A Bayesian network model for fault diagnosis of a lock mechanism based on degradation data
Introduction
The fault diagnosis method of mechanical systems has gained wide attention because of the growing demands for the landing gear system’s reliability and safety. The lock mechanism system is an essential part of the landing gear system, consisting of many components. Revolute joints connect the components to transfer motion and load and complete the function of unlocking and closing the lock. As the working time increases, each revolves joint’s degeneration may lead to faults of the mechanism. On the one hand, fault patterns in the lock mechanism are not easy to identify. On the other hand, sensors are not easily placed on the component to diagnose unique lock mechanisms. It is essential to establish a fault diagnosis model to overcome these problems.
Over the last few decades, a lot of researchers have investigated the fault diagnosis methods. Fault diagnosis methods can be divided into three categories, including model-based [1], [2], signal-based [3], [4], and knowledge-based approaches [5]. Gao et al. [6] revealed that a signal-based method uses detected signals to diagnose possible abnormalities, and a knowledge-based approach requires a large amount of historical data. Cai et al. [7] and Liu et al. [8] compared the three categories and point out that knowledge-based approaches are suitable for complex mechanical systems because difficulty occurs in building accurate mathematical models and obtaining accurate signal patterns for complex mechanical systems. For complex mechanical systems, some mechanical systems have fewer experiment data because of high-reliability experiment cost. Even it is difficult for some special systems to set up the necessary sensors to judge the system’s state. The relationship between the components is difficult to determine due to the components’ coupling relationship [9]. A mechanical system consisted of interconnected components, and the degradation of components cannot be ignored [10], [11], [12], [13]. These strongly interacting components usually cause intrinsic complexity. Fault diagnosis based on the Bayesian network [14] is a classical knowledge-based approach that can deal effectively with various uncertainty problems based on probabilistic information representation inference. The Bayesian network can deal with fault diagnosis’s complexity for mechanism systems [7], [15], [16]. Oukhellou et al. [17] proposed a Bayesian network approach for structural systems by combining sensor data and mechanical knowledge. Liu et al. [8] proposed a new dynamic Bayesian network-based fault diagnosis method considering component degradation to deal with the problem that components’ performance decreased over working time.
However, each node’s logical relation in the Bayesian network structure must be determined first to build a Bayesian network model. In a mechanical system, the logical relation between components cannot be determined because of strong dependence. In a previous study, some researchers used the copula function to analyze each component’s dependency to address this problem [18]. Shen et al. [19] assumed that the logical relationship between components was series using the copula function. Yontay and Pan [20] developed a Bayesian network model to determine the logical relationship between components in series or parallel, making the relationship between components more definite. Yu et al. [21] and Johnson et al. [22] proposed a new hierarchical Bayesian model based on the technique to overcome drawbacks of traditional causation-based approaches and predict system reliability. Cai et al. [23] proposed a multi-source information fusion basing diagnosis methodology using the Bayesian network, considering the connection between two layers of nodes in building a Bayesian network structure. Components were usually placed in the same layer. However, the relationship between the same layer nodes was not considered when the strong dependence of components existed.
When building a Bayesian network model, the degradation of components in the same Bayesian network layers cannot be ignored. The Bayesian network structure can be constructed by learning from data related to fault and fault symptoms when a Bayesian network model is built [7]. Jin et al. [24] presented a Bayesian network-based fault diagnosis method and proposed a structure learning method to obtain causal relationships among fixtures and sensor nodes. Lin et al. [25] developed a methodology and utilized a Bayesian network to current internetwork in which the K2 algorithm was used for Bayesian network structure learning. Because continuous data is not applicable for the K2 algorithm, Ratnapinda et al. [26] compared three approaches to learn numerical parameters of discrete Bayesian networks from continuous data streams. Liu et al. [27] proposed an improved Algorithm Based on CACC for the discretization of Continuous Data. In mechanical systems, the K2 algorithm can determine the logical relationships between components in the Bayesian network based on historical experimental data because of the strong dependence among components.
