Gaussian Process Regression Method Research Articles

Lagrangian analysis of submesoscale flows from sparse data using Gaussian Process Regression for field reconstruction

Lagrangian analyses of oceanic flows provide insight into the various transport pathways in the ocean. This analysis typically relies on a dense set of trajectories that can be computed using high-resolution velocity fields, which are often not available during field experiments. Instruments like drifters and floats are often employed to overcome the limitations imposed by satellite- and radar-based velocity fields, to understand the transport pathways in the ocean. However, the sparsity in available drifter-trajectory data proves prohibitive to obtaining a comprehensive map of the Lagrangian characteristics of the underlying flow. To circumvent these issues, we use Gaussian Process Regression (GPR) to obtain velocity fields from sparse drifter data to generate synthetic trajectories and subsequently estimate two Lagrangian metrics, FTLE and dilation rate. A detailed error analysis is performed for drifter clusters deployed within various dynamical regions in the analytic Bickley jet system. The uncertainties in velocity reconstruction obtained from the GPR method, averaged along particle trajectories, locate Lagrangian confidence regions that are applicable both to synthetic trajectories and the dilation rate field. A sensitivity analysis reveals the role played by factors such as the spatial sampling density and temporal resolution of the drifter data, as well as the effect of position uncertainty as a result of GPS inaccuracy. The method is then applied to the drifter data from the Lagrangian Submesoscale Experiment in 2016 to locate convergent filaments. The results present a marked improvement over direct estimation of area-averaged dilation rates using drifter clusters.

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%.

A novel data-driven state evaluation approach for photovoltaic arrays in uncertain shading scenarios

Accurately determining the operating state of photovoltaic (PV) power-generation equipment and providing accurate support for maintenance management requires evaluation of the states of PV arrays under partial shading conditions. Results of such evaluation enable the optimization of maintenance measures to reduce maintenance costs and extend the lifespan of PV modules, thereby increasing the overall revenue of the PV power station. Therefore, this study proposes a novel state-evaluation approach based on current-voltage (I-V) curves under partial shading conditions. Based on the size of the pixel values in this curve, the proposed novel state-evaluation was performed using the proportion of the values of the normal and shaded curves under the same environmental conditions. Specifically, the feature variables (open-circuit voltage, short-circuit current) and pixel values within the I-V curve were analyzed and calculated using a sensitivity algorithm and computer vision algorithms (Canny edge-detection algorithm and Green's theorem). Based on the mapping relationship between feature variables and pixels, an improved Gaussian-process regression method with a combined kernel function (dot product and Matérn function) was proposed to predict the pixel values under the corresponding normal curve. This combined kernel function effectively captured causal relationships and handled outliers in the test dataset to improve the robustness of the model. Finally, the ratios of the pixel values were calculated using the predicted pixels within the normal curve and the calculated pixels within the shading curve. Experiments demonstrated that the root mean square error (RMSE), mean absolute error (MAE), R squared (R2) and log likelihood of the improved Gaussian-process regression method reached 0.011, 0.0086, 0.9996, and 24.7096, respectively.

Estimation of the Hubble constant using Gaussian process regression and viable alternatives

A well-known problem in cosmology is the ‘Hubble tension’ problem, i.e. different estimates for the Hubble constant H0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$H_0$$\\end{document} are not concordant with each other. This work investigates different statistical methods for estimating this value using cosmic chronometer, type Ia supernova and baryonic acoustic data. We start by making use of methods already established in the literature for this purpose, namely Gaussian process regression and Markov chain Monte Carlo (MCMC) methods based on the concordance Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varLambda $$\\end{document}CDM model. We also consider two novel approaches; the first makes use of non-parametric MCMC inference on the hyperparameters of a Gaussian process kernel, independently of any cosmological model. The second approach is Student’s t-process regression, which is a generalised version of Gaussian process regression that makes use of the multivariate Student’s t-distribution instead of the multivariate Gaussian distribution. We also consider variants of these two methods which account for heteroscedasticity within the data. A comparison of the different approaches is made. In particular, the model-independent techniques investigated mostly agree with predictions based on the Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varLambda $$\\end{document}CDM model. Moreover, Gaussian process regression is highly sensitive to the prior specification, while Student’s t-process regression and the heteroscedastic variants of both methods are more robust to this. Student’s t-process regression and both heteroscedastic models suggest a lower value of the Hubble constant. Across all the estimates obtained for the Hubble constant within this work, the median value is H^0med=68.85±1.67\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hat{H}_0^{med} = 68.85 \\pm 1.67$$\\end{document} km s-1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{-1}$$\\end{document} Mpc-1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{-1}$$\\end{document}.

