Gaussian process regression and conditional Karhunen-Loève models for data assimilation in inverse problems

The increasing effects of climate change require the accurate measurement and prediction of carbon emissions from building construction operations. This study aims to assess the performance of Gaussian Process Regression (GPR) and Support Vector Machine (SVM) in predicting emissions and determine which model is best suited for improving sustainable construction practices. The GPR and SVM models were trained and tested using empirical datasets with varying parameter values. Model performance is evaluated using correlation coefficient (R), root mean square error (RMSE), and mean absolute error (MAE). The analysis reveals that GPR consistently performs better than SVM across diverse datasets, especially in intricate and varied data situations. The superior performance of GPR highlights its robustness and versatility in handling the complexities of construction-related emissions data. The results indicate that GPR has the potential to assist significantly many stakeholders in the construction sector, including planners and environmental managers, in making better-informed decisions that are in line with carbon reduction objectives. Further studies could examine the incorporation of further predictive variables into the GPR model, such as economic indicators and the effects of material innovation.

Gaussian process regression to determine water content of methane: Application to methane transport modeling

A new maximum a posteriori (MAP) formulation is shown to be a straightforward and intuitive way to derive optimal blind equalization cost functions. This MAP method provides a general, systematic way to derive blind adaptation methods using the given pdf of the input and a convolutional noise model. A general blind equalization/deconvolution cost function known as Gray's Variable Norm, is shown to be derivable using the MAP formulation presented here. Gray's Variable Norm (1979) is a superset of existing blind equalization cost functions, including the Godard and Sato algorithms as special cases. The MAP method is capable of deriving cost functions needed for a wide variety of problems, including those with infinite variance pdfs and even multichannel problems. >

Gaussian process regression with skewed errors

The growth of rice is a sequence of three different phenological phases. This sequence of change in rice phenology implies that the condition of the plant during the vegetative phase relates directly to the health of leaves functioning during the reproductive and ripening phases. As such, accurate monitoring is important towards understanding rice growth dynamics. Leaf Area Index (LAI) is an important indicator of rice yields and the availability of this information during key phenological phases can support more informed farming decisions. Satellite remote sensing has been adopted as a proxy to field measurements of LAI and with the launch of freely available high resolution Satellite images such as Sentinel-2, it is imperative that accurate retrieval methods are adopted towards monitoring LAI at irrigated rice fields. Here, we evaluate the potential of a hybrid radiative transfer model (i.e., PROSAIL - Gaussian Process Regression (GPR), for estimating the phenological dynamics of irrigated rice LAI using imager derived from the Sentinel-2 multispectral instrument. LAI field measurements were obtained from an experimental rice field in Nasarawa state, Nigeria during the dry season. We used the PROSAIL radiative transfer model to create a look up table (LUT) that was subsequently used to train a GPR model. Afterwards, we evaluated the potential of the hybrid modelling approach by assessing the overall model accuracy and the extent to which LAI was able to accurately predict LAI during key rice phenological phases. We compared the predicted hybrid GPR LAI values with LAI values generated from the SNAP toolbox, based on a hybrid Artificial Neural Network (ANN) modelling approach. Our results show that the overall predictive accuracy of the hybrid GPR model (R2 = 0.82, RMSE = 1.65) was more accurate than that of the hybrid ANN model (R2 = 0.66, RMSE = 3.89) for retrieving LAI values from Sentinel-2 imagery. Both models underestimated LAI values during the reproductive and ripening phases . However, the accuracy during the phenological phases were more significant when using the hybrid GPR model (P < 0.05). During the different phenological phases, the hybrid GPR model predicted LAI more accurately during the reproductive (R2 = 0.7) and ripening (R2 = 0.59) phases compared to the hybrid ANN reproductive and ripening phases. When monitoring LAI phenological profiles of both hybrid models, the hybrid GPR and ANN models underestimated LAI during the reproductive and ripening phases. However, the ANN model underestimations were statistically significantly greater than those for the hybrid GPR model (P < 0.05). Our results highlight the potential of hybrid GPR models for estimating the phenological dynamics of irrigated rice LAI from Sentinel-2 data. They provided more accurate estimation of LAI patterns from varying nitrogen and water applications than hybrid ANN models.

