Gaussian Process Regression Approach Research Articles

Car-Following Described by Blending Data-Driven and Analytical Models: A Gaussian Process Regression Approach

Traffic engineers rely on microscopic traffic models to design, plan, and operate a wide range of traffic applications. Recently, large data sets, yet incomplete and from small space regions, are becoming available thanks to technology improvements and governmental efforts. With this study we aim to gain new empirical insights into longitudinal driving behavior and to formulate a model which can benefit from these new challenging data sources. This paper proposes an application of an existing formulation, Gaussian process regression (GPR), to describe individual longitudinal driving behavior of drivers. The method integrates a parametric and a non-parametric mathematical formulation. The model predicts individual driver’s acceleration given a set of variables. It uses the GPR to make predictions when there exists correlation between new input and the training data set. The data-driven model benefits from a large training data set to capture all driver longitudinal behavior, which would be difficult to fit in fixed parametric equation(s). The methodology allows us to train models with new variables without the need of altering the model formulation. And importantly, the model also uses existing traditional parametric car-following models to predict acceleration when no similar situations are found in the training data set. A case study using radar data in an urban environment shows that a hybrid model performs better than parametric model alone and suggests that traffic light status over time influences drivers’ acceleration. This methodology can help engineers to use large data sets and to find new variables to describe traffic behavior.

Comprehensive Modeling in Predicting Biodiesel Density Using Gaussian Process Regression Approach.

In this study, four Gaussian process regression (GPR) approaches by various kernel functions have been proposed for the estimation of biodiesel density as the functions of pressure, temperature, molecular weight, and the normal melting point of fatty acid esters. Comparing the actual values with GPR outputs shows that these approaches have good accuracy, but the performance of the rational quadratic GPR model is better than others. In this GPR model, RMSE = 0.47, MSE = 0.22, MRE = 0.04, R2 = 1, and STD is equal to 0.3. In addition, for the first time, this study shows that the effective parameters affect the biodiesel density. According to this analysis, it was shown that among the input parameters, pressure has the greatest effect on the target values with a relevancy factor of 0.59. This study can be used as a suitable and valuable work/tool for chemical and petroleum engineers who attempt environment protection and recovery improvement.

Developing a Robust Model Based on the Gaussian Process Regression Approach to Predict Biodiesel Properties

Biodiesel is assumed a renewable and environmentally friendly fuel that possesses the potential to substitute petroleum diesel. The basic purpose of the present study is to design a precise algorithm based on Gaussian Process Regression (GPR) model with several kernel functions, i.e., Rational Quadratic, Squared Exponential, Matern, and Exponential, to estimate biodiesel properties. These properties include kinematic viscosity (KV), pour point (PP), iodine value (IV), and cloud point (CP) as a function of fatty acid composition. In order to develop this model, some variables are assumed, such as molecular weight, carbon number, double bond numbers, monounsaturated fatty acids, polyunsaturated fatty acid, weight percent of saturated acid, and temperature. The performance and efficiency of the GPR model are measured through several statistical criteria and the results are summarized in root mean square error (RMSE) and coefficients of determination ( R 2 ). R 2 and RMSE are sorted as 0.992 & 0.15697, 0.998 & 0.96580, 0.966 & 1.38659, and 0.968 & 1.56068 for four properties such as KV, IV, CP, and PP, respectively. It is worth to mention this point that the kernel function Squared Exponential shows a great performance for IV and PP and kernel functions Exponential and Matern indicate appropriate efficiency for CP and KV properties, respectively. On the other hand, the results of the offered GPR models are compared with those of the previous models, LSSVM-PSO and ANFIS. The outcomes proved the superiority of this model over two former models in point of estimating the biodiesel properties.

A novel combined multi-battery dataset based approach for enhanced prediction accuracy of data driven prognostic models in capacity estimation of lithium ion batteries

To ensure smooth and reliable operations of battery systems, reliable prognosis with accurate prediction of State of Health of lithium ion batteries is of utmost importance. However, battery degradation is a complex challenge involving many electrochemical reactions at anode, separator, cathode and electrolyte/electrode interfaces. Also, there is significant effect of the operating conditions on the battery degradation. Various machine learning techniques have been applied to estimate the capacity and State of Health of lithium ion batteries to ensure reliable operation and timely maintenance. In this paper, we study the Gaussian Process Regression (GPR) and Support Vector Machine (SVM) model-based approaches in estimating the capacity and State of Health of batteries. Battery capacity and State of Health estimations are carried out using GPR and SVM models and the predictions comparatively studied for accuracy based on RMSE values. The prediction accuracy is further compared with respect to single sensor and multi sensor data. Further, a combined multi battery data set model is used to improve the prediction accuracy. Combining the data of multiple batteries with similar operating conditions for training a model resulted in higher prediction accuracy.