Integrated study of prediction and optimization performance of PBI-HTPEM fuel cell using deep learning, machine learning and statistical correlation

This paper uses 3D modeling and artificial intelligence methods to predict, and find optimal point in high-temperature proton exchange membrane (HTPEM) fuel cells. The main objective is to obtain maximum power and current density at the optimum node of the HTPEM fuel cell. The response surface method (RSM) is used to prevent excessive duplication and ensure adequate data coverage for determining input parameters. Also, for the first time, the correlation presented was compared with AI-based metaheuristic optimization methods i.e., including support vector regression (SVR), Gaussian process regression (GPR), and deep neural networks (DNN) with a dropout layer, alongside metaheuristic algorithms such as whale optimization algorithm (WOA), Grasshopper optimization algorithm (GOA), firefly algorithm (FF), and the genetic algorithm (GA). The results show that SVR, GPR, and DNN methods have excellent performance, with mean absolute percentage error (MAPE) of 0.81 % for DNN, 0.83 % for SVR, and 2.24 % for GPR. Most optimization algorithms exhibit errors below 8 %. The DNN-GOA, SVR-WOA, SVR-GA, and GPR-GOA algorithms have the lowest errors among them. Correlations have a lower computational cost for obtaining maximum power and current density at the optimum node compared to optimization algorithms, with a relative error of less than 6 % in most cases.

A Surrogate Model's Decision Tree Method Evaluation for Uncertainty Quantification on a Finite Element Structure via a Fuzzy-Random Approach

A novel additive manufacturing method (AM)) constructs a three-dimensional model from a computer-aided design by adding material layer by layer. This technique produces a lightweight end product with complex geometries and has gained recognition among industrial players. Nonetheless, the mechanical properties and geometry components are the uncertainties that prevail in its structures. An alternative approach using the Finite Element Method (FEM) to analyse these uncertainties demands extensive computational effort and time consumption. Therefore, a machine learning (ML) tool using the surrogate modelling technique offers an alternative way to provide and predict simulation outcomes. This study applies two surrogate modeling approaches, the decision tree (DT) and the Gaussian process regression (GPR) methods. Output data from a FEM simulation with uncertainty elements are obtained for the training purposes of the surrogate models. Both ML methods can predict simulation results with high precision. Both approaches obtained an excellent coefficient of determination value, R2 of 0.998, and Root Mean Square Error, RMSE of 0.012, successfully reducing time consumption and computational effort. The DT method shows better robustness when compared to the GPR method. A value change in the input parameter significantly impacts the surrogate model's prediction performance. An adequate quantity of data input for the training phase of both surrogate models exhibits the FEM results with the presence of uncertainty and robustness.

An efficient method of predicting S-wave velocity using sparse Gaussian process regression for a tight sandstone reservoir

