Fuzzy ARTMAP Ensemble Based Decision Making and Application

Abstract

Because the performance of single FAM is affected by the sequence of sample presentation for the offline mode of training, a fuzzy ARTMAP (FAM) ensemble approach based on the improved Bayesian belief method is supposed to improve the classification accuracy. The training samples are input into a committee of FAMs in different sequence, the output from these FAMs is combined, and the final decision is derived by the improved Bayesian belief method. The experiment results show that the proposed FAMs’ ensemble can classify the different category reliably and has a better classification performance compared with single FAM.

1. Introduction

Recently, artificial neural networks (ANNs) have been widely used as an intelligent classifier to identify the different categories based on learning pattern from empirical data modeling in complex systems [1]. For example, the BP, RBF, and SVM models have been developed quickly and utilized to classify the different fault classes of the machine equipment [2–6]. However, these traditional neural network methods have limitation on generalization, which can give rise to overfitting models for training samples. To solve the problem, the fuzzy ARTMAP (FAM) neural network is created and applied to the classification field [7–9], which is an incremental and supervised network model and designed in accordance with adaptive resonance theory. Although the FAM is able to overcome the stability-plasticity dilemma [10], in real-world application, the performance of FAM is affected by the sequence of sample presentation for the offline mode of training [11, 12].

For this drawback, some preprocessing procedures, known as the ordering algorithms such as min-max clustering and genetic algorithm [13, 14], have been proposed for FAM. Furthermore, a number of fusion techniques have been proposed for FAM to overcome this problem. Tang and Yan employed the voting algorithm of FAM to diagnose the bearings faults [15], Loo and Rao applied the multiple FAM based on the probabilistic plurality voting strategy to medical diagnosis and classification problems [16]. Since these voting algorithms do not consider the effect of the number of the sample in each class, an improved Bayesian belief method (BBM) is used to combine multiple FAM classifiers which are offline trained in different sequence of samples in this paper.

In view of the above principles, a novel ensemble FAM classifiers is proposed to improve the classification performance of single FAM. The identification schematic graph is shown in Figure 1. Firstly, through different features extraction methods, some feature parameters are extracted from the raw signals. Secondly, by the modified distance discrimination technique, the optimal feature set is selected from the original feature set. Finally, multiple FAM classifiers ensemble based on the improved BBM is employed to come up with the final classification results. The proposed method is applied to the fault diagnosis of hydraulic pump. The experiment results show the effectiveness of the proposed ensemble FAM classifiers.

Figure 1 

Flowchart of classification system.

2. Fuzzy ARTMAP Ensemble Using the Improved Bayesian Belief Method

2.1. Fuzzy ARTMAP (FAM)

FAM consists of two ART modules, namely, ART_𝑎 and ART_𝑏 modules which are bridged via a map field [10], which is capable to forming associative maps between clusters of input domain in which ART_𝑎 module functions as clustering and output domain in which the module ART_𝑏 functions as clustering. Each module comprises three layers: normalization layer 𝐹₀, input layer 𝐹₁, and recognition layer 𝐹₂. The structure of FAM is shown in Figure 2. When the output domain is a finite set of class labels, FAM can be utilized as a classifier. The algorithm of FAM can be depicted simply as follows.

Figure 2 

The basic structure of fuzzy ARTMAP.

The ART_𝑎 module receives the input pattern, and the normalization of a 𝑀-dimensional input vector 𝐚, is complement-coded to a 2𝑀-dimensional vector 𝐀𝐀=𝐚,𝐚^𝑐=𝑎₁,…,𝑎_𝑀,1−𝑎₁,…,1−𝑎_𝑀. (1) Then, the dimension of the input vector is kept constant: |𝐀|=𝐚,𝐚^𝑐=^𝑀_𝑖=1𝑎_𝑖+𝑀−^𝑀_𝑖=1𝑎_𝑖=𝑀. (2) Afterward, the input sample 𝐀 selects the category node stored in the network by the category choice function (CCF): 𝐴∧𝑤^𝑎_𝑗𝑤^𝑎_𝑗+𝛼_𝑎=𝑇_𝑗(𝐴), (3) where ∧ is a min operator, 𝛼_𝑎 is the choice function of ART_𝑎, and 𝑤^𝑎_𝑗 is the weight vector of the 𝑗th category node.

