Gaussian Process Research Articles

Deep Reinforcement Multiagent Learning Framework for Information Gathering with Local Gaussian Processes for Water Monitoring

The conservation of hydrological resources involves continuously monitoring their contamination. A multiagent system composed of autonomous surface vehicles is proposed herein to efficiently monitor the water quality. To achieve a safe control of the fleet, the fleet policy should be able to act based on measurements and fleet state. It is proposed to use local Gaussian processes and deep reinforcement learning to jointly obtain effective monitoring policies. Local Gaussian processes, unlike classical global Gaussian processes, can accurately model the information in a dissimilar spatial correlation which captures more accurately the water quality information. A deep convolutional policy is proposed, that bases the decisions on the observation on the mean and variance of this model, by means of an information gain reward. Using a double deep Q‐learning algorithm, agents are trained to minimize the estimation error in a safe manner thanks to a Consensus‐based heuristic. Simulation results indicate an improvement of up to 24% in terms of the mean absolute error with the proposed models. Also, training results with 1–3 agents indicate that our proposed approach returns 20% and 24% smaller average estimation errors for, respectively, monitoring water quality variables and monitoring algae blooms, as compared to state‐of‐the‐art approaches.

Predicting CBR values using gaussian process regression and meta-heuristic algorithms in geotechnical engineering

Predicting CBR values using gaussian process regression and meta-heuristic algorithms in geotechnical engineering

Constraints on cosmological models from quasars calibrated with type Ia supernova by a Gaussian process

Abstract In this paper, we use quasars calibrated from type Ia supernova (SN Ia) to constrain cosmological models. We consider three different X-ray luminosity (LX) - ultraviolet luminosity (LUV) relations of quasars, i.e. the standard LX − LUV relation and two redshift-evolutionary relations (Type I and Type II) respectively constructed from copula and considering a redshift correction to the luminosity of quasars. Only in the case of the Type I relation, quasars can always provide effective constraints on the ΛCDM model. Furthermore, we show that, when the observational Hubble data (OHD) are added, the constraints on the absolute magnitude M of SN Ia and the Hubble constant H0 can be obtained. In the ΛCDM model, the OHD measurements plus quasars with the Type I relation yields M =$-19.321^{+0.085}_{-0.076}$, which is in good agreement with the measurement from SH0ES (M = −19.253 ± 0.027), and H0 = 70.80 ± 3.6 km s−1 Mpc−1, falling between the measurements from SH0ES and the Planck cosmic microwave background radiation data.

Prediction of mechanical properties of LPBF built part based on process monitoring and Gaussian process regression

Abstract As a highly promising technology in additive manufacturing, the laser powder bed fusion (LPBF) has only limited application due to its low reproducibility. In this study, the image information of the 316L specimen after laser scanning and powder paving of each layer was acquired by a CMOS industrial camera. The important features were selected,extrated and quantificated by analyzing the tensile test results. Finally,combined with the laser power, the quantified features were as input of a Gaussian process regression model based on optimisation algorithm of grid search to predict the tensile strength of 316L specimen. The results show that the quantized image features have a significant improvement on the regression effect, and the coefficient of determination(R²) is improved from 63% to 90.57% compared to using only the laser power as input.

An optimization method for ITER radial x-ray camera line-of-sight design basing on Bayesian uncertainty analysis

This paper presents a novel uncertainty optimization algorithm for the design of line-of-sight (LOS) systems used in tomographic inversion. By extending Gaussian process tomography from discrete pixel space to continuous function space through Bayesian inference, we introduce an uncertainty function and analyze its typical distributions. We develop an algorithm to minimize the uncertainty, which is then applied to optimize the LOS configuration of the internal camera in the ITER project. Uncertainty analysis and phantom testing are conducted to validate the effectiveness of the proposed algorithm. The results demonstrate improved accuracy and stability in tomographic reconstructions. This study contributes to the advancement of LOS design for tomographic inversion, offering a practical solution for optimizing diagnostic systems in complex experimental settings.

Signal Processing Using a Circular Sensor Array to Measure the Torsional Angle of a Bolted Joint.

This study presents a new approach to determining the preload force of bolted joints. The concept involves measuring the torsional angle without contact. For this purpose, we present a circular magnetic sensor array integrated into the torque wrench. The torsional angle in bolted joints depends on the dimensions of the screw and the materials used and is typically less than four degrees. For this reason, one requirement is a high angular resolution so that a continuous recording of the torsion angle is feasible during the assembly process. This can be achieved using the circular sensor array and adapted signal processing methods. Two signal processing approaches are utilized. First, the direct method uses the discrete Fourier transformation to calculate the rotation angle from the signal phase. This approach is robust to signal distortion and does not depend on signal amplitude. Second, the method with a learning phase employs Gaussian process regression to minimize the angle error. In an experiment, both approaches were applied within a test bench and showed promising results. The direct method demonstrated a very good angular resolution without training and calibration. For mobile and less-complex applications where a reference system is unavailable, the direct method is preferable. However, in complex measurement systems where reference systems can be utilized initially, significant enhancements to an excellent resolution can be achieved through prior training.

