Fault Signal Classification using Adaptive Boosting Algorithm

In recent years, researchers seldom investigate how to boost the classification performance of any learning algorithm for fault signal detection. We propose a fault signal classification method based on adaptive boosting (adaboost) in this paper. Adaboost is able to select an optimal linear combination of classifiers to form an ensemble whose joint decision rule has relatively high accuracy on the training set. First, we extract statistical features from sample signals. And then we make use of a decision tree to identify optimal features, which are used to classify the sample set by adaboost algorithm. To verify its accuracy, we set up the roller bearing experiment. Practical results show that the method can precisely identify fault signals, and be comparable to SVM based traditional method. DOI: http://dx.doi.org/10.5755/j01.eee.18.8.2635


I. INTRODUCTION
Roller bearing is one of the most widely used in rotating machinery.Condition monitoring of such an element is greatly advantageous for economical and security value, and can be regarded as a pattern recognition problem [1].A basic framework of a roller bearing is composed of rolling elements, inner and outer races, and a cage.The main failure mode of rolling bearings is localized defects, which is dislodging of a sizable piece of contact surface during operation as a result of fatigue cracking under cyclic contact stressing in the bearing metal [2]- [11].
According to the traditional signal processing methods, we might calculate several symptom values under each condition, such as the wavelet energy coefficients [10], the Fourier coefficients [11], the statistical measurements [8], and the frequencies obtained from envelop analysis.However, these symptoms cannot be automatically recognized by computers.Researchers began to be interested in investigating a machine learning method for monitoring the bearing conditions.Jayanta [7] and Samantha [8] use Artificial Neural Network (ANN) to recognize fault types.Some researchers use SVM [5], [6], [9] and Petri Nets [4] as the classifier because of the high accuracy and good generalization capability.
Although several fault diagnosis systems have been proposed, the development of systems is still very limited.Moreover, identification accuracy of existent methods needs to improve.
In this letter, we propose a fault signal classification method based on adaptive boosting (Adaboost).Boosting is a general methodology for improving the performance of any given learning algorithms, and adaboost is a representative one of boosting algorithms, which is firstly introduced by Freund and Schapire [3], and which is a machine learning meta-algorithm for performing supervised learning.

II. ROLLER BEARING FAULT DIAGNOSIS
The block diagram of proposed fault signal diagnosis system is shown in Fig. 1.There are three main phases: feature extraction, feature selection (dimensionality reduction) and classification.In our experiment, we set up a monitoring system of roller bearing where a dataset from a vibration signal was used.The dataset included about 4 conditions including normal condition, inner race defect, ball defect, and outer race defect.And then, we divided signal length on each condition into 25 pieces (samples).The set of database consists of 100 samples in total.Each feature vector was built by computing the 12 statistical features for each sample.We used a decision tree to select important features for classification, and the selection results composed the input of the classifier.Finally, we use an adaboost algorithm for classification.

III. FEATURE EXTRACTION
The vibration signal of the machine is a typical nonstationary random signal.The statistical features can be considered as the descriptors, which can reflect the change tendency of non-stationary random signal.Several statistical parameters are adopted such as mean, standard error, median, standard deviation, variance, kurtosis, skewness, range, minimum, maximum, and sum [8].In our research, we added the steepest gradient, which denotes the maximal change rate in neighborhood.The gradient (or gradient vector field) of a scalar function 12 ( , , ) x is defined as the vector field whose components are the partial derivatives of f .That is 12 ( / , / , , / ).
Table I shows the whole mathematical expressions of the statistical parameters.