When a winning category node is selected, a vigilance test (VT), namely, a similarity check against a vigilance parameter 𝜌_𝑎 of the chosen category node, is taken place: 𝐴∧𝑤^𝑎_𝑗|𝐴|≥𝜌_𝑎, (4) where 𝑤^𝑎_𝑗 is the winning 𝑗th node. When the above category match function (CMF) is satisfied with criterion, the resonance occurs and learning takes place; namely, the weight vector 𝑤_𝑗 is updated according to the following equation:𝑤^new_𝑗=𝛽𝐴∧𝑤^old_𝑗+1−𝛽𝑤^old_𝑗, (5) where 𝛽∈[0,1] is the learning rate. Otherwise, a new node is created in 𝐹^𝑎₂ which codes the input pattern. In the meantime, for the ART_𝑏 the same learning algorithm occurs simultaneously using the target pattern.

After the resonance occurs in the ART_𝑎 and ART_𝑏, the winning node in 𝐹^𝑎₂ will send a prediction to ART_𝑏 via the map field. The map field vigilance test is used to detect the test. If the test fails, it indicates that the winning node of ART_𝑎 predicts an incorrect target class in ART_𝑏; then a match tracking process initiates. During the match tracking, the value of 𝜌_𝑎 is increased until it is slightly higher than |𝐴∧𝑤^𝑎_𝑗||𝐴|⁻¹; then a new search for the other winning node in ART_𝑎 is carried out, and the process continues until the selected 𝐹^𝑎₂ node can make a correct prediction in ART_𝑏.

2.2. Decision Fusion Using Bayesian Belief Method

The novel Bayesian belief method is supposed in [17]. It is based on the assumption of mutual independency of classifiers and considers the error of each classifier. Assume that in pattern space 𝑍 there are 𝑀 classes and 𝐾 classifiers. A classifier 𝑒_𝑘 can be considered as a function: 𝑒_𝑘(𝑥)=𝑗,𝑘=1,2,…,𝐾,𝑗∈{1,2,…,𝑀,𝑀+1}. (6) It signifies that the sample 𝑥 is assigned to class 𝑗 by the classifier 𝑒_𝑘. And its two-dimensional confusion matrix can be represented as CM_𝑘=𝑛^𝑘₁₁𝑛^𝑘₁₂⋯𝑛^𝑘_1𝑀𝑛^𝑘_1()𝑀+1𝑛^𝑘₂₁𝑛^𝑘₂₂⋯𝑛^𝑘_2𝑀𝑛^𝑘_2()𝑀+1𝑛⋯⋯⋯⋯⋯_𝑘𝑀1𝑛^𝑘_𝑀2𝑛^𝑘_𝑀𝑀𝑛^𝑘_𝑀()𝑀+1,(𝑘=1,…,𝐾),𝑀+1isanunknownlabel (7) which is obtained by executing 𝑒_𝑘(𝑥) on the test data set after 𝑒_𝑘(𝑥) is trained. Each row 𝑖 corresponds to class 𝑐_𝑖 and each column 𝑗 corresponds to 𝑒_𝑘(𝑥)=𝑗. The matrix unit 𝑛^𝑘_𝑖𝑗 means the input samples from class 𝑐_𝑖 while are assigned to class 𝑐_𝑗 by classifier 𝑒_𝑘(𝑥). The number of samples in class 𝑐_𝑖 is 𝑛^𝑘_𝑖.=∑^𝑀+1_𝑗=1𝑛^𝑘_𝑖𝑗, where 𝑖=1,…,𝑀, and the number of samples labeled 𝑗 by 𝑒_𝑘(𝑥) is 𝑛^𝑘_.𝑗=∑^𝑀_𝑖=1𝑛^𝑘_𝑖𝑗, where 𝑗=1,…,𝑀+1. Considering the difference of the number of samples in each class, on the basis of the confusion matrix a belief measure of classification can be calculated for each classifier by the following belief function [18]:𝐵_𝑘𝑐𝑥∈^𝑖𝑒_𝑘(𝑥)𝑐=𝑃𝑥∈^𝑖𝑒_𝑘(𝑥)=𝑛=𝑗^𝑘𝑖𝑗/∑^𝑀+1_𝑗=1𝑛^𝑘_𝑖𝑗∑^𝑀_𝑖=1𝑛^𝑘_𝑖𝑗/∑^𝑀+1_𝑗=1𝑛^𝑘_𝑖𝑗,𝑖=1,2,…,𝑀,𝑗=1,2,…,𝑀+1. (8) When multiple classifiers 𝑒₁,𝑒₂,…,𝑒_𝑘 are developed, their correspondent beliefs 𝐵₁,𝐵₂,…,𝐵_𝑘 are computed based on the performance of base classifiers. Combining the belief measures of all fusion classifiers can result in the final belief measure of the multiple classifier system. In case of equal a priori class probabilities, the combination rule can be depicted as follows:𝐵(𝑖)=𝐵𝑥∈𝑐_𝑖∣𝑒₁(𝑥),𝑒₂(𝑥),…,𝑒_𝑘(𝑥),EN=𝑃𝑥∈𝑐_𝑖∣𝑒₁(𝑥),𝑒₂(𝑥),…,𝑒_𝑘(𝑥)=∏,EN_𝐾𝑘=1𝐵_𝑘𝑥∈𝑐_𝑖∣𝑒₁(𝑥),EN∑_𝑖∏^𝐾_𝑘=1𝐵_𝑘𝑥∈𝑐_𝑖∣𝑒₁(𝑥),EN,𝑖=1,2,…,𝑀+1. (9) Thus, 𝑥 is classified into a class 𝑗(𝑗=1,2,…,𝑀+1) according to the belief of making the final decision Bel(𝑗)=max^𝑀+1_𝑖=1𝐵(𝑖).