Experimental validation of a short-term damping estimation method for wind turbines in nonstationary operating conditions

Abstract. Modal properties and especially damping of operational wind turbines can vary over short time periods as a consequence of environmental and operational variability. This study seeks to experimentally test and validate a recently proposed method for short-term damping and natural frequency estimation of structures under the influence of varying environmental and operational conditions from measured vibration responses. The method is based on Gaussian process time-dependent auto-regressive moving average (GP-TARMA) modelling and is tested via two applications: a laboratory three-storey shear frame structure with controllable, time-varying damping and a flutter test of a full-scale 7 MW wind turbine prototype, in which two edgewise modes become unstable. Damping estimates for the shear frame compare well with estimates obtained with stochastic subspace identification (SSI) and standard impact hammer tests. The efficacy of the GP-TARMA approach for short-term damping estimation is illustrated through comparison to short-term SSI estimates. For the full-scale flutter test, GP-TARMA model residuals imply that the model cannot be expected to be entirely accurate. However, the damping estimates are physically meaningful and compare well with a previous study. The study shows that the GP-TARMA approach is an effective method for short-term damping estimation from vibration response measurements, given that there are enough training data and that there is a representative model structure.

Reliability Analysis and Optimization of a Reconfigurable Matching Network for Communication and Sensing Antennas in Dynamic Environments through Gaussian Process Regression.

During the implementation of the Internet of Things (IoT), the performance of communication and sensing antennas that are embedded in smart surfaces or smart devices can be affected by objects in their reactive near field due to detuning and antenna mismatch. Matching networks have been proposed to re-establish impedance matching when antennas become detuned due to environmental factors. In this work, the change in the reflection coefficient at the antenna, due to the presence of objects, is first characterized as a function of the frequency and object distance by applying Gaussian process regression on experimental data. Based on this characterization, for random object positions, it is shown through simulation that a dynamic environment can lower the reliability of a matching network by up to 90%, depending on the type of object, the probability distribution of the object distance, and the required bandwidth. As an alternative to complex and power-consuming real-time adaptive matching, a new, resilient network tuning strategy is proposed that takes into account these random variations. This new approach increases the reliability of the system by 10% to 40% in these dynamic environment scenarios.

Enhancing photovoltaic energy forecasting: a progressive approach using wavelet packet decomposition

Abstract Accurate photovoltaic (PV) energy forecasting plays a crucial role in the efficient operation of PV power stations. This study presents a novel hybrid machine-learning (ML) model that combines Gaussian process regression with wavelet packet decomposition to forecast PV power half an hour ahead. The proposed technique was applied to the PV energy database of a station located in Algeria and its performance was compared to that of traditional forecasting models. Performance evaluations demonstrate the superiority of the proposed approach over conventional ML methods, including Gaussian process regression, extreme learning machines, artificial neural networks and support vector machines, across all seasons. The proposed model exhibits lower normalized root mean square error (nRMSE) (2.116%) and root mean square error (RMSE) (208.233 kW) values, along with a higher coefficient of determination (R2) of 99.881%. Furthermore, the exceptional performance of the model is maintained even when tested with various prediction horizons. However, as the forecast horizon extends from 1.5 to 5.5 hours, the prediction accuracy decreases, evident by the increase in the RMSE (710.839 kW) and nRMSE (7.276%), and a decrease in R2 (98.462%). Comparative analysis with recent studies reveals that our approach consistently delivers competitive or superior results. This study provides empirical evidence supporting the effectiveness of the proposed hybrid ML model, suggesting its potential as a reliable tool for enhancing PV power forecasting accuracy, thereby contributing to more efficient grid management.

