One of the most common parts to maintain system balance and support the various load in rotating machinery is the rolling element bearing. The breakdown of the element in bearings leads to inefficiency and sometimes catastrophic events across various industries. The main challenge over the last few years for fault diagnosis of bearings is the early detection of fault signature. In this paper, an adaptive online dictionary learning algorithm is developed for early fault detection of bearing elements. The dictionary is trained using a set of vibration signal from a heavily damaged bearing. The enveloped signal of the bearing is obtained using the Kurtogram and split into several sections. The K-SVD algorithm is implemented to the dictionaries corresponding to the enveloped signal. OMP is implemented with the calculated dictionaries to obtain the sparse representation of the testing signal. Then the envelope analysis is implemented to obtain the fault signal from the recovered signal by the dictionaries. The adaptive algorithm is added to the dictionary learning to update the dictionary based on newly acquired data with the weighted least square method. Without retraining the dictionaries using the K-SVD algorithm, the computation speed is significantly improved. The proposed algorithm is compared with a traditional dictionary learning algorithm to show the improvement in detection of new fault frequency and improved signal to noise ratio.

中文翻译：

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用于轴承故障诊断的自适应在线词典学习。

保持系统平衡并支持旋转机械中各种负载的最常见零件之一是滚动轴承。轴承中元素的分解会导致各个行业的效率低下，有时甚至发生灾难性事件。过去几年中，轴承故障诊断的主要挑战是及早发现故障特征。本文提出了一种自适应的在线词典学习算法，用于轴承元件的早期故障检测。使用来自严重损坏轴承的一组振动信号来训练字典。使用Kurtogram获得轴承的包络信号，并将其分成几部分。对与包络信号相对应的字典执行K-SVD算法。OMP与计算出的字典一起实现，以获得测试信号的稀疏表示。然后，通过字典执行包络分析以从恢复的信号中获取故障信号。将自适应算法添加到字典学习中，以使用加权最小二乘法基于新获取的数据更新字典。无需使用K-SVD算法重新训练字典，可显着提高计算速度。将该算法与传统的字典学习算法进行了比较，表明在检测新故障频率方面的改进和改进的信噪比。将自适应算法添加到字典学习中，以使用加权最小二乘法基于新获取的数据更新字典。无需使用K-SVD算法重新训练字典，可显着提高计算速度。将该算法与传统的字典学习算法进行了比较，表明在检测新故障频率方面的改进和改进的信噪比。将自适应算法添加到字典学习中，以使用加权最小二乘法基于新获取的数据更新字典。无需使用K-SVD算法重新训练字典，可显着提高计算速度。将该算法与传统的字典学习算法进行了比较，表明在检测新故障频率方面的改进和改进的信噪比。