XIE Fengyun

School of Mechanical and Electronical Engineering，East China Jiaotong University，Nanchang 330013，China

On-line Condition Monitoring Based on Empirical Mode Decomposition and Neural Network

XIE Fengyun*

School of Mechanical and Electronical Engineering，East China Jiaotong University，Nanchang 330013，China

On-line condition monitoring in machining processes plays a significant role to improve the machining stability and precision.In this paper，an approach based on empirical mode decomposition(EMD)and neural network for on-line condition monitoring is proposed.The root mean square(RMS)of intrinsic mode functions(IMFs)by EMD is regarded as machining processing feature.The three layers Back-propagation(BP)neural network model taking the machining feature as target input of neural network，the IMFs as characteristic parameter，and the 3 types of processing states as output are established to identify the processing state.The result shows that the proposed method can effectively identify the state of of process.

empiricalmode decomposition，neuralnetwork，condition monitoring，root mean square

Jiangxi Province Natural Science Foundation(20114BAB206 003)，Key Laboratory of the Ministry of Education for Vehicles and Equipment(09JD03)，Jiangxi Province Nature Science Foundation(20132BAB201047)

*XIE Fengyun，PhD.E-Mail:xiefyun@163.com

On-line condition monitoring in machining operations is very crucial in order to prevent tool failures，increase machine utilization and decrease production cost in an automated manufacturing environment.Online system diagnostics and prognostics can be performed by using the real time monitoring data［1］.

However，the on-line condition monitoring is not an easy task for some reasons，for instance，the machining processes are usually non-linear，and timevariant systems，which make them difficult to be modeled;the acquired signals from sensors are dependent on other kind of measuring factors，it is not a direct method for measuring;the acquired signals are disturbed by such as geometry variances，work piece material properties，digitizers noise，sensor nonlinearity，and chatter.

For many years，lots of scholars have studied condition monitoring by various methods.There are important contributions presented for condition monitoring，for instance，a method of state recognitions based on wavelet and hidden Markov model was presented by Xie［2］;an approach for monitoring the cutting tool condition by self-organizing feature maps (SOFM)was presented by Owsley，et al［3］;A new hybrid technique for cutting tool wear monitoring，which fuses a physical process model with an artificial neural networks(ANN)model is proposed for turning by Sick［4］;A real time monitoring method of tool wear using multiple modeling method was proposed by Ertunc et al［5］;Dey and Stori proposed a Bayesian network(BN)method for monitoring and diagnosis of machining operations states［6］;Yao，et al proposed an on-line chatter detection by using the wavelet and support vector machine［7］.

In this paper，an approach based on empirical mode decomposition(EMD)for extracting feature and Back-propagation(BP)neural network for identification of processing state is proposed.To monitor processing states in machining process，an accelerometer sensor is used for data acquisition.The EMD is used to decompose the acceleration signals of machining process. The intrinsic mode functions (IMFs)of different frequency bandwidth can be ob-tained by EMD.The root mean square(RMS)of IMFs is proposed as eigenvector to effectively express the machining feature.The BP neural network model is used to identify the machining process states.The result shows that the proposed method can effectively identify the stable，transition and chatter state after being trained by the experiment data.

1.Background

1.1.Empirical mode decomposition(EMD)

EMD is a direct，intuitive，and adaptive method for signal decomposition proposed by Huang，et al to deal with data from non-stationary and nonlinear processes.The method is based on the assumption that any signal consists of different simple intrinsic modes of oscillation.Each of these intrinsic oscillatory modes is represented by an intrinsic mode function(IMF).The EMD process of a signalx(t)［8］can be demonstrated as follows:

1)Initializer0=x(t)and i=1

2)Extract the ith IMF

①Initializehi(k－1)=ri;

② Extractthelocalmaximaand minima ofhi(k－1);

③Find the local maximum and the minimum by cubic spline lines to form upper and lower envelopes ofhi(k－1)，the upper and lower envelopes should cover all the data between them;

④Calculate the meanmi(k－1)of the upper and lower envelopes ofhi(k－1)，let hik=hi(k－1)－mi(k－1);

⑤ Ifhikis a IMF，then set IMFi=hik，otherwise，go back to b)withk=k+1.

3)Defineri+1=ri－IMFi

4)Ifri+1still has least two extreme then go back to step 2)else decomposition process is finished andri+1is the residue of the signal.

1.2.BP neural network

BP neural network was presented by McClelland and Rumelhart in 1986.It is widely-used in the statistical computation and data mining field due to the high nonlinear mapping ability.The structure of BP neural network as shown in Fig.1 consists of three main layers，namely input，hidden，and output layers.The variable“M”means the total neuron number in the input layer，the variable“N”means the total neuron number in the hidden layer，and the variable“L”means the total neuron number in the output layer.

