中文摘要：

针对机械故障诊断中缺乏大量故障样本进行训练的问题,提出基于图论和直推式支持矢量机（Graph theory and transductive support vector machine,GTSVM）的故障诊断方法。通过建立数据矩阵的完全图,定义一种基于密度敏感的距离描述图中各个节点即样本之间的相异性,有效地利用数据空间结构信息,并以Iris数据进行仿真分析。对齿轮箱在三种运行模式（正常、齿面轻微剥落、齿面严重剥落）下的振动信号进行分析,提取11个时域特征指标,用主元分析对11个特征进行选择,采用图论方法对选择后的特征数据进行处理,然后用梯度下降法训练直推式支持矢量机,实现故障检测和分类。将GTSVM法与支持矢量机法、直推式支持矢量机法进行对比,结果表明,GTSVM法的分类正确率最高。此外,经过主元方法进行特征选择后,故障检测性能也得到较大提高,表明该方法能应用于齿轮早期故障诊断。

英文摘要：

In view of the severe shortage of samples for training in mechanical fault diagnosis,a novel method based on graph theory and transductive support vector machine（GTSVM） is presented for gear incipient fault diagnosis.By building a complete graph of original data matrix,a density-sensitive distance is defined to evaluate the dissimilarity between samples,which reflects the data structure well,and the well-known Iris data is used to verify the effectiveness.The vibration signals of gearbox under three running conditions（normal,slight spalling and severe spalling） are analyzed,and 11 time domain features are extracted from original data.Principal component analysis is adopted to select discriminative features,and graph theory is used to process the selected feature sets.Then,transductive support vector machine is trained by gradient descent learning and applied in fault detection and faults classification.The results using GTSVM method are compared with those using support vector machine and transductive support vector machine,which indicates the high classification accuracy of the proposed approach.Besides,the performance in failure detection is also improved through principal component analysis feature selection.Experiments show that the proposed method is effective in gear incipient fault diagnosis.