Predicting flammability-leading properties for liquid aerosol safety via machine learning

Flammable and explosive hazards, which have been well studied, are major safety concerns in industrial processes. However, the liquid aerosolization phenomenon, which increases the fire and explosion hazard of bulk liquids, has not been widely recognized. This work aims at identifying the contributors influencing liquid aerosol flammability and solving their data deficiencies by developing quantitative structure − property relationship (QSPR) models. 1215 liquid chemicals and 14 predictors have been input to train the developed machine learning models via k-fold cross validation with the consideration of principal component analysis. Three rounds of model performance comparisons are conducted to find the optimal models for liquid dynamic viscosity (LDV), surface tension (ST), and liquid vapor pressure (LVP). The most persuasive model for LDV is obtained by the exponential Gaussian process regression (GPR) approach with seven principal components, while the Matern 5/2 GPR algorithm is the most robust model for predicting ST and LVP. Due to their good interpretation and prediction performance, the optimized machine learning models can be used to predict flammability-leading properties for aerosols and can therefore help design inherently safer processes involving potential liquid aerosolization.

Robust Non-Parametric Mortality and Fertility Modelling and Forecasting: Gaussian Process Regression Approaches

A rapid decline in mortality and fertility has become major issues in many developed countries over the past few decades. An accurate model for forecasting demographic movements is important for decision making in social welfare policies and resource budgeting among the government and many industry sectors. This article introduces a novel non-parametric approach using Gaussian process regression with a natural cubic spline mean function and a spectral mixture covariance function for mortality and fertility modelling and forecasting. Unlike most of the existing approaches in demographic modelling literature, which rely on time parameters to determine the movements of the whole mortality or fertility curve shifting from one year to another over time, we consider the mortality and fertility curves from their components of all age-specific mortality and fertility rates and assume each of them following a Gaussian process over time to fit the whole curves in a discrete but intensive style. The proposed Gaussian process regression approach shows significant improvements in terms of forecast accuracy and robustness compared to other mainstream demographic modelling approaches in the short-, mid- and long-term forecasting using the mortality and fertility data of several developed countries in the numerical examples.

A Gaussian process regression approach to predict the k-barrier coverage probability for intrusion detection in wireless sensor networks

Sensors in a Wireless Sensor Network (WSN) sense, process, and transmit information simultaneously. They mainly find applications in agriculture monitoring, environment monitoring, smart city development and defence. These applications demand high-end performance from the WSN. However, the performance of a WSN is highly vulnerable to various types of security threats. Any intrusion may reduce the performance of the WSN and result in fatal problems. Hence, fast intrusion detection and prevention is of great use. This paper aims towards fast detection and prevention of any intrusion using a machine learning approach based on Gaussian Process Regression (GPR) model. We have proposed three methods (S-GPR, C-GPR and GPR) based on feature scaling for accurate prediction of k-barrier coverage probability. We have selected the number of nodes, sensing range, Sensor to Intruder Velocity Ratio (SIVR), Mobile to Static Node Ratio (MSNR), angle of the intrusion path, and required k as the potential features. These features are extracted using an analytical approach. Simulation results demonstrate that the proposed method III accurately predicts the k-barrier coverage probability and outperforms the other two methods (I and II) with a correlation coefficient (R = 0.85) and Root Mean Square Error (RMSE = 0.095). Further, the proposed methods achieve a higher accuracy as compared to other benchmark schemes.

A Gaussian Process Regression approach within a data-driven POD framework for engineering problems in fluid dynamics

<abstract><p>This work describes the implementation of a data-driven approach for the reduction of the complexity of parametrical partial differential equations (PDEs) employing Proper Orthogonal Decomposition (POD) and Gaussian Process Regression (GPR). This approach is applied initially to a literature case, the simulation of the Stokes problem, and in the following to a real-world industrial problem, within a shape optimization pipeline for a naval engineering problem.</p></abstract>

State-of-Charge Dependent Battery Model Identification Using Gaussian Process Regression

Abstract This paper investigates the parameter identification of a state-of-charge dependent equivalent circuit model (ECM) for Lithium-ion batteries. Different from most existing ECM identification methods, we focus on identifying the functional relations between ECM parameters and state-of-charge (SOC). By transforming the ECM into an ARX model, a Gaussian process regression (GPR) approach is proposed, without using parametric functions to describe the SOC dependence of ARX coefficients. The proposed approach derives the posterior distributions of ECM parameters, thus is capable to quantify the estimation uncertainties. Another advantage lies in the flexibility of incorporating the knowledge of batteries into the prior distributions used in GPR, which enhances the estimation performance in the presence of noises. The effectiveness of the proposed GPR approach is illustrated by simulation examples under both low and high noise levels.

