PROCEEDINGS of the23rd International Congress on Acoustics
9 to 13 September 2019 in Aachen, Germany

Classification of operating conditions of machinery combined withtransmissibility function methodPeidong JIA1; Jing Wang2; Mingmei HAN3;Xun WANG4;Xiaobin CHENG5;Jun YANG6
1-6

Key Laboratory of Noise and Vibration Research, Institute of Acoustics, Chinese Academy of Sciences,Beijing, China.

ABSTRACT
Condition monitoring of machinery is concerned for the purpose of maintenance, productivity andavoiding potential downtime. In the trend of smart factory, the virtual representation of machining process
can be built by measuring the vibration. Different working conditions and fault conditions should beidentified. Different working conditions have different characteristics with the general signal processing
parameters in time and frequency domain. The dimension reduction method like PCA, and the cluster method
like k-means can be used for further classification. In order to accurately classify different operating
conditions, the feature extracted from the measured signal should be distinct enough. In this case, multiple
vibration sensors have to be implemented, and transmissibility function between different sensors of thedynamic system can be considered as the characteristic parameters. This paper combines transmissibility
function and signal processing parameters for classification of different operating conditions to extract more
information about operating process.
Keywords: Operating condition, Transmissibility function, Machine learning
1.

INTRODUCTION
In the trend of smart factory, the manufacture process is monitored by various kinds of sensors
for the purpose of maintenance, optimization and productivity. As for machining process, states ofthe machine tool are represented by vibration sensors. The vibration signal of operating condition
can be simply characterized by signal processing features, such as mean, standard deviation,
variance in time domain, and spectrum, resonance frequency, central frequency, wavelet(1, 2),
cepstrum(3, 4) and so on.
The modern machine learning technique is implemented in the field of condition monitoring(5),which does not require sufficient diagnostic knowledge on the characteristics of vibration signals.
However, there are many working conditions during the machining process, the features extract fromthe vibration signals should be distinct enough.
In a complex mechanical system, not only the characteristics of the source but also the transfer
path should be analyzed. Transfer path analysis is commonly used in the automotive industry, where
the each source’s contribution to the overall noise(6) are analyzed. In different machining process,modal parameters should be analyzed as well, and these modal parameters are time-variant during
the process. Another technique is invented which is called operational modal parameter
estimation(7). In case the exact input source, the excitation force, and the transfer function cannot bemeasured, modal parameter data can be estimated by operating data.
The relationship between the sensor signals at the desired location and measured loc ation can beexpressed as the transmissibility function by the methodology of operational transfer path
1

jiapeidong@mail.ioa.ac.cn
wangjing175@mails.ucas.ac.cn
3hanmingmei16@mails.ucas.ac.cn
4
xun.wang@mail.ioa.ac.cn
5xb_cheng@mail.ioa.ac.cn
6jyang@mail.ioa.ac.cn
2

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analysis(8). As the state of machining changes, the cutting force and the stress of the structure varyconsequently. This kind of difference can be represented in the transmissibility matrix.
This paper demonstrates a novel method which uses the transmissibility function to monitor themachining process. This feature is distinct for different operating conditions, and the experimental
work is shown.

2. METHOD
2.1 Classification
The purpose of condition monitoring is to classify the data. If the label is available, theclassifier such as KNN(9), random forest(10), CNN(11) can be used for classification. If the label isunavailable, the k-means(12), DBSCAN(13), Graph Community Detection(14) is used to clusteringthe data.
Before the classification can be implemented, the high dimensional data should be reduced to
the low dimensional data, and PCA(15) is commonly used, and the charactistics has to be carefully
chosen when performing PCA.
2.2 Transmissibility Function
Assuming that the transfer function of the system is linear and time invariant, the vibration signal
at the one location can be derived by the signal from other locations, which can be denote as Y=AX,
where A is the transmissibility function from the sensors X to the sensor Y.

Figure 1 Diagram of the transmissibility function
The transmissibility function can be obtained by the operational condition A YX* (XX* ) 1 incase the system is time-invariant. Then the signal at locations Y, can be estimated by the reference
sensors at location XYpredict = AXnew(1)
If the system is time-invariant, the predicted data Ypredict should be exactly the same as themeasured data Ynew . In case the system is time-variant, matrix A changes continually and thepredicted data Ypredict is different from the measured data Ynew . Therefore the error between Ypredictand Ynew (error = Ypredict  Ynew ) points to the variance of the transmissibility functions. This gives
a way to monitor the variance of the system.

