**1. Introduction**

An autonomous underwater vehicle (AUV) is one of the most important exploration tools in the ocean underwater environment. As an important part of AUV, the thruster directly determines the efficiency and safety with strong working intensity for AUV, However, the thruster fault usually happens in engineering practice [1,2]. Therefore, how to make thruster fault diagnosis and fault tolerant control for AUV is the premise for completing underwater missions [3,4].

There have been many works applied to AUV fault diagnosis. A Gaussian particle filtering algorithm is presented to estimate the AUV failure model, the Bayes algorithm is used to realize the AUV thruster fault detection [5]. For solving the fault diagnosis of AUV actuators, a diagnostic network is proposed based on extreme learning and a wide convolutional neural network [6]. Through experimental data analysis, a feature calculation method is presented to solve the weak faults thruster faults, which provides accurate and concise information for fault severity identification [7]. A fault diagnosis method is presented based on deep learning and attention mechanism for AUV, a data attention mechanism is developed for realizing dynamic decorrelation, multi-layer perceptron is used for fault detection [8]. From training datasets gathered in previous AUV operations directly, the Bayesian nonparametric technique is used for modelling the vehicle's performance including faults, in the light of the Kullback-Leibler divergence measure, a nearest-neighbor classifier is used to accomplish the fault diagnosis [9]. In summary, the above studies have given some methods to solve the AUV fault diagnosis. However, ocean currents perturbations could produce noise for thruster fault diagnosis, the above methods are

**Citation:** Tian, Q.; Wang, T.; Liu, B.; Ran, G. Thruster Fault Diagnostics and Fault Tolerant Control for Autonomous Underwater Vehicle with Ocean Currents. *Machines* **2022**, *10*, 582. https://doi.org/10.3390/ machines10070582

Academic Editor: Ahmed Abu-Siada

Received: 26 May 2022 Accepted: 12 July 2022 Published: 18 July 2022

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difficult to be used for AUV fault diagnosis with ocean currents in practice effectively. The above methods also do not consider how to control AUV to complete the underwater missions with minor faults.

Fault tolerant control is the technology to ensure the AUV for completing the underwater mission with faults [10,11]. In order to realize the fault tolerant control, it develops a model-parameter-free control strategy for AUV trajectory tracking, tracking controller is designed through the employment of sliding mode control technology without utilizing model parameters. However, the sliding mode control easily lead to the chattering of the AUV control system [12]. In order to solve the problem of thruster fault tolerant control for AUV, a fault tolerant control method is proposed in the light of the sliding mode theory, the adaptive law is developed for the proposed controller to mitigate the chattering phenomenon [13]. In order to further improve the performance of the fault tolerant control, some intelligent methods are investigated [4,14,15]. An iterative learning algorithm is proposed to process the propeller failure for AUV based on an extended state observer, a fuzzy logic controller is introduced to deal with the fuzzification of the parameters of a saturated proportional-derivative controller and extended state observer [14]. Combined with the backstepping method, a single critic network based on adaptive dynamic programming is used to deal with the AUV fault tolerant control. It designs an online policy iteration algorithm in light of the estimated system states [4]. To further conduct the effect of the ocean currents, the fault tolerant issue is transformed into an optimal control problem by the adaptive dynamic programming method, the neural-network estimator is developed to estimate ocean currents [15], however, it is difficult to establish the ocean current accurately in practice. In summary, although the above research has given some methods for fault tolerant control for AUV, they are difficult to be used in an environment with ocean currents.

Ocean currents perturbations could produce noise for thruster fault diagnosis. In this paper, in order to solve the problem of the thruster fault diagnostics and fault tolerant control for AUV with ocean currents, the possibilistic fuzzy C-means (PFCM) algorithm is proposed for realizing the thruster fault diagnostics effectively. Once the thruster fault is diagnosed, based on the fault diagnosis results, a fault tolerant control is presented by the fuzzy controller, to improve the performance of the fuzzy controller, a robust optimization problem is proposed by considering the uncertainty of ocean currents, which is solved by the proposed co-evolutionary (CPSO) algorithm, finally, it forms a mechanism of diagnostics and control strategy to accomplish the missions.

The rest of this paper is given as follows. Section 2 presents the AUV mathematical models; Section 3 gives the algorithm for AUV fault diagnostics and fault tolerant control; Section 4 discusses the effectiveness of the proposed method based on different scenarios; Section 5 concludes the paper.

### **2. Mathematical Models of AUV**

In this section, the problem description is given for the AUV firstly, and then the AUV models are discussed.
