Adaptive sparse polynomial chaos expansions for global sensitivity analysis based on support vector regression

In this study, a hybrid metamodel using the orthogonal constraints of radial basis function and sparse polynomial chaos expansions is proposed for the global sensitivity analysis of time-consuming models. Firstly, the orthogonal conditions of radial basis functions (RBF) and polynomial chaos expansions (PCE) were derived to construct the hybrid metamodel. Then, the variance of the metamodel was decoupled into the variances of the RBF and PCE independently by using the orthogonal condition. Furthermore, the analytical formulations of Sobol indices for the hybrid metamodel were derived according to the orthogonal decomposition. Thus, the interaction items of radial basis function and polynomial chaos expansions were eliminated, which significantly simplifies the Sobol indices. Two analytical cases were employed to investigate the influence of the number of the polynomial chaos expansions items, and several analytical and engineering cases were tested to demonstrate the accuracy and efficiency of the proposed method. In the engineering cases, the proposed method yielded significant improvements in terms of both accuracy and efficiency comparing with the existing global sensitivity analysis approaches, which indicates that the proposed method is more appropriate to the global sensitivity analysis of time-consuming engineering problems.

A method to determine the norm vacuum of duplex pressure condenser based on the support vector regression (SVR) model was proposed, The norm vacuum of condenser is usually obtained from the characteristic curve given by the manufactory. But the method is only fit for the condition that both of the flow of cooling water and exhaust steam of steam turbine are maintained at designed valves. In this paper, the factors which affected the norm vacuum of condenser were analyzed, and then a new method was studied with SVR model's parameters optimized by genetic algorithm (GA). Data from duplex pressure condenser of a 600MW unit were validated by the proposed method. The results show that the SVR model has high prediction accuracy and very strong stability. The studying results fall foundations for diagnosing the faults of low vacuum for condenser.

Mixed kernel function support vector regression for global sensitivity analysis

The absorption of capillary water is one of the most crucial factors in the flow of groundwater in rocks (CWA). Although meticulous experimental studies are needed to determine a rock’s CWA, predictive techniques might cut down on the expense and effort. There are various data mining methods for this purpose, but the considered algorithms in this study were not proposed so far for predicting the CWA. Different rock samples were taken for this purpose from various locations, yielding diverse rocks. For the prediction procedures, four support vector regression (SVR) models were created: a traditional SVR, two ensembled models, and a hybrid SVR model using the whale optimization technique (WOA - SVR). Results show that all models have acceptable performance in predicting the CWA with R2 larger than 0.797 and 0.806 for the training and testing data, respectively, representing the acceptable correlation between observed and predicted values. Regarding developed models, the conventional SVR model has the worst performance of all models. All statistical evaluation criteria were improved by assembling models, which present the ability of additive regression and bagging predictions in improving prediction processes. The hybrid WOA - SVR model has the best performance considering all indices. This hybrid model could also gain the lowest values of error indices between all SVR models, which leads to outperforming the WOA - SVR model compared to other methods.

The application of support vector regression and virtual sample generation technique in the optimization design of transonic compressor

The main focus of this thesis is the uncertainty propagation (UP) and global sensitivity analysis (GSA) in complex hydrogeological numerical models. Various methods are presented with applications on numerical models for the groundwater flow and mean lifetime expectancy (MLE) in the scope of Andra's (French National Radioactive Waste Management Agency) project for the geological disposal of high-level and intermediate-level long-lived radioactive wastes in a highly impermeable layer from Callovo-Oxfordian age (COX) in France. <br> A state of the art is provided for the theory of uncertainty propagation and for the methodologies of sensitivity analyses in a broad sense. Methods for UP are provided from 2-levels Factorial Designs to quasi-random samplings. GSA techniques encompass screening methods such as the Morris Measures and the Derivative-based Global Sensitivity Measures (DGSM), and also the so-called Sobol' indices based upon the variance decomposition of the response of interest. Meta-modelling techniques such as polynomial regression and Polynomial Chaos Expansions (PCE) meta-models are employed as surrogate models for UP and GSA purpose at negligible computational-costs. A comparison of GSA techniques upon various complex analytical test-functions was undertaken with the purpose of determining a relevant method to be employed in the context of “screening” out unimportant variables in computer-intensive, high-dimensional models. <br> A numerical model of groundwater flow and lifetime expectancy is employed for assessing the effect of uncertain advection-dispersion parameters and their spatial distributions upon the MLE from a target zone inside the domain. The model is a 2-dimensions synthetic cross-section of the eastern region of the Paris Basin (Meuse/Haute-Marne sector). This model was used as an exploratory tool for sensitivity analysis methods applied upon numerous sets of uncertain hydrodynamic and dispersion parameters in 15 layers. The uncertainty characterizing the permeability-porosity values in aquifer formations encompassing the COX have proved to add much of variability to the MLE calculated from the target zone. The model also served at exploring the effect of the spatial variability of permeability-porosity parameters in two main aquifer sequences on the groundwater flow rates and MLE in the model. The variabilities of the output responses are mainly due to the uncertainty upon the means and variances of the permeability-porosity distributions, as well as the longitudinal correlation lengths, in each sequence. <br> Then, a 3-dimensions high-definition hydrogeological model representing the Meuse/Haute-Marne sector in the eastern region of the Paris Basin is a more comprehensive numerical model incorporating realistic geometries, fractures, heterogeneities and discontinuities encountered on field. A sensitivity analysis of the MLE from a given zone located in the middle of the COX layer was performed by perturbing the hydraulic conductivities and porosities values in fourteen hydrogeological formations. The uncertain permeability-porosity parameters in the aquifer formations from Bathonian in the Dogger sequence, and Rauracian-Sequanian in the Oxfordian sequence, have strong and rather non-linear effects on the variability of the output response of interest. <br> The methodologies for UP and GSA employed in the present thesis have proved to be very efficient when applied to large hydrogeological models of groundwater flow and MLE. In particular, quasi-random sampling methods offer a flexible frame for providing the uncertainty distribution of the output response of interest at low computational costs. Screening techniques provide a fast estimation for the overall contribution of each input variable to the variability of the output. Meta-modelling techniques such as PCE proved highly accurate in individualising the low- and high-order effects of each input variable upon the output response of interest.