3. Case Study

In order to evaluate the effectiveness of the supposed ensemble FAM, the fault identification of hydraulic pump is taken as example. Figure 3 shows the schematic diagram of experiment rig. Four accelerometers are attached to the housing with magnetic bases and mounted at the positions P1, P2, P3, and P4. Pressure sensor is mounted at the position P5. Considering the sensitivity to the fault conditions of hydraulic pump, the vibration signal which is acquired by the accelerometer at the position P2 is utilized to identify the fault categories. And the vibration signals are acquired, respectively, under normal condition and the different fault conditions, such as inner plunger wear, inner race wear, ball wear, swashplate wear, portplate wear, and paraplungers wear.

Figure 3 

The schematic diagram of the experimental setup.

3.1. Data Preparation

The data set contains 490 samples. These data samples are divided into 245 training and 245 test samples. The detailed descriptions of three data sets are shown in Table 1. In order to identify the different fault categories, a seven-class classification problem need be solved.

Table 1 

Sample subset statistics.

3.2. Feature Extraction and Selection

3.2.1. Feature Extraction

Feature parameters are used to characterize the information relevant to the conditions of the hydraulic pump. To acquire more fault-related information, many features in different symptom domains are extracted from the measured signals.

Frequency domain is another description of a signal. In [19], some novel features which can give a much fuller picture of the frequency distribution in each band of frequencies are proposed. Supposed 𝑁 points of normalized PSD, 𝑃_𝑥𝑥, of the vibration signal, 𝑃_𝑥𝑥 are divided into 𝐿 segments, where 𝐿 is 1 in this study. The four features based on the moment estimates of power can be obtained as follows: 𝑘₁=1𝑁^′_𝑁′𝑃_𝑥𝑥(𝑛),𝑘₂=1𝑁^′−1_𝑁′𝑃_𝑥𝑥(𝑛)−𝑘₁²,𝑘₃=1𝑁^′𝑘₂^3/2_𝑁′𝑃_𝑥𝑥(𝑛)−𝑘₁³,𝑘₄=1𝑁^′𝑘²_2𝑁′𝑃_𝑥𝑥(𝑛)−𝑘₁⁴, (3.2.1) where “𝑛” is the number of total data points and 𝑁′ is the number of sample points in the lth segment.

In order to characterize the spectrum with a higher accuracy, the moment estimates of frequency weighed by power are calculated by the following formulas: 𝑘₅=1𝐾_𝑙𝑁′𝑓(𝑛)𝑃_𝑥𝑥(𝑛),𝑘₆=∑_𝑁′𝑓(𝑛)−𝑘₅²𝑃_𝑥𝑥(𝑛)𝐾_𝑙,𝑘₇=1𝐾_𝑙𝑘³_6𝑁′𝑓(𝑛)−𝑘₅³𝑃_𝑥𝑥(𝑛,𝑘₈)=1𝐾_𝑙𝑘⁴_6𝑁′𝑓(𝑛)−𝑘₅⁴𝑃_𝑥𝑥(𝑛), (11) where 𝑓(𝑛) is the corresponding frequency of 𝑃_𝑥𝑥(𝑛) and 𝐾_𝑙 is the total power in the segment. Then, the total number of features extracted for each spectrum is 1 × 8.

