Motor fault diagnosis has gained much attention from academic research and industry to guarantee motor reliability. Generally, there exist two major approaches in the feature engineering for motor fault diagnosis: (1) traditional feature learning, which heavily depends on manual feature extraction, is often unable to discover the important underlying representations of faulty motors; (2) stateoftheart deep learning techniques, which have somewhat improved diagnostic performance, while the intrinsic characteristics of black box and the lack of domain expertise have limited the further improvement. To cover those shortcomings, in this paper, two manual feature learning approaches are embedded into a deep learning algorithm, and thus, a novel fault diagnosis framework is proposed for threephase induction motors with a hybrid feature learning method, which combines empirical statistical parameters, recurrence quantification analysis (RQA) and long shortterm memory (LSTM) neural network. In addition, weighted batch normalization (BN), a modification of BN, is designed to evaluate the contributions of the three feature learning approaches. The proposed method was experimentally demonstrated by carrying out the tests of 8 induction motors with 8 different faulty types. Results show that compared with other popular intelligent diagnosis methods, the proposed method achieves the highest diagnostic accuracy in both the original dataset and the noised dataset. It also verifies that RQA can play a bigger role in realworld applications for its excellent performance in dealing with the noised signals.
An induction motor is one of the most critical components in industrial processes due to its high reliability, low cost, and robust performance. It has been widely used as the key machine dynamical equipment to generate electromagnetic torque. However, the mechanical degradation with natural aging process, coupled with the fact that motors are often exposed to multifarious harsh environments, makes motors vulnerable to various sorts of faults [
Recently, owing to the significant development of the computing ability [
However, the abovementioned methods still have some shortcomings. The performances of the traditional methods [
To tackle those issues, a deep learning framework is integrated with manual feature learning techniques to preserve the advantages of both sides. RQA is seamlessly embedded into the stacked LSTM architecture. RQA’s antinoise capability is verified by a weighted BN layer. The major contributions of this paper are summarized as follows:
Propose a new hybrid feature learning approach that combines statistical parameters, RQA and LSTM neural network, for motor fault detection. Neither RQA nor LSTM has been applied on motors before.
A modification of BN named weighted BN is designed to assign dynamic weights to the hybrid feature set and then perform batch normalization. It shares BN’s advantages and possesses the capability to evaluate the contributions of the three various feature learning approaches [
Two datasets, respectively, the original dataset and the noised dataset, are acquired from tests to verify the proposal’s adaptability and robustness to different levels of noise.
The remainder of this paper is organized as follows. In Section
In order to experimentally verify the performance of this proposed approach, tests of 8 threephase induction motors with different fault types under a uniform operation condition were carried out in a drivetrain diagnostics simulator platform. As shown in Figure
The test platform and data acquisition devices. (a) Test rig: drivetrain diagnostic simulator (DDS). (b) Data acquisition card NI9234. (c) Acceleration sensor BWBJ14530.
Specifically, the tests were under the operating condition of 33.90 N m (25 lbf. ft.) load. The motor frequency was set to 15 Hz, and thus, the rotation rate was 900 r/min. Under this uniform operating condition, 8 motors with different fault types (1 healthy and 7 faulty) were used to generate the required dataset. Data from the healthy motor are used as a benchmark for comparison with the experimental data from other faulty motors. The faulty types are as follows: (1) builtin broken rotor bars (BB), (2) builtin bowed rotor (BR), (3) rotor misalignment (RM), (4) stator winding faults (SW), (5) voltage unbalance and single phasing (VP), (6) builtin rotor unbalance (RU), and (7) faulted bearings (FB). The faulty types and the corresponding causes are listed in Table
Motors with 8 fault types in tests.
Fault condition  Abbreviations  Class  Description 

