Online Gaussian Process Regression Research Articles

Fault Detection for Re-initialization of Online Gaussian Process Regression Using Kernel Linear Independence Test

Fault Detection for Re-initialization of Online Gaussian Process Regression Using Kernel Linear Independence Test

Fault-Tolerant Control for Aircraft with Structural Damage Using Sparse Online Gaussian Process Regression

This paper presents the design of data-driven fault-tolerant control using sparse online Gaussian process regression (SOGPR) to stabilize an aircraft with left-wing damage. The structural damage causes changes in mass, moment of inertia, center of gravity, and aerodynamic coefficients. These parameter variations deteriorate the performance of model-based nonlinear control methods. Hence, Gaussian process-based nonlinear dynamic inversion (GP-NDI) is proposed to compensate for uncertainties in situations of structural damage. Unlike parametric adaptive control approaches, Gaussian process regression is a non-parametric method that does not need prior information about uncertainties. And the proposed method implements SOGPR to reduce computational time and memory by incrementally updating the mean and variance. To compensate for the error in the estimated uncertainty, a robust control input is designed. In addition, a weighted delete score is used to improve the transient response. Numerical simulation results are compared with model reference adaptive control (MRAC) and nonlinear disturbance observer (NDO) to analyze a stabilizing and tracking performance in a structural damage situation.

Reinforcement learning with Gaussian process regression using variational free energy

Abstract The essential part of existing reinforcement learning algorithms that use Gaussian process regression involves a complicated online Gaussian process regression algorithm. Our study proposes online and mini-batch Gaussian process regression algorithms that are easier to implement and faster to estimate for reinforcement learning. In our algorithm, the Gaussian process regression updates the value function through only the computation of two equations, which we then use to construct reinforcement learning algorithms. Our numerical experiments show that the proposed algorithm works as well as those from previous studies.

Consistent online Gaussian process regression without the sample complexity bottleneck

Gaussian processes provide a framework for nonlinear nonparametric Bayesian inference widely applicable across science and engineering. Unfortunately, their computational burden scales cubically with the training sample size, which in the case that samples arrive in perpetuity, approaches infinity. This issue necessitates approximations for use with streaming data, which to date mostly lack convergence guarantees. Thus, we develop the first online Gaussian process approximation that preserves convergence to the population posterior, i.e., asymptotic posterior consistency, while ameliorating its intractable complexity growth with the sample size. We propose an online compression scheme that, following each a posteriori update, fixes an error neighborhood with respect to the Hellinger metric centered at the current posterior, and greedily tosses out past kernel dictionary elements until its boundary is hit. We call the resulting method Parsimonious Online Gaussian Processes (POG). For diminishing error radius, asymptotic statistical stationarity is achieved (Theorem 1ii) at the cost of unbounded memory in the limit. On the other hand, for constant error radius, POG converges to a neighborhood of stationarity (Theorem 1ii) but with finite memory at-worst determined by the metric entropy of the feature space (Theorem 2). Here stationarity refers to the distributional distance between sequential marginal posteriors approaching null with the time index. Experimental results are presented on several nonlinear regression problems which illuminates the merits of this approach as compared with alternatives that fix the subspace dimension defining the history of past points.

Multi-Horizon Forecasting of Global Horizontal Irradiance Using Online Gaussian Process Regression: A Kernel Study

In the present paper, global horizontal irradiance (GHI) is modelled and forecasted at time horizons ranging from 30 min to 48 h, thus covering intrahour, intraday and intraweek cases, using online Gaussian process regression (OGPR) and online sparse Gaussian process regression (OSGPR). The covariance function, also known as the kernel, is a key element that deeply influences forecasting accuracy. As a consequence, a comparative study of OGPR and OSGPR models based on simple kernels or combined kernels defined as sums or products of simple kernels has been carried out. The classic persistence model is included in the comparative study. Thanks to two datasets composed of GHI measurements (45 days), we have been able to show that OGPR models based on quasiperiodic kernels outperform the persistence model as well as OGPR models based on simple kernels, including the squared exponential kernel, which is widely used for GHI forecasting. Indeed, although all OGPR models give good results when the forecast horizon is short-term, when the horizon increases, the superiority of quasiperiodic kernels becomes apparent. A simple online sparse GPR (OSGPR) approach has also been assessed. This approach gives less precise results than standard GPR, but the training computation time is decreased to a great extent. Even though the lack of data hinders the training process, the results still show the superiority of GPR models based on quasiperiodic kernels for GHI forecasting.

