Gaussian process regression is widely used to model an unknown function on a continuous domain by interpolating a discrete set of observed design points. We develop a theoretical framework for proving new moderate deviations inequalities on different types of error probabilities that arise in GP regression. Two specific examples of broad interest are the probability of falsely ordering pairs of points (incorrectly estimating one point as being better than another) and the tail probability of the estimation error at an arbitrary point. Our inequalities connect these probabilities to the mesh norm, which measures how well the design points fill the space.

The superposition of data sets with internal parametric self-similarity is a longstanding and widespread technique for the analysis of many types of experimental data across the physical sciences. Typically, this superposition is performed manually, or recently through the application of one of a few automated algorithms. However, these methods are often heuristic in nature, are prone to user bias via manual data shifting or parameterization, and lack a native framework for handling uncertainty in both the data and the resulting model of the superposed data. In this work, we develop a data-driven, nonparametric method for superposing experimental data with arbitrary coordinate transformations, which employs Gaussian process regression to learn statistical models that describe the data, and then uses maximum a posteriori estimation to optimally superpose the data sets. This statistical framework is robust to experimental noise and automatically produces uncertainty estimates for the learned coordinate transformations. Moreover, it is distinguished from black-box machine learning in its interpretability—specifically, it produces a model that may itself be interrogated to gain insight into the system under study. We demonstrate these salient features of our method through its application to four representative data sets characterizing the mechanics of soft materials. In every case, our method replicates results obtained using other approaches, but with reduced bias and the addition of uncertainty estimates. This method enables a standardized, statistical treatment of self-similar data across many fields, producing interpretable data-driven models that may inform applications such as materials classification, design, and discovery.

Population-based structural health monitoring (PBSHM) provides a means of accounting for inter-turbine correlations when solving the problem of wind farm anomaly detection. Across a wind farm, where a group of structures (turbines) is placed in close vicinity to each other, the environmental conditions and, thus, structural behavior vary in a spatiotemporal manner. Spatiotemporal trends are often overlooked in the existing data-based wind farm anomaly detection methods, because most current methods are designed for individual structures, that is, detecting anomalous behavior of a turbine based on the past behavior of the same turbine. In contrast, the idea of PBSHM involves sharing data across a population of structures and capturing the interactions between structures. This paper proposes a population-based anomaly detection method, specifically for a localized population of structures, which accounts for the spatiotemporal correlations in structural behavior. A case study from an offshore wind farm is given to demonstrate the potential of the proposed method as a wind farm performance indicator. It is concluded that the method has the potential to indicate operational anomalies caused by a range of factors across a wind farm. The method may also be useful for other tasks such as wind power and turbine load modeling.

Cyber–physical–social systems (CPSS) are physical devices that are embedded in human society and possess highly integrated functionalities of sensing, computing, communication, and control. CPSS rely on their intense collaboration and information sharing through networks to be functioning. In this paper, topology-informed network information dynamics models are proposed to characterize the evolution of information processing capabilities of CPSS nodes in networks. The models are based on a mesoscale probabilistic graph model, where the sensing and computing capabilities of the nodes are captured as the probabilities of correct predictions. A topology-informed vector autoregression model and a latent variable vector autoregression model are proposed to model the correlations between prediction capabilities of nodes as linear functional relationships. A hybrid Gaussian process regression model is also developed to capture both the nonlinear spatial and temporal correlations between nodes. The new information dynamics models are demonstrated and tested with a simulator of CPSS networks. The results show that the topological information of networks can improve the efficiency in constructing the time series models. The network topology also has influences on the prediction capabilities of CPSS.

In this paper, a Gaussian process regression (GPR)-based novel method is proposed for non-linear aerodynamic modelling of the aircraft using flight data. This data-driven regression approach uses the kernel-based probabilistic model to predict the non-linearity. The efficacy of this method is examined and validated by estimating force and moment coefficients using research aircraft flight data. Estimated coefficients of aerodynamic force and moment using GPR method are compared with the estimated coefficients using maximum-likelihood estimation (MLE) method. Estimated coefficients from the GPR method are statistically analysed and found to be at par with estimated coefficients from MLE, which is popularly used as a conventional method. GPR approach does not require to solve the complex equations of motion. GPR further can be directed for the generalised applications in the area of aeroelasticity, load estimation, and optimisation.

