Interval Evidential Reasoning-based Fault Detection of Electromagnetic Relay

The electromagnetic relay is a key switch control component, and its fault detection under uncertainties is a challenging problem. In this paper, a fault detection method based on interval evidential reasoning (IER) is proposed and applied to detect the relay’s fault. The method can handle fuzzy uncertainty and interval uncertainty in relay test data, and iteratively aggregate evidence by using the IER algorithm. Firstly, the relay super-path time data is transformed into the form of an interval belief distribution by using the fuzzy threshold, which is optimized by using training data. Secondly, historical and current information is aggregated to update interval belief distribution. Finally, the fault detection result can be obtained from interval belief distribution by a rule. The experimental results show that the presented method can improve the detection effect significantly.


Introduction
Electromagnetic relay has been widely used in industrial, military, and aerospace systems, its reliability is crucial for these systems.With the increase in the number of actions, the relay fails due to components degeneration and may cause serious results.Fault detection is necessary for replacing faulty relays.Relay characteristic parameters such as pick-up time and super-path time can reflect the degradation of relay performance and can be a feature for fault detection.However, owing to the strong uncertainty of relays fault feature data, existing methods are difficult to effectively detect faults in relays.Hence, the fault detection of relays under uncertainties has important theoretical and engineering significance.
In current literature, fault detection methods mainly include three categories: methods based on the system model, methods based on probability theory and methods based on machine learning probability theory.Because of the complex degradation mechanism of relays, it is hard to build the mathematical model of relays fault, the methods based on the system model is difficult to be applied to the fault detection problem of relay.The other two methods are based on data-driven, which can handle uncertain information without a precise mathematical model.Lang et al. [1] proposed a fault detection method based on kernel density estimation (KDE) for faults in the semiconductor manufacturing process, which is capable of being trained with limited amounts of successful run data.Han et al. [2] proposed a novel fault diagnosis method for modular multilevel converters, which involves the implementation of the long short-term memory network (LSTM).
The Dempster-Shafer (D-S) evidence theory introduced the concept of belief distribution to expand traditional probability distribution [3], so it can be considered as the extension of probability theory.Different from other methods based on probability theory, it can describe the information given by expert knowledge [4].As a development of the D-S theory, the evidential reasoning (ER) rule can effectively deal with conflicting evidence [5] and is applied to fault detection [6,7].Weng et al. [8] proposed a data-driven industrial alarm method based on ER approach.Compared with the classical method, it has better performance.Information in interval form is common and ER approach cannot aggregate evidence in interval form.To address this, Wang et al. [9] proposed the interval evidential reasoning (IER) algorithm, which can handle both determined and interval evidence well.
Aiming at uncertainty in relay test data, a new IER-based fault detection method is proposed in this paper.The main contributions of this paper are given as follows: (1) The belief distribution structures are established by using a fuzzy threshold and an optimization model for determining the fuzzy threshold is proposed.The constraints of the optimization model are given by expert knowledge, which effectively combines expert experience and historical data.
(2) The fault feature data of relays are adaptive expanded to interval and transformed into interval belief distribution.Historical and current information are aggregated iteratively by using the IER algorithm.All of the above can improve the anti-interference ability of the proposed method.
The rest of the paper is organized as follows.In Section 2, the IER-based fault detection method is proposed, which includes the establishment of belief distribution and evidence aggregation by using the IER algorithm; In Section 3, an experiment is done to verify the effect of the method; Section 4 concludes this paper.