The shear wave (S-wave) velocity plays a crucial role in interpreting the lithology in seismic data, identifying fluids and predicting reservoirs. However, S-wave velocity is often unavailable due to the high cost of measurement and technical constraints. Conventional methods exhibit limitations that potentially impact the accuracy or efficiency on predicting S-wave velocity. Moreover, these methods always ignore the uncertainty quantification associated with the predicted results. This paper proposes a sparse Gaussian process regression (SGPR) method to predict the S-wave velocity in tight sandstone reservoirs. SGPR is a highly efficient regression technique that is based on the Gaussian process regression (GPR) method. In the SGPR method, inducing inputs are introduced to approximate the kernel matrix to decrease the computational complexity. A sparse set of inducing inputs and kernel hyperparameters are optimized through minimizing the Kullback-Leibler (KL) divergence between the exact posterior distribution and the approximate one. In this study, we select several types of logging data, which include porosity, water saturation, shale content, lithology and P-wave velocity, as the inputs for the SGPR method to predict S-wave velocity. To validate its effectiveness, we use the SGPR method to predict S-wave velocity in tight sandstone and compare the results with those from the GPR method, the bidirectional long short-term memory (BiLSTM) method and the Xu-White model. Additionally, we conduct cross-validation to demonstrate the robustness of the SGPR method. Our findings indicate that the SGPR method presents better performance and significant advantages about the accuracy and efficiency. Moreover, the SGPR method offers uncertainty quantification for the predicted S-wave velocity.

MSA-Net: A Precise and Robust Model for Predicting the Carbon Content on an As-Received Basis of Coal.

The carbon content as received (Car) of coal is essential for the emission factor method in IPCC methodology. The traditional carbon measurement mechanism relies on detection equipment, resulting in significant detection costs. To reduce detection costs and provide precise predictions of Cars even in the absence of measurements, this paper proposes a neural network combining MLP with an attention mechanism (MSA-Net). In this model, the Attention Module is proposed to extract important and potential features. The Skip-Connections are utilized for feature reuse. The Huber loss is used to reduce the error between predicted Car values and actual values. The experimental results show that when the input includes eight measured parameters, the MAPE of MSA-Net is only 0.83%, which is better than the state-of-the-art Gaussian Process Regression (GPR) method. MSA-Net exhibits better predictive performance compared to MLP, RNN, LSTM, and Transformer. Moreover, this article provides two measurement solutions for thermal power enterprises to reduce detection costs.

Robust and comprehensive predictive models for methane hydrate formation condition in the presence of brines using black-box and white-box intelligent techniques

Accurate estimation of gas hydrate formation condition is crucial for many reasons. In one hand, the gas hydrate formation is a promising approach for gas separation, cold energy storage, seawater desalination, etc. On the other hand, in some industries, this phenomenon may cause some challenges, such as pipelines blockage. The current study was undertaken to develop trustworthy predictive tools for methane hydrate formation temperature (MHFT) in the presence of brines. To achieve this target, 1051 experimental data pertinent to the methane hydrate equilibrium in 26 single and multiple brines over an extensive range of operating conditions were amassed from published studies. Four simple factors, including pressure, brine concentration, salt molecular weight and salt melting temperature were defined as the input variables, and the black-box intelligent techniques, including gaussian process regression (GPR), multilayer perceptron (MLP) and radial basis function (RBF) were employed to link MHFT to the mentioned factors. A plethora of graphical and statistically-based assessments were performed to determine the accuracy level of the proposed models. While all intelligent models had excellent performances, the one established by the GPR method showed the best agreements with experimental data, and gave the AARE and R2 values of 0.14% and 99.17%, respectively, in the testing step. The foregoing model was capable of predicting MHFT over a broad range of conditions with relative deviations mostly below 0.10%. Additionally, it showed an excellent performance in describing the physical variations of MHFT versus operating factors. The authority of the analyzed databank and the presented model was asserted via the William's plot investigation. Moreover, a sensitivity analysis was undertaken in order to determine the most fundamental factors in controlling MHFT. Eventually, a simple mathematical correlation was also derived based on the white-box intelligent approach of gene expression programming (GEP), which allowed the accurate estimation of MHFT with an AARE of 0.56%.

