Combining the symplectic variations theory, the homogeneous control equation and isopaxametric element homogeneous formulations for piezothermoelastic hybrid laminates problems were deduced. Firstly, based on the gene...Combining the symplectic variations theory, the homogeneous control equation and isopaxametric element homogeneous formulations for piezothermoelastic hybrid laminates problems were deduced. Firstly, based on the generalized Hamilton variation principle, the non-homogeneous Hamilton canonical equation for piezothermoelastic bodies was derived. Then the symplectic relationship of variations in the thermal equilibrium formulations and gradient equations was considered, and the non-homogeneous canonical equation was transformed to homogeneous control equation for solving independently the coupling problem of piezothermoelastic bodies by the incensement of dimensions of the canonical equation. For the convenience of deriving Hamilton isopaxametric element formulations with four nodes, one can consider the temperature gradient equation as constitutive relation and reconstruct new variation principle. The homogeneous equation simplifies greatly the solution programs which axe often performed to solve nonhomogeneous equation and second order differential equation on the thermal equilibrium and gradient relationship.展开更多
Typically, relationship between well logs and lithofacies is complex, which leads to low accuracy of lithofacies identification. Machine learning (ML) methods are often applied to identify lithofacies using logs label...Typically, relationship between well logs and lithofacies is complex, which leads to low accuracy of lithofacies identification. Machine learning (ML) methods are often applied to identify lithofacies using logs labelled by rock cores. However, these methods have accuracy limits to some extent. To further improve their accuracies, practical and novel ensemble learning strategy and principles are proposed in this work, which allows geologists not familiar with ML to establish a good ML lithofacies identification model and help geologists familiar with ML further improve accuracy of lithofacies identification. The ensemble learning strategy combines ML methods as sub-classifiers to generate a comprehensive lithofacies identification model, which aims to reduce the variance errors in prediction. Each sub-classifier is trained by randomly sampled labelled data with random features. The novelty of this work lies in the ensemble principles making sub-classifiers just overfitting by algorithm parameter setting and sub-dataset sampling. The principles can help reduce the bias errors in the prediction. Two issues are discussed, videlicet (1) whether only a relatively simple single-classifier method can be as sub-classifiers and how to select proper ML methods as sub-classifiers;(2) whether different kinds of ML methods can be combined as sub-classifiers. If yes, how to determine a proper combination. In order to test the effectiveness of the ensemble strategy and principles for lithofacies identification, different kinds of machine learning algorithms are selected as sub-classifiers, including regular classifiers (LDA, NB, KNN, ID3 tree and CART), kernel method (SVM), and ensemble learning algorithms (RF, AdaBoost, XGBoost and LightGBM). In this work, the experiments used a published dataset of lithofacies from Daniudi gas field (DGF) in Ordes Basin, China. Based on a series of comparisons between ML algorithms and their corresponding ensemble models using the ensemble strategy and principles, conclusions are drawn: (1) not only decision tree but also other single-classifiers and ensemble-learning-classifiers can be used as sub-classifiers of homogeneous ensemble learning and the ensemble can improve the accuracy of the original classifiers;(2) the ensemble principles for the introduced homogeneous and heterogeneous ensemble strategy are effective in promoting ML in lithofacies identification;(3) in practice, heterogeneous ensemble is more suitable for building a more powerful lithofacies identification model, though it is complex.展开更多
This paper is concerned with the inverse problem of scattering of time-harmonic acoustic waves by an inhomogeneous penetrable obstacle in a piecewise homogeneous medium. The well-posedness of the direct problem is fir...This paper is concerned with the inverse problem of scattering of time-harmonic acoustic waves by an inhomogeneous penetrable obstacle in a piecewise homogeneous medium. The well-posedness of the direct problem is first established by using the integral equation method. We then proceed to establish two tools that play important roles for the inverse problem： one is a mixed reciprocity relation and the other is a priori estimates of the solution on some part of the interfaces between the layered media. For the inverse problem, we prove in this paper that both the penetrable interfaces and the possible inside inhomogeneity can be uniquely determined from a knowledge of the far field pattern for incident plane waves.展开更多
基金Project supported by the National Natural Science Foundation of China(No.50276041)
文摘Combining the symplectic variations theory, the homogeneous control equation and isopaxametric element homogeneous formulations for piezothermoelastic hybrid laminates problems were deduced. Firstly, based on the generalized Hamilton variation principle, the non-homogeneous Hamilton canonical equation for piezothermoelastic bodies was derived. Then the symplectic relationship of variations in the thermal equilibrium formulations and gradient equations was considered, and the non-homogeneous canonical equation was transformed to homogeneous control equation for solving independently the coupling problem of piezothermoelastic bodies by the incensement of dimensions of the canonical equation. For the convenience of deriving Hamilton isopaxametric element formulations with four nodes, one can consider the temperature gradient equation as constitutive relation and reconstruct new variation principle. The homogeneous equation simplifies greatly the solution programs which axe often performed to solve nonhomogeneous equation and second order differential equation on the thermal equilibrium and gradient relationship.