Normal  NO  1  Healthy state 
Broken rotor bars  BB  2  Fitted with an already broken rotor bar 
Bowed rotor  BR  3  Consists of a centrally intentionally bent rotor 
Rotor misalignment  RM  4  Caused by custommachined end bells with asymmetric structure 
Stator winding faults  SW  5  Copper wires around the stator with shorted stator winding turns 
Voltage unbalance and single phasing  VP  6  Controlled by the control console to disrupt voltage balance and to disconnect one phase 
Rotor unbalance  RU  7  Intentionally removing one of the balanced rotors from induction motor and destroying the inner balance 
Faulted bearings  FB  8  Composed of one inner race faulted bearing and one outer race faulted bearing 
The acceleration sensor was used in the experiment and installed at the shell of motors to measure the vibration signals in radial direction. The acceleration signals were collected by the data acquisition card, and the sampling frequency was set to 10.24 kHz. Each test lasted approximately 120 s, and thus, the number of raw data points acquired from one motor is approximately 1228800. Figure
The waveforms of the measured acceleration signals of 8 motors.
From the 120 s acceleration signals, the middle 100 s stable signals are selected as the training and test data. A sliding window is used to obtain the samples of the same length. Suppose the length of window as
In this paper, the step size and window length are both set to 1024. It means that every 0.1second signal which contains 1024 data points (10.24 kHz) represents a sample. Thus, there are 1000 samples of each fault type, and those samples form the original dataset named dataset 1.
As the motor frequency is 15 Hz, one sample consists of 1.5 cycle of motor periodic rotation signals. Therefore, the difference between samples is more distinct, compared with the samples containing integral cycles of signals in previous works [
For the sake of investigating the antinoise capability of the proposed algorithm and verifying its effectiveness in realworld fault diagnosis applications, Gaussian noise with a signaltonoise ratio of 5 dB is artificially embedded into the dataset 1. This noising method is based on the assumption that the acceleration signals of motors in real world contain a higherlevel Gaussian noise [
To obtain a precise diagnostic accuracy, a fivefold crossvalidation method is adopted to split the training and test data. The dataset is segmented into 5 subsets, and the holdout method is repeated 5 times. Each time, one of the subsets is used as the test set and the rest as the training set.
This section describes the specific procedures of the proposed fault diagnosis method, illustrates the basic principles of the RQA, LSTM, and weighted BN, and presents the details of the whole neural network architecture. The flow diagram of the proposal is shown in Figure
Manual feature learning: draw the recurrence plots (RPs) of every sample and extract 10 RQA features from RPs; extract 29 empirical statistical features from time domain and frequency domain.
Deep learning feature learning: construct threelayer stacked LSTM of 0.25 dropout with hidden layer sizes of 256, 128, and 64.
Form the hybrid feature set with aforementioned features and put it into the weighted BN block which consists of a weight assignment layer and a BN layer.
Put the outputs of the previous step into a threelayer fully connected neural network with layer sizes of 64, 32, and 8, and the output is the diagnostic result.
The flow diagram of the proposed method.
RQA is a kind of nonlinear analysis for the dynamical system based on the view of a phase space concept, aiming at quantifying the recurrence plots (RPs) [
8 RPs of 8 faulty motors. (a) NO. (b) BB. (c) BR. (d) RM. (e) SW. (f) VP. (g) RU. (h) FB.
In RQA, three major parameters, respectively, embedding dimension
It is highly impracticable to directly use RPs to classify faulty types for their low resolution. Thus, RQA appears as a good tool to quantify RPs with recurrence statistics. The core of RQA is to identify and quantify the transient recurrent patterns which characterize the dynamic change behaviors. In this paper, 10 recurrence parameters named
The recurrence rate (RR) is the simplest parameter of crosscorrelation sum. It is defined as
Determinism (DET) is a criterion of the predictability of a system. It is given by
Shannon entropy (LENTR) denotes the complexity of a system. It is calculated as
Laminarity (LAM) corresponds with the number of laminar phases of a system. It is defined as
Trapping time (TT) represents the average vertical line length. It is given by
TT estimates the average time in which a state of RPs is trapped.
Average diagonal length (ADL) is the average diagonal line length. It is the mean length of diagonal parallel lines. Similarity, longest diagonal length (LDL) is the longest diagonal parallel line length, longest vertical length (LVL) is the longest vertical line length, and average vertical length (AVL) is the average vertical line length. Besides these 9 parameters from the distribution of RPs, recurrence time is chosen as the 10th parameter, which evaluates the complexity of RPs though the calculation time.
Recurrent neural network (RNN) is one of the deepest neural networks, which can address the data series with arbitrary length and has been applied successfully in many endtoend tasks [
At time step
The schematic diagram of LSTM architecture.
In order to establish a better LSTM architecture with higher diagnostic accuracy, several parameters, such as layer number, time steps, and learning rate, need to be determined. The quantification of these parameters is mainly based on a comparative evaluation of the performances of various optional values in dataset 1. The accuracy and cost time at different layer numbers are shown in Figure
Accuracy and cost time at different layer numbers. The accuracy curve has a distinct rise at the first 3 layers and then tends to be stable, while the cost time always increases as the layers get deeper.
During the construction of the stacked LSTM, the backpropagation is used for the update of weights, of which the learning rate is the main parameter. Different learning rates and corresponding results of 10 times of repeat tests are visualized in the boxplot in Figure
Diagnostic accuracy at different optional values. (a) Learning rate. (b) Time steps.
The hidden layer size of each stacked layer is empirically, respectively, 256, 128, and 64 in a descending order, and thus, the output size of each layer is 4 × 256, 4 × 128, and 4 × 64.
The maxpooling function is used to eliminate the dimensionality curse and retain the most useful information of a region by returning the maximum value. In this method, a maxpooling layer is added after the stacked LSTM layers to convert the 4 × 64 output to a flatten 64dimensional vector. To prevent model form overfitting, dropout based on early stopping mechanism is adopted in the training process [
Twentynine statistical features, including 16 timedomain features and 13 frequencydomain features, are extracted [
Statistical features.
Domain  Features  Expression 