GHI forecasting using Gaussian process regression: kernel study

Abstract In this paper, online Gaussian process regression (GPR) is used to model and forecast Global Horizontal Irradiance, at forecast horizons ranging from 30 min to 5 h. It is shown that the covariance function (or kernel) is a key element, deeply influencing forecast results. As a consequence, Gaussian processes with simple kernels and with more complex kernels have been tested and compared to the classic persistence model. Using two datasets of 45 days, it is shown that online GPR models based on quasiperiodic kernels outperform both the persistence model and GPR models based on simple kernels, including the widely used squared exponential kernel.

Three-Dimensional Deformable Object Manipulation Using Fast Online Gaussian Process Regression

In this letter, we present a general approach to automatically visual servo control the position and shape of a deformable object whose deformation parameters are unknown. The servo control is achieved by online learning a model mapping between the robotic end-effector's movement and the object's deformation measurement. The model is learned using the Gaussian process regression (GPR) to deal with its highly nonlinear property, and once learned, the model is used for predicting the required control at each time step. To overcome GPR's high computational cost while dealing with long manipulation sequences, we implement a fast online GPR by selectively removing uninformative observation data from the regression process. We validate the performance of our controller on a set of deformable object manipulation tasks and demonstrate that our method can achieve effective and accurate servo control for general deformable objects with a wide variety of goal settings. Experiment videos are available at https://sites.google.com/view/mso-fogpr.

Hybrid Control Scheme of a Hydraulically Actuated Lower Extremity Exoskeleton for Load-Carrying

In this paper, a lower extremity exoskeleton is developed to help human beings walk and carry heavy loads. The exoskeleton is actuated by a pump-based hydraulic actuation system. The hydraulic actuation system has a high speed on/off valve and a unidirectional cylinder with embedded springs on the cylinder rod. The hybrid control scheme, including two modes, i.e., position control and following control, is proposed to drive the exoskeleton system. The position control mode is employed to support the carrying load in the stance phase. The following control mode is used to shut down the DC motor to disable the pump and open the relief valve in the swing phase. In the position control, an online Gaussian process regression algorithm is proposed to estimate the human gait trajectory using the human robot interaction signals. A general position control strategy, i.e., proportion integration differentiation (PID), is utilized to control the exoskeleton to shadow the estimated human gait trajectory. In the following control, the operator can lead the mechanical legs with the help of embedded springs on the cylinder rod. Experiments are performed on the healthy human subject, who walks on the level ground at natural speed. The experimental results demonstrate that the proposed hybrid control strategy is suitable for the pump-based hydraulically actuated lower extremity exoskeleton.

A Data‐Driven Gaussian Process Regression Model for Two‐Chamber Microbial Fuel Cells

AbstractRapidly and accurately modeling of microbial fuel cells (MFCs) plays an important role not only in thorough understanding of the effects of operating conditions on system performance, but also in the successful implementation of real‐time maximization of power output. Although the first principle electrochemical model has better generalization performance, it is often time‐consuming for model construction and is hard to real‐time application. In this study, a nonparametric Gaussian process regression (GPR) model is used to capture the nonlinear relationship between operating conditions and output voltage in the MFCs. A simple online learning strategy is proposed to recursively update the hyper‐parameters of the GPR model. The applicability and effectiveness of the proposed method is validated by both the simulation and experimental datasets from the acetate and the glucose and glutamic acid two‐chamber MFCs. The results illustrate that the online GPR model provides a promising method for capturing the complex nonlinearity phenomenon in MFCs, which can be greatly helpful for further real‐time optimization of MFCs.

Recursive Gaussian process: On-line regression and learning

Two approaches for on-line Gaussian process regression with low computational and memory demands are proposed. The first approach assumes known hyperparameters and performs regression on a set of basis vectors that stores mean and covariance estimates of the latent function. The second approach additionally learns the hyperparameters on-line. For this purpose, techniques from nonlinear Gaussian state estimation are exploited. The proposed approaches are compared to state-of-the-art sparse Gaussian process algorithms.