{ , } H H  
be a set of relay working statuses,  includes two statuses: failure 1 ( ) H and normal 2 ( ) H .The evidence of relay working statuses can be described as the following form of belief distribution: where 1  represents that the belief degrees of e points to 1  denotes the belief degrees of e points to 2 H .The super-path time is a fault feature of relays and can be used to generate evidence.With the increase in the number of actions, the super-path time showed a decreasing tendency, and the relay gradually transited from a normal status to a failure status.Considering that the boundary between two statuses is fuzzy, the fuzzy threshold is designed to model fuzzy uncertainty.
It is supposed that x denotes super-path time, the fuzzy threshold of x is denoted by The belief degrees can be derived by using Equation (2) and are shown as ( ), ( ) The fuzzy threshold can be given by expert knowledge, but it is difficult to accurately estimate the uncertainties.So it is necessary to optimize the fuzzy threshold.An optimization model is established to determine the fuzzy threshold and the constraints of the model are given by expert knowledge.
It is supposed that ( )( 1,2, , ) The difference between i e and i e can be measured by using Euclidian distance: where ( , ) To minimize the total evidence distance, the fuzzy threshold optimization model is derived as follows: where 1 2 1 2 , , , a a b b can be given by prior knowledge.By solving the optimization model ( 4), the optimal fuzzy threshold , [ ] To model the interval uncertainty of super-path time data, x is expanded to interval become an interval form of belief distribution, as shown in the following: The interval belief structure of evidence e is shown as

Interval evidential reasoning (IER) algorithm
The relay super-path time data can be transformed into interval belief distribution by using a fuzzy threshold, which includes relay working status assessment information.The next step is to aggregate the information by an IER algorithm.The IER algorithm is composed of the following steps.Firstly, before aggregating, the interval degrees of belief are transformed into interval basic probability masses below:  where p represents the interval expanded factor.Suppose that W denotes the sliding window size, p can be calculated by: It is supposed that , which suggests that the relay is normal at 0 times.When 0 t  , the expert specifies the aggregation parameters { , , , } , where ,  , the relay has failed, then ( ) ) D t D t   .This rule is similar to the dead band method, when the width of interval belief degrees increases to a certain level, the fault detection result remains unchanged, which amounts to a dynamic dead band.

Experimental process
As shown in Figure 1, a relay testing system was used to test a relay and measure characteristic parameters once every 500 actions.After testing, 5000 sets of super-path time data were obtained, as shown in Figure 2. The relay failed near the 3750th set of data.
As can be seen from Figures 4 and 5, when t closes to 401, the width of interval belief degrees increases, which suggests that uncertainties increase.Due to the application of the IER approach, the anti-interference ability of the proposed method is improved.Our method also aggregates history and current information, which reduces uncertainties and makes relay faults easier to distinguish.

Comparative analysis of experiment
To verify the effectiveness of the proposed method, we compared it with three typical methods: the method based on kernel density estimation (KDE), the LSTM classifier and the ER alarm method proposed by [10].In the KDE method, the Gaussian kernel is chosen as the kernel function.The bandwidth of the Gaussian kernel is obtained by solving an optimization model which uses Euclidean distance and maximum distance as fitness indicators.The architecture of the LSTM network is established by using the following configurations.The input size is set to 1.An LSTM layer with 64 hidden units is defined and configured to output only the final element of the sequence followed by a Sigmoid layer.
We applied the above methods to test data and compare the false alarm rate (FAR) and missed alarm rate (MAR) of each method.The results are as shown in Table 1.According to these results, the IERbased approach gives the lowest FAR and the lowest MAR.

Conclusion
In this paper, a new IER-based fault detection method is proposed for detecting relay faults.It considers fuzzy uncertainty and interval uncertainty in relay test data and aggregates historical and current information for reducing the uncertainty.The experiment was done to verify the effect of the method. With membership function, the membership degrees of x to  are shown below:1

Figure 1 .Figure 2 .
Figure 1.Relay testing The 3001-3200 sets of data are selected as the normal training data (1), (2), , (200) train train train x x x  , and the 4201-4400 sets of data are selected as the failure training data (201), (202), , train train x x  Figure 5.

,
where  , ,  , denotes the weighted interval basic probability masses, and  , is a basic probability in  , ,  , where r Then, ER algorithm is used to aggregate probability masses on L piece of evidence:

)
Finally, the upper and lower bounds of n

Table 1 .
Comparison of fault detection effects