Fig.1 Structure of BP neural network

In Fig.1，xis an input data vector，and the bias vectorbsummed with the weightedwinputs to form the net inputu.The activation functionfon the excitation signal and provides the neuron’s output vectory，sending it to the next layer or to the network output.The output vector of the neuron is given by

By modifying the connection weight to training the initial network，the anticipated output and optimal network can be obtained.The optimal network can be used to monitor the machining state by the neural network pattern recognition method.

2.Feature extraction based on EMD

In order to acquire machining process data，an accelerometer sensor is adopted.An experiment is setup in machining process.Fig.2 is a data acquisition scheme.

Fig.2 Data acquisition scheme

The machining processing states are divided into the stable，transitional，and chatter state according to spectrum analysis.To analyze each processing state in machining process，the processing signal is decomposed into 11 IMFs by applying EMD method as shown in Fig.3.In Fig.3，(a)shows the EMD of stable state，and(b)shows the EMD of chatter state.We can see that it is an evidently different in corresponding IMFs.The RMS values of the IMFS in different frequency bands were calculated，and 8 RMS of IMFS is elected as eigenvector to express the machining processing feature.3 groups RMS of IMFs in different processing conditions and processing state are shown in Tab.1.

Fig.3 EMD of the processing signal

3.Condition monitoring by neural network

The classical three layers BP neural network model is set up in this paper which puts the RMS of IMF as the target input of neural network to monitor the processing states.The group 1 and 2 in Tab.1 are chosen as characteristic parameters to form the training sample.The 3 output samples are noted as stable state(1 0 0)，transitional state(0 1 0)，and chatter state(0 0 1).Because the input features are 8，the network node number of input layer(n)can be chosen as 8，and the node number of output layer can be chosen as 3 related to corresponding 3 machining processing state.The network training curve is shown in Fig.4.

Fig.4 Curve of training error of BP network

The group 3 in Tab.1 regarded as test sample is substituted in the corresponding trained model.The output vector of test sample is shown in Tab.2.The maximum value of the output row vector with respect to state is selected as the identification state.We can obtain the result of stable，transition，and chatter state with respect to the test sample stable，transition，and chatter state.The results can be seen that it is correct by using the neural network identification method.

Tab.1 The RMS of IMF

Continued from previous table

Tab.2 The output of BP neural network

4.Conclusions

The condition monitoring in machining process is very important for mechanical manufacturing process.In this paper，a method of condition monitoring based on EMD and BP neural network is proposed.The main idea of the work relies on the transformation of the accelerometer signals into BP network model that captures the processing state.A method of feature extracting from processing signals is used by EMD.The RMS of IMFs by EMD is used as eigenvector to express the processing feature.The machining process is divided into three states.Finally，a correct identification result is obtained by the proposed method.It can ensure the machine is in a healthy working condition according to the identification results.

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［2］ XIE F Y.A Method of State Recognition in Machining Process Based on Wavelet and Hidden Markov Model.In Proceedings of the ISMR 2012，2012:639－643.

［3］ Owsley L M，Atlas L E，Bernard G D.Self-Organizing Feature Maps and Hidden Markov Models for Machine-Tool Monitoring.IEEE Transactions on Signals Processing，1997，45:2787－2798.

［4］ Sick B.On-Line and Indirect Tool Wear Monitoring in Turning with Artificial Neural Networks:A review of more than a decade of research.Mechanical Systems and Signal Processing，2002，16:487－546.

［5］ Ertunc H M，Loparo K A，et al.Real time monitoring of tool wear using multiple modeling method［C］//In Proceedings of the IEMDC 2001.2001:687－691.

［6］ Dey S，Stori J A，Dey S，et al.A Bayesian Network Approach to Root Cause Diagnosis of Process Variations［J］.International Journal of Machine Tools＆Manufacture，2004，45:75－91.

［7］ Yao Z H，Mei D Q，Chen Z C.On-line chatter detection and identification based on wavelet and support vector machine［J］.Journal of Materials Processing Technology，2010，210:713－719.

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基于经验模态分解与神经网络的在线状态监测

谢锋云*
华东交通大学机电学院，南昌 330013

在机械加工过程，为了提高加工稳定性和精度，在线状态监测具有十分重要的作用。基于经验模态分解与神经网络模型，提出了一个在线状态监测方法。该方法将EMD分解的本征模态函数均方根作为机械加工特征量。为识别实时加工状态，以加工特征为神经网络的目标输入，建立起将IMF作为特征参数及把3种加工状态作为输出的3层后向神经网络模型。识别的结果显示，提出的方法能有效地识别加工状态。

经验模态分解;神经网络模;状态监测;均方根

TH133;TP391

10.3969/j.issn.1001－3881.2013.24.010

2013－08－30