Validation of target tracking performance through signal feature extraction method based on 1D convolutional neural network Dongwoo Hong 1 Yeungnam University 280 Daehak-Ro, Gyeongsan, Gyeongbuk 38541, Republic of Korea Junhee Kwon 2 Yeungnam University 280 Daehak-Ro, Gyeongsan, Gyeongbuk 38541, Republic of Korea Byeongil Kim 3

Yeungnam University 280 Daehak-Ro, Gyeongsan, Gyeongbuk 38541, Republic of Korea

ABSTRACT In order to perform active vibration and noise control, a variety of adaptive algorithms have been investigated and developed. Especially, neural network-based signal tracking algorithms, such as the radial basis function neural network (RBFNN), are being widely utilized. For signal tracking problems, a reference signal has a significantly important role, while it is difficult to determine the reference signal when it has relatively complex spectrum. Thus, this study focuses on the signal feature extraction for manipulating appropriate reference signals easily and validation of signal tracking performance with it. In order to carried out the signal feature extraction, 1D convolutional neural network (1D CNN) is implemented and trained based on the CWRU bearing dataset. In addition, multi normalized least mean square (NLMS), neural network-based signal tracking algorithm, and diagonal recurrent neural network (DRNN) is employed to confirm the signal tracking performance. The proposed method shows that the 1D CNN-based signal feature extraction method could find the signal feature properly and the reference signal obtained from this methodology is employed to a target tracking problem, which shows a great performance.

1. INTRODUCTION

In the mechanical system, such as robot mechanism, machining tool, and rotary system, the vibration and noise control are required since uncomfortable vibration and noise can be occurred through interference between each part. Furthermore, they directly contribute to the comfortableness of worker. In order to perform the active vibration control (AVC) and active noise control (ANC), a variety of adaptive algorithms, such as NLMS and filtered-x LMS (FXLMS), have been developed and applied in mechanical system. In recent year, the deep learning methods are attracted in engineering research field and widely applied in diagnosis, control, and data generation. Especially,

1 dongwoo229@naver.com 2 rnjswns02@ynu.ac.kr 3 bikim@yu.ac.kr

a Shea mar ce 21-24 AUGUST SCOTTISH BENT caso

neural network-based signal tracking algorithm, such as RBFNN and DRNN, are being widely utilized to control the system motion. Currently, many researches are devoted on AVC[1, 2] and ANC[4, 5] based on the adaptive algorithm and controller. Tian et al. [3] performed the active vibration control for laminated composite beams with piezoelectric layers using genetic algorithm (GA)-based LQR controller. Through the simulation, the proposed structure shows effectiveness control performance. Kim et al. [6–8] improved the performance of LMS algorithm using the sliding mode control algorithm focused on the active vibration control of incommensurate sinusoids. In addition, a novel control algorithm, model predictive sliding mode control, is proposed to overcome the drawbacks of adaptive filtering algorithms. Zhao et al. [9] proposed the novel FXLMS based on offline and online secondary-path modeling. Through the simulation and experiment, the proposed algorithm shows great performance.

In order to perform the system control, such as vibration [10] or motion control [11], applying deep learning methods, a variety of research has been being contributed as follows. Fei et al. [12, 13] improved the sliding mode control applying the recurrent neural network (RNN) to track the trajectory for signal and solve the chattering phenomenon. The proposed controller shows great performance. Bessa et al. [14] proposed intelligent controller framework which is based on fully connected neural network having single hidden layer to control position of micro diving agent. As a literature researches, the proposed methods have a great performance for each parts, but those focus on the system feedback control. In order to perform suitable controls, signal feature analysis should be conducted first. Furthermore, dealing with the signal or trajectory tracking problems, a reference signal has a significantly important role, while it is difficult to determine the reference signal when it has relatively complex spectrum.

Thus, this paper focuses on two parts: 1) 1D CNN-based signal feature extraction is conducted to analyze signal characteristic and provide reference signal into signal tracking algorithm, and 2) verification of signal tracking performance is conducted based on extracted signal features. The main contributions are summarized as follows: 1) the signal feature extraction is carried out based on the 1D CNN. 2) signal tracking performance is demonstrated through multi-NLMS, neural network- based signal tracking algorithm, and DRNN. When conducting the signal feature extraction and verification of tracking performance, the Case Western Reserve University (CWRU) bearing dataset is used.

2. TRANINING DATASET AND SIGNAL PROCESSING

This section discusses the CWRU bearing dataset and signal processing process. In order to perform training of signal feature extraction model, the CWRU bearing dataset has been utilized and it is summarized in Table 1. The measuring conditions are summarized as follows: 1) the motor load and speed are set to 0, 1, 2, and 3 HP and 1797, 1772, 1750, 1730 rpm, respectively. 2) The bearing fault types consists of outer race, inner race, and ball, 3) fault sizes are 0.007, 0.014, 0.021 inch. When the feature extraction model is trained, overall cases (load, speed, fault size) are shuffled and utilized as training set. Also, the training, validation, and test data are divided into 0.01s with 50% overlap between consecutive signals.

Table 1: Case Western Reserve University bearing dataset

Fault type Motor load [HP] Fault size [inch] Motor speed [rpm]

Normal 0 / 1 / 2 / 3

- 1797 / 1772 /

1750 / 1730 Outer race 0.007 / 0.014 / 0.021 Inner race

Ball

In order to consider the frequency range of 0Hz to 3000Hz, the dataset is processed with 1D CNN- based low pass filter having only one convolutional layer, whose schematic structure is shown in Figure 1.

Figure 1: Schematic of 1D CNN-based low pass filter The trained 1D CNN-based low pass filter will be placed in the feature extraction algorithm to deal with the directly raw data. The detailed algorithm structure will be described in section 3. 3. SIGNAL FEATURE EXTRACTION

This section mainly focuses on the 1D CNN-based signal feature extraction process. The section 3.1 deal with the 1D CNN structure to extract the signal feature, and the section 3.2 discusses the performance of feature extraction about normal and outer race fault.

3.1. Feature Extraction Structure Based on 1D Convolutional Neural Network

In order to directly deal with the raw data and extract the signal feature, the 1D CNN structure is mainly utilized, and schematic of structure is expressed in Figure 2. In Figure 2, the proposed model consists of low pass filter, which is described in previous section, four convolutional layers, and fully connected layer. Also, in order to compensate the signal loss, the residual connection is applied in between low pass filter and front three convolutional layer, and it is expressed as the orange line in Figure 2. When the proposed model is trained, the Adam optimizer is utilized. The signal feature extraction has been performed through trained model. Furthermore, the extracted feature is utilized as the reference signal to track the signal.

Iwi Training data Y (Filtered signal) Error => Predicted X (Bearing data)

Figure 2: 1D convolutional neural network structure about feature extraction

3.2. Performance of Feature Extraction

Using the trained model described in section 2, the signal feature extraction has been performed, and it results summarize only two case, normal and outer race. In order to analyze the signal feature (frequency), the output signals of convolutional 2 to 4 layer are used, and the detailed criteria of signal feature extraction is summarized as follows: 1) the output of convolutional layer is converted by FFT, 2) RMS values are calculated using FFT signal, and 3) in order to extract and save the index of maximum peak value, the specific sweep range is defined. When performing the step 3), maximum

Maii ly used layer for signal feature extraction ==> Residual connection ie | -|-|-= Flatten Fully connected layer layer Input signal Low pass filter Convolutional (Measuring signal) layer layer

peak value must have higher than a threshold value (RMS value). Through above process, the signal feature extraction is performed about normal and outer race, and the results are shown in Figure 3.

Input (Normal) ‘Convolutional layer output (Normal) 005 — 2.0200 oa oan $003 goers Foca] Len , 2.0030 oor coowo cccoog heel Hi ab 0.00930 60! 00 3700 6 8 08 ABU 3700 00 200" tho_ 00 Soo 5006 3 3550 000 frequen ‘reueey ie Input (Outer) Convolutional layer output (Outer) ou j ~ Cony ayer output Eo.006 0.002 artis '.0009-“"390" 600 “B00 1300 1500 1800 260 2400 2700 3000 °° 399° a9 300" i200" 1500 i800 posteond ro pcb rary

Figure 3: Signal feature extraction about input and output of convolutional layer In Figure 3, the blue line and blue dot line represents the FFT result corresponding to input and convolutional layer output, respectively, and the red mark represents saved signal feature through above process. Also, yellow box stands for the emphasized frequency range through passing away the convolution layers. The normal and outer case are emphasized two and three parts, respectively, and it means that the convolutional layer can catch those signal features. Thus, through above results, it is demonstrated that the signal feature extraction can be performed based on the 1D CNN structure. Furthermore, using the extracted signal feature, the verification of signal tracking performance is performed in section 4. 4. VALIDATION OF TARGET TRACKING PERFORMANCE

This section mainly focuses on the verification of signal tracking performance using extracted signal feature. The section 4.1 deal with the signal tracking algorithm, and the section 4.2 discusses the signal tracking performance about outer race fault.

‘Tracking Algorithm

4.1. Signal Tracking Algorithm

In order to perform the verification of signal tracking performance, three tracking algorithms are utilized, and it is summarized in Figure 4.

(a) Schematic of Signal Tracking Algorithm (b) Multi-NLMS

-4 Uy (k) >} Wl ion e(k) >| NLMS Z Up (ke) >) W2(k) y(k) = e(k) >| NLMS ig Un (Kk) >] Wall) 1 e(k) >| NLMS

(c) Neural Network (d) Diagonal Recurrent Neural Network Figure 4: Signal tracking algorithm – (a) schematic of signal tracking algorithm, (b) multi-NLMS, (c) neural network, (d) diagonal recurrent neural network In Figure 4, (a), (b), (c), and (d) stand for schematic of signal tracking algorithm, multi-NLMS, neural network, and DRNN, respectively. Also, in Figure 4 (a), 𝑢𝑢(𝑘𝑘) represents the plant input signal. 𝑑𝑑(𝑘𝑘) and 𝑦𝑦(𝑘𝑘) stand for plant output (desired signal) and tracking algorithm, respectively. 𝑒𝑒(𝑘𝑘) represents the error signal between 𝑑𝑑(𝑘𝑘) and 𝑦𝑦(𝑘𝑘) . In Figure 4 (b), (c), and (d), 𝑢𝑢 𝑛𝑛 (𝑘𝑘) stand for the reference signal defining through extracted feature, which is described in section 3. 𝑊𝑊 𝐼𝐼𝐼𝐼 and 𝑊𝑊 𝐻𝐻𝐻𝐻 stand for the weight corresponding to input to hidden and hidden to output, respectively. Especially, DRNN has a recurrent unit 𝑊𝑊 𝐻𝐻

𝑅𝑅 in hidden layer, and it shows in Figure 4 (d). The weight update equation for those algorithms is summarized Equation 1 to 3.

𝑊𝑊(𝑘𝑘+ 1) = 𝑊𝑊(𝑘𝑘) + 𝜇 ‖𝑈 𝑈 (𝑘 𝑘 )‖ 2 + 𝛿 𝛿 𝑈𝑈(𝑘𝑘)𝑒𝑒(𝑘𝑘) (1)

Equation 1 represents weight update equation corresponding to multi-NLMS. When neural network training is performed, the backpropagation method is utilized. Thus, in order to update the network weight, Equation 2 and Equation 3 is defined, and it is corresponding to network output to hidden layer and recurrent unit, respectively.

Input layer Hiddenlayer Output layer

𝑤𝑤 𝐻𝐻𝐻𝐻 (𝑘𝑘+ 1) = 𝑤𝑤 𝐻𝐻𝐻𝐻 (𝑘𝑘) + 𝜂 𝜂 𝜕 𝜕 𝜕 𝜕 𝜕 𝑤 𝑤 𝐻 𝐻 𝐻

(2)

𝑤𝑤 𝑗𝑗 𝑅𝑅 (𝑘𝑘+ 1) = 𝑤𝑤 𝑗𝑗 𝑅𝑅 (𝑘𝑘) + 𝜂𝜂 𝜕 𝜕 𝜕 𝜕 𝜕 𝑤 𝑤 𝑗 𝑅 𝑅 (3)

Through above algorithms, the verification of signal tracking performance is performed based on the extracted signal feature.

4.2. Verified Signal Tracking Performance

This section focuses on the verification of signal tracking performance for outer race. When signal tracking is performed, using the extracted feature, which is described in section 3, the signal tracking is performed through three tracking algorithms, multi-NLMS, neural network, and DRNN. The tracking results show in Figure 5. Table 2: Comparison each signal tracking error based on RMS value

Comparison Tracking

Neural Network Diagonal Recurrent

Multi-NLMS

Performance

Neural Network

Tracking Error (RMS) 0.0356 0.00011 0.00082

Input layer Hidden layer Output layer

(a) Multi-NLMS

Signal Tracking Performance - Multi NLMS Time [s] 1.0 < — Target : Outer — 05 Traking Output © 0.0 2 3-05 “18.00 0.01. +0.02.~«0.03.~=~O04~~=~OS~«~—UOGSS*C*~«~COTSC«i 0.05 5 0.03) ~ Error i ip 0-02 5 -0.01 8 £ -0.03 “900 0.01. ~+«20.02~=S=«0.03.-—=—«0.04_~=S*0.0S.-—SC«iGSSC«OTSC«OB

(b) Neural Network

‘Tracking Error 1.0 0.5 0.0 Outer Signal -0.5 -19 0.005 0.003 0.001 -0.001 -0.003 -0.005 Signal Tracking Performance - Neural Network —— Target : Outer Traking Output 00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 —— Error ee os Hh 00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 Time [s]

(c) Diagonal Recurrent Neural Network Figure 5: Verification of signal tracking performance – (a) multi-NLMS, (b) neural network, and (c) diagonal recurrent neural network In Figure 5, the blue line and red dot line stand for the desired and filter output signal, respectively, and the red line stands for the error signal. The overall tracking algorithm can track the outer race signal, but the error signal has a different performance, and it means that each algorithms have different ability for the tracking. Thus, in order to compare the tracking performance, the error RMS values are summarized in Table 2. In multi-NLMS case (Figure 5 (a)), the error RMS has 0.0356, and

Tracking Error 1.0 0.5 Outer Signal -0.5 -19, 0.005 0.003 0.001 -0.001 -0.003 —0.005 Signal Tracking Performance - Diagonal Recurrent Neural Network —— Target : Outer Traking Output 0.0 a a ae 00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 — Error —— a =f Him il id 00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 Time [s] 0.08

in neural network (Figure 5 (b)) and DRNN (Figure 5 (c)), the error RMS have 0.00011 and 0. 00082, respectively. The multi-NLMS shows poor ability to track the signal having complex spectrum than another algorithm. The reason for these results can be seen as a structural problem of the algorithm, and it will be dealt with future research. Through the tracking results, the proposed method shows that the 1D CNN-based signal feature extraction method could find the signal feature properly and the reference signal obtained from this methodology is employed to a target tracking problem, which shows a great performance. 5. CONCLUSIONS

In order to perform the signal feature extraction and validate the signal tracking performance, this paper focuses on two parts as follows: 1) 1D CNN-based signal feature extraction is performed to obtain the reference signal, and 2) the verification of signal tracking performance is carried out based on extracted signal feature. When feature extraction model training is performed, CWRU bearing dataset has been utilized. Also, the proposed feature extraction model consists of 1D convolutional layer. In order to extract the signal feature, the criteria of signal feature extraction are summarized as follows: 1) the output of convolutional layer is converted by FFT, 2) RMS values are calculated using FFT signal, and 3) in order to extract and save the index of maximum peak value, the specific sweep range is defined. When performing the step 3), maximum peak value must have higher than a threshold value (RMS value). Furthermore, using the extracted signal feature, the signal tracking is performed through three tracking algorithms, multi-NLMS, neural network, and DRNN. Through the tracking results, it shows that the 1D CNN-based signal feature extraction method could find the signal feature properly and the reference signal obtained from this methodology is employed to a target tracking problem, which shows a great performance. In the future, based on the results of this study, several researches will be conducted as follows: 1) the signal tracking will be conducted for real-time measuring signal, which have at least two state (normal to fault). Also, 2) the active vibration and noise control will be conducted for mechanical system utilizing the tracking signal. 6. ACKNOWLEDGEMENTS

This research was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education(NRF-2021R1A6A1A03039493) 7. REFERENCES

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