(1. School of Mechanical Engineering, Hebei University of Technology, Tianjin 300130, China; 2. Tianjin Navigation Instruments Research Institute, Tianjin 300131, China; 3. School of Control Science and Engineering, Hebei University of Technology, Tianjin 300130, China)

(1. School of Mechanical Engineering, Hebei University of Technology, Tianjin 300130, China; 2. Tianjin Navigation Instruments Research Institute, Tianjin 300131, China; 3. School of Control Science and Engineering, Hebei University of Technology, Tianjin 300130, China)

To meet the reliability requirement of electro mechanical gyroscopes, a new method for accurately detecting and diagnosing the faults of gyro motors is presented, which is a pattern recognition method based on hidden markov model (HMM) and uses time domain features extracted from the bus current signals as health indicators. By using a sequential backward selection (SBS) method, the best features are selected to build the representation space and train the parameters of HMM. Then the HMMs are used as classifier for failure detection and diagnosis. The proposed method has been tested on a brushless DC gyro motor to detect bearing faults and stator faults at different temperature levels. The experimental results show that the accuracy of the proposed method is 96.8% for failure detection and diagnosis of gyro motors.

failure detection; failure diagnosis; hidden Markov models; gyro motor

Gyro motors, as a class of important inertial sensors, are widely used in all kinds of electro mechanical gyroscopes. Failure detection and diagnosis of gyro motors have been a focus for all gyro-motor researchers, because the malfunction can lead to a catastrophic failure of gyroscope if undetected. Although gyro motors have been extensively used for a century, their failure detection and diagnosis are a relatively new research area. The aim of such work is to accurately diagnose the health condition of gyro motors, and improve the reliability of gyroscopes.

In previous work, some research has been carried out for failure detection and diagnosis, which was based on Motor Current Signature Analysis (MCSA)[1-2]. The techniques can be classified into time domain, frequency domain and time-frequency domain. However, the electrical signals of gyro motors are very noisy, and it is necessary to use a new type of method to reduce the effect of noise measurements. One of the popular choices is pattern recognition method, combining MCSA and feature signatures extraction. The proposed approach is that the Hidden Markov Model is used as a new type of classification technique to detect and diagnose the abnormal condition.

The Hidden Markov Model is a powerful statistical modeling tool, which is widely used for speech recognition[3], bearing and gear faults prognosis[4-5]and diagnosis of induction motor fault[6-8]. In this paper, we present a feature extraction method based on time domain representation, and the features extracted from transformations are used to train HMMs, which stand for various fault conditions, such as bearing faults, stator faults and so on. Then the HMMs are used to detect and diagnose the faults of brushless DC gyro motor.

1 Failure diagnosis architecture

Fig.1 HMM-based failure diagnosis approach

Fault detection and diagnosis, based on Hidden Markov Model, includes two stages: signal processing and classification. The first stage includes feature extraction and feature selection, and it is necessary to build the representation space using the set of features, but not all of them are sensitive to faults, so some appropriate features should be selected by the feature selection method. In the second stage, Hidden Markov Models are used, and the kinds of fault states will be divided into the M different classes (M-classes) by clustering techniques. In the d-dimensional space, every class can be represented by a geometric area, and all are used to design HMMs. A feature vector, xi=(x1, x2,…,xd)，is characterized by a d-dimensional vector, and the aim is to decide if the measurexishould be assigned to one of the M-classes (HMM1, HMM2,…or HMMm). The HMM, for which the probability to come into being the measure is maximum, determines the type of faults. The process is shown in Fig.1.

2 Feature extraction and selection

The Motor Current Signature Analysis (MCSA) is one of the popular machine diagnosis techniques, and it has been successfully applied for the fault detection and diagnosis of major machines[9]. So the time domain features can be used as diagnosis indicators for gyro motors, and it can give information on bearing faults and stator faults. One can distinguish the following:

An experimental value: xi

The mean value of current：

The standard deviation of current:

Crest factor：

Kurtosis：

Skewness：

The average power of current:

In order to build the multidimensional feature space, effective features should been extracted, but it is possible that the extracting features are irrelevant and redundant, which affects the quality of diagnosis. In the paper [10], the Sequential Backward Selection (SBS) method was presented, and the principles of the feature selection were conducive to: - better classification results; - removing irrelevant, noisy and misleading features; - reducing complex computation; - better understanding the essential process characteristics.

3 Hidden Markov Model

A Hidden Markov Model, as a kind of statistical model, is used to characterize a modeling system for the future state estimation. Each HMM is defined by states, which include a set of feature vectors. To estimate the HMM parameters, the features are converted into observation sequences and grouped into classes. With the Markov Process, an addition has been finished, and the observations are probabilistic functions of the states rather than the states themselves. The Markov Process is shown in Fig.2.