To depict the fault-related information about the hydraulic pumps quantitatively, the first-order continuous wavelet grey moment (WGM) [20] of vibration signal is extracted. Assuming the wavelet coefficients matrix [𝑊]_𝑀×𝑁 which can be displayed by the continuous wavelet transform (CWT) scalogram, 𝑀 and 𝑁 are the scales and the time of the scalogram, respectively, the matrix [𝑊]_𝑀×𝑁 is divided into 𝑚 parts along the scale equally, and the first-order wavelet grey moment 𝑔₁ of each part can be calculated by the following equation: 𝑔₁=1(𝑀/𝑚)×𝑁^{𝑀/𝑚𝑁}_𝑖=1𝑗𝑤¹_𝑖𝑗(𝑖−1)²+𝑗−1², (12) where 𝑤_𝑖𝑗 is the element of matrix [𝑊]_{(𝑀/𝑚)×𝑁}. In this paper, the 𝑚 is set as 8 and the wavelet function is Morlet wavelet.

In addition, due to sensitiveness of these model parameters to the shape of the vibration data, AR model parameters are utilized to characterize the information about the conditions of hydraulic pumps. The AR model is written as follows: 𝑥_𝑡=𝜙₁𝑥_𝑡−1+𝜙₂𝑥_𝑡−2+⋯+𝜙_𝑝𝑥_𝑡−𝑝, (13) where 𝑥_𝑡−1,𝑥_𝑡−2,…,𝑥_𝑡−𝑝 are the 𝑟 previous samples, 𝑥_𝑡 is the predicted sample of the signal, and 𝜙₁,𝜙₂,…,𝜙_𝑡−𝑝 is AR model parameters, which can be obtained by the least square method in [21] and expressed by the following formula: 𝜙=𝑋^𝑇𝑋⁻¹𝑋^𝑇𝑌, (14) where 𝑥𝑋=^𝑛𝑥_𝑛−1⋯𝑥₁𝑥_𝑛+1𝑥_𝑛⋯𝑥₂⋮𝑥_𝑁−1𝑥_𝑁−2⋯𝑥_𝑁−𝑛,𝑌=𝑥_𝑛+1,𝑥_𝑛+2,…,𝑥_𝑁^𝑇. (15) In this study, the parameter 𝑝 is set as 8.

Thus, 24 features constitute the original feature set.

3.2.2. Feature Selection

In order to improve the identification accuracy and reduce the computation burden, some sensitive features providing characteristic information for the classification system need to be selected, and irrelevant or redundant features must be removed. In this study, based on [22], a modified distance discriminant technique is employed to select the optimal features.

Supposing that a feature set of 𝐽 classes consists of 𝑁 samples, in the 𝑗th class there are 𝑁_𝑗 samples, where 𝑗=1,2,…,𝐽, and 𝑁=∑^𝐽_𝑗=1𝑁_𝑗. Each sample is represented by 𝑀 features, and the 𝑚th feature of the 𝑖th sample is written as 𝑓^𝑚_𝑖. Then, the feature selection process can be described as follows.

Step 1. Calculate the standard deviation and the mean of all samples in the 𝑚th feature: 𝜎²_𝑚=1𝑁^𝑁_𝑖=1𝑓^𝑚_𝑖−𝑓^𝑚2,𝑓^𝑚=1𝑁^𝑁_𝑖=1𝑓^𝑚_𝑖. (16)

Step 2. Calculate the standard deviation and the mean of the sample in the 𝑗th class in the 𝑚th feature, respectively, 𝜎_𝑚^′2𝑗=1𝑁_𝑗−1^𝑁𝑗_𝑗=1𝑓^𝑚_𝑗−𝑓^𝑚_𝑗²,𝑓^𝑚_𝑗=1𝑁_𝑗^𝑁𝑗_𝑗=1𝑓^𝑚_𝑗. (17)