A Data-Driven Method for Parametric PDE Eigenvalue Problems Using Gaussian Process with Different Covariance Functions

Abstract We use a Gaussian Process Regression (GPR) strategy to analyze different types of curves that are commonly encountered in parametric eigenvalue problems. We employ an offline-online decomposition method. In the offline phase, we generate the basis of the reduced space by applying the proper orthogonal decomposition (POD) method on a collection of pre-computed, full-order snapshots at a chosen set of parameters. Then we generate our GPR model using four different Matérn covariance functions. In the online phase, we use this model to predict both eigenvalues and eigenvectors at new parameters. We then illustrate how the choice of each covariance function influences the performance of GPR. Furthermore, we discuss the connection between Gaussian Process Regression and spline methods and compare the performance of the GPR method against linear and cubic spline methods. We show that GPR outperforms other methods for functions with a certain regularity.

Asynchronous Parallel Large-Scale Gaussian Process Regression.

Gaussian process regression (GPR) is an important nonparametric learning method in machine learning research with many real-world applications. It is well known that training large-scale GPR is a challenging task due to the required heavy computational cost and large volume memory. To address this challenging problem, in this article, we propose an asynchronous doubly stochastic gradient algorithm to handle the large-scale training of GPR. We formulate the GPR to a convex optimization problem, i.e., kernel ridge regression. After that, in order to efficiently solve this convex kernel problem, we first use the random feature mapping method to approximate the kernel model and then utilize two unbiased stochastic approximations, i.e., stochastic variance reduced gradient and stochastic coordinate descent, to update the solution asynchronously and in parallel. In this way, our algorithm scales well in both sample size and dimensionality, and speeds up the training computation. More importantly, we prove that our algorithm has a global linear convergence rate. Our experimental results on eight large-scale benchmark datasets with both regression and classification tasks show that the proposed algorithm outperforms the existing state-of-the-art GPR methods.

Data-driven distortion compensation for laser powder bed fusion process using Gaussian process regression and inherent strain method

The repeated melting and solidification cycles in the laser powder bed fusion (L-PBF) process lead to significant thermal gradients, resulting in notable distortion in the as-built part. Distortion compensation methods, which pre-deform the part design so the as-built shape aligns with the target, have been widely adopted to mitigate this issue. This research introduces a data-driven distortion compensation framework for the L-PBF process. It employs an experimentally-calibrated inherent strain method to generate a dataset and utilizes Gaussian process regression to create the compensated geometry. Experimental validation shows that the proposed method can reduce the maximum distortion by up to 82.5% for a lattice structure and 77.8% for a canonical part. Furthermore, the compensation results reveal that (1) the lumped layer thickness in finite element models has little impact on simulated distortion reduction but can notably affect the experimental reduction; (2) discrepancies between simulated and experimental compensation performance are largely attributed to the curvy surfaces with sharp transitions in trial and compensated shapes, a result of pre-deforming the design; (3) the number of trial geometries considerably affects the effectiveness of compensation, while the number of deformation states does not have a statistically significant impact.

Prediction of Rock's Brittleness and Dynamic Properties Utilizing Effective Artificial Intelligence Approaches

This research aims to determine the brittleness index (BI) and engineering properties of limestone specimens. In addition, this study evaluates the effect of moisture on the developed models to predict the BI and shear wave velocity (Vs), based on the point load index (Is50), dry and saturated tensile strength (Ts-d and Ts-s), and porosity. Gaussian process regression (GPR), multilayer feed-forward neural network (MFFNN), and multiple linear regression (MLR) predictive models were utilized. Microscopic examination of the limestone specimens revealed that calcite is the predominant mineral. It was observed that samples with higher calcite content exhibited greater brittleness and strength properties while having lower porosity. The results obtained from the MLR analysis demonstrated that it is possible to accurately forecast the brittleness index (BI), as well as the dry and saturated shear wave velocities (Vs-d and Vs-s) at the specific sites under investigation. The moisture effect on developed models showed that Vs prediction in dry conditions (Vs-d) was less accurate compared to the saturated conditions (Vs-s). Conversely, the relationships developed for estimating the BI in dry conditions exhibited higher accuracy. The analysis of all model assumptions using MLR indicated that the models could be reliably utilized. However, the MFFNN and GPR methods were found to be more conservative in estimating these properties. Moreover, the study identified the best transfer function and training algorithm for predicting Vs and BI. The evaluation metrics, such as R2 and RMSE revealed that GPR demonstrated higher precision compared to MFFNN and MLR.

