基于特征空间邻域结构分析的故障识别方法
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摘要
故障诊断对于提高设备运行的可靠性起着至关重要的作用。故障诊断系统要求能够快速有效的判断故障位置、类型、性质以及严重性等,并要求具有实时性、在线更新以及准确性。基于知识发现的方法是故障诊断方法中最有效的方法之一。目前的故障识别模块在稳定性以及准确度方面还难以满足应用要求,本文从故障特征子空间的探索与利用角度出发,在邻域粒化后寻找保持原始特征空间近似能力的多个属性约简,然后通过优化方法融合不同约简的信息,以提高故障识别的泛化性能与稳定性。从以下几方面进行了探索:
第一,提出了基于邻域辨识矩阵的属性约简方法以及基于样本对选择的快速约简方法。将基于辨识矩阵的约简方法引入到邻域粗糙集中,建立了邻域辨识关系下的属性约简方法。在基于辨识矩阵的约简方法中,仅最小元素影响约简的结果,因此给出了通过寻找最小元素求得属性约简的快速方法。同时分析了邻域大小对于属性约简的影响,检验了约简评价指标的有效性。
第二,提出了基于邻域属性依赖度寻找所有约简的方法和邻域随机约简方法。邻域属性依赖度已被用于构造寻找单个约简的算法,通过幂集的形式可利用属性依赖度求得所有约简。为了寻求一种快速高效的多约简求解方法,构建了基于属性依赖度的随机约简算法。这两种属性约简方法不仅适用于邻域粗糙集,也可以拓展到经典粗糙集以及模糊粗糙集中。
第三,提出了基于间隔分布熵的集成学习方法。本文提出了间隔分布熵的概念,以表示间隔分布的均匀程度,在最大化间隔的同时最大化间隔分布熵。由此设计了相应的集成学习方法并检验了其分类性能和间隔分布的变化。
第四,提出了基于间隔分布优化正则化的集成学习方法。多分类器决策融合问题本质上是一个特殊的分类问题,从分类器设计的角度去解决分类集成中的权学习问题是本文的主要思路。通过把最小化融合损失和正则化学习结合起来,提出了基于平方损失、logistic损失以及线性损失的正则化集成学习方法,并给出了平方损失对应的泛化性能的界。测试了所提出方法的分类性能、间隔分布的变化以及不同优化目标下学习的权值,检验了该方法的有效性。
第五,提出了基于邻域约简集成的故障识别方法。从单个故障特征子空间学到的判别函数稳定性和泛化性能较差,,把不同特征子空间的信息集成起来,可提高故障识别的稳定性以及准确性。本文通过邻域随机约简获得不同的故障可分子空间,并通过基于间隔分布优化的方式集成从这些子空间建立的分类函数,在齿轮裂纹故障中检验了提出方法的有效性。
本文的研究统一了基于邻域粗糙集的属性约简方法,由于最小邻域可分子空间泛化性能以及稳定性方面的局限,提出了基于间隔分布优化的邻域约简集成学习方法。提出了间隔分布熵的概念,通过优化间隔分布熵改变间隔分布。通过把最小化融合损失和正则化学习结合起来,提出了三种损失函数不同正则和约束下的基于间隔分布优化的集成学习方法。
Fault diagnosis plays a crucial role in improving the reliability of equipments. Faultdiagnosis users expect that the fault location, fault classes and the trend could be effec-tively and rapidly judged. Meanwhile, the instantaneity, online update ability and accu-racy are essential. Fault analysis based on knowledge discovery is one of the most effec-tive ways. In view of the constraint of the stability and the accuracy for the present faultrecognition module in practical application, in this paper, from the angle of explorationand usage of fault feature subspace, multiple reducts that keep the approximation abilityof original feature space can be obtained, and then information in different reducts can befused through optimization methods to improve generalization capability and stability offault recognition. The main contributions of the work are listed as follows:
Firstly, attribute reduction based on neighborhood discernibility matrix and a fastmethod based on sample pair selection are put forward. Attribute reduction based on dis-cernibility matrix is introduced into neighborhood rough set. As to the method based ondiscernibility matrix, only the minimum elements in the matrix are useful for attributereduction. Hence, reducts can be found by looking for minimum elements. Besides, theimpact of neighborhood size on attribute reduction is analyzed. Finally, test the effective-ness of reduct evaluation indexes.
