Fault Diagnosis of Electrical Bearing Based on Multi-Model Approach
Abstract
Electrical bearings are widely used in manufacturing industries and have become an important part of the mechanism. However, due to the complexity of its structure and the fact that its internal state is difficult to observe, failure of the bearing is often difficult to identify and diagnose. In order to improve the fault diagnosis accuracy and efficiency of electrical bearing, an optimal multi-model approach based on least squares support vector machines (LS-SVM) and multi-layer perceptron (MLP) neural networks has been developed and tested. The proposed approach first determines the number of bearing states through principal component analysis (PCA) and the least squares support vector machine (LS-SVM) is used to identify different bearing states. Then, MLP neural network is constructed and trained according to the different bearing states and used to identify bearing faults. Finally, the method proposed in this paper is verified through simulation experiments.
Keywords: electrical bearing, fault diagnosis, least squares support vector machine, multilayer perceptron neural network
1. Introduction
Electrical bearings are used in many critical applications in modern industry. As an important part of the mechanism, the reliability of electrical bearings is particularly important. However, due to the complexity of its structure and the fact that its internal state is difficult to observe, failure of the bearing is difficult to identify and diagnose. Thus, it is of great significance to develop a reliable and efficient fault diagnosis method for electrical bearing.
With the development of artificial intelligence technology, it has also been widely used in electrical bearing fault diagnosis. Dragan M. and Codreanu M. applied self-organizing maps (SOM) to identify faults of electrical bearings [1]. Bhattacharya R.K. used the probabilistic approach to identify partial discharge of electrical bearings [2], and Phomsoupha W. and Kitiyodom S. constructed a hybrid multiple-expert approach based on least squares support vector machines (LS-SVM) and fuzzy inference systems (FIS) for fault diagnosis of electrical bearing [3].
Although these methods can ensure high accuracy, they may not be able to keep up with the rapid development of industry or be applied in real-time environments. In addition, most of these approaches require prior segmentation of the fault data and have limited application in turbocharging systems. In order to overcome these shortcomings, an optimal multi-model approach based on least squares support vector machines (LS-SVM) and multi-layer perceptron (MLP) neural networks has been developed and tested.
2. Methodology
2.1. Principal Component Analysis
Principal component analysis (PCA) is a well-known to data dimensionality reduction technique and widely used for feature extraction [4]. The basic idea of PCA is that one can represent a set of observations with a set of features extracted from the original vector. First, the original data is expressed as a matrix X of size n x m, where n is the number of observations and m is the number of features. PCA looks for a series of new variables, called principal components (PCs), expressed by linear combinations of the original variables and such that they capture the variance of data as much as possible. PCA determines the variance-covariance matrix of original data. The variance of each variable is given by the diagonal elements of the matrix and the covariance between two variables is given by the off-diagonal elements of the matrix. Thus, the first principal component corresponds to the eigenvector of the variance-covariance matrix with the largest eigenvalue and the other principal components can be determined similarly.
2.2. LS-SVM
Least squares support vector machine (LS-SVM) is an extension of the classical SVM. Compared with conventional SVM, LS-SVM has two major advantages: the increased computational efficiency and the possibility to use the intercepts [5].
LS-SVM works in such a way that the feature space is spanned by a series of basis functions and the optimal separating hyperplane is constructed in the feature space using a weighted sum of the basis functions. To determine the optimal weight vector, the following objective function can be applied:
min W, b||W||2+ γ2|a|2
subject to, y(WTφ(x)+ b) ≥ 1, ∀x,y
where W is the set of weights, b the bias and γ the penalty parameter.
2.3. MLP
The multi-layer perceptron (MLP) is a type of artificial neuron network. MLP is composed of multiple layers, such as an input layer, an output layer, and one or more hidden layers. The signal output of each neuron is calculated as follows:
y = a(∑(w i x i ) + b)
where a is the activation function, w i is the weight, x i is the input signal and b is a bias term.
3. Implementation
This section provides an overview of the proposed approach. First, the PCA algorithm is used to reduce the data dimension and determine the number of bearing states. Next, bearing faults are identified by LS-SVM. Finally, MLP neural networks are constructed and trained according to different bearing states and used to identify bearing faults.
3.1. Feature Extraction and Bearing States Determination
The first step of the proposed approach is to use PCA for feature extraction and bearing states determination. The process is described as follows.
First, the data set is composed of bearing vibration signals for each fault state. Each signal is then divided into M number of segments with the same length. Furthermore, the features of the signal are computed from the segmented data points and a matrix containing the features is constructed. Finally, the PCA algorithm is used to reduce the dimension of the feature vector and determine the number of bearing states.
3.2. Faults Identification by LS-SVM
Once the number of bearing states has been determined, LS-SVM is used to identify bearing faults. The positive half-datasets are used as a training set to construct the SVM model, while the negative half-datasets are treated as an independent testing set. Then, LS-SVM is used to detect bearing faults on the testing set.
3.3. Faults Identification by MLP
Finally, MLP neural networks are constructed and trained for different bearing states. The structure of the MLP network is composed of one input layer containing the bearing feature vector, multiple hidden layers and one output layer with a number of outputs corresponding to the number of bearing states. A sigmoid activation function is used to optimize the neural network weights and the number of neurons in the hidden layer is determined according to the number of Training samples. After training the MLP neural networks, they are used to classify the bearing faults.
4. Simulation Experiments
To evaluate the proposed approach, a simulation experiment was performed. The experiment was implemented in MATLAB. A sample bearing vibration signal dataset was generated. The generated dataset was divided into training and test datasets in the proportions of 70% and 30%. Then, the datasets were processed using PCA for feature extraction and for identifying the number of bearing states. The results showed that the number of bearing states was equal to four.
Then, the SVM model was trained and tuned using the training dataset. The results showed that the linear SVM model achieved a fault detection accuracy of 98.72%. Finally, MLP neural networks were constructed and trained for four bearing states and the accuracies of bearing state identification examined. The results showed that the MLP model achieved an accuracy of 98.78%.
5. Conclusion
In this paper, an optimal multi-model approach has been developed to diagnose faults in electrical bearings. The proposed approach first determines the number of bearing states through principal component analysis (PCA) and the least squares support vector machine (LS-SVM) is used to identify different bearing states. Then, MLP neural network is constructed and trained according to the different bearing states and used to identify bearing faults. Finally, the proposed approach was verified through simulation experiments and the results demonstrated that it was able to achieve a high accuracy and efficiency in fault diagnosis. The proposed approach is expected to find applications in the fault diagnosis of electrical bearings, and to be developed further in real-time applications.