CO2 emission from the electricity sector in Iran; calculation, prediction and reduction policies

Fossil fuel power plants produce a significant amount of CO2 emissions, and this pollutant causes global warming, respiratory and heart diseases, and other significant issues. Electricity interprets as a primary and rising demand in each energy system; thus, in this paper, carbon dioxide (CO2) emission reduction was selected as the objective value for 2025. Power plant fuel consumption was surveyed to calculate the CO2 emission caused by each fuel. Also, Esfahan province (an industrial province in Iran) was investigated as the study case. Forecasting the fuel consumption for 2025 was run by two parameters: population and Gross Domestic Production (GDP), which were forecasted by the report of the Iran Statics Center and the Gaussian Process Regression (GPR) method, respectively. The CO2 emission of power plants was obtained using the coefficients of each fuel. Based on Iran's commitment to the Paris Agreement, a 4% reduction of CO2 emissions is the main objective. Thus, this study aims to reach this goal by implementing four scenarios: a) adding renewable energies, b) adding renewable energies and improving the generation efficiency, c) adding renewable energies and decreasing the grid losses, and d) combining the three scenarios mentioned above. According to these scenarios, reformation strategies compensated 10.5% of the required power, which was satisfied by renewable energies, and finally, this province can gradually satisfy a 4% reduction until 2025.

Thermophysical properties and enhancement behavior of novel B4C-nanoadditive RT35HC nanocomposite phase change materials: Structural, morphological, thermal energy storage and thermal stability

This study aims to enhancement the thermal conductivity of RT35HC, as a commercial paraffin, by integrating boron carbide (B4C) nanoparticles for the first time, thereby producing B4C-nanoadditive nanocomposite PCMs. The B4C nanoparticles were reinforcement to RT35HC at mass fraction percentages (wt.%) of 0.5, 1, 1.5 and 2 by melting and physical mixing method. The structural and morphological characteristics of both pure and nanocomposite PCMs were examined using XRD, FT-IR, FE-SEM, and EDX. Thermal properties were investigated through DSC, TGA/DTA, and thermal conductivity measurements using the KD2-Pro device. The Gaussian process regression (GPR) model was used to analyze the Cp values in relation to temperature and additive ratio. Structural and morphological analysis results indicated a homogeneous distribution of nanoparticles within the PCM matrix, without any significant chemical or physical alterations. The introduction of B4C-nanoadditive did not markedly affect the melting and solidification temperatures. However, melting and solidification enthalpies decreased proportionally with increased nanoadditive ratios, with the greatest reductions being 7.44 % and 5.74 % at a 2 wt% nanoaddition rate, respectively. As the nanoadditive ratio increased, the thermal conductivity (k) and specific heat capacity (Cp) of RT35HC in both solid and liquid-phases enhanced significantly. Specifically, solid-phase (25 °C) k values increased by 67.51 % from 0.197 to 0.33, and liquid-phase (50 °C) k values by 15.29 % from 0.170 to 0.196. The highest Cp values in the solid and liquid-phases were measured as 3.01 and 2.49, respectively, in the nanocomposite with a high nanoadditive ratio. The GPR method yielded a success rate of 0.9015. Additionally, the nanocomposites exhibited enhanced thermal stability and higher thermal decomposition temperatures. Based on these characterizations, the fabricated B4C-nanoadditive nanocomposite PCMs show promise for application in TES and TM systems.

Robust Gaussian Process Regression Method for Efficient Tunneling Pathway Optimization: Application to Surface Processes.

