## 1 Introduction  
An autonomous underwater vehicle (AUV) usually performs various tasks in the complex marine environment, but the occurrence of failure will cause a loss that cannot be measured. Therefore, there is a need for an intelligent vehicle capable of responding to an emergency; that is, it should be able to perform automatic fault diagnosis [1]. The AUV consists of several components, of which the actuator is the key component and the most heavily loaded component. In the marine environment, there are external random disturbances, such as currents and strong measurement noise. AUV itself is a strong nonlinear system with large inertia and large time-delay characteristics, which makes the theory and method of the actuator fault diagnosis. Many scholars have made research results in AUV actuator fault diagnosis technology, but most of them focus on the hard faults of the actuator and the large loss of output, but less on the weak fault diagnosis. At the same time, the weak faults of the actuators are mostly early faults. Effective detection and diagnosis of early faults as early as possible plays an important role in avoiding \"catastrophic accidents\" caused by AUVs [2; 3; 4]. The main problems of fault diagnosis for AUV actuators are: [PERSON] et al. [5] established an AUV fault diagnosis model with four horizontal and two vertical thrusters. The methodology defines that, in the case of partial fault or complete fault (failure) in horizontal thrusters located in different action planes (which defines the axis or plane where component(s) of forces are actuating in this plane), horizontal propelling forces are calculated through the allocation matrix, used in the pseudo-inverse method, without any change, and a modified weighted matrix. [PERSON] et al. [6] presented how the model is learned using the Expectation Maximization algorithm for Gaussian Mixtures and how the testbed is monitored by probabilistic inference. The jamming fault of the motor and other faults are simulated and diagnosed by using a GMM classifier through the motor temperature, current, voltage, and other data. They described how the framework deals with non-Gaussian data and how it reflects in the accuracy overall. [PERSON] et al. [7] introduced an improved Elman neural network, which was applied to the underwater vehicle motion modeling. Through designing a self-feedback connection with fixed gain in the unit connection, as well as increasing the feedback of the output layer node, the improved Elman network has faster convergence speed and generalization ability. This method for a high-order nonlinear system has stronger identification ability. [PERSON] et al. [8] improved the multi-fault pattern classifier training speed and fault diagnosis accuracy of the fuzzy weighted support vector domain description (FWSVDD), and a multi-fault mode classification method based on a hierarchical strategy was proposed. A model-based fault diagnosis method was established on the Livingstone 2 system, and a fault tree was established to classify faults by level [9]. The main problems of weak fault diagnosis for AUV actuators are: [PERSON] et al. [10] presented an evaluation of Recurrent Neural Networks (RNN) for a data-driven fault detection and diagnosis scheme for underwater thrusters with empirical data. The nominal behavior of the thruster was modeled using the measured control input, voltage, rotational speed, and current signals. They evaluated the performance of fault classification using all the measured signals compared to using the computed residuals from the nominal model as features. Partial kernel principal component analysis (PKPCA) was studied for sensor fault detection and isolation (FDI) of an autonomous underwater vehicle. In order to achieve fault isolation, partial KPCA was proposed where a set of residual signals was generated based on the parity relation concept.