Secondly, the method finding all reducts and randomized reduction based on neigh-borhood attribute dependency are constructed. Neighborhood attribute dependence hasalready been used to construct the algorithm looking for a single reduct. In fact, powersets can be used to find all reducts based on attribute dependency. To find a fast and effec-tive methods finding multiple reducts, neighborhood randomized reduction is proposed.The two attribute reduction methods are not only applicable to neighborhood rough set,but can be expanded to classic rough sets and fuzzy rough sets.
Thirdly, ensemble learning method based on margin distribution entropy is proposed.In this paper, the concept of margin distribution entropy is put forward to indicate the uni-formity degree of margin distribution. To maximize margin and simultaneously maximizemargin distribution entropy, an ensemble learning method is designed. The classificationperformance and the variation of margin distribution are examined.
Fourth, an ensemble learning method based on margin distribution optimization andregularization is proposed. Multiple Classifiers fusion in essence is a special classifi-cation problem. From the angle of classifier design to solve the problem of ensemblelearning is the main idea of this paper. By combining fusion loss minimization and regu-larized learning together, square loss, logistic loss and linear loss are respectively used toconstruct regularization based ensemble learning methods. The boundary of generationability for square loss is given. The classification performance, variation of margin distri-bution and learned weights as to different optimization objectives are tested to prove theeffectiveness of the proposed method.
Finally, due to the poor stability and generation ability of the discrimination functionlearned from a single fault feature subspace , by fusing the information in different fea-ture subspaces, it can greatly enhance the stability and accuracy of the fault recognition.Different feature subspaces are obtained through the neighborhood randomized reductionand then they are integrated by margin distribution optimization. The effectiveness of thismethod is tested in gears crack level recognition.
In this paper, attribution reduction methods based on neighborhood rough set areunified. Due to the limitation of generalization performance and stability for minimalneighborhood separable subspace, neighborhood reducts ensemble leaning based on mar-gin distribution optimization is constructed. The margin distribution entropy is proposedand optimized to change margin distribution. By combining fusion loss minimization andregularized learning, ensemble learning methods based on three loss functions, differentregularization items and constraints are put forward.
第一,提出了基于邻域辨识矩阵的属性约简方法以及基于样本对选择的快速约简方法。将基于辨识矩阵的约简方法引入到邻域粗糙集中,建立了邻域辨识关系下的属性约简方法。在基于辨识矩阵的约简方法中,仅最小元素影响约简的结果,因此给出了通过寻找最小元素求得属性约简的快速方法。同时分析了邻域大小对于属性约简的影响,检验了约简评价指标的有效性。
第二,提出了基于邻域属性依赖度寻找所有约简的方法和邻域随机约简方法。邻域属性依赖度已被用于构造寻找单个约简的算法,通过幂集的形式可利用属性依赖度求得所有约简。为了寻求一种快速高效的多约简求解方法,构建了基于属性依赖度的随机约简算法。这两种属性约简方法不仅适用于邻域粗糙集,也可以拓展到经典粗糙集以及模糊粗糙集中。
第三,提出了基于间隔分布熵的集成学习方法。本文提出了间隔分布熵的概念,以表示间隔分布的均匀程度,在最大化间隔的同时最大化间隔分布熵。由此设计了相应的集成学习方法并检验了其分类性能和间隔分布的变化。
第四,提出了基于间隔分布优化正则化的集成学习方法。多分类器决策融合问题本质上是一个特殊的分类问题,从分类器设计的角度去解决分类集成中的权学习问题是本文的主要思路。通过把最小化融合损失和正则化学习结合起来,提出了基于平方损失、logistic损失以及线性损失的正则化集成学习方法,并给出了平方损失对应的泛化性能的界。测试了所提出方法的分类性能、间隔分布的变化以及不同优化目标下学习的权值,检验了该方法的有效性。
第五,提出了基于邻域约简集成的故障识别方法。从单个故障特征子空间学到的判别函数稳定性和泛化性能较差,,把不同特征子空间的信息集成起来,可提高故障识别的稳定性以及准确性。本文通过邻域随机约简获得不同的故障可分子空间,并通过基于间隔分布优化的方式集成从这些子空间建立的分类函数,在齿轮裂纹故障中检验了提出方法的有效性。
本文的研究统一了基于邻域粗糙集的属性约简方法,由于最小邻域可分子空间泛化性能以及稳定性方面的局限,提出了基于间隔分布优化的邻域约简集成学习方法。提出了间隔分布熵的概念,通过优化间隔分布熵改变间隔分布。通过把最小化融合损失和正则化学习结合起来,提出了三种损失函数不同正则和约束下的基于间隔分布优化的集成学习方法。
