to its complex and nonlinear hydrological processes. This study assessed the amount of suspended sediment at the Bagh-e-Kalayeh hydrometric station on the Alamut River in the Qazvin province of Iran using two hydrological and meteorological variables, including discharge and rainfall, by considering three scenarios (discharge, discharge + monthly rainfall, and discharge + monthly rainfall + daily rainfall). For modeling, kernel-based data-driven methods, including Gaussian process regression (GPR) and support vector regression (SVR), and tree models, including the M5 tree, random forest (RF), random tree (RT), extra trees, reduced error pruning tree (REPT), and multi-search methods, were used. The results showed that the best performance was achieved by the SVR, with r = 0.948, Wilmot index = 0.965, and RMSE = 0.011 in the first scenario (only discharge). Discharge had the most significant impact on sediment estimation compared to rainfall. It was determined that the suspended sediment load in the Alamut River can be successfully estimated by the SVR method, where only the discharge was used as the input parameter. Additionally, the results indicated that given its characteristics and inherent features, the multi-search method can be used as a complementary approach in sediment modeling, especially in situations where the data volume is not extensive.

Optimization of Linear Loading Strategy for Fuel Cell Initiation Based on Gaussian Process Regression Model

Optimization of Linear Loading Strategy for Fuel Cell Initiation Based on Gaussian Process Regression Model

A novel sparse Gaussian process regression with time-aware spatiotemporal kernel for remaining useful life prediction and uncertainty quantification of bearings

A novel sparse Gaussian process regression with time-aware spatiotemporal kernel for remaining useful life prediction and uncertainty quantification of bearings

Accelerating Optimal Synthesis of Atomically Thin MoS2: A Constrained Bayesian Optimization Guided Brachistochrone Approach

AbstractA machine learning (ML) guided approach is presented for the accelerated optimization of chemical vapor deposition (CVD) synthesis of 2D materials toward the highest quality, starting from low‐quality or unsuccessful synthesis conditions. Using 26 sets of these synthesis conditions as the initial training dataset, our method systematically guides experimental synthesis towards optoelectronic‐grade monolayer MoS2 flakes. A‐exciton linewidth (σA) as narrow as 38 meV could be achieved in 2D MoS2 flakes after only an additional 35 trials (reflecting 15% of the full factorial design dataset for training purposes). In practical terms, this reflects a decrease of the possible experimental time to optimize the parameters from up to one year to about two months. This remarkable efficiency was achieved by formulating a constrained sequencing optimization problem solved via a combination of constraint learning and Bayesian Optimization with the narrowness of σA as the single target metric. By employing graph‐based semi‐supervised learning with data acquired through a multi‐criteria sampling method, the constraint model effectively delineates and refines the feasible design space for monolayer flake production. Additionally, the Gaussian Process regression effectively captures the relationships between synthesis parameters and outcomes, offering high predictive capability along with a measure of prediction uncertainty. This method is scalable to a higher number of synthesis parameters and target metrics and is transferrable to other materials and types of reactors. This study envisions that this method will be fundamental for CVD and similar techniques in the future.

System fragility analysis of highway bridge using multi-output Gaussian process regression surrogate model

This study presents a multi-output Gaussian process regression (GPR) surrogate model for seismic-fragility analysis of bridge structural systems. Multi-output GPR can model the correlations among multiple outputs, accuracy and stability are achieved with fewer training data, which reduces the computational cost of fragility analysis. Furthermore, the explainability of the constructed surrogate model is implemented by adopting an automatic relevance-determination (ARD) kernel in the GPR. The estimated hyperparameters can provide the contribution of the uncertainty of each input parameter to the outputs. The fragility analysis using the multi-output GPR surrogate model was verified by applying it to a seismic isolation highway bridge with multiple spans and a curved geometry. The effectiveness of the multi-output GPR was demonstrated by the construction of an accurate and stable surrogate model with 46 inputs and 28 outputs. The relative contributions of the uncertainties to the structural properties and input earthquake loads could also be understood. The fragility curves, at both the component and system levels, were appropriately obtained using a sufficient number of samples in a Monte Carlo calculation. Furthermore, the failure modes were evaluated, identifying which structural components contributed to the system failure. This enabled discussions on structural system failures from the viewpoint of the structural dynamic characteristics of the bridge and earthquake-load properties.

Predicting low-velocity impact on the CNTs-reinforced plate using machine learning models

Purpose The study aims to predict a low-velocity impact on a plate reinforced with carbon nanotubes (CNTs) using machine learning models. Design/methodology/approach The first-order shear deformation plate theory (FSDT) is used to express the plate displacements filed. The Hertz nonlinear contact law is used to predict the contact between impactor and plate. Using the energy method and Hamilton’s principle, the motion equations are extracted. The six main parameters considered as inputs to machine learning models are CNTs percentage, impactor radius, plate thickness, plate length and width, CNTs distribution profile and impactor initial velocity. These input parameters are used to predict two impact targets including contact force and contact time. Findings As the values of the targets are continuous, the machine learning task is considered a regression problem. Therefore, this study uses different regression models to predict the targets. These regression models include linear regression, stochastic gradient descent regressor, Bayesian regression, partial least squares regression, Gaussian process regression, multilayer perceptron regressor, support vector regression and decision tree regression. To validate the effectiveness of the regression models, experiments are designed based on different evaluation metrics. The results of the experiments demonstrate that the machine learning models achieve promising performance in predicting the contact force and contact time based on the input parameters. Originality/value Due to the volume of high numerical calculations of impact mechanics to reach the response, the targets of the impact problem are predicted using a variety of machine learning methods.