Due to the harsh circumstances, planetary gearboxes as the important transmission component of mechanical equipment inevitably incur unexpected failures. Due to the merits of encoder signal, the research of encoder signal for fault detection have recently received much attention. However, the research on how to apply encoder signal to the fault detection of planetary gearbox under variation speed conditions is still not sufficient. Therefore, this paper proposes a three-stage variable speed encoder signal analysis approach for extracting fault-related transient features in original encoder signal and detecting potential fault of planetary gearboxes. In the proposed method, we first employ difference method to original encoder signal to convert it into more meaningful instantaneous angular speed (IAS) in time domain. Then, self-resampling technique is introduced to transform IAS in time domain into the new one in angular domain. At last, low-pass filter and sparsity based algorithm (LpfSpaA) is established for separating fault-induced IAS fluctuation from noisy IAS in angular domain. In the proposed LpfSpaA that is the core of the paper, a unique convex optimization problem is constructed and an iterative algorithm is derived to solve it. Meanwhile, to obtain the perfect performance of proposed LpfSpaA, an adaptive parameter determination scheme is also analyzed. The efficacy of proposed method in feature extraction and fault detection is assessed using synthetic and actual signals.

由于恶劣的环境，行星齿轮箱作为机械设备的重要传动部件不可避免地会引起意外故障。由于编码器信号的优点，用于故障检测的编码器信号的研究近来备受关注。然而，如何在变速箱条件下将编码器信号应用于行星齿轮箱故障检测的研究还不够。因此，本文提出了一种三阶段变速编码器信号分析方法，用于提取原始编码器信号中与故障相关的暂态特征，并检测行星齿轮箱的潜在故障。在提出的方法中，我们首先对原始编码器信号采用差分方法，以将其转换为时域中更有意义的瞬时角速度（IAS）。然后，引入自重采样技术将时域的IAS转换为角域的新IAS。最后，建立了基于低通滤波器和稀疏性的算法（LpfSpaA），以将故障引起的IAS波动与嘈杂的IAS进行分离。在本文的核心LpfSpaA中，构造了一个独特的凸优化问题，并推导了迭代算法来求解。同时，为了获得理想的LpfSpaA性能，还分析了一种自适应参数确定方案。提出的方法在特征提取和故障检测中的功效通过综合信号和实际信号进行评估。建立了基于低通滤波器和稀疏性的算法（LpfSpaA），用于在角域中将故障引起的IAS波动与噪声IAS分开。在本文的核心LpfSpaA中，构造了一个独特的凸优化问题，并推导了迭代算法来求解。同时，为了获得理想的LpfSpaA性能，还分析了一种自适应参数确定方案。提出的方法在特征提取和故障检测中的有效性通过综合信号和实际信号进行评估。建立了基于低通滤波器和稀疏性的算法（LpfSpaA），以将故障引起的IAS波动与噪声IAS的角域分开。在本文的核心LpfSpaA中，构造了一个独特的凸优化问题，并推导了迭代算法来求解。同时，为了获得理想的LpfSpaA性能，还分析了一种自适应参数确定方案。提出的方法在特征提取和故障检测中的功效通过综合信号和实际信号进行评估。还分析了自适应参数确定方案。提出的方法在特征提取和故障检测中的功效通过综合信号和实际信号进行评估。还分析了自适应参数确定方案。提出的方法在特征提取和故障检测中的功效通过综合信号和实际信号进行评估。