Fig.2 Generalized architecture of an HMM[6]

3.1 Elements of HMM

HMM is characterized by five elements:

M: The number of observation symbols per state from v1to vM.

The qtdenotes the current state, the aijis the probability of being in state Sjat time t+ 1, provided that it is in state Siat time t.

The otdenotes the observation at time t.

The evaluation, decoding and learning are three basic problems which have been solved by the HMM, and the evaluation and learning can be used to solve the classification problem.

3.2 Evaluation

The αt(i ) denotes the probability of the observation sequence O= (o1,o2,…, oT) and state Siat time t. Initialization:

Recursion:

Termination:

In this way, we can calculate P(O |λ).

In the backward algorithms, the variable βt(i ) is defined as:

Where, βT(i ) =1.

Initialization:

Recursion:

Termination:

In this way, we can also calculate P(O |λ).

3.3 Training

The Baum-Welch method is used to solve the learning problem for finding the best HMM parameters. The ξt(i,j )denotes the probability of obtaining the model in state Siat time t and the state Sjat time t+ 1, given a training observation sequence and the model λ. The ξt(i,j )is defined as:

This probability can also be expressed as:

The γt(i ) is defined as:

The current model is defined as λ= (A,B,π) and the re-estimated model is defined as= (,,). By using ξt(i,j )and γt(i ), we can obtain the re-estimated formulas as:

3.4 Diagnosis

To identify the gyro motor faults, firstly we need train HMM parameters by the above method, and the process is shown in Fig.3. Once the models are trained, the sequence λ is gained, and a gyro motor fault can be diagnosed by the steps shown in Fig.4.

Fig.3 HMM training

Fig.4 Approach of HMM-based diagnosis

4 Experimental results

To acquire the current signals, a brushless DC gyro motor (24 V, 6000rpm, 1.5 W) is selected as a specimen. The acquisition of current signals is the bus current signals, which are the easiest acquired signals. The number of samples per signal is 3000, and the sampling rate is 20 Hz. A gyro motor usually operates at the same speed to gain a constant moment of momentum, and the work temperature will affect the motor state. So the data acquisition consists of 3 levels of temperature: -40℃, 20 ℃, and 50 ℃.

The gyro motor is artificially introduced three kinds of condition: healthy, bearing faults and stator faults. Every condition is sampled 10 examples at the same temperature, and 90 acquisitions have been made. Among the 90 examples, the 27 acquisitions are used to select the best feature, and the remaining 63 acquisitions are used to verify the method efficiency. The training and test samples are defined in Tab.1.

Tab.1 Composition of the training and test samples

The Fig.5 shows the best three features space (Fo= [δt,,σ]) by the sequential backward selection (SBS) method, the features are: - Attack timeδt: the time from the motor start to the current stable;

- The mean value of the bus current;

- The standard deviation of the bus currentσ.

Fig.5 Feature space by the best feature

We use a set of 3 observation sequences (Oi={oi1, oi2, …, oiT}, for i= 1,2,3 and T= 3) to train each HMM, with S1,S2,and S3stand for the healthy mode, the bearing faults, and stator faults separately. The initial parameters are defined as:

The observation matrix B is given by:

where: μjis the gravity center of the training date in the class Sj; Ejis the training data of the class Sj; (·)′ is matrix transpose;Covdenotes the covariance matrix.

By training each HMM, the best HMMs parameters (Ai,πi), which make the probabilityP(Oi|λi)maximum, are given in Tab.2 to Tab.4.

Tab.2 HMM of the healthy mode

Tab.3 HMM of bearing faults mode

Tab.4 HMM of stator faults mode

The remaining 63 classification results are presented in Tab.5, which shows that the right rate is equal to 96.8%. These results show that the new scheme can detect and diagnose the typical faults of gyro motors.

Tab.5 The results of diagnosis

5 Conclusion

In this paper, we present a new method for failure detection and diagnosis of gyro motors based on Hidden Markov Model (HMM). In this new approach, the motor bus current signature is analyzed, and the features are extracted from transformation made on the bus current signals based on the time domain. The most valuable feature vectors by using HMM models are used to detect and diagnose two faults of gyro motors: bearing faults and stator faults. The experimental data are collected from a brushless DC gyro motor, and the obtained results prove that the method is effective in faults detection and diagnosis of gyro motors.