Time  TF_{1} 

TF_{2} 


TF_{3} 
 
TF_{4} 


TF_{5} 


TF_{6} 


TF_{7} 
 
TF_{8} 
 
TF_{9} 
 
TF_{10} 
 
TF_{11} 
 
TF_{12} 
 
TF_{13} 
 
TF_{14} 
 
TF_{15} 
 
TF_{16} 
 


Frequency  FF_{1} 

FF_{2} 
 
FF_{3} 
 
FF_{4} 
 
FF_{5} 


FF_{6} 
 
FF_{7} 
 
FF_{8} 
 
FF_{9} 
 
FF_{10} 
 
FF_{11} 
 
FF_{12} 
 
FF_{13} 

BN is a popular type of normalization method which can transform the distribution of any neuron’s input during a batch of iterations to Gaussian distribution in deep NNs [
The weighting layer can be regarded as a customized neural network layer before BN layer and optimized during the whole training process. The role of the weighting layer is to assign dynamic weights to the hybrid features. For the RQA feature set
Three fully connected layers with the size of {64, 32, 8} is added. In these layers, the neurons at different layers are all connected to each other; activation functions of ReLU are used at the first two layers, and SoftMax is used at the last layer.
The whole architecture is constructed through minimizing the following crossentropy loss function between the predicted values and real labels [
The batch gradient descent and backpropagation algorithm are used for optimization and to minimize the cost function
In addition, the programs are performed on a GeForce GTX TITAN X graphics card and a E52630 processor with 126 GB memory, using TensorFlow as backend.
In this section, the performance of the proposed method is illustrated and discussed. Several other methods are tested and contrasted.
Figure
The training process of dataset 1 and dataset 2. A significant convergence trend occurs in both datasets with bigger fluctuations in dataset 2.
Visualization of the outputs of every step of 8 different samples.
Figure
Confusion matrix of the classification results of two datasets. (a) Dataset 1. (b) Dataset 2.
Figure
The proportions of RQA features.
In order to illustrate how the proposed method executes the classification task stepbystep, the different layers’ outputs are visualized with 3dimensional sketches using a nonlinear dimension reduction method, tdistributed stochastic neighbour embedding (tSNE) [
3D representations of highdimensional outputs at different layers with dataset 1 by tSNE.
To verify the superiority of the proposed method, several stateoftheart intelligent fault diagnosis methods are employed for comparison:
RQA + SVM [
LSTM: independent use of the proposed LSTM architecture on raw data
MLP [
CNN [
SIFT + CNN [
CDFL [
In (1) and (2), the separate use of RQA and LSTM aims at proving its indispensability in the hybrid method. In (1), 10 RQA features mentioned in Section
3D representations of highdimensional outputs at different layers with dataset 2 by tSNE.
The kernel length of the convolutional layers is set to 64, and the maxpooling function is utilized in the pooling layers. In (5), 1D data are converted to a 2D timefrequency maps through shorttime Fourier transform. Then, the maps are compressed into 100
The performances of all methods.
Several conclusions can be drawn from Figure
In this paper, a novel fault diagnosis framework with high accuracy for threephase induction motors is presented. A hybrid feature learning approach that combines empirical statistical parameters, RQA and LSTM, is proposed to integrate the stateoftheart deep learning techniques with the manual feature learning approaches to gain a superior and robust performance. In addition, a modification of BN named weighted BN is designed to evaluate the contributions of each feature learning approach and facilitate validating the noise resistance performance.
The tests of 8 motors (1 healthy and 7 faulty) are carried out to form datasets 1 and 2. It verifies that the proposed method, with the highest accuracies of 99.3% and 98.9% in fault recognition, performs better than other methods and possesses good noise resistance. More specifically, it yields 18.5% and 8.1% average performance improvements compared with RQA + SVM and MLP; it yields 3.6%, 4.7%, 9.2%, and 2.1% average performance improvements compared with the four deep learning methods, LSTM, CNN, SIFT + CNN, and CDFL. The weight distribution of the weighted BN illustrates RQA is more effective in dealing with the realworld noised data.
In future research, our effort will be devoted to two aspects. (1) Make the proposed method reliable for practical use, which demands a large amount of accumulated industry data. (2) Make attempts to figure out the connections between the intermediate representations of deep learning networks and traditional manual features.
The .tdms data used to support the findings of this study are available from the corresponding author upon request.
The authors declare that they have no conflicts of interest.
This project was supported by the National Key Technology R&D Program of China (No. 2017YFB1302004) and National Nature Science Foundation of China project (No. 51305258).