Motion compensation is a significant part of an airborne remote sensing system. A Position and Orientation System (POS) can directly measure the motion information of an airborne remote sensing payload that can improve the quality of airborne remote sensing images. Gravity disturbance, information on which is often ignored due to being difficult to acquire in real-time, has become the main error source of POS in the development of inertial components. In this paper, a new real-time gravity compensation method is proposed, which includes the gravity disturbance as the error states of a POS Kalman filter, and an accurate gravity disturbance model is constructed using a time-varying Gaussian-Markov model based on a high-precision gravity map, whose resolution is enhanced by a new interpolation method based on Gaussian Process Regression (GPR). A flight experiment was conducted to evaluate the efficiency of the proposed method and the results showed that the proposed method performs well when compared with other real-time gravity compensation methods.

For the integrated navigation system, the correctness and the rapidity of fault detection for each sensor subsystem affects the accuracy of navigation. In this paper, a novel fault detection method for navigation systems is proposed based on Gaussian Process Regression (GPR). A GPR model is first used to predict the innovation of a Kalman filter. To avoid local optimisation, particle swarm optimisation is adopted to find the optimal hyper-parameters for the GPR model. The Fault Detection Function (FDF), which has an obvious jump in value when a fault occurs, is composed of the predicted innovation, the actual innovation of the Kalman filter and their variance. The fault can be detected by comparing the FDF value with a predefined threshold. In order to verify its validity, the proposed method is used in a SINS/GPS/Odometer integrated navigation system. The comparison experiments confirm that the proposed method can detect a gradual fault more quickly compared with the residual chi-squared test. Thus the navigation system with the proposed method gives more accurate outputs and its reliability is greatly improved.

Advanced machine learning techniques like Gaussian process regression and multi-task learning are novel in the area of wine price prediction; previous research in this area being restricted to parametric linear regression models when predicting wine prices. Using historical price data of the 100 wines in the Liv-Ex 100 index, the main contributions of this paper to the field are, firstly, a clustering of the wines into two distinct clusters based on autocorrelation. Secondly, an implementation of Gaussian process regression on these wines with predictive accuracy surpassing both the trivial and simple ARMA and GARCH time series prediction benchmarks. Lastly, an implementation of an algorithm which performs multi-task feature learning with kernels on the wine returns as an extension to our optimal Gaussian process regression model. Using the optimal covariance kernel from Gaussian process regression, we achieve predictive results which are comparable to that of Gaussian process regression. Altogether, our research suggests that there is potential in using advanced machine learning techniques in wine price prediction. (JEL Classifications: C6, G12)

Gaussian process regression (GPR) is used in a Spare-grid Quadrature Kalman filter (SGQKF) for Strap-down Inertial Navigation System (SINS)/odometer integrated navigation to bridge uncertain observation outages and maintain an estimate of the evolving SINS biases. The SGQKF uses nonlinearized dynamic models with complex stochastic nonlinearities so the performance degrades significantly during observation outages owing to the uncertainties and noise. The GPR calculates the residual output after factoring in the contributions of the parametric model that is used as a nonlinear SINS error predictor integrated into the SGQKF. The sensor measurements and SINS output deviations from the odometer are collected in a data set during observation availability. The GPR is then applied to predict SINS deviations from the odometer and then the predicted SINS deviations are fed to the SGQKF as an actual update to estimate all SINS biases during observation outages. We demonstrate our method's effectiveness in bridging uncertain observation outages in simulations and in real road tests. The results agree with the theoretical analysis, which demonstrate that SGQKF using GPR can maintain an estimate of the evolving SINS biases during signal outages.