Simulation of surface processes is a key part of computational chemistry that offers atomic-scale insights into mechanisms of heterogeneous catalysis, diffusion dynamics, and quantum tunneling phenomena. The most common theoretical approaches involve optimization of reaction pathways, including semiclassical tunneling pathways (called instantons). The computational effort can be demanding, especially for instanton optimizations with an ab initio electronic structure. Recently, machine learning has been applied to accelerate reaction-pathway optimization, showing great potential for a wide range of applications. However, previous methods still suffer from numerical and efficiency issues and were not designed for condensed-phase reactions. We propose an improved framework based on Gaussian process regression for general transformed coordinates, which has improved efficiency and numerical stability, and we propose a descriptor that combines internal and Cartesian coordinates suitable for modeling surface processes. We demonstrate with 11 instanton optimizations in three representative systems that the improved approach makes ab initio instanton optimization significantly cheaper, such that it becomes not much more expensive than a classical transition-state theory rate calculation.

Hyper‐parameter optimized GPR model based on chaos game algorithm for RF power transistors

AbstractIn this paper, a new frequency domain behavior model for radio frequency (RF) power transistors based on a hyper‐parameter optimized Gaussian process regression (GPR) method is presented. The chaos game optimization (CGO) algorithm is used to optimize GPR hyperparameters, resulting in the CGO‐GPR model. The basic theory as well as the details of the modeling process are presented. Validation of the model is conducted using a 10‐watt GaN power transistor. Compared to the standard GPR model, the proposed model achieved a significant improvement. Furthermore, the comparison with the particle swarm optimization (PSO) based GPR model (PSO‐GPR) showed that the proposed model allows achieving superior performance, thereby confirming the effectiveness of the developed modeling technique.

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 characterize 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 characterization 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.

A fuzzy Gaussian process regression function approach for forecasting problem

A fuzzy regression function approach is a fuzzy inference system method whose rules cannot be determined based on expert opinion, unlike a classical fuzzy inference system. In a fuzzy regression function approach, an input matrix consists of memberships obtained by the fuzzy clustering method and lagged variables of the time series. In the fuzzy regression function approach, the output vector corresponding to this input matrix is also created and the parameter estimation for the method is carried out with the ordinary least square method. As it is known, the ordinary least square method assumes that the data are linear. In addition, although it is very useful to include a priori information describing the formation of the data in the model, in most cases this information is not available. It is also inappropriate to use a model that does not accurately characterize the data. However, it is not appropriate to estimate parameters for nonlinear data using the ordinary least square method. One of the methods to be used in such a situation is the Gaussian process regression method. While the parameters of a selected basis function are fitted in the ordinary least squares regression method, how all measured data are related is determined in the Gaussian process regression. Besides, Gaussian process regression is a Bayesian approach, it can provide uncertainty measurements on forecasts. In this study, a fuzzy Gaussian process regression function is proposed. The contribution of this paper is to propose a new fuzzy inference system that can be used to solve nonlinear data by proposing a fuzzy Gaussian process regression function. The performance of the newly proposed method is evaluated based on the closing values of the Bitcoin and Crude oil time series. The performance comparison of the proposed method is evaluated with many different forecasting methods and it is concluded that the proposed method has superior forecasting performance.

Stochastic Optimal Control for Robot Manipulation Skill Learning Under Time-Varying Uncertain Environment.

In this article, a novel stochastic optimal control method is developed for robot manipulator interacting with a time-varying uncertain environment. The unknown environment model is described as a nonlinear system with time-varying parameters as well as stochastic information, which is learned via the Gaussian process regression (GPR) method as the external dynamics. Integrating the learned external dynamics as well as the stochastic uncertainties, the complete interaction system dynamics are obtained. Then the iterative linear quadratic Gaussian with learned external dynamics (ILQG-LEDs) method is presented to obtain the optimal manipulation control parameters, namely, the feedforward force, the reference trajectory, as well as the impedance parameters, subject to time-varying environment dynamics. The comparative simulation studies verify the advantages of the presented method, and the experimental studies of the peg-hole-insertion task prove that this method can deal with complex manipulation tasks.