Predicting jet-grout column diameter to mitigate the environmental impact using an artificial intelligence algorithm

Prediction of TVB-N content in eggs based on electronic nose

Non-Linear Partial-Least-Squares-based Polynomial Chaos Expansion (NLPLS-based PCE) approach for global sensitivity analysis of a High-Q Partially Air-Filled Pedestal Resonator Integrated in a Printed Circuit Board (PCB)

This paper extends previous works related to the assessment of component degradation, through Markov multi-state physic models. The extension includes the evaluation of the effects of uncertain parameters in the model, and the definition of their importance with respect to their influence on the output of the model. Global Sensitivity Analysis (GSA) is selected as the technique because it enables us to 1) consider the simultaneous effects of parameters variations, and 2) to define importance indexes that allow a ranking of the components. GSA requires a large number of evaluations for specific points, identified by an appropriate design of experiment. To avoid the many costly evaluations, a meta-model is built based on polynomial chaos expansion (PCE). A PCE is a multi-dimensional polynomial approximation of the model with coefficients determined by evaluating the model in a reduced set of predetermined points. Importance index values are then derived directly from the PCE. Because, in the problem considered, the model provides the time-dependent behavior of the state probabilities, the importance indexes are also functions of time. An application is presented, related to the cracking process in an Alloy 82/182 dissimilar metal weld in the primary coolant system of a nuclear power plant.

Nonlinear QSAR models with high-dimensional descriptor selection and SVR improve toxicity prediction and evaluation of phenols on Photobacterium phosphoreum

A stacking ensemble model for predicting soil organic carbon content based on visible and near-infrared spectroscopy

Global sensitivity analysis for multivariate outputs using generalized RBF-PCE metamodel enhanced by variance-based sequential sampling

It is necessary to develop general and efficient models for the representation of vapor-liquid equilibria (VLE) for the binary mixtures containing R1234ze(E) which will be new alternatives to conventional refrigerants. This work investigates the applicability of four machine learning models, including K-nearest neighbor (KNN), support vector regression (SVR), random forests (RF), and multi-layer perceptron (MLP), in representing VLE for 10 binary mixtures. The accuracy, stability, computational complexity and extrapolation ability of these machine learning models are analyzed and compared with two thermodynamic models including Soave–Redlich–Kwong (SRK) and Peng–Robinson (PR). The results show the KNN, RF and MLP models are not suitable to accurately represent the experimental pressure and vapor-phase mole fraction. The SVR model is the most accurate machine learning model in representing the experimental pressure with a mean absolute relative error of 0.71%, basically as accurate as the PR and SVR models. Meanwhile, the SVR model describes the experimental vapor-phase mole fraction more accurately with a mean absolute error of 0.0049 compared to the PR and SVR models. In addition, the SVR model has a low running-time cost and a certain extent of extrapolation ability.

The rod ejection accident (REA) is the design-basis reactivity initiated event and an important aspect for a pressurized water reactor (PWR). The consequence of REA is that it introduces a large positive reactivity insertion in a core, which leads to a fast large power excursion and other parameters changing. Thus, it is important to understand the uncertainty in the parameters of reactor core when REA happens. This paper applies support vector regression (SVR) to analyze accident scenarios with control rod ejection. SVR is an approach based on machine learning and soft computing. SVR, by definition, is an application of support vector machine (SVM) to nonlinear regression problem. Furthermore, the objective of this paper is to train SVR model to identify both safe and potentially unsafe power plant conditions based on real time plant data. The data is obtained from computer generated accident scenarios and is divided into two datasets, training datasets and test datasets. The training dataset are used to train the SVR model and the test dataset are used to test the validation of this model. And then the results obtained by SVR model are compared with that of artificial neural network (ANN) model. The comparison results show that SVR model has superior performance over ANN model and agree well with the general understanding. Because the proposed methodology achieve accurate results, it is likely to be suitable for other data processing of nuclear engineering.