The Enhanced Adsorption Capacity of Ziziphus jujuba Stones Modified with Ortho-Phosphoric Acid for Organic Dye Removal: A Gaussian Process Regression Approach

Here, the chemical modification of Ziziphus jujuba stones (ZJS) treated with ortho-phosphoric acid (ZJS-H3PO4) is investigated to enhance its adsorption properties for organic dyes. The physicochemical properties of ZJS-H3PO4 reveal increased porosity (87.29%), slightly higher bulk density (0.034 g mL−1), and enhanced acidity (31.42 m eq g g−1) compared to untreated ZJS. XRF analysis confirms the successful incorporation of orthophosphoric acid during treatment due to a significant increase in phosphorus content. The maximum adsorption capacity of methylene blue on ZJS-H3PO4 is found to be 179.83 mg g−1, demonstrating its efficacy as a potential adsorbent for organic dyes. These findings suggest that modifying ZJS with orthophosphoric acid could be a promising strategy to enhance its adsorption performance in various environmental applications. Furthermore, Gaussian process regression (GPR) is employed to model MB adsorption by ZJS-H3PO4. Optimization of the GPR model involves evaluating different kernel functions and meticulously adjusting parameters to maximize its ability to capture complex relationships in the data. The obtained GPR model demonstrates remarkable performance with high correlation coefficients (R) and low root mean square errors (RMSEs) across all study phases. Model validation is performed through residual analysis, confirming its effectiveness and accuracy in predicting MB adsorption. Finally, a user-friendly interface is developed to facilitate the usage of the GPR model in future applications, representing a significant advancement in environmental process modeling and ecosystem management.

Development of an Emulator for Radiation Physics Simulator Using Stochastic Variational Gaussian Process Model

This paper describes an emulator that uses a Stochastic Variational Gaussian process (SVGP) regression model to parameterize radiation in a numerical weather prediction (NWP) model that meteorologically models the Earth's weather system. The computation of radiative processes is very large, accounting for most of the total NWP model computation. Statistical emulators are surrogate models that represent simulators and can overcome the computational limitations of very complex simulators such as radiative processes. Recently, artificial neural network-based radiative transfer emulators have been developed, and in this study, a statistical model, GP, is used to develop a radiative transfer emulator. The GP model has the advantage of calculating the uncertainty of the prediction along with the prediction, so the uncertainty of the prediction can be utilized appropriately. However, the computational complexity of the conventional GP model is very high, making it difficult to apply to large data. To solve this problem, an approximate approach, the SVGP model, was utilized. To further reduce the dimensionality of the input variables, we used a combined neural network and SVGP model. As a result, the SVGP-based radiative physics emulator improved its accuracy by about 20% compared to the artificial neural network emulator. However, the computation speed was about 3 to 9 times slower than the neural network emulator, but it was faster than the computation speed of the NWP model. This suggests that statistical emulators can be used to replace NWP model simulators.

Bayesian estimation of large-scale simulation models with Gaussian process regression surrogates

Large scale, computationally expensive simulation models pose a particular challenge when it comes to estimating their parameters from empirical data. Most simulation models do not possess closed-form expressions for their likelihood function, requiring the use of simulation-based inference, such as simulated method of moments, indirect inference, likelihood-free inference or approximate Bayesian computation. However, given the high computational requirements of large-scale models, it is often difficult to run these estimation methods, as they require more simulated runs that can feasibly be carried out. The aim is to address the problem by providing a full Bayesian estimation framework where the true but intractable likelihood function of the simulation model is replaced by one generated by a surrogate model trained on the limited simulated data. This is provided by a Linear Model of Coregionalization, where each latent variable is a sparse variational Gaussian process, chosen for its desirable convergence and consistency properties. The effectiveness of the approach is tested using both a simulated Bayesian computing analysis on a known data generating process, and an empirical application in which the free parameters of a computationally demanding agent-based model are estimated on US macroeconomic data.

Evaluating Multi-target Regression Framework for Dynamic Condition Prediction in Wellbore

AbstractIn recent years, the focus has shifted towards leveraging physics-based modelling and data-driven analysis to predict drilling incidents and anomalies in real time, with the goal of reducing non-productive periods. However, much of this attention has directed at specific drilling operations like drilling and tripping, leaving other vital processes, such as wellbore conditioning, comparatively overlooked. The primary objective of this study is to employ data-driven techniques for predicting the dynamic state of the wellbore by utilising sensor data, operating parameters, and surface measurements. Accurate predictions are pivotal for automating these processes, promising significant savings in both redundant time and associated costs, ultimately elevating operational efficiency.In this research, the surface drilling parameters such as flowrate, rotation speed, block position, and drill string length are incorporated with the surface measurements such as hookload, pressure, and torque during wellbore conditioning operation to predict further surface sensor measurements. Different parameter settings are evaluated to find the best approach. Six supervised learning algorithms are used to select the best prediction method. The findings reveal that considering all surface parameters and measurements yields the most accurate predictions. Among various single and multi-target regression methods, including deep learning approaches, the Gaussian process and random forest models exhibit the lowest prediction errors.By reliably predicting and understanding wellbore behaviour, this research paves the way for more efficient and autonomous drilling operations in the future, bridging a critical gap in the industry's automation capabilities.