Cross Trajectory Gaussian Process Regression Model for Battery Health Prediction

Accurate battery capacity prediction is important to ensure reliable battery operation and reduce the cost. However, the complex nature of battery degradation and the presence of capacity regeneration phenomenon render the prediction task very challenging. To address this problem, this paper proposes a novel and efficient algorithm to predict the battery capacity trajectory in a multi-cell setting. The proposed method is a new variant of Gaussian process regression (GPR) model, and it utilizes similar trajectories in the historical data to enhance the prediction of desired capacity trajectory. More importantly, the proposed method adds no extra computation cost to the standard GPR. To demonstrate the effectiveness of the proposed method, validation tests on two different battery datasets are implemented in the case studies. The prediction results and the computation cost are carefully benchmarked with cutting-edge GPR approaches for battery capacity prediction.

Predicting the delamination factor in carbon fibre reinforced plastic composites during drilling through the Gaussian process regression

The carbon fibre reinforced plastic (CFPR) has been widely used in aircraft structural applications due to the superior modulus, specific tensile strength, and fatigue strength. The inhomogeneous and anisotropic nature of these composites poses great challenges on the machining process. Particularly, the delamination is one of major defects associated with drilling, which has a significant impact on CFRP’s structure integrity and application. Machine learning approaches can help facilitate the optimization of machining processes. In this study, we develop the Gaussian process regression (GPR) model to predict delaminations in carbon fibre reinforced plastic composites during drilling from machining parameters. The model is simple and highly accurate and stable that contributes to fast delamination estimations. By combining the optimization results from the Taguchi method and GPR approach, it is expected that more quantitative data can be extracted from fewer experimental trials at the same time.

PARAMETRIC AND NON-PARAMETRIC REGRESSION APPROACHES FOR NON-INVASIVE BLOOD GLUCOSE MONITORING

Blood glucose monitoring systems (BGMSs) play a crucial role in health care applications. Invasive measurements are more accurate while non-invasive BGMS encourage self monitoring and reduce the cost of health care. Though multiple sensor data acquisition and suitable processing improve accuracy, self-monitoring becomes difficult in such non-invasive systems due to multiple signal acquisition. This paper investigates a non-invasive BGMS prototype that renders accurate measurements by statistically processing a single sensor data. The developed prototype is based on near-infrared (NIR) spectroscopy, which provides an electronic voltage that gets mapped to corresponding blood glucose level. This mapping is proposed using two different statistical regression approaches, parametric Bayesian Regression (BR) approach and the non-parametric Gaussian Process Regression (GPR) approach. Dataset is acquired from 33 subjects who visited Ramaiah Medical College Hospital, India. On each subject, voltage from the BGMS prototype and corresponding invasively obtained blood glucose level have been recorded. The BR and GPR approaches are trained with 75% of the data while the remaining 25% is used for testing. Test results show that BR approach renders root mean square error (RMSE) of 3.7[Formula: see text]mg/dL, while the mean absolute percentage error (MAPE) is around 2.5. The GPR with different radial basis function kernels revealed that a multiquadric kernel provides a lowest RMSE of 3.28[Formula: see text]mg/dL and lowest MAPE of 2.2, thus outperforming the parametric BR approach. Investigations also show that for a training data of less than 15 entries, BR renders better accuracy than the GPR approach.

A novel approach for solid particle erosion prediction based on Gaussian Process Regression

Based on Gaussian Process Regression (GPR) method, a novel non-linear approach is adopted to predict solid particle erosion in standard elbows. Several data sets extracted from Computational Fluid Dynamics (CFD) results and experimental tests are used to evaluate the effectiveness of the approach for gas-solid as well as gas-liquid-solid flows. Elbow diameter, particle size and density, fluid density and viscosity, and flow velocity are considered as input parameters. By combining input parameters into dimensionless groups, dimensionality reduction is performed. This is conducted to understand the dimensionless numbers governing the erosion phenomenon and effect of dimensionality reduction on erosion prediction. Results and error analysis show that for gas-solid flow, over 80% of the predictions have relative error less than 20% compared to the experimental data. In gas-liquid-solid flow conditions, effect of mixture Reynolds number and ratio of the superficial velocities on erosion rate for both churn and annular flows are investigated. A GPR-based framework is demonstrated to predict erosion distributions over the elbow and results are compared with experimental measurements. Results demonstrate that the GPR approach can accurately and reliably predict solid particle erosion.

