A locking-free rectangular Mindlin plate element with a new multi-resolution analysis (MRA) is proposed and a new finite element method is hence presented. The MRA framework is formulated out of a mutually nesting dis...A locking-free rectangular Mindlin plate element with a new multi-resolution analysis (MRA) is proposed and a new finite element method is hence presented. The MRA framework is formulated out of a mutually nesting displacement subspace sequence whose basis functions are constructed of scaling and shifting on the element domain of basic full node shape function. The basic full node shape function is constructed by extending the split node shape function of a traditional Mindlin plate element to other three quadrants around the coordinate zero point. As a result, a new rational MRA concept together with the resolution level (RL) is constituted for the element. The traditional 4-node rectangular Mindlin plate element and method is a mono-resolution one and also a special case of the proposed element and method. The meshing for the monoresolution plate element model is based on the empiricism while the RL adjusting for the multiresolution is laid on the rigorous mathematical basis. The analysis clarity of a plate structure is actually determined by the RL, not by the mesh. Thus, the accuracy of a plate structural analysis is replaced by the clarity, the irrational MRA by the rational and the mesh model by the RL that is the discretized model by the integrated.展开更多
Since traditional machine learning methods are sensitive to skewed distribution and do not consider the characteristics in multiclass imbalance problems,the skewed distribution of multiclass data poses a major challen...Since traditional machine learning methods are sensitive to skewed distribution and do not consider the characteristics in multiclass imbalance problems,the skewed distribution of multiclass data poses a major challenge to machine learning algorithms.To tackle such issues,we propose a new splitting criterion of the decision tree based on the one-against-all-based Hellinger distance(OAHD).Two crucial elements are included in OAHD.First,the one-against-all scheme is integrated into the process of computing the Hellinger distance in OAHD,thereby extending the Hellinger distance decision tree to cope with the multiclass imbalance problem.Second,for the multiclass imbalance problem,the distribution and the number of distinct classes are taken into account,and a modified Gini index is designed.Moreover,we give theoretical proofs for the properties of OAHD,including skew insensitivity and the ability to seek a purer node in the decision tree.Finally,we collect 20 public real-world imbalanced data sets from the Knowledge Extraction based on Evolutionary Learning(KEEL)repository and the University of California,Irvine(UCI)repository.Experimental and statistical results show that OAHD significantly improves the performance compared with the five other well-known decision trees in terms of Precision,F-measure,and multiclass area under the receiver operating characteristic curve(MAUC).Moreover,through statistical analysis,the Friedman and Nemenyi tests are used to prove the advantage of OAHD over the five other decision trees.展开更多
文摘A locking-free rectangular Mindlin plate element with a new multi-resolution analysis (MRA) is proposed and a new finite element method is hence presented. The MRA framework is formulated out of a mutually nesting displacement subspace sequence whose basis functions are constructed of scaling and shifting on the element domain of basic full node shape function. The basic full node shape function is constructed by extending the split node shape function of a traditional Mindlin plate element to other three quadrants around the coordinate zero point. As a result, a new rational MRA concept together with the resolution level (RL) is constituted for the element. The traditional 4-node rectangular Mindlin plate element and method is a mono-resolution one and also a special case of the proposed element and method. The meshing for the monoresolution plate element model is based on the empiricism while the RL adjusting for the multiresolution is laid on the rigorous mathematical basis. The analysis clarity of a plate structure is actually determined by the RL, not by the mesh. Thus, the accuracy of a plate structural analysis is replaced by the clarity, the irrational MRA by the rational and the mesh model by the RL that is the discretized model by the integrated.
基金Project supported by the National Natural Science Foundation of China(Nos.61802085 and 61563012)the Guangxi Provincial Natural Science Foundation,China(Nos.2021GXNSFAA220074and 2020GXNSFAA159038)+1 种基金the Guangxi Key Laboratory of Embedded Technology and Intelligent System Foundation,China(No.2018A-04)the Guangxi Key Laboratory of Trusted Software Foundation,China(No.kx202011)。
文摘Since traditional machine learning methods are sensitive to skewed distribution and do not consider the characteristics in multiclass imbalance problems,the skewed distribution of multiclass data poses a major challenge to machine learning algorithms.To tackle such issues,we propose a new splitting criterion of the decision tree based on the one-against-all-based Hellinger distance(OAHD).Two crucial elements are included in OAHD.First,the one-against-all scheme is integrated into the process of computing the Hellinger distance in OAHD,thereby extending the Hellinger distance decision tree to cope with the multiclass imbalance problem.Second,for the multiclass imbalance problem,the distribution and the number of distinct classes are taken into account,and a modified Gini index is designed.Moreover,we give theoretical proofs for the properties of OAHD,including skew insensitivity and the ability to seek a purer node in the decision tree.Finally,we collect 20 public real-world imbalanced data sets from the Knowledge Extraction based on Evolutionary Learning(KEEL)repository and the University of California,Irvine(UCI)repository.Experimental and statistical results show that OAHD significantly improves the performance compared with the five other well-known decision trees in terms of Precision,F-measure,and multiclass area under the receiver operating characteristic curve(MAUC).Moreover,through statistical analysis,the Friedman and Nemenyi tests are used to prove the advantage of OAHD over the five other decision trees.