Surface water quality index forecasting using multivariate complementing approach reinforced with locally weighted linear regression model.

River water quality management and monitoring are essential responsibilities for communities near rivers. Government decision-makers should monitor important quality factors like temperature, dissolved oxygen (DO), pH, and biochemical oxygen demand (BOD). Among water quality parameters, the BOD throughout 5 days is an important index that must be detected by devoting a significant amount of time and effort, which is a source of significant concern in both academic and commercial settings. The traditional experimental and statistical methods cannot give enough accuracy or solve the problem for a long time to detect something. This study used a unique hybrid model called MVMD-LWLR, which introduced an innovative method for forecasting BOD in the Klang River, Malaysia. The hybrid model combines a locally weighted linear regression (LWLR) model with a wavelet-based kernel function, along with multivariate variational mode decomposition (MVMD) for the decomposition of input variables. In addition, categorical boosting (Catboost) feature selection was used to discover and extract significant input variables. This combination of MVMD-LWLR and Catboost is the first use of such a complete model for predicting BOD levels in the given river environment. In addition, an optimization process was used to improve the performance of the model. This process utilized the gradient-based optimization (GBO) approach to fine-tune the parameters and better the overall accuracy of predicting BOD levels. To assess the robustness of the proposed method, we compared it to other popular models such as kernel ridge (KRidge) regression, LASSO, elastic net, and gaussian process regression (GPR). Several metrics, comprising root-mean-square error (RMSE), R (correlation coefficient), U95% (uncertainty coefficient at 95% level), and NSE (Nash-Sutcliffe efficiency), as well as visual interpretation, were used to evaluate the predictive efficacy of hybrid models. Extensive testing revealed that, in forecasting the BOD parameter, the MVMD-LWLR model outperformed its competitors. Consequently, for BOD forecasting, the suggested MVMD-LWLR optimized with the GBO algorithm yields encouraging and reliable results, with increased forecasting accuracy and minimal error.

Nonlinear response modelling of material systems using constrained Gaussian processes

AbstractThis article investigates the suitability of constrained Gaussian process regression in predicting nonlinear mechanical responses of material systems with notably reduced uncertainties. This study reinforces the conventional Gaussian processes with mechanics‐informed prior knowledge observed in various kinematic responses. Stiffening and softening responses of material systems mostly demonstrate at least one of the boundedness, monotonicity and convexity conditions with respect to some kinematic variables. These relationships or impositions in turn are encoded into a constrained Gaussian process for prediction, uncertainty quantification and extrapolation. Using numerous examples and comparative studies, this article evidently proves that the use of constrained Gaussian processes is data‐efficient, highly accurate, yields low uncertainties, recovers model overfitting and extrapolates very well compared to unconstrained or conventional Gaussian processes. Moreover, the usability of the proposed numerical method across various engineering modelling domains such as multiscale homogenisation, experimentation, structural optimisation, material constitutive modelling and structural idealisation is demonstrated.

Modelling stochastic and quasi-periodic behaviour in stellar time-series: Gaussian process regression versus power-spectrum fitting

Abstract As the hunt for an Earth-like exoplanets has intensified in recent years, so has the effort to characterise and model the stellar signals that can hide or mimic small planetary signals. Stellar variability arises from a number of sources, including granulation, supergranulation, oscillations and activity, all of which result in quasi-periodic or stochastic behaviour in photometric and/or radial velocity observations. Traditionally, the characterisation of these signals has mostly been done in the frequency domain. However, the recent development of scalable Gaussian process regression methods makes direct time-domain modelling of stochastic processes a feasible and arguably preferable alternative, obviating the need to estimate the power spectral density of the data before modelling it. In this paper, we compare the two approaches using a series of experiments on simulated data. We show that frequency domain modelling can lead to inaccurate results, especially when the time sampling is irregular. By contrast, Gaussian process regression results are often more precise, and systematically more accurate, in both the regular and irregular time sampling regimes. While this work was motivated by the analysis of radial velocity and photometry observations of main sequence stars in the context of planet searches, we note that our results may also have applications for the study of other types of astrophysical variability such as quasi-periodic oscillations in X-ray binaries and active galactic nuclei variability.