The existing fault diagnosis method cannot solve the complicated relationship among the lock mechanism system components and cannot consider its degradation. Besides, the absence of sensor data is an engineering problem. To increase the diagnostic accuracy, especially for strong dependence among components and multiple-simultaneous fault, an improved Bayesian network method of the lock mechanism is proposed based on the wear data in this paper. A wear experiment is conducted to monitor the wear in the joints in the other lock mechanisms. Based on other lock mechanisms’ historical experiment data, an improved Bayesian network model is established considering dependence among components. The Bayesian network model without considering the dependence of components is built based on the experimental data. Then, to consider the logical relation between components, the K2 algorithm is used to learn the Bayesian network structure. Finally, a fused fault diagnosis model is established by combining the two Bayesian network models. With the model, the fault types can be distinguished when the wear of the multi-joints is known, and the weakest joint can be identified based on the occurred fault and the wear depth of other joints.
More importantly, this paper aims to study the diagnosis of the lock mechanism in which the number of the sensor is less. The lock mechanism’s fault diagnosis result is carried out using the established improved Bayesian network model and the components’ wear detection data in this lock mechanism. The improved model can also allow a more accurate diagnosis with limited sensors, verified by analyzing the results’ difference.
The remainder of this paper is organized as follows. Section 2 introduces the lock mechanism system in this paper and presents the fault mode and fault symptoms. Section 3 presents the wear experiment of the lock mechanism. An improved Bayesian network-based fault diagnosis model is proposed in Section 4. Section 5 shows the diagnosis result. Three diagnosis cases are used to compare the improved diagnosis model with the model without considering the dependence among components. Finally, the conclusion work is summarized in Section 6.
Section snippets
Functional principles
The lock mechanism system is an essential part of the landing gear system, consisting of a series of components. The lock mechanism can implement an open and close motion for the cabin door. The schematic diagram of the lock mechanism system is depicted in Fig. 1. The Lock mechanism system consists of four linkages, two rails, a tension spring, a guide rod, and a support. The plane schematic diagram of the lock mechanism is shown in Fig. 2. Slider 1 and linkage AB are connected by joint A.
Wear experiment of lock mechanisms
A wear experiment of the lock mechanism is conducted. To simply the experiment, the journal and the bearing in the joints are made of brass H58 and 0.45C steel, respectively. Since brass and steel’s hardness differs significantly, the wear on the journal’s surface is scarce and can be ignored. Only wear of the bearing is considered. The typical configuration of a joint is composed of the bearing and journal, as shown in Fig. 3.
The experiment equipment for the lock mechanism and the lock
Proposed fault diagnosis model
The fault diagnosis model of the lock mechanism is established by using the experimental data. The proposed Bayesian network model consists of two layers: fault layer and fault symptom layer. The Bayesian network model includes two steps: the network structure construction and network parameters estimation. The framework of the modeling process in this section is shown in Fig. 8. There are three modules: experimental data preprocessing, diagnosis modeling without considering dependence, and
Model verification
In the previous section, an improved Bayesian network-based fault diagnosis model is established according to the wear data in the lock mechanism analyzed. To research the effects of dependence among components, the fault diagnosis using evidence from wear data of joints is performed. Three fault diagnosis cases express three identical lock mechanisms to verify the fault diagnostic model, as shown in Table 8. The evidence from wear data of five revolute joints is utilized in those cases at the
Conclusion
This study focuses on analyzing a lock mechanism system with a strong dependence of wear in joints and less wear detection data in this lock mechanism. An improved Bayesian network model is proposed to identify faulty components and distinguish the fault types, especially considering joints’ dependence. An experiment of other lock mechanisms is conducted, and wear data of the joints is obtained. The database obtained by the experiment needs to be discretized by the CACC algorithm before
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgment
This work was supported by the National Natural Science Foundation of China (Grant No. 52075443).
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