Reference:

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[2] Pineda-Sanchez M, Riera-Guasp M, Roger-Folch J, et al. Diagnosis of induction motor faults in time-varying conditions using the polynomial-phase transform of the current[J]. IEEE Transactions on Industrial Electronics, 2011, 58(4): 1428-1439.

[3] Rabiner L, Juang B H. An introduction to hidden Markov models[J]. ASSP Magazine, IEEE, 1986, 3(1): 4-16.

[4] Soualhi A, Razik H, Clerc G, et al. Prognosis of Bearing Failures using Hidden Markov Models and the Adaptive Neuro-Fuzzy Inference System[J]. Industrial Electronics, IEEE Transactions on, 2014, 61(6): 2864-2874.

[5] Zaidi S S H, Aviyente S, Salman M, et al. Prognosis of gear failures in DC starter motors using hidden Markov models[J]. IEEE Transactions on Industrial Electronics, 2011, 58(5): 1695-1706.

[6] Soualhi A, Clerc G, Razik H, et al. Fault detection and diagnosis of induction motors based on hidden Markov model[C]//Electrical Machines (ICEM), 2012 XXth International Conference on. IEEE, 2012: 1693-1699.

[7] Abdesselam L, Guy C. Diagnosis of induction machine by time frequency representation and hidden Markov modelling[C]//2007 IEEE International Symposium on Diagnostics for Electric Machines, Power Electronics and Drives. 2007: 272-276.

[8] Nakamura H, Chihara M, Inoki T, et al. Impulse testing for detection of insulation failure of motor winding and diagnosis based on Hidden Markov Model[J]. IEEE Transactions on Dielectrics and Electrical Insulation, 2010, 17(5): 1619-1627.

[9] Pineda-Sanchez M, Riera-Guasp M, Roger-Folch J, et al. Diagnosis of induction motor faults in time-varying conditions using the polynomial-phase transform of the current[J]. IEEE Transactions on Industrial Electronics, 2011, 58(4): 1428-1439.

[10] Ondel O, Boutleux E, Clerc G. Feature selection by evolutionary computing: Application on diagnosis by pattern recognition approach[C]//Proceedings of the 18th International Conference on Computer Applications in Industry and Engineering. 2005: 219-225.

1005-6734(2014)06-0829-05

10.13695/j.cnki.12-1222/o3.2014.06.024

用隱Markov模型的陀螺電機(jī)故障診斷方法

董 磊1,2，李德才2，韋俊新2，李為民1，潘龍飛2，孫曉晉3，陳云飛3
(1. 河北工業(yè)大學(xué) 機(jī)械工程學(xué)院，天津 300130；2. 天津航海儀器研究所 天津 300131；3. 河北工業(yè)大學(xué) 控制科學(xué)與工程學(xué)院，天津 300130)

為滿足機(jī)電陀螺儀高可靠性的要求，準(zhǔn)確地檢測和診斷陀螺儀核心部件——陀螺電機(jī)的各類故障是十分必要的。提出了一種陀螺電機(jī)檢測和診斷的新方法，即基于隱Markov模型的模式識(shí)別方法。該方法從母線電流時(shí)域信號(hào)提取特征并作為電機(jī)狀態(tài)的監(jiān)測指標(biāo)，通過順序后推法選擇最佳信號(hào)特征建立特征空間，并用于隱Markov模型的參數(shù)訓(xùn)練，進(jìn)而使用隱Markov模型作為分類器對(duì)陀螺電機(jī)進(jìn)行故障檢測和診斷。為驗(yàn)證方法的有效性，用一臺(tái)無刷直流陀螺電機(jī)作為樣本進(jìn)行了實(shí)驗(yàn)，構(gòu)造了軸承故障和定子故障，并在不同的溫度條件下進(jìn)行了測試。實(shí)驗(yàn)結(jié)果表明：該方法對(duì)于陀螺電機(jī)故障檢測和診斷的正確率達(dá)到96.8%。

故障檢測；故障診斷；隱Markov模型；陀螺電機(jī)

TH165.3

A

2014-07-07；

2014-11-11

裝備預(yù)研支撐技術(shù)項(xiàng)目（62101050802）；國防預(yù)先研究重點(diǎn)項(xiàng)目（513090501）

董磊（1979—），男，博士研究生，高工，主要從事慣性元件及可靠性的研究。E-mail：dongleihit@126.com

聯(lián) 系 人：李為民（1964—），男，教授，博士生導(dǎo)師。E-mail：vmin@hebut.edu.cn

Failure detection and diagnosis of gyro motors using hidden Markov models

DONG Lei1,2, LI De-cai2, WEI Jun-xin2, LI Wei-min1, PAN Long-fei2, SUN Xiao-jin3, CHEN Yun-fei3