Step 3. Calculate the weighted standard deviation of the class center 𝑔_𝑗 in the 𝑚th feature: 𝜎_𝑚^′′2=^𝐽_𝑗=1𝜌_𝑗𝑔^𝑚_𝑗−𝑔^𝑚2=𝜇₁−𝜇²₂, (18) where 𝜇₁=∑^𝐽_𝑗=1𝜌_𝑗(𝑔^𝑚_𝑗)², 𝜇₂=∑^𝐽_𝑗=1𝜌_𝑗𝑔^𝑚_𝑗, 𝑔^𝑚=∑^𝐽_𝑗=1𝜌_𝑗𝑔^𝑚_𝑗, and 𝑔^𝑚 are the centers of all samples in the 𝑚th feature; 𝑔^𝑚_𝑗 is the center of the samples of the 𝑗th class in the 𝑚th feature; 𝜇₁, 𝜇₂ are the weighted means of the squared class center 𝑔²_𝑗 and the class center 𝑔_𝑗 in the 𝑚th feature; 𝜌_𝑗 is the prior probability of the 𝑗th class, respectively; and ∑^𝐽_𝑗=1𝜌_𝑗=1.

Step 4. Calculate the distance discriminant factor of the 𝑚th feature: 𝑑^𝑚_𝑏−𝛽𝑑^𝑚_𝑤=1𝜎²_𝑚𝜎_𝑚^′′2−𝛽^𝐽_𝑗=1𝜌_𝑗𝜎_𝑚^′2𝑗, (19) where 𝑑^𝑚_𝑏 is the distance of the 𝑚th feature between different classes, 𝑑^𝑚_𝑤 corresponds to the distance of the 𝑚th feature within classes, and 𝛽 is used to control the impact of 𝑑^𝑚_𝑤, which is set as 2 in this paper.
Considering the overlapping degree among different classes, a compensation factor is calculated as follows.
Firstly, define and calculate the variance factor of 𝑑^𝑚_𝑤 in the 𝑚th feature as follows: 𝑣^𝑚_𝑤=max𝑑^𝑚_𝑤min𝑑^𝑚_𝑤. (20)
Secondly, define and calculate the variance factor of 𝑑^𝑚_𝑏 in the 𝑚th feature as follows: 𝑢^𝑚_𝑏=max𝑓^𝑚_𝑖−𝑓^𝑚_𝑗min𝑓^𝑚_𝑖−𝑓^𝑚_𝑗,𝑓^𝑚_𝑖−𝑓^𝑚_𝑗=𝑓^𝑚_𝑖−𝑓^𝑚_𝑗𝜎²_𝑚,𝑖,𝑗=1,2,…,𝐽,𝑖≠𝑗. (21)
Then, the compensation factor of the 𝑚th feature can be defined and calculated as follows: 𝜂_𝑚=1𝑣^𝑚_𝑤+1𝑢^𝑚_𝑏. (22)
Thus, the modified distance discriminant factor can be calculated as follows: 𝑑^𝑚_𝑏−𝛽^′𝑑^𝑚_𝑤=𝑑^𝑚_𝑏−𝛽𝜂_𝑚𝑑^𝑚_𝑤=1𝜎²_𝑚𝜎_𝑚^′′2−𝛽^𝐽_𝑗=11𝑣^𝑤_𝑗+1𝑢^𝑏_𝑗𝜌_𝑗𝜎_𝑚^′2𝑗,(𝑚=1,2,…,𝑀). (23)

Step 5. Rank 𝑀 features in descending order according to the modified distance discriminant factors (1/𝜎²_𝑚)[𝜎_𝑚^′′2−𝛽((1/𝑣^𝑤_𝑗)+(1/𝑢^𝑏_𝑗))∑^𝐽_𝑗=1𝜌_𝑗𝜎_𝑚^′2(𝑗)]=𝜆_𝑚; then normaliz 𝜆_𝑚 by 𝜆_𝑚=(𝜆_𝑚−min(𝜆_𝑚))/(max(𝜆_𝑚)−min(𝜆_𝑚)) and get the distance discriminant criteria. Clearly, bigger 𝜆_𝑚(𝑚=1,2,…,𝑀) signifies that the correspondent feature is better to separate 𝐽 classes.

Step 6. Set a threshold value 𝛾 and select the sensitive features whose distance discriminant factor 𝜆_𝑚≥𝛾 from the set of 𝑀 features.

3.3. Diagnosis Analysis

It is well known that the data-ordering of training samples can affect the classification accuracy of single FAM, and that a single output used to represent multiple classes may lead to lower classification accuracy. In order to know how well the proposed FAMs’ ensemble work, that is, how significant the generalization ability is improved by utilizing the improved Bayesian belief method to combine the classification results from a committee of single FAM trained with different data-ordering of training samples, the performance of single FAM is also conducted.