基金financially supported by the National Natural Science Foundation of China(Grant No.42002134)China Postdoctoral Science Foundation(Grant No.2021T140735)Science Foundation of China University of Petroleum,Beijing(Grant Nos.2462020XKJS02 and 2462020YXZZ004).
文摘Typically, relationship between well logs and lithofacies is complex, which leads to low accuracy of lithofacies identification. Machine learning (ML) methods are often applied to identify lithofacies using logs labelled by rock cores. However, these methods have accuracy limits to some extent. To further improve their accuracies, practical and novel ensemble learning strategy and principles are proposed in this work, which allows geologists not familiar with ML to establish a good ML lithofacies identification model and help geologists familiar with ML further improve accuracy of lithofacies identification. The ensemble learning strategy combines ML methods as sub-classifiers to generate a comprehensive lithofacies identification model, which aims to reduce the variance errors in prediction. Each sub-classifier is trained by randomly sampled labelled data with random features. The novelty of this work lies in the ensemble principles making sub-classifiers just overfitting by algorithm parameter setting and sub-dataset sampling. The principles can help reduce the bias errors in the prediction. Two issues are discussed, videlicet (1) whether only a relatively simple single-classifier method can be as sub-classifiers and how to select proper ML methods as sub-classifiers;(2) whether different kinds of ML methods can be combined as sub-classifiers. If yes, how to determine a proper combination. In order to test the effectiveness of the ensemble strategy and principles for lithofacies identification, different kinds of machine learning algorithms are selected as sub-classifiers, including regular classifiers (LDA, NB, KNN, ID3 tree and CART), kernel method (SVM), and ensemble learning algorithms (RF, AdaBoost, XGBoost and LightGBM). In this work, the experiments used a published dataset of lithofacies from Daniudi gas field (DGF) in Ordes Basin, China. Based on a series of comparisons between ML algorithms and their corresponding ensemble models using the ensemble strategy and principles, conclusions are drawn: (1) not only decision tree but also other single-classifiers and ensemble-learning-classifiers can be used as sub-classifiers of homogeneous ensemble learning and the ensemble can improve the accuracy of the original classifiers;(2) the ensemble principles for the introduced homogeneous and heterogeneous ensemble strategy are effective in promoting ML in lithofacies identification;(3) in practice, heterogeneous ensemble is more suitable for building a more powerful lithofacies identification model, though it is complex.
基金the first author (XL) was supported by the China Postdoctoral Science Foundation (20100480494)the NSF of China (11101412)+1 种基金K.C. Wong Education Foundation, Hong Kongthe second author (BZ) was supported by the NSF of China (11071244,11161130002)
文摘This paper is concerned with the inverse problem of scattering of time-harmonic acoustic waves by an inhomogeneous penetrable obstacle in a piecewise homogeneous medium. The well-posedness of the direct problem is first established by using the integral equation method. We then proceed to establish two tools that play important roles for the inverse problem： one is a mixed reciprocity relation and the other is a priori estimates of the solution on some part of the interfaces between the layered media. For the inverse problem, we prove in this paper that both the penetrable interfaces and the possible inside inhomogeneity can be uniquely determined from a knowledge of the far field pattern for incident plane waves.
