Signal pre-processing method and application design of edge nodes for distributed electromechanical system

LIU Peijin，ZHANG Xiangxiang，SUN Yu，SHI Mengtao，HE Ning

(School of Mechatronic Engineering，Xi’an University of Architecture and Technology，Xi’an 710055，China)

Abstract：A signal pre-processing method based on optimal variational mode decomposition (OVMD)is proposed to improve the efficiency and accuracy of local data filtering and analysis of edge nodes in distributed electromechanical systems.Firstly,the singular points of original signals are eliminated effectively by using the first-order difference method.Then the OVMD method is applied for signal modal decomposition.Furthermore,correlation analysis is conducted to determine the degree of correlation between each mode and the original signal,so as to accurately separate the real operating signal from noise signal.On the basis of theoretical analysis and simulation,an edge node pre-processing system for distributed electromechanical system is designed.Finally,by virtue of the signal-to-noise ratio (SNR)and root-mean-square error (RMSE)indicators,the signal pre-processing effect is evaluated.The experimental results show that the OVMD-based edge node pre-processing system can extract signals with different characteristics and improve the SNR of reconstructed signals.Due to its high fidelity and reliability,this system can also provide data quality assurance for subsequent system health monitoring and fault diagnosis.

Key words：distributed electromechanical system；electromechanical signal；edge node；optimal variational mode decomposition(OVMD)；signal pre-processing system

0 Introduction

Signal pre-processing is of great significance for the health monitoring and fault diagnosis of distributed electromechanical systems.Edge nodes in different directions are responsible for filtering and efficient analysis of local device data,supporting real-time intelligent processing and execution of local devices.Accounting for 39% of cloud computing cost alone,its efficiency can greatly affect the entire system research performance[1-2].In the era where “data is the king”,it is the quality of data involved in the analysis that will eventually determine the accuracy of monitoring and diagnosis results.However，the signals collected at the edge nodes under actual operating conditions will exhibit “secondary effect”due to serious signal overlap resulting from various physical effects.And most useful signals are buried in strong noise signals.The overlapping of signals and noise has caused great difficulties in analyzing noise laws and signal characteristics[3-6].Therefore,it is vital for diagnostic monitoring or device anti-jamming analysis to extract the real and interference signals of reaction operation status efficiently and accurately from the edge node signal.

In recent years,researchers have carried out a lot of pre-processing research work such as related filtering and noise reduction in response to the signal pollution in monitoring and diagnosis.The short-time Fourier transform (STFT)proposed by Gabor made up for the defects of non-stationary signal processing methods in traditional frequency domain[7].Wu et al.analyzed the spectral characteristics of vibration signals based on STFT,and further obtained decomposed signals at different frequencies[8].However,the usage of this method is limited to time window function fixation,which makes the pre-processing technology not universal.Furthermore,the wavelet transform (WT)proposed in Ref.[9] addresses the issues of the fixed window size of STFT.In addition,many other scholars have made their contributions in the improvements and optimizations based on WT with respect to different scenarios.Unfortunately,it is more difficult to choose proper wavelet basis functions,which have great impacts on the filtering effect[10-13].In recent years,empirical modal decomposition (EMD)has been widely used in the decomposition of complex signals,which can be adaptively decomposed into several relatively stable modal components[14].Xie et al.realized multi-channel signal processing based on EMD[15].Nevertheless,EMD has a serious modal aliasing effect.Although some methods such as ensemble EMD (EEMD)and complementary ensemble EMD (CEEMD)can effectively overcome the modal aliasing phenomenon of EMD,the tremendous computations are not affordable for the signal pre-processing stage[16-17].In response to the drawbacks of EMD,dragomiretskiy et al.proposed a variational modal decomposition (VMD)method such that the modal ambiguities and endpoint effect can be successfully suppressed[18].Compared with the methods in the aforementioned Refs.[7-17],VMD not only achieves the purpose of noise reduction,but also retains the signals of different levels in the signal resulting in higher fidelity of the system.It is more suitable for electromechanical signal processing where different fields are inter-coupled in a distributed electromechanical system.Thus,based on the research of VMD,a signal pre-processing system with the implementation of optimal VMD (OVMD)is designed.Firstly,by taking advantage of the first-order difference method,the singular points of the original signals are effectively eliminated.Then,OVMD is applied to decompose the singularity-eliminated signals.Finally,correlation analysis is performed to determine the degree of correlation between each mode and the original signal,and then accurately distinguish the real operating signal and noise signal to accomplish the signal pre-processing functionalities of the edge node for the electromechanical system.

1 Pre-processing method

The pre-processing method is mainly composed of several sequential steps,in which the first-order difference method,OVMD method and correlation analysis are applied accordingly.The pre-processing evaluation index is also provided at last,so as to fulfill the entire pre-processing function of edge node electromechanical signal.

1.1 First difference method

Based on the 3σcriterion,the first difference method[19]is proposed to handle the scenarios with a large amount of data to be processed.In this study,the first difference method is used to eliminate the singular points of the experimental data.In the case of a higher sampling rate,the continuous sampling data interval becomes small,so it satisfies

x(t)-x(t-1)≈x(t+1)-x(t),

(1)

wherex(t)is the sampled value at timet.

Therefore,according to the sampling value at timet-1 andt,the estimation at timet+1 is recorded as

x′(t+1)=2x(t)-x(t-1),

(2)

wherex′(t+1)is the predicted value at timet+1.Assuming thatωis the threshold,if the criteria |x(t)-x′(t)|>ωis satisfied,the value at timetis considered to be a singular point,which should be eliminated and replaced with the predicted valuex′(t)ofx(t).Takeω=nσ,whereσis the sample standard deviation,andnis generally an integer and selected according to the sampling rate and data characteristics.

1.2 VMD

The goal of VMD is to decompose the original signal into the optimal solutionKintrinsic mode function (IMF)by iterative method.In this study,VMD is adopted to realize the effective separation of the original signalffrom low frequency to high frequency in the frequency domain.Its variational model is constructed as

(3)

In order to take advantages of reconstruction accuracy and the strictness of constraint execution to solve the variational model of Eq.(3),the quadratic penalty factorαand Lagrange multiplierλare introduced to convert the constrained variational problem into an unconstrained variational problem.The enhanced Lagrange equation is expressed as

L({uk},{ωk},λ(t))=

(4)

k∈{1,K}.

(5)

1.3 Determination of optimal number K

When using the VMD method,the number of decomposition modesKdirectly affects the accuracy of the decomposition.If over-decomposition occurs,the components will show intermittence,leading to frequency aliasing,while under-decomposition will cause modal aliasing effects[20].This study uses the instantaneous frequency average method to determine theKvalue instead of empirical selection method to increase the system reliability.The instantaneous frequency characterizes the frequency change of the modal components.If there are too many decomposition layers,the magnitude of instantaneous frequency change of each mode will be greater,and the frequency curve will mutate.According to the principle of instantaneous frequency ambiance[21],the average instantaneous frequency value of the modal component is expressed as

(6)

whereiis theith IMF of VMD;Nis the number of instantaneous frequencies of the component;m means there aremsample points;andjis thejth sampling point.

In the decomposition process,the VMD algorithm is taken for modal decomposition first,and then the Hilbert transform is performed on each modal component such that the average instantaneous frequency value is obtained.Finally,from the average value curve of each instantaneous frequency,after locating the curvature mutation point,theKvalue can be found by taking the critical value before the mutation.

1.4 Correlation analysis

1.5 Evaluation index

In this study,the signal-to-noise ratio (SNR)and root-mean-square error (RMSE)are combined together to evaluate the signal pre-processing effect.SNR represents the signal-to-noise ratio change before and after reconstruction,while the RMSE represents the deviation change before and after reconstruction.The larger the SNR,the smaller the RMSE,the better extraction effect of effective components is expected[22].The SNR and RMSE values can be obtained as

(7)

(8)

wherex(t)is original signal;x(t)′ is the reconstructed signal;andNis the number of samples.

2 Simulation

The operating signal of the electromechanical system has considerable interference,including the high-order harmonics and singular points.In combination with the actual working conditions,a current simulation signal is established containing white Gaussian noise with the standard deviation of 1 together with both the seventh and ninth harmonics and singular points.The fundamental frequency is 50 Hz,and the harmonic frequencies are 350 Hz and 450 Hz,respectively.The time-domain waveform of the simulated signal is shown in Fig.1,and the simulation signal is

f(t)=20sin(100πt)+7sin(700πt)+

3sin(900πt)+u(t)+v(t),

(9)

whereu(t)is white Gaussian noise with a standard deviation of 1,andv(t)is the singularity signal.

The result after the removal of singular points by using the first difference method is shown in Fig.2.Compared with the original waveform in Fig.1,the singular points are apparently eliminated while all other data point information remains untouched.

Fig.1 Time-domain waveform of simulated signal

Fig.2 Waveform after eliminating signal singular points

Through the calculation on the mean value of instantaneous frequency of IMF decomposed for 6 times by VMD in Fig.2,the result curves are obtained as shown in Fig.3.

Fig.3 Curve of mean instantaneous frequency

It can be seen from Fig.3 that when the signal is decomposed at the fifth time,the mean value of instantaneous frequency has mutation,so we chooseK=4 as the decomposition number.Then the decomposition effects are compared and analyzed with different methods.The modal components and frequencies of each modal component and frequency decomposed by VMD and EMD methods are shown in Fig.4.

(a)VMD decomposition diagram

It can be found from Figs.4(a)and (c)that the VMD method can decompose the fundamental wave,the seventh and ninth harmonics as well as noise components more effectively compared with the EMD method.Also it can be noticed from Figs.4(b)and (d)that serious spectrum aliasing occurs in the EMD decomposition mode,and the main frequency component cannot be decomposed.Therefore,it can be concluded that OVMD method is capable of decomposing signals of various levels.

On the basis of the correlation principle,the pre-processed signals are explored further with the correlation analysis completed between the modal components obtained by VMD and EMD decomposition and the original signals.The correlation coefficients are shown in Table 1.

Table 1 Correlation coefficients of components with different methods

From Table 1,strong correlation is observed between the IMF1 obtained by the OVMD and the original signal with coefficient 0.988,while for EMD method,the maximum correlation modal component is IMF4 with the coefficient value 0.84.Combined with Fig.4(b),it can be seen that IMF4 is far from the fundamental wave of the simulated signal 50 Hz and 20 mA,while the IMF1 decomposed by the VMD method is basically the same as the fundamental wave.

After the VMD and EMD components are reconstructed respectively with the correlation coefficients greater than the threshold,the SNR and RMSE are compared to evaluate the reconstruction outcome.The reconstructed signals and the original total harmonic distortion (THD)as well as the SNR and RMSE of reconstructed signals under different methods are shown in Table 2.Significant improvement is observed with both methods,despite the fact that the original signal has been seriously polluted by noise and harmonics.Specifically,the SNR using OVMD for pre-processing is improved by 1.9 dB compared with EMD.And the THD after OVMD pre-processing and reconstruction is reduced by 36.9%,8.5% lower than EMD pre-processing,which means that the collected signal can be processed better.

Table 2 Reconstructed values of SNR,RMSE and THD

3 Design of pre-processing system

3.1 Scheme design

The hardware architecture and experimental platform of the edge node pre-processing system of the distributed electromechanical system are shown in Figs.5 and 6,respectively,which mainly consists of three parts as follows:

Fig.5 Architecture of system hardware

1)Research object.Data are fed from electromechanical systems and high-performance sensors;

2)Data collection and transmission.The data acquisition and transmission functions are implemented with the aid of the virtual instrument cRIO controller;

3)Signal pre-processing and storage.The related functionalities are realized on the upper computer at the edge node.

Fig.6 Experimental platform

3.2 Signal acquisition and transmission

The embedded FPGA and industrial-grade I/O acquisition card is used in the system for signal acquisition.The data are retrieved from the acquisition program of the LabVIEW FPGA module,and then transmitted from the FPGA chassis to the real-time system through the PCI bus.The FPGA on the chassis is directly connected to the I/O acquisition card,and the hardware data can be directly accessed when collected under FPGA.vi,which reaches microsecond level of signal acquisition with almost no response delay,such that the high-speed and completeness of signal acquisition is achieved.In order to improve the real-time performance of the system,data reading and transmission function blocks are accomplished by the RT main program,and the pre-processing work is completed at the PC layer.The data transmission between FPGA and RT adopts DMA FIFO mode.To avoid FIFO buffer overflow,the FIFO depth can be set according to the sampling rate,and data transmission is carried out in the way of network flow between RT and upper computer.

3.3 Signal pre-processing and storage

The edge node pre-processing and storage functions are developed and debugged by LabVIEW and Matlab.The pre-processing process is illustrated in Fig.7.

Fig.7 Signal pre-processing process

To facilitate independent development and debugging,the functions of data acquisition,processing and storage are developed by virtue of modularized programming,and the data and messages between modules are transmitted in queued mode.The different characteristic signals after pre-processing are respectively transmitted to the data storage module in queued mode,and stored in terms of the unique TDMS data format of LabVIEW,which is a binary mode to support high-speed data management.

4 Experiments

A V-phase input current signal of the variable frequency motor in an edge node for pre-processing analysis is selected for the experimental case studies.With the frequency of the variable frequency motor at 50 Hz,the sampling rate at 10 kHz,and we take part of the signal to verify the pre-processing method.The signal time-domain waveform is shown in Fig.8.

Fig.8 Time-domain waveform of actual signal

There are obvious zero-valued singular points between 0.03 s and 0.04 s in the actual obtained signal.After the singular points are eliminated by the system,the signal waveform is much cleaner,as shown in Fig.9.The singular points are successfully eliminated and then the result of Eq.(2)is taken instead of zero.

Fig.9 Waveform of singularity eliminated signal

With the instantaneous frequency mean value method,the number of decomposition levelsKis determined to be 4.The result of 4-order decomposition by VMD is shown in Fig.10.It can be seen from Fig.10(a)that theoriginal signal is nicely decomposed.Combined with Fig.10(b),it can be seen that the fundamental components,harmonic components and noise components are extracted after using OVMD.

(a)Decomposition diagram

The result of correlation analysis on the original signal and each IMF as well as its auto-correlation function are shown in Fig.11.

Fig.11 Analysis of IMF (h)auto-correlation function

Combining Fig.10(b)and Fig.11,it can be determined preliminarily that IMF 2 is the harmonic component on the motor input side.From the auto-correlation diagrams of IMF 3 and IMF 4 in Fig.11,the peak value is higher with low auto-correlation delay.And the autocorrelation approximates to 0 gradually as the delay grows.Moreover,there is a trend of oscillation,which is obviously aperiodic.Combined with the actual working conditions,it can be determined that IMF3 and IMF4 components are high-frequency noise signals.Based on the calculation of the correlation coefficient between each IMF and the original signal,the component withrgreater than the threshold value for reconstruction is taken and the noise component with the auto-correlation analysis result is extracted.The reconstructed signal and the noise extraction result are shown in Fig.12.

(a)Result of reconstruction

The SNR,RMSE and THD calculation results of the reconstructed signal and the original signal are shown in Table 3.

Table 3 Calculation results of various indicators

The following conclusions can be drawn from Fig.10 and Table 3.

1)The THD after pre-processing and reconstruction is reduced by 4.5%.The SNR and RMSE of the reconstructed signal with the OVMD method are calculated and compared,in which the former indicates the improvement by about 22 dB,while the RMSE of the latter is at small value.Therefore,better performance is achieved and verified.

2)The pre-processing system can reliably decompose the original signal,effectively improve the SNR and extract signals of different levels,hence high fidelity and reliability is guaranteed.

5 Conclusions

In this study,as the traditional filtering technology “one-size-fits-all”processing method was broken,a hybrid pre-processing method suitable for edge node signal of the electromechanical system was proposed.The edge node signal pre-processing system was designed and developed,which realized a primary development at the edge nodes of distributed systems.Experimentally,the application of pre-processing system not only can achieve reliable extraction and reconstruction of analytical signals,but also provides a reliable data base for subsequent accurate analysis and diagnosis while maintaining high signal fidelity.It is proved to be practical to certain extents for the health detection and fault diagnosis of distributed electromechanical systems.Additionally,by the analysis index this method can solve the problem of signal pollution at the edge node of the distributed electromechanical system very well,which lays solid foundation for further development of the remote monitoring and diagnosis platform of the distributed electromechanical system.