On the assessment of specific heat capacity of nanofluids for solar energy applications: Application of Gaussian process regression (GPR) approach

To characterize the performance of nanofluids for heat transfer applications in solar systems, an accurate estimation of their specific heat capacity (SHC) is of paramount importance. To this end, having such properties of nanofluids via computational approaches has gained attention as an effective method to eliminate the time-consuming process of experimental investigations. This study focuses on modeling the SHC of different carbon-based and metal oxide-based nanoparticles dispersed in various base fluids. Herein, we propose a novel data-driven dynamic model based on the Gaussian process regression (GPR) technique in comparison with the random forest (RF) approach and generalized regression neural network (GRNN) to predict the SHC of nanofluids. The developed models employ the solid volume fraction (ϕ), temperature (T), mean diameter of nanoparticle (Dp), and SHC of base fluid (CPBase) as the input parameters. The data has been collected from 10 reliable references. The results showed that the GPR model (R=0.99974, RMSE=0.01506 J/K.g) shows superior performance than the results of the RF (R=0.99761, RMSE=0.04598 J/K.g) and GRNN (R=0.99563, RMSE=0.06085 J/K.g). The results proved that the developed model would accurately estimate the SHC of the studied nanofluids. In addition, the sensitivity analysis of the dependence of input variables on the SHC of nanofluids revealed that the mean diameter of nanoparticles and the SHC of base fluid are the major critical factors in the determination of SHC of nanofluids.

A New Predictive Model for Evaluating Chlorophyll-a Concentration in Tanes Reservoir by Using a Gaussian Process Regression

Chlorophyll-a (hereafter referred to as Chl-a) is a recognized indicator for phytoplankton abundance and biomass –hence, an effective estimation of the trophic condition– of water bodies as lakes, reservoirs and oceans. Indeed, Chl-a is the primary molecule responsible for photosynthesis. A strong and robust Bayesian nonparametric technique, termed Gaussian process regression (GPR) approach, for foretelling the dependent variable Chl-a concentration in Tanes reservoir from a dataset concerning to 268 samples is shown in this paper. Ten years (2006–2015) of monitoring water quality variables (biological and physico-chemical independent variables) in the Tanes reservoir were used to build this mathematical GPR-relied model. As an optimizer, the method known as Limited-memory Broyden-Fletcher-Goldfarb-Shanno (LBFGSB) iterative algorithm was used; this allows the selection of kernel optimal parameters during the GPR training phase, which greatly determines the regression precision. The results of the current investigation can be summarized in two. Firstly, the relevance of each input variable on Chl-a concentration in Tanes reservoir is determined. Secondly, the Chl-a can be successfully predicted using this hybrid LBFGSB/GPR–relied model (R2 and r values were 0.8597 and 0.9306, respectively). The concordance between observed data and the model clearly proves the high efficiency of this innovative approach.

A new hybrid model to foretell thermal power efficiency from energy performance certificates at residential dwellings applying a Gaussian process regression

An energy performance certificate (EPC) provides information on the energy performance of an energy system. The objective of this research aimed at obtaining a predictive model for early detection of thermal power efficiency (TPE) for energy conversion and preservation in buildings. This article expounds a sound and solid nonparametric Bayesian technique known as Gaussian process regression (GPR) approach, based on a set of data collected from different dwellings in an oceanic climate. Firstly, this model introduces the relevance of each predictive variable on energy performance in residential buildings. The second result refers to the statement that we can predict successfully the TPE by using this model. A coefficient of determination equal to 0.9687 was thus established in order to predict the TPE from the observed data, using the GPR approach in combination with the differential evolution (DE) optimiser. The concordance between experimental observed data and the predicted data from the best-proposed novel hybrid DE/GPR-relied model demonstrated here the adequate efficiency of this innovative approach.

A Gaussian process regression model to predict energy contents of corn for poultry

The present study proposes a Gaussian process regression (GPR) approach to develop a model to predict true metabolizable energy corrected for nitrogen (TMEn) content of corn samples (as model output) for poultry given levels of feed chemical compositions of crude protein, ether extract, crude fiber, and ash (as model inputs). A 30 corn samples obtained from 5 origins [Brazil (n = 9), China (n = 5), Iran (n = 7), and Ukraine (n = 9)] were assayed to determine chemical composition and TMEn content using chemical analyses and bioassay technique. In addition to GPR model, data were also analyzed by multiple linear regression (MLR) model. Results revealed that corn samples of different origins differ in their gross energy and chemical composition of crude protein, crude fiber, and ash, but no differences were observed for their ether extract and TMEn contents. Based on model evaluation criteria of R2 and root mean square error (RMSE), the GPR model showed satisfactory performance (R2 = 0.92 and RMSE = 33.68 kcal/kg DM) in predicting TMEn and produced relatively better prediction values than those produce by MLR (R2 = 0.23 and RMSE = 104.85 kcal/kg DM). The GPR model may be capable of improving our aptitude and capacity to precisely predict energy contents of feed ingredients to formulate optimal diets for poultry.