Simulating root length density dynamics of sunflower in saline soils based on machine learning

PurposeEnsuring the early detection of structural issues in aircraft is crucial for preserving human lives. One effective approach involves identifying cracks in composite structures. This paper employs experimental modal analysis and a multi-variable Gaussian process regression method to detect and locate cracks in glass fiber composite beams.Design/methodology/approachThe present study proposes Gaussian process regression model trained by the first three natural frequencies determined experimentally using a roving impact hammer method with crystal four-channel analyzer, uniaxial accelerometer and experimental modal analysis software. The first three natural frequencies of the cracked composite beams obtained from experimental modal analysis are used to train a multi-variable Gaussian process regression model for crack localization. Radial basis function is used as a kernel function, and hyperparameters are optimized using the negative log marginal likelihood function. Bayesian conditional probability likelihood function is used to estimate the mean and variance for crack localization in composite structures.FindingsThe efficiency of Gaussian process regression is improved in the present work with the normalization of input data. The fitted Gaussian process regression model validates with experimental modal analysis for crack localization in composite structures. The discrepancy between predicted and measured values is 1.8%, indicating strong agreement between the experimental modal analysis and Gaussian process regression methods. Compared to other recent methods in the literature, this approach significantly improves efficiency and reduces error from 18.4% to 1.8%. Gaussian process regression is an efficient machine learning algorithm for crack localization in composite structures.Originality/valueThe experimental modal analysis results are first utilized for crack localization in cracked composite structures. Additionally, the input data are normalized and employed in a machine learning algorithm, such as the multi-variable Gaussian process regression method, to efficiently determine the crack location in these structures.

This paper describes a real-time data collection framework and an adaptive machining learning method for constructing a real-time energy prediction model for a machine tool. To effectively establish the energy consumption pattern of a machine tool over time, the energy prediction model is continuously updated with new measurement data to account for time-varying effects of the machine tool, such as tool wear and machine tool deterioration. In this work, a real-time data collection and processing framework is developed to retrieve raw data from a milling machine tool and its sensors and convert them into relevant input features. The extracted input features are then used to construct the energy prediction model using Gaussian Process (GP) regression. To update the GP regression model with real-time streaming data, we investigate the use of sparse representation of the covariance matrix to reduce the computational and storage demands of the GP regression. We compare computational efficiency of sparse GP to that of full GP regression model and show the effectiveness of the sparse GP regression model for tracking the variation in the energy consumption pattern of the target machine.

Due to the recent advances in digitisation of the manufacturing industry and the generation of manufacturing data, there is increasing interest to integrate machine learning on the shop floor to improve efficiency and quality control. Ultrasonic welding is an emerging joining process used in various manufacturing industries, and is an energy efficient, cost-effective method of joining similar or dissimilar materials. However, the quality of the joint achievable is heavily dependent on process input parameters. In this study, a Gaussian Process Regression (GPR) model is developed to map the relationship between process parameters and joint performance for ultrasonically welded aluminium joints, with a view to improving quality control in a manufacturing setting. Initially, a 33 full factorial design of experiments is conducted to investigate the influential parameters, then a GPR model is trained on the experimental data. In-process sensor data is also used to infer process performance. To assess the prediction performance of the model, ten unseen parameter combinations are predicted and compared to their respective experimental result. The model demonstrates a high level of accuracy producing a Pearson’s correlation coefficient of 0.982 between the predicted and actual results for all data. The mean relative predictive error for unseen data is 7.35%.KeywordsUltrasonic weldingMachine learningGaussian process regressionQuality control

There is increasing interest in real-time brain-computer interfaces (BCIs) for the passive monitoring of human cognitive state, including cognitive workload. Too often, however, effective BCIs based on machine learning techniques may function as “black boxes” that are difficult to analyze or interpret. In an effort toward more interpretable BCIs, we studied a family of N-back working memory tasks using a machine learning model, Gaussian Process Regression (GPR), which was both powerful and amenable to analysis. Participants performed the N-back task with three stimulus variants, auditory-verbal, visual-spatial, and visual-numeric, each at three working memory loads. GPR models were trained and tested on EEG data from all three task variants combined, in an effort to identify a model that could be predictive of mental workload demand regardless of stimulus modality. To provide a comparison for GPR performance, a model was additionally trained using multiple linear regression (MLR). The GPR model was effective when trained on individual participant EEG data, resulting in an average standardized mean squared error (sMSE) between true and predicted N-back levels of 0.44. In comparison, the MLR model using the same data resulted in an average sMSE of 0.55. We additionally demonstrate how GPR can be used to identify which EEG features are relevant for prediction of cognitive workload in an individual participant. A fraction of EEG features accounted for the majority of the model’s predictive power; using only the top 25% of features performed nearly as well as using 100% of features. Subsets of features identified by linear models (ANOVA) were not as efficient as subsets identified by GPR. This raises the possibility of BCIs that require fewer model features while capturing all of the information needed to achieve high predictive accuracy.

The Gaussian process regression (GPR) model, which is a powerful machine learning tool for probabilistic prediction, is introduced into slope displacement prediction. Using this model, the displacements of the slope of the permanent ship lock of the Three Gorges Project, the Wolongsi slope, and the high slope of Longtan hydropower station were predicted. In addition, the predictive uncertainty index (PUI) for describing the uncertainty of the predicted results was proposed, and the corresponding classification of the PUI was established. The study results demonstrate that the GPR model can self-adaptively acquire model parameter values and has satisfactory adaptability for predicting nonlinear time series of slope displacement. The proposed PUI and its classification based on the GPR model enable quantitative uncertainty analysis and, in turn, reliability evaluation of the predicted results. The GPR model provides a new approach to displacement prediction and safety management in slope engineering.

Super-resolution (SR) aims at generating a high resolution image or image sequence from several slightly different low-resolution images. In previous work, we have showed that a Maximum A Posteriori (MAP) SR algorithm can yield significant image quality enhancement of the individual respiratory gated PET frames. However, in the past it has been also argued that image-based motion correction algorithms yield sub-optimal results, particularly when images are reconstructed using iterative methods. Here, we evaluate the results incorporating MAP SR directly as part of the One-Step-Late (OSL) reconstruction algorithm. The evaluation used GATE simulated data. The IEC phantom with lesions between 10–37mm (contrast 8/1) was used to simulate 200 noise realizations of 6 frames, each shifted by 3mm along the z-axis relative to each other. The algorithm was also tested on four realistic phantoms. Gated respiratory images were reconstructed with the OPL-EM algorithm. Superresolution was performed through a MAP algorithm either as part of the reconstruction process or as a post-processing step applied to the individually reconstructed gated frames. A Huber prior was used as regularization term while the function yielded by the MAP method was optimized through a quasi-Newton algorithm. We compared signal-to-noise ratio (SNR) and contrast, as well as the bias-variance tradeoff for each algorithm. SR incorporated reconstruction led to 9% and 14% higher SNR and contrast respectively compared to the image-based SR. The bias-variance tradeoff showed that reconstruction-incorporated SR has a bias and variance of 39% lower and 60% higher respectively compared to image-based SR.

In recent years, environmental pollution has become more and more serious, especially water pollution. In this study, the method of Gaussian process regression was used to build a prediction model for the sulphate content of lakes using several water quality variables as inputs. The sulphate content and other variable water quality data from 100 stations operated at lakes along the middle and lower reaches of the Yangtze River were used for developing the four models. The selected water quality data, consisting of water temperature, transparency, pH, dissolved oxygen conductivity, chlorophyll, total phosphorus, total nitrogen and ammonia nitrogen, were used as inputs for several different Gaussian process regression models. The experimental results showed that the Gaussian process regression model using an exponential kernel had the smallest prediction error. Its mean absolute error (MAE) of 5.0464 and root mean squared error (RMSE) of 7.269 were smaller than those of the other three Gaussian process regression models. By contrast, in the experiment, the model used in this study had a smaller error than linear regression, decision tree, support vector regression, Boosting trees, Bagging trees and other models, making it more suitable for prediction of the sulphate content in lakes. The method proposed in this paper can effectively predict the sulphate content in water, providing a new kind of auxiliary method for water detection.

This article proposes a constrained Gaussian process regression (GPR)-based multiobjective distribution optimal power flow (GPR-DOPF) framework to coordinate the voltage-regulating devices [capacitor banks (CBs) and voltage regulators (VRs)] with smart inverter (SI) controls. The GPRs are well suited for the complexity and nonlinearity that characterizes power distribution networks. This work provides a detailed mathematical formulation of the GPR, proposes a ­scalable GPR-DOPF to address computational inefficiency with large datasets, and models the SI control modes and other voltage-regulating devices for application in the DOPF. The GPR is trained (assuming no significant physical changes in the network) using the extensive power flow data obtained from the power distribution network. To determine the optimal settings of the SIs and the legacy devices using the GPR-DOPF, a multiobjective mixed integer nonlinear problem (MINLP) is formulated. The GPR model is coupled with the Non-Dominated Sorting Genetic Algorithm II (NSGA II) to determine the pareto optimal solutions (POSs) of the proposed MINLP formulation. The mathematical objectives include minimizing the voltage deviation and the overall network active power loss.

In this paper, Gaussian Process Regression (GPR)‐based models which use the Bayesian approach to regression analysis problem such as load forecasting (LF) are proposed. The GPR is a non‐parametric kernel‐based learning method having the ability to provide correct predictions with uncertainty in measurements. The proposed model provides an hourly and monthly load forecast for an Australian city and four Indian cities in the Maharashtra state. Twelve GPR models are trained with historical datasets including hourly load and environmental data. To evaluate the trained model, the actual and predicted load demand curve is plotted and mean average percentage error (MAPE) is calculated corresponding to different kernel functions of the GPR model. To the best of the author's knowledge, the prediction of load demand using GPR for Indian cities of Maharashtra state has been made for the first time. The calculated MAPE in LF is 0.15% for Australia and 0.002%, 0.209%, 0.077%, and 0.140% for Indian cities viz. Nasik, Bhusawal, Kolhapur, and Aurangabad, respectively. The test results illustrate that minimum MAPE in load prediction is obtained using the proposed model that is GPR with ‘Exponential’ kernel functions. Furthermore, the comparative analysis with the existing approaches confirms the dominance of the proposed model.