Fault diagnosis plays a crucial role in improving the reliability of equipments. Faultdiagnosis users expect that the fault location, fault classes and the trend could be effec-tively and rapidly judged. Meanwhile, the instantaneity, online update ability and accu-racy are essential. Fault analysis based on knowledge discovery is one of the most effec-tive ways. In view of the constraint of the stability and the accuracy for the present faultrecognition module in practical application, in this paper, from the angle of explorationand usage of fault feature subspace, multiple reducts that keep the approximation abilityof original feature space can be obtained, and then information in different reducts can befused through optimization methods to improve generalization capability and stability offault recognition. The main contributions of the work are listed as follows:
Firstly, attribute reduction based on neighborhood discernibility matrix and a fastmethod based on sample pair selection are put forward. Attribute reduction based on dis-cernibility matrix is introduced into neighborhood rough set. As to the method based ondiscernibility matrix, only the minimum elements in the matrix are useful for attributereduction. Hence, reducts can be found by looking for minimum elements. Besides, theimpact of neighborhood size on attribute reduction is analyzed. Finally, test the effective-ness of reduct evaluation indexes.
Secondly, the method finding all reducts and randomized reduction based on neigh-borhood attribute dependency are constructed. Neighborhood attribute dependence hasalready been used to construct the algorithm looking for a single reduct. In fact, powersets can be used to find all reducts based on attribute dependency. To find a fast and effec-tive methods finding multiple reducts, neighborhood randomized reduction is proposed.The two attribute reduction methods are not only applicable to neighborhood rough set,but can be expanded to classic rough sets and fuzzy rough sets.
Thirdly, ensemble learning method based on margin distribution entropy is proposed.In this paper, the concept of margin distribution entropy is put forward to indicate the uni-formity degree of margin distribution. To maximize margin and simultaneously maximizemargin distribution entropy, an ensemble learning method is designed. The classificationperformance and the variation of margin distribution are examined.
Fourth, an ensemble learning method based on margin distribution optimization andregularization is proposed. Multiple Classifiers fusion in essence is a special classifi-cation problem. From the angle of classifier design to solve the problem of ensemblelearning is the main idea of this paper. By combining fusion loss minimization and regu-larized learning together, square loss, logistic loss and linear loss are respectively used toconstruct regularization based ensemble learning methods. The boundary of generationability for square loss is given. The classification performance, variation of margin distri-bution and learned weights as to different optimization objectives are tested to prove theeffectiveness of the proposed method.
Finally, due to the poor stability and generation ability of the discrimination functionlearned from a single fault feature subspace , by fusing the information in different fea-ture subspaces, it can greatly enhance the stability and accuracy of the fault recognition.Different feature subspaces are obtained through the neighborhood randomized reductionand then they are integrated by margin distribution optimization. The effectiveness of thismethod is tested in gears crack level recognition.
In this paper, attribution reduction methods based on neighborhood rough set areunified. Due to the limitation of generalization performance and stability for minimalneighborhood separable subspace, neighborhood reducts ensemble leaning based on mar-gin distribution optimization is constructed. The margin distribution entropy is proposedand optimized to change margin distribution. By combining fusion loss minimization andregularized learning, ensemble learning methods based on three loss functions, differentregularization items and constraints are put forward.
引文
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