Document Type : Article

**Authors**

College of Mechanical and Electrical Engineering, Harbin Engineering University, Harbin 150001, Heilongjiang，China

**Abstract**

The paper aims to develop a harmonic identification scheme for a hydraulic shaking table’s sinusoidal acceleration response. Nonlinearities are inherent in a hydraulic shaking table. Some of them are dead zone of servo valve, backlash and friction between joints, and friction in actuator. Nonlinearities cause harmonic distortion of the system shaking response when it correspondsto a sinusoidal excitation. This lowers the system control performance. An efficient, time-domain acceleration harmonic identification is developed by using Hopfield neural network. Due to the introduction of energy function used to optimize the computation for the identification harmonic method, the fully connected, single layer feedback neural network does not require training in advance and is able to identifyharmonic amplitudes and phase angles. Each harmonic,as well asthe fundamental response,can be directly obtained.Simulations and experiments show very promising results that the proposed scheme is really applicable to identify harmonicswith high precision and good convergence. Comparisons between the presented method and other method are carried out to further demonstrate its efficiency.

**Keywords**

- Electro-hydraulic shaking table
- Acceleration harmonic
- Harmonic identification
- Hopfield neural network
- Real-time performance

**Main Subjects**

References

1. Yao, J.J., Hu, S.H., Fu, W. and Han, J.W. Impact of

excitation signal upon the acceleration harmonic distortionof an electro-hydraulic shaking table", Journalof Vibration and Control, 17(7), pp. 1106-1111 (2011).

2. Chung, Y.L., Nagae, T., Hitaka, T. and Nakashima,

M. Seismic resistance capacity of high-rise buildings subjected to long-period ground motions: E-defense shaking table test", Journal of Structural Engineering,

136(6), pp. 637-644 (2010).

excitation signal upon the acceleration harmonic distortionof an electro-hydraulic shaking table", Journalof Vibration and Control, 17(7), pp. 1106-1111 (2011).

2. Chung, Y.L., Nagae, T., Hitaka, T. and Nakashima,

M. Seismic resistance capacity of high-rise buildings subjected to long-period ground motions: E-defense shaking table test", Journal of Structural Engineering,

136(6), pp. 637-644 (2010).

3. Merritt, H.E., Hydraulic Control Systems, New York:

Wiley (1967).4. Lin, H.C. Intelligent neural network based dynamic

power system harmonic analysis", International Conference

on Power System Technology, Singapore, pp.

244-248 (2004).

5. Wang, X.H., He, Y.G. and Long, Y. Neural network

based high accuracy frequency harmonic analysis in

power system", 4th International Symposium on Neural

Networks, Nanjing, China, pp. 1006-1014 (2007).

6. Hamad, M.S., Gadoue, S.M. and Williams, B.W.

Harmonic compensation of a six-pulse current source

controlled converter using neural network-based shunt

active power lter", IET Power Electronics, 5(6), pp.

747-754 (2012).

7. Abdeslam, D.O., Wira, P., Fliellert, D. and Merckle, J.

Power harmonic identication and compensation with

an articial neural network method", IEEE International

Symposium on Industrial Electronics, Montreal,

QC, Canada, pp. 1732-1737 (2006).

8. Almaita, E. and Asumadu, J.A. On-line harmonic

estimation in power system based on sequential training

radial basis function neural network", Proceedings

of the IEEE International Conference on Industrial

Technology, Auburn, AL, United states, pp. 139-144

(2011).

9. Arabaci, H. An articial neural network approach for

sensorless speed estimation via rotor slot harmonics",

Turkish Journal of Electrical Engineering and Computer

Sciences, 22(4), pp. 1076-1084 (2014).

10. Nascimento, C.F., Oliveira Jr., A.A., Goedtel, A. and

Dietrich, A.B. Harmonic distortion monitoring for

nonlinear loads using neural-network-method", Applied

Soft Computing Journal, 13(1), pp. 475-482

(2013).

11. Ulinuha, A., Masoum, M.A.S. and Islam, S. Hybrid

genetic-fuzzy algorithm for volt/var/total harmonic

distortion control of distribution systems with high

penetration of non-linear loads", IET Generation,

Transmission and Distribution, 5(4), pp. 425-439

(2011).

12. Zamanan, N., Sykulski, J. and Al-Othman, A.K. A

digital technique for online identication and tracking

of power system harmonics based on real coded genetic

algorithm", 6th IASTED International Conference on

European Power and Energy Systems, Rhodes, Greece,

pp. 144-148 (2006).

13. Xue, Z.H., Du, P.J. and Su, H.J. Harmonic analysis

for hyperspectral image classication integrated with

PSO optimized SVM", IEEE Journal of Selected Topics

in Applied Earth Observations and Remote Sensing,

7(6), pp. 2131-2146 (2014).

14. Yin, Y.N., Lin, W.X. and Li, W.L. Estimation

amplitude and phase of harmonic based on improved

PSO", 8th IEEE International Conference on Control

and Automation, Xiamen, China, pp. 826-831 (2010).