Statistical parameter Mathematical expression
Mean ( ) The goal of feature selection is to find such a lower dimensional subset that holds most of the information (suitable for classification or regression).In order to improve the efficiency of adaboost classification, we selected the optimal features from the candidate features in advance by an implementation of J48 decision tree.
The construction criterion of decision tree for feature selection is as follows: The extracted features are the input of the feature selection algorithm, and the output is a generated decision tree; Each node represents a subset of classes, which will be partitioned successively in the child nodes; Each leaf node is associated with a class label; The branch of the tree denotes a threshold, which originates from the attribute; In the decision tree, the optimal features are selected by an importance criterion of each node.The importance criterion is based on the theories of entropy reduction and information gain.More details of entropy reduction and information gain are introduced below.
For a sample set S , the information gain of an attribute A is defined as follows: The first term denotes the entropy of original sample set S; entropy reflects the homogeneity of the set and is defined as follows: where c is the number of classes, i P is the distribution on the proportion of S belonging to class label i .The next term is the expected value of the entropy using attribute A .
() Value A is the set of all possible values for attribute A , and v S is the subset of S for which attribute A has value . || v is defined as the number of sample set.

V. CLASSIFICATION BOOSTING
The adaboost algorithm achieves strong classifier by combining many weak learners where t  denotes the weight coefficient, and in our study the weak learner is defined as a decision stump.The detailed implementation of adaboost is as follows: First, the weights are initialized

VI. EXPERIMENTAL RESULTS AND DISCUSSION
In our experiment, we use the 1200ATN self-aligning ball bearing as experimental subject, equipped in test rig of ZHX-3A rotor.The parameters of roller bearing are shown in Table II.The vibration signals from YDI-12 sensor are acquired by NI PXI4472 DAQ (data acquisition), which is equipped in PXI-1042Q industrial computer.The sampling frequency is 10 kHz.The sampling length is 8192 for the speed of 900RPM in all conditions.Fig. 2 shows the vibration signals from roller bearing in 4 conditions including normal condition, inner race defect, ball defect, and outer race defect.In this study, we utilize 12 statistical features for each sample, which are reduced to 5 features by J48 decision tree, as shown in Fig. 3. Successively, we implemented adaboost for classification.The iteration number of adaboost algorithm is empirically set 20.The test details are given by comparing classification of one versus one: 1. Normal condition vs inner race defect; 2. Normal condition vs ball defect; 3. Normal condition vs outer race defect; 4. Inner race defect vs ball defect; 5. Inner race defect vs outer race defect; 6. Ball defect vs outer race defect.We summarized the experimental results as follows.
We integrated twelve statistical features, including mean, standard error, median, standard deviation, variance, kurtosis, skewness, range, minimum, maximum, sum and an introduced feature-steepest gradient.
Decision tree reduces the dimensionality of statistical features, and selects optimal features for the next classification.In the experiment, we found that the decision tree selected five features, including standard variance, mean, min, median, and the steepest gradient due to their significant contributions.Fig. 3 gives the visualized result.
Referring to Table III and Table IV, different speeds (600RPM, 900RPM) for the same test identities are experimented.The reason of using two different speeds is that magnitude of vibration changes is proportional to shaft speed and hence the statistical features changes with speed.We engaged the adaboost algorithm for classification, and the classification accuracy under different speeds is given in Table III and Table IV.And meanwhile, SVM based fault signal classification 5 is taken for comparison in order to prove the superiority of our algorithm.Here the kernel function of SVM is radial basis function.
The result indicates that the accuracy of the proposed method is superior to that of SVM based fault signal classification.

VII. CONCLUSIONS
Fault diagnosis of roller bearing is a challenging issue in the field of condition monitoring of rotary machines.The theory and experiment in this paper have demonstrated the ability to make an efficient fault diagnosis for machine system.

Fig. 1 .
Fig. 1.The block diagram of the proposed method.

Fig. 2 .
Fig. 2. The time-domain signals at the speed of 900 PRM taken from roller bearings in 4 conditions, including the normal condition, the inner race defect, the outer race defect, and the ball defect.

TABLE 1 .
MATHEMATICAL EXPRESSION OF STATISTICAL PARAMETERS.

TABLE II .
PARAMETERS OF THE ROLLER BEARING.