**1. Introduction**

In order to address global warming issues, many countries have reduced carbon emissions year by year as one of their targets for economic and social development. As one typical source of clean energy, wind power has significant advantages in terms of environmental and ecological impact compared with hydropower and nuclear power [1]. In recent years, wind power has been rapidly developed in many countries, and the installed capacity has been increasing year by year [2].

The working environment of wind turbines is often complex, so the failure rate of the components of wind turbines is relatively high [3]. If the key components of the wind turbine system fail, it will cause damage and even stop the whole turbine, resulting in huge economic losses. Therefore, in recent years, a large number of research work has been focused on fault diagnosis of wind turbines. The failures typically include blade failures, transmission system failures, generator failures, and tower failures. Among them, misalignment of the transmission system is one of the common failures [4]. Many reasons, such as bearing eccentricity, installation error, and coupling misalignment, can cause misalignment of the wind turbine transmission system that connects the gearbox and generator for a typical doubly-fed wind turbine [5]. The misalignment of the transmission system can inevitably lead to vibration of the unit, which will reduce the reliability of the power generation system. In addition, the misalignment failure can cause damage to gears

**Citation:** Xiao, Y.; Xue, J.; Zhang, L.; Wang, Y.; Li, M. Misalignment Fault Diagnosis for Wind Turbines Based on Information Fusion. *Entropy* **2021**, *23*, 243. https://doi.org/10.3390/ e23020243

Academic Editors: Philip Broadbridge, Yongbo Li, Xihui (Larry) Liang and Fengshou Gu

Received: 13 January 2021 Accepted: 18 February 2021 Published: 20 February 2021

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**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

and bearings [6]. Therefore, it is necessary to monitor and diagnose the misalignment of the transmission system in doubly-fed wind turbines.

Although there is much work on the misalignment fault diagnosis for a conventional rotating system, there is little work for wind turbine misalignment diagnosis. In particular, a wind turbine presents additional and unique challenges as it operates under variable rotational conditions [7,8]. At present, the main research on detecting the misalignment of wind turbines includes the following work. Zhao et al. applied variational mode decomposition (VMD) to decompose the fault vibration signal to isolate features and diagnose the misalignment faults in a direct drive wind turbine [9]. Abdalla et al. diagnosed misalignment of planetary gearbox based on vibration measurements using spectrum analysis and modulation signal bispectrum (MSB) analysis [10]. Huang et al. applied the Hilbert–Huang transform (HHT) method for fault diagnosis of wind turbine rotors and discussed three typical faults by the HHT, including rotor mass imbalance, aerodynamic asymmetries, and yaw misalignment [11]. An and Kong proposed a modified empirical mode decomposition (EMD) method to extract characteristics from vibration signals and applied a back-propagation neural network to data from various sensors to diagnose faults of offshore wind turbines included stator imbalanced, rotor unbalanced, and bearing misalignment [12]. Villa et al. developed a statistical diagnosis algorithm based on the significance level of the modeled fault to detected unbalance fault and misalignment fault of wind turbine, and tested the algorithm on vibration from a test-bed [13]. He et al. analyzed the vibration characteristics of the transmission chain of a wind turbine based on double-elastic support with natural axial misalignment between the output shaft of gearbox and the shaft of generator causing vibration signals of normal gearbox blend with serious high-order gear mesh frequency and smooth modulation [14]. However, these methods mainly applied rely on single information, and their performance could be limited owing to the limited source of information.

Because the diagnosis based on single information often cannot reflect the overall condition, the information fusion methodology for multiple source information is needed for the diagnostic system. Information fusion is a synchronous and comprehensive processing of the information obtained from multiple sensors. It can ensure the integrity of the information from a different perspective and overcome the shortcomings of traditional single information to form a more objective and closer understanding of the system [15], which can greatly improve the accuracy of diagnosis.

Information fusion can be divided into three levels: data level, feature level, and decision level [16,17].


At present, there are many research methods and achievements in decision level fusion, including Bayesian theory [18], Dempster–Shafer (D–S) evidence theory [19], fuzzy set theory [20,21], rough set theory [22], and so on. The classification principle of Bayesian theory is to calculate the posterior probability of an object (the probability that the object belongs to a certain class) using the prior probability and Bayes formula, and select the class with the largest posterior probability as the one to which the object belongs. In D–S evidence theory, trust function and likelihood function are obtained by calculating the orthogonal sum of basic probability distribution functions of different evidences. After fusing multiple evidences, the final decision is made according to decision rules. Among them, basic probability distribution function is the probability distribution of all possible faults in each state, trust function is the lower bound of fault event probability, and likelihood function is the upper bound. Fuzzy set theory (FS) was founded by Zadeh. Membership T(x) was used to describe fuzzy information. At this time, non-membership F(x) did not appear. Then, intuitionistic fuzzy sets (IFSs) and interval intuitionistic fuzzy sets (IVIFSs) appeared successively. The fuzzy information processing technology developed from fuzzy set theory can provide a simple and effective means to explore uncertainty and simulate human recognition mechanism. Rough set theory, initially developed by Pawlak (1982), is a mathematical tool that deals with vague, uncertain, and incomplete information. Rough set theory has been successfully applied in many fields such as machine learning, pattern recognition, control systems, data mining, and image classification.

The advantages and limitations of the above four methods are listed in Table 1.


**Table 1.** Comparison of information fusion algorithms. D–S, Dempster–Shafer.

In this paper, based on the good theoretical basis and application effect of D–S evidence theory [23–27], it is used to complete decision fusion, which provides a sufficient fault diagnosis solution for wind turbine misalignment fault.

The aim of this paper is to use multiple sources of information to distinguish the misalignment-free (normal condition) and three different types of transmission misalignment. The main contributions are summarized as follows.

Multiple sources of information and integrated approach are used for wind turbine transmission misalignment detection. More specifically, the vibration, temperature, and stator current signal are taken as the original source, and their time domain features, frequency domain features, and time-frequency domain features are extracted as fault characteristics. t-distributed stochastic neighbor embedding (t-SNE) is used to reduce the vibration and current characteristics dimensionality, and then three posterior probability least squares support vector machine with parameters optimized by improved artificial bee colony algorithm are constructed. The probability outputs of the three LSSVM are taken as the basic probabilities of evidence fusion. The probability distribution after fusion is calculated according to the Dempster fusion rule. Compared with the non-fusion models, it is demonstrated that the model based on D–S evidence fusion has higher diagnostic accuracy for wind turbine misalignment faults.

The remainder of the paper is organized in the following way. In Section 2, the formulas of D–S evidence theory, posterior probability least squares support vector machines, and the improved artificial bee colony are presented in detail. Section 3 describes the specific steps for D–S fault diagnosis. Section 4 presents the fault diagnosis case study based on the simulation model. Section 5 presents the fault diagnosis case study based on the experimental platform. Section 6 concludes the current work.