Complementing Drawability Assessment of Deep-Drawn Components With Surrogate-Based Global Sensitivity Analysis

Abstract In the early-stage development of sheet metal parts, key design properties of new structures must be specified. As these decisions are made under significant uncertainty regarding drawing configuration changes, they sometimes result in the development of new parts that, at a later design stage, will not be drawable. As a result, there is a need to increase the certainty of experience-driven drawing configuration decisions. Complementing this process with a global sensitivity analysis (GSA) can provide insight into the impact of various changes in drawing configurations on drawability, unveiling cost-effective strategies to ensure the drawability of new parts. However, when quantitative global sensitivity approaches, such as Sobol's method, are utilized, the computational requirements for obtaining Sobol indices can become prohibitive even for small application problems. To circumvent computational limitations, we evaluate the applicability of different surrogate models engaged in computing global design variable sensitivities for the drawability assessment of a deep-drawn component. Here, we show in an exemplary application problem, that both a standard Gaussian process regression (GPR) model and an ensemble model can provide commendable results at a fraction of the computational cost. We compare our surrogate models to existing approaches in the field. Furthermore, by comparing drawability measures we show that the error introduced by the surrogate models is of the same order of magnitude as that from the choice of drawability measure. In consequence, our surrogate models can improve the cost-effective development of a component in the early design phase.

Experimental study and machine learning modeling of water removal efficiency from crude oil using demulsifier

This study deals with the investigation of the water removal efficiency (WRE) from crude oil using a commercial demulsifier. The impacts of time, demulsifier concentration, and temperature on WRE were experimentally studied. The results implied the fact that temperature plays a substantial role in the demulsification and has a direct correlation with WRE. In addition, while increasing the concentration up to 40 ppm contributed to reaching a higher WRE, it did not have positive effects on efficiency at higher concentrations (overdose) and just led to more demulsifier consumption. The concentration dependence of WRE was also diminished at high temperatures. At higher levels of temperature and concentration, the time required to reach a high WRE was noticeably reduced. In order to generalize the findings of this study, the measured experimental data were employed to design predictive methods for WRE based on two smart soft-computing paradigms, including Multilayer perceptron (MLP) and Gaussian process regression (GPR). Despite the high accuracy of both models, the MLP model presented the best consistencies with experimental data with average absolute relative error and relative root mean squared error of 0.84%, and 0.01%, respectively during the testing (validation) step. Also, a visual description through the contour diagram confirmed the capability of the recently proposed models to describe the physical variations of WRE under various operating conditions. Ultimately, a sensitivity analysis based on the MLP model was undertaken to shed light on the order of significance of operational factors in controlling WRE. Overall, the findings of the current research, in turn, have a satisfactory contribution to the efficient design of the water removal process from crude oil based on demulsifiers.

Fossil energy market price prediction by using machine learning with optimal hyper-parameters: A comparative study

Fossil energy markets are important commodities, and their price fluctuations impact worldwide economy and financial markets. Hence, it is essential to forecast the prices of fossil energy commodities. In this study, various machine learning systems are optimized by using Bayesian optimization method and implemented to forecast prices in 12 different fossil energy markets including crude oil, natural gas, propane, kerosene, gasoline, heating oil, and coal based on price information from all fossil energy markets. The optimized machine learning systems considered in modeling and simulations are Gaussian regression process, support vector regression, regression trees, k-nearest neighbor algorithm, and deep feedforward neural networks. The simulation results show that Gaussian regression process is the best system to forecast fossil energy markets. In addition, the deep learning feedforward neural networks system yields to stable forecasts. Furthermore, the prediction of the prices in natural gas, coal, and propane markets is a difficult task compared to the prediction of the prices in crude oil markets. The understanding of the effectiveness of machine learning systems in pricing different fossil energy markets can help international economic agents establish appropriate investment strategies.

Migraine aura discrimination using machine learning: an fMRI study during ictal and interictal periods.

Functional magnetic resonance imaging (fMRI) studies on migraine with aura are challenging due to the rarity of patients with triggered cases. This study optimized methodologies to explore differences in ictal and interictal spatiotemporal activation patterns based on visual stimuli using fMRI in two patients with unique aura triggers. Both patients underwent separate fMRI sessions during the ictal and interictal periods. The Gaussian Process Classifier (GPC) was used to differentiate these periods by employing a machine learning temporal embedding approach and spatiotemporal activation patterns based on visual stimuli. When restricted to visual and occipital regions, GPC had an improved performance, with accuracy rates for patients A and B of roughly 86-90% and 77-81%, respectively (p < 0.01). The algorithm effectively differentiated visual stimulation and rest periods and identified times when aura symptoms manifested, as evident from the varying predicted probabilities in the GPC models. These findings contribute to our understanding of the role of visual processing and brain activity patterns in migraine with aura and the significance of temporal embedding techniques in examining aura phenomena. This finding has implications for diagnostic tools and therapeutic techniques, especially for patients suffering from aura symptoms.