3.

EXPERIMENTAL RESULTS

3.1 Experimental set-up
The experiment was implemented on a 3-axis milling machine. One accelerometer was mounted
on the spindle, while the other two were mounted on bench clamp and workbench. A rectangularaluminum work piece with the length of 60 cm, was cut by different depth of cutting, feed rate andspindle speed, as shown in Table 1.

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Table 1 – Different machining parameters
Operating Condition

Cutting depth, mm

Feed rate,mm/min

Spindle speed,RPM

11500

1500

21500

2500

33500
1500
The work piece was rigidly fixed in the middle, while the left-hand side and right-hand side wereleft free. The milling cutter was moving from left side to right side as shown in Figure 2. As thecutter was moving, excitation point was moving, thus the transfer function and modal response werechanging.

Figure 2 Test rig
3.2 Classification using the one accelerometer
For the huge amount of data, manually observing the data in time and frequency domain istedious. Principal Component Analysis(PCA) is a commonly-used approach to extract unknown
underlying features. As shown in Figure 3, different working conditions, different cutting depth,
feed rate and spindle speed can be grouped into different clusters.

Figure 3 Scatter plot by PCA, the vibration is picked up on bench clamp

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3.3 The transmissibility matrix variance during the process
In order to distinguish different characteristics at different cutting positions, the transmissibility
function is considered. Calculated with the operational data, a spectrogram-like figure is drawn in
Figure 4, which is the transmissibility from the spindle to workbench. It shows the time-variance ofthe transmissibility from the spindle to the workbench when the cutter moves from left to right. At
the left-most side and right-most side, there are resonance responses between 1k-2kHz, and since themiddle part is fixed, the magnitude is smaller. This figure illustrates variance of the transmissibility
and gives additional information for condition monitoring.

Figure 4 Transmissibility function from the spindle to the workbench
3.4 Classification of different operating conditionsPerforming PCA on the time-variant transmissibility function calculated by one-third octave SPLof different operating conditions, the data is distinct in the scatter plot, as shown in Figure 5.
Therefore, this feature can be used for the further classification algorithm like KNN.

Figure 5 Scatter plot of different operating conditions
3.5 Classification of different cutting positions
During the process when the tool moves from the free-vibrating side to the rigid-fixed side, themodal response is changed, and variance should be monitored as well. According to Equation 1, asimple way is to compare the difference. For example, the measured signal at the leftmost -10cm isused to estimate transmissibility matrix A, then estimated signal is calculated when the tool iscutting the middle position. Since the transmissibility function is changed, error could be large atcertain frequencies. Figure 6 compares the measured and the estimated spectrum from different
training condition. If the matrix A changes too much, the estimation error increases. Training
Condition 2 means the cutter processes at center position of the work piece. The Condition 1 and4743

Condition 3 means the position of leftmost 10 cm and rightmost 10 cm respectively. The measured
condition is real measured data when the tool is cutting the middle rigidly fixed part of the workpiece.

Figure 6 Estimation error corresponding to the reference sensor
Furthermore, PCA is implement on the estimation error, the difference caused by the change oftransmissibility function is distinct.
During the experiment, the tool is continuously moving from the leftmost side to the rightmost
side. Figure 7a shows the scatter plot when performing k-means clustering algorithms to divide thedata into three groups. Figure 7b shows, the manually-divided groups by the position 15 cm and 45cm. The mismatches between the groups are only 3.9%, 3.8%, 11.7% respectively, and this meansthat the transmissibility function at the left and right free -vibrating side are different from that at therigidly-fixed position. This gives a way to automatically classify the different operating conditions.

a)b)Figure 7 Scatter plot by PCA of estimation error

4.

CONCLUSIONSThis paper presents the transmissibility function as the feature to represent different operating
conditions of machining process. The transmissibility gives a distinct feature which helps to classify
not only the different feed rate, spindle speed and cutting depth, but also the different cuttingposition. The further work should research on different classification methods which can classify theworking conditions of machining process automatically.

ACKNOWLEDGEMENTS
This paper is supported by the Strategic Priority Research Program of Chinese Academy ofSciencesˈGrant No. XDC02020400.

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