In the diagnosis phase performed by the single FAM and FAM ensemble, they are all trained in the fast learning and conservative mode (i.e., setting 𝛽=1 in (5) and 𝛼_𝑎=0.001 in (3)). Besides, in order to ensure the performance of stability-plasticity, the vigilance parameter of FAM is set as 𝜌_𝑎=0.5, and the ensemble size is set as 5.

In order to improve the classification accuracy and reduce the computation time, in each case some salient features are selected from each feature set by the modified distance discriminant technique, respectively, and then input into the five single FAM in different sequence in the process of training. Figure 4 shows the modified distance discriminant factor 𝜆_𝑚 of all features in the feature sets. From the figure it can be seen that the threshold 𝛾 corresponding to the optimal features are different for the case. That is to say, the number of salient features is different.

Figure 4 

Feature selection for three different data sets.

Figure 5 summarizes the classification results in terms of test accuracy of single FAM and FAMs’ ensemble. From the figure, it can be seen that the FAMs’ ensemble (0.988) outperforms the single FAMs’ in terms of accuracy. And the test accuracy is getting higher when the number of single FAM increases. These indicate that FAMs’ ensemble can identify the different fault categories of hydraulic pump well.

Figure 5 

Relationship between the test accuracy and the number of single FAM used in FAMs’ ensemble.

3.3.1. Effect of Different Threshold for Feature Selection

As shown in Figure 4, when the threshold value 𝛾 is set properly, some redundant and irrelevant features can be removed from the original feature set. To test the effect of the proposed feature selection method based on the modified distance discriminant technique, a series of experiments is carried out against the threshold value 𝛾, in which the parameter of the single FAM is the same as the above, and the size of ensemble FAM is set as 5.

Figure 6 lists the classification accuracy of five individual FAMs’ and FAM ensemble against the different thresholds. From the figure, it can be noticed that when 𝛾=0 (original feature set), the test accuracy of single FAM and FAM ensemble is 0.824 and 0.845, respectively. The highest test accuracy of single FAM and FAMs’ ensemble (0.915 and 0.988) is arrived synchronously when 𝛾=0.8, where the optimal feature set is selected. However, when the threshold value continues to increase, the test accuracy of single FAM and FAMs’ ensemble tends to decrease. And when threshold 𝛾>0.9, the test accuracy of single FAM and FAMs’ ensemble is lower than that used in all features with threshold 𝛾=0. This is mainly because the smaller number of features leads to the overfitting; namely, the drastic reduction of features can lead to a decrease in the test accuracy.

Figure 6 

Classification accuracy comparison for different threshold.

3.3.2. Classification Performance Comparison with Other Classification Methods

In order to test the superiority of the proposed FAMs’ ensemble method, the test results produced by FAMs’ ensemble and single FAM are compared with those produced by other classification methods. In this experiment, the parameters of FAM ensemble and single FAM are the same as the above.

Table 2 shows the test results of the FAMs’ ensemble versus other classification methods. From the table it can be seen that the average test accuracy using single FAMs’ is the lowest. However, the test accuracy produced by two FAMs’ ensemble methods is higher than that produced by the single classifier, and the test success rate of the proposed FAMs’ ensemble is highest and higher than that of FAM ensemble with voting algorithm. These indicate that the proposed FAMs’ ensemble has comparatively superior diagnosis performance.

Table 2 

Test accuracy produced by different classification methods.

4. Conclusions

The classification performance of FAM is affected by the sequence of training samples. A novel and reliable FAMs’ ensemble based on the improved Bayesian belief method is described and proposed to improve the classification performance of FAM in this paper, which combines the output from a committee of FAM fed with different orderings of training samples and derives the combined decision.

And the supposed FAMs’ ensemble method is applied to the fault identification of hydraulic pump. The experiment results testify that the proposed FAM ensemble can diagnose the fault categories accurately and reliably and has better diagnosis performance compared with single FAM. These indicate that the proposed FAMs’ ensemble has a good promise in the engineering of classification and decision making.

Acknowledgments

This work is supported by the National Scientific and Technological Achievement Transformation Project of China (Grant no. 201255), Electronic Information Industry Development Fund of China (Grant no. 2012407), the National Natural Science Foundation of China (Grant no. 61374172), and the Fundamental Research Funds for the Central Universities, Hunan University, China.