A Comparison of Estimating Crop Residue Cover from Sentinel-2 Data Using Empirical Regressions and Machine Learning Methods

Quantifying crop residue cover (CRC) on field surfaces is important for monitoring the tillage intensity and promoting sustainable management. Remote-sensing-based techniques have proven practical for determining CRC, however, the methods used are primarily limited to empirical regression based on crop residue indices (CRIs). This study provides a systematic evaluation of empirical regressions and machine learning (ML) algorithms based on their ability to estimate CRC using Sentinel-2 Multispectral Instrument (MSI) data. Unmanned aerial vehicle orthomosaics were used to extracted ground CRC for training Sentinel-2 data-based CRC models. For empirical regression, nine MSI bands, 10 published CRIs, three proposed CRIs, and four mean textural features were evaluated using univariate linear regression. The best performance was obtained by a three-band index calculated using (B2 − B4)/(B2 − B12), with an R2cv of 0.63 and RMSEcv of 6.509%, using a 10-fold cross-validation. The methodologies of partial least squares regression (PLSR), artificial neural network (ANN), Gaussian process regression (GPR), support vector regression (SVR), and random forest (RF) were compared with four groups of predictors, including nine MSI bands, 13 CRIs, a combination of MSI bands and mean textural features, and a combination of CRIs and textural features. In general, ML approaches achieved high accuracy. A PLSR model with 13 CRIs and textural features resulted in an accuracy of R2cv = 0.66 and RMSEcv = 6.427%. An RF model with predictors of MSI bands and textural features estimated CRC with an R2cv = 0.61 and RMSEcv = 6.415%. The estimation was improved by an SVR model with the same input predictors (R2cv = 0.67, RMSEcv = 6.343%), followed by a GPR model based on CRIs and textural features. The performance of GPR models was further improved by optimal input variables. A GPR model with six input variables, three MSI bands and three textural features, performed the best, with R2cv = 0.69 and RMSEcv = 6.149%. This study provides a reference for estimating CRC from Sentinel-2 imagery using ML approaches. The GPR approach is recommended. A combination of spectral information and textural features leads to an improvement in the retrieval of CRC.

Precessing numerical relativity waveform surrogate model for binary black holes: A Gaussian process regression approach

Gravitational wave astrophysics relies heavily on the use of matched filtering both to detect signals in noisy data from detectors, and to perform parameter estimation on those signals. Matched filtering relies upon prior knowledge of the signals expected to be produced by a range of astrophysical systems, such as binary black holes. These waveform signals can be computed using numerical relativity techniques, where the Einstein field equations are solved numerically, and the signal is extracted from the simulation. Numerical relativity simulations are, however, computationally expensive, leading to the need for a surrogate model which can predict waveform signals in regions of the physical parameter space which have not been probed directly by simulation. We present a method for producing such a surrogate using Gaussian process regression which is trained directly on waveforms generated by numerical relativity. This model returns not just a single interpolated value for the waveform at a new point, but a full posterior probability distribution on the predicted value. This model is therefore an ideal component in a Bayesian analysis framework, through which the uncertainty in the interpolation can be taken into account when performing parameter estimation of signals.

Modeling total resistance and form resistance of movable bed channels via experimental data and a kernel-based approach

AbstractAn accurate prediction of roughness coefficient in alluvial channels is of substantial importance for river management. In this study, the total and form resistance in alluvial channels with dune bedform were assessed using experimental data. First, the data of experiments carried out at the Hydraulic Laboratory of University of Tabriz was used to investigate the impact of hydraulic and sediment parameters on roughness coefficient. Then, these data were combined with other laboratory data, and the total and bedform resistance were modeled via a Gaussian Process Regression (GPR) approach. For models, developing different input combinations were considered based on flow and sediment characteristics. The obtained results from the experiments showed that the Reynolds number has a better correlation with flow resistance in comparison with other hydraulic parameters. It was found that the roughness variations due to bedform are almost between 40 and 80% of the total roughness coefficient. Also, the obtained results proved the capability of the GPR method in the modeling process. It was found that the model which took the advantages of both flow and sediment characteristics performed better compared to the other models. The sensitivity analysis results showed that the Reynolds number has the most significant impact in the prediction process.