15. Yang, X.F. and Wang, J.L. An analysis method for

power system transient signal based on improved prony

algorithm and PSO algorithm", International Conference

on Information Technology and Applications,

Chengdu, China, pp. 209-213 (2013).

310 J. Yao et al./Scientia Iranica, Transactions B: Mechanical Engineering 25 (2018) 299{310

16. Vasumathi, B. and Moorthi, S. Implementation of

hybrid ANNPSO algorithm on FPGA for harmonic

estimation", Engineering Applications of Articial Intelligence,

25(3), pp. 476-483 (2012).

17. Ray, P.K. and Subudhi, B. Ensemble-Kalman-lterbased

power system harmonic estimation", IEEE

Transactions on Instrumentation and Measurement,

61(12), pp. 3216-3224 (2012).

18. Singh, S.K., Sinha, N., Goswami, A.K. and Sinha, N.

Several variants of Kalman Filter algorithm for power

system harmonic estimation", International Journal of

Electrical Power and Energy Systems, 78(1), pp. 793-

800 (2016).

19. Jatoth, R.K. and Reddy, G.A. A hybrid GA-adaptive

particle swarm optimization based tuning of unscented

Kalman lter for harmonic estimation", Lecture Notes

in Computer Science, Chennai, India, pp. 380-388

(2010).

20. Ren, J. and Kezunovic, M. A wavelet method for

power system frequency and harmonic estimation",

North American Power Symposium, Arlington, TX,

United states, pp. 1052-1056 (2010).

21. Jain, S.K., Saxena, D. and Singh, S.N. Adaptive

wavelet neural network based harmonic estimation of

single-phase systems", Proceedings of the 2011 International

Conference and Utility Exhibition on Power

and Energy Systems: Issues and Prospects for Asia,

Pattaya City, Thailand, pp. 1113-1117 (2012).

22. Yang, J.N. and Cheng, L. A wavelet model for online

tracking of power system: Time-varying harmonics

using Kaman ltering", International Conference on

Informationization, Automation and Electrication in

Agriculture, Zhengjiang, China, pp. 351-358 (2008).

23. Yao, J.J., Jiang, G.L., Di, D.T. and Liu, S. Acceleration

harmonic identication for an electro-hydraulic

servo shaking table based on the normalized leastmean-

square adaptive algorithm", Journal of Vibration

and Control, 19(1), pp. 47-55 (2013).

24. Yao, J.J., Di, D.T., Jiang G.L. and Gao, S. Acceleration

amplitude-phase regulation for electro-hydraulic

servo shaking table based on LMS adaptive ltering

algorithm", Journal of Vibration and Control, 85(10),

pp. 1581-1592 (2012).

25. Yao, J.J., Zhang, L., Chen, S., Wan, Z.S., Wang, T.

and Niu, Q.T. Translational shaking tests achieved on

a 6-DOF hydraulic parallel manipulator", Industrial

Robot: An International Journal, 43(1), pp. 103-111

(2016).

26. Hillar, C., Mehta, R. and Koepsel, K. A hopeld

recurrent neural network trained on natural images

performs state-of-the-art image compression", IEEE

International Conference on Image Processing, Paris,

France, pp. 4092-4096 (2014).

27. Martin, T.H., Neural Network Design, Beijing: China

Machine Press (2007).

28. Singh, S.K., Nath, A., Chakraborty, R., Kalita, J.,

Sinha, N. and Goswami, A.K. Fast transverse-RLS

algorithm based power system harmonic estimation",

2014 International Conference on Information Communication

and Embedded Systems, Chennai, India,

pp. 1253-1257 (2015).

29. Garanayak, P., Panda, G. and Ray, P.K. Harmonic

estimation using RLS algorithm and elimination with

improved current control technique based SAPF in a

distribution network", International Journal of Electrical

Power and Energy Systems, 73(12), pp. 209-217

(2015).

30. Ray, P.K. and Subudhi, B. BFO optimized RLS

algorithm for power system harmonics estimation",

Applied Soft Computing Journal, 12(8), pp. 1965-1977

(2012).

Wiley (1967).4. Lin, H.C. Intelligent neural network based dynamic

power system harmonic analysis", International Conference

on Power System Technology, Singapore, pp.

244-248 (2004).

5. Wang, X.H., He, Y.G. and Long, Y. Neural network

based high accuracy frequency harmonic analysis in

power system", 4th International Symposium on Neural

Networks, Nanjing, China, pp. 1006-1014 (2007).

6. Hamad, M.S., Gadoue, S.M. and Williams, B.W.

Harmonic compensation of a six-pulse current source

controlled converter using neural network-based shunt

active power lter", IET Power Electronics, 5(6), pp.

747-754 (2012).

7. Abdeslam, D.O., Wira, P., Fliellert, D. and Merckle, J.

Power harmonic identication and compensation with

an articial neural network method", IEEE International

Symposium on Industrial Electronics, Montreal,

QC, Canada, pp. 1732-1737 (2006).

8. Almaita, E. and Asumadu, J.A. On-line harmonic

estimation in power system based on sequential training

radial basis function neural network", Proceedings

of the IEEE International Conference on Industrial

Technology, Auburn, AL, United states, pp. 139-144

(2011).

9. Arabaci, H. An articial neural network approach for

sensorless speed estimation via rotor slot harmonics",

Turkish Journal of Electrical Engineering and Computer

Sciences, 22(4), pp. 1076-1084 (2014).

10. Nascimento, C.F., Oliveira Jr., A.A., Goedtel, A. and

Dietrich, A.B. Harmonic distortion monitoring for

nonlinear loads using neural-network-method", Applied

Soft Computing Journal, 13(1), pp. 475-482

(2013).

11. Ulinuha, A., Masoum, M.A.S. and Islam, S. Hybrid

genetic-fuzzy algorithm for volt/var/total harmonic

distortion control of distribution systems with high

penetration of non-linear loads", IET Generation,

Transmission and Distribution, 5(4), pp. 425-439

(2011).

12. Zamanan, N., Sykulski, J. and Al-Othman, A.K. A

digital technique for online identication and tracking

of power system harmonics based on real coded genetic

algorithm", 6th IASTED International Conference on

European Power and Energy Systems, Rhodes, Greece,

pp. 144-148 (2006).

13. Xue, Z.H., Du, P.J. and Su, H.J. Harmonic analysis

for hyperspectral image classication integrated with

PSO optimized SVM", IEEE Journal of Selected Topics

in Applied Earth Observations and Remote Sensing,

7(6), pp. 2131-2146 (2014).

14. Yin, Y.N., Lin, W.X. and Li, W.L. Estimation

amplitude and phase of harmonic based on improved

PSO", 8th IEEE International Conference on Control

and Automation, Xiamen, China, pp. 826-831 (2010).

15. Yang, X.F. and Wang, J.L. An analysis method for

power system transient signal based on improved prony

algorithm and PSO algorithm", International Conference

on Information Technology and Applications,

Chengdu, China, pp. 209-213 (2013).

310 J. Yao et al./Scientia Iranica, Transactions B: Mechanical Engineering 25 (2018) 299{310

16. Vasumathi, B. and Moorthi, S. Implementation of

hybrid ANNPSO algorithm on FPGA for harmonic

estimation", Engineering Applications of Articial Intelligence,

25(3), pp. 476-483 (2012).

17. Ray, P.K. and Subudhi, B. Ensemble-Kalman-lterbased

power system harmonic estimation", IEEE

Transactions on Instrumentation and Measurement,

61(12), pp. 3216-3224 (2012).

18. Singh, S.K., Sinha, N., Goswami, A.K. and Sinha, N.

Several variants of Kalman Filter algorithm for power

system harmonic estimation", International Journal of

Electrical Power and Energy Systems, 78(1), pp. 793-

800 (2016).

19. Jatoth, R.K. and Reddy, G.A. A hybrid GA-adaptive

particle swarm optimization based tuning of unscented

Kalman lter for harmonic estimation", Lecture Notes

in Computer Science, Chennai, India, pp. 380-388

(2010).

20. Ren, J. and Kezunovic, M. A wavelet method for

power system frequency and harmonic estimation",

North American Power Symposium, Arlington, TX,

United states, pp. 1052-1056 (2010).

21. Jain, S.K., Saxena, D. and Singh, S.N. Adaptive

wavelet neural network based harmonic estimation of

single-phase systems", Proceedings of the 2011 International

Conference and Utility Exhibition on Power

and Energy Systems: Issues and Prospects for Asia,

Pattaya City, Thailand, pp. 1113-1117 (2012).

22. Yang, J.N. and Cheng, L. A wavelet model for online

tracking of power system: Time-varying harmonics

using Kaman ltering", International Conference on

Informationization, Automation and Electrication in

Agriculture, Zhengjiang, China, pp. 351-358 (2008).

23. Yao, J.J., Jiang, G.L., Di, D.T. and Liu, S. Acceleration

harmonic identication for an electro-hydraulic

servo shaking table based on the normalized leastmean-

square adaptive algorithm", Journal of Vibration

and Control, 19(1), pp. 47-55 (2013).

24. Yao, J.J., Di, D.T., Jiang G.L. and Gao, S. Acceleration

amplitude-phase regulation for electro-hydraulic

servo shaking table based on LMS adaptive ltering

algorithm", Journal of Vibration and Control, 85(10),

pp. 1581-1592 (2012).

25. Yao, J.J., Zhang, L., Chen, S., Wan, Z.S., Wang, T.

and Niu, Q.T. Translational shaking tests achieved on

a 6-DOF hydraulic parallel manipulator", Industrial

Robot: An International Journal, 43(1), pp. 103-111

(2016).

26. Hillar, C., Mehta, R. and Koepsel, K. A hopeld

recurrent neural network trained on natural images

performs state-of-the-art image compression", IEEE

International Conference on Image Processing, Paris,

France, pp. 4092-4096 (2014).

27. Martin, T.H., Neural Network Design, Beijing: China

Machine Press (2007).

28. Singh, S.K., Nath, A., Chakraborty, