## 1 Introduction
In addition, in the work of speech recognition, SincNet has also achieved great success due to its special filter structure and interpretability. This is a great inspiration for working with time series data [15]. Since the working states of various systems and machines are stable most of the time, the scarcity of labeled data has become one of the data problems in the field of fault detection and anomaly detection. The absence of large labeled datasets has led researchers to turn their attention to Transfer Learning (TL) [16, 17]. Transfer learning transfers knowledge in related but different domains to improve the learning machine's ability to complete related tasks in the target domain [18]. According to the feature space and label space of the target and source domains in transfer learning, transfer learning can be divided into homogeneous transfer learning and heterogeneous transfer learning. If the feature space of the target and source domains is \(X_{S}=X_{T}\) and the label space \(Y_{S}=Y_{T}\); this situation is called isomorphic transfer learning. If \(X_{S}\
eq X_{T}\) or \(Y_{S}\
eq Y_{T}\), then this situation is called heterogeneous transfer learning. According to the knowledge transfer strategy, transfer learning can also be divided into four transfer methods: instance-based, feature-based, parameter-based, and model-based [19]. Transfer learning not only solves the problem of less labeled data in the field of fault and anomaly detection but also can greatly shorten the model convergence time through pre-training and other means. One of the main characteristics of fault diagnosis tasks is the imbalance of fault data. Models trained on smaller datasets generally generalize poorly and are prone to overfitting, so pre-training on larger datasets is needed for knowledge transfer. Whether in the military field or in the civilian field, it is of great significance to quickly adapt to new problems that arise. Operating a spacecraft is a complex, multi-stage process that spans a long cycle. It involves ground launch, acceleration and escape, deceleration and berthing into orbit, attitude adjustment, and more. Despite the lack of an atmospheric environment, space poses extreme temperatures and exposure to cosmic rays, both of which can impact the spacecraft's components and performance over time. To ensure the spacecraft's reliable operation, it is crucial to study the conditions that lead to anomalies. These conditions include the spacecraft's environmental state (e.g., temperature, radiation) and mission state (e.g., acceleration, deceleration, attitude adjustment). By classifying and studying different working conditions, we can more precisely monitor the spacecraft's health status and prevent or eliminate faults. Furthermore, by modeling the spacecraft's operation data under different working conditions, we can improve the accuracy and recall rate of anomaly detection while minimizing false positives and missed detections. Based on the reference of the above fields for spacecraft anomaly detection methods, this paper proposes a Sinc-LSTM neural network for spacecraft actuator anomaly detection based on transfer learning and working condition classification. We selected the important inertial actuator CMG of the spacecraft as the research object. In the field of spacecraft anomaly detection, labeled data is generally insufficient to support model establishment, so a transfer learning method is introduced to introduce anomaly knowledge of different spacecraft into model tasks. The main contributions of this paper are as follows:  
1. The anomaly detection of CMG data is carried out using the transfer learning method, and a two-stage pre-training is designed. The features of general time series data and the features of the same type of spacecraft are extracted respectively to solve the problems of less CMG public data, difficult modeling, and less labeled data. 2. A Sinc-LSTM network is designed for fitting and reconstructing time series data in anomaly detection.