Crack localization in glass fiber composite beams by experimental modal analysis and multi variable Gaussian process regression method

Abstract. An accurate spatially continuous air temperature data set is crucial for multiple applications in the environmental and ecological sciences. Existing spatial interpolation methods have relatively low accuracy, and the resolution of available long-term gridded products of air temperature for China is coarse. Point observations from meteorological stations can provide long-term air temperature data series but cannot represent spatially continuous information. Here, we devised a method for spatial interpolation of air temperature data from meteorological stations based on powerful machine learning tools. First, to determine the optimal method for interpolation of air temperature data, we employed three machine learning models: random forest, support vector machine, and Gaussian process regression. A comparison of the mean absolute error, root mean square error, coefficient of determination, and residuals revealed that a Gaussian process regression had high accuracy and clearly outperformed the other two models regarding the interpolation of monthly maximum, minimum, and mean air temperatures. The machine learning methods were compared with three traditional methods used frequently for spatial interpolation: inverse distance weighting, ordinary kriging, and ANUSPLIN (Australian National University Spline). Results showed that the Gaussian process regression model had higher accuracy and greater robustness than the traditional methods regarding interpolation of monthly maximum, minimum, and mean air temperatures in each month. A comparison with the TerraClimate (Monthly Climate and Climatic Water Balance for Global Terrestrial Surfaces), FLDAS (Famine Early Warning Systems Network (FEWS NET) Land Data Assimilation System), and ERA5 (ECMWF, European Centre for Medium-Range Weather Forecasts, Climate Reanalysis) data sets revealed that the accuracy of the temperature data generated using the Gaussian process regression model was higher. Finally, using the Gaussian process regression method, we produced a long-term (January 1951 to December 2020) gridded monthly air temperature data set, with 1 km resolution and high accuracy for China, which we named GPRChinaTemp1km. The data set consists of three variables: monthly mean air temperature, monthly maximum air temperature, and monthly minimum air temperature. The obtained GPRChinaTemp1km data were used to analyse the spatiotemporal variations of air temperature using Theil–Sen median trend analysis in combination with the Mann–Kendall test. It was found that the monthly mean and minimum air temperatures across China were characterised by a significant trend of increase in each month, whereas monthly maximum air temperatures showed a more spatially heterogeneous pattern, with significant increase, non-significant increase, and non-significant decrease. The GPRChinaTemp1km data set is publicly available at https://doi.org/10.5281/zenodo.5112122 (He et al., 2021a) for monthly maximum air temperature, at https://doi.org/10.5281/zenodo.5111989 (He et al., 2021b) for monthly mean air temperature, and at https://doi.org/10.5281/zenodo.5112232 (He et al., 2021c) for monthly minimum air temperature.

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.

Oil-paper insulation is the key insulation structure of the transformers, whose aging condition is closely related to the operations of the equipment. The degree of polymerization (DP) is the direct parameter characterizing the aging condition of oil-paper insulation. Recently, the near infrared spectroscopy (NIRS) measurement powered by quantitative analysis is used to evaluate DP of the insulating papers mainly. While the applications of NIRS for DP evaluation is constrained because the present spectral quantitative analysis method is not accurate and stable enough, especially for onsite tests. In this paper, we propose a Gaussian process regression (GPR) method to predict DP of the oil- paper insulation in laboratory as well as in field. Firstly, the basic principles of GPR algorithm are illustrated. A GPR model for DP prediction is established based on the spectra of differently aged insulating paper samples which are prepared in laboratory. The GPR model show a high prediction accuracy both for training set and testing set. The established GPR model is finally applied on the DP prediction of insulating papers originating from a de-tanked transformer. The accurate predicted DP and the reliable aging assessment results indicate that the established model can be implemented on site.

Gaussian process regression with skewed errors

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

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

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

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.

In the task of 3-D topography measurement by fringe projection profilometry (FPP), it is crucial to establish mapping from the phase map to the 3-D coordinates, known as 3-D calibration. The traditional methods are prone to select some specific functions to fit the phase-to-coordinates’ relationship, which needs to make a compromise between measurement accuracy and efficiency. This article proposes a novel calibration method based on the Gaussian process (GP) regression to solve this problem. In this work, according to the geometric and other systemic constraints, a pixel-dependent semiparameterized calibration model is derived to guarantee the efficiency of computation and data storage. Based on the spatial correlations of the calibration data, the GP regression method is applied to enhance the fitting ability and flexibility of the calibration model without any specific functions and parameters. The GP regression method is also applied to remove random noise from the phase map, which further improves the accuracy of 3-D coordinates. The experimental results of measuring a whiteboard and a double ball bar demonstrate the superiority of the proposed GP-based calibration model in terms of accuracy and robustness when compared with the traditional models.

We present a Python-based multi-fidelity tool to estimate rotorcraft performance metrics. We use Gaussian-Process regression (GPR) methods to adaptively build a surrogate model using a small number of high-fidelity CFD points to improve estimates of performance metrics from a medium-fidelity comprehensive analysis model. To include GPR methods in our framework, we used the EmuKit Python package. Our framework adaptively chooses new high-fidelity points to run in regions where the model variance is high. These high-fidelity points are used to update the GPR model; convergence is reached when model variance is below a pre-determined level. To efficiently use our framework on large computer clusters, we implemented this in Galaxy Simulation Builder, an analysis tool that is designed to work on large parallel computing environments. The program is modular, and is designed to be agnostic to the number and names of dependent variables and to the number and identifying labels of the fidelity levels. We demonstrate our multi-fidelity modeling framework on a rotorcraft collective sweep (hover) simulation and compare the accuracy and time savings of the GPR model to that of a simulation run with CFD only.

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

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.

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.

Su kaynaklarının planlanması ve tarımsal su yönetimi için referans bitki su tüketiminin (ET0) doğru tahmin edilmesi oldukça önemlidir. Bu çalışmada üç farklı makine öğrenimi yönteminin, yapay sinir ağları (YSA), rassal ağaç (RT) ve gauss süreç regresyonu (GPR), yarı nemli iklim koşullarına sahip bir bölgeden alınan iklim verileri kullanılarak günlük ET0’ı tahmin etme performansları araştırılmıştır. Modelleri eğitmek ve test etmek için Bafra’da 2018–2020 döneminde toplanan günlük meteorolojik verilerin beş girdi kombinasyonu [günlük ortalama (Tort), maksimum (Tmax) ve minimum sıcaklık (Tmin), rüzgar hızı (u2), bağıl nem (RHort) ve güneşlenme şiddeti (Rs) hem tam hem de eksik kombinasyonları dahil] kullanılmıştır. Makine öğrenimi modellerinin performansı ise FAO-56 Penman Monteith (FAO-56 PM) standart denklemi ile karşılaştırılmıştır. Modellerin doğruluğunu değerlendirmek için dört farklı istatistiksel performans indeksi kullanılmıştır [belirleme katsayısı (R2), ortalama mutlak hata (MAE), hata kareleri toplamının karekökü (RMSE) ve Nash–Sutcliffe etkinlik katsayısı (NSE)]. Sonuçlar, her beş senaryoda da YSA modellerinin RT ve GPR modellerinden daha iyi performans gösterdiğini ortaya koymuştur. Tüm verilerin girdi olarak kullanıldığı beşinci senaryo için YSA modelleri tarafından tahmin edilen ET0 değerlerinin FAO-56 PM değerleri ile iyi bir uyum içinde olduğu belirlenmiştir (R2=0.988, MAE=0.166, RMSE=0.205, NSE=0.984). Bununla birlikte meteorolojik veriler tam olmadığında bile sadece Tort, RHort ve Rs ile oldukça yüksek günlük ET0 tahminleri elde edilmiştir. Genel olarak, radyasyona dayalı makine öğrenimi modelleri, sıcaklığa dayalı makine öğrenimi modellerinden daha iyi performans göstermiştir. Sonuçlar, yarı nemli iklim özelliklerine sahip bir bölgede YSA modelinin ET0'ı oldukça verimli ve doğru bir şekilde modellemek için etkili bir şekilde kullanılabileceğini göstermektedir.

Gaussian Process Regression (GPR) is a nonparametric machine learning model that provides uncertainty quantification in making predictions. GPR utilizes several covariance functions (CFs) in the process of developing models to ensure high accuracy. There are five common CFs in GPR, which are the Radial Basis Function (RBF), Rational Quadratic (RQ), Periodic (Per), Matérn 3/2 (Mat 3/2), and Matérn 5/2 (Mat 5/2), where each covariance function (CF) has different characteristics and behaviors. This paper is to investigate the comparative performances of each CF when applied to the Global Wheat Prices dataset. Error metric measurement like Mean Square Error (MSE) and Root Mean Square Error (RMSE), while Coefficient of Variation (CV) for uncertainty quantification measurement is computed for each CF, and comparisons was made among the CFs to conclude the best CF for this application. The lowest values among them will be the best CF for the data. It should be noted that the CV for each model should be less than 5%, and the CF with the smallest value of CV is considered reliable. The five CFs were fit to the Global Wheat Prices dataset, and it was found that the Mat 3/2 produced the best performances with the lowest values of MSE, RMSE, and CV. Mat 3/2 is the most efficient CF for making predictions since it gives the lowest value of error metric measurement and the lowest value of CV under 5% among the other CFs, making it more reliable for modeling. Overall, the outcome shows that Mat 3/2 is the best CF to be used in developing a GPR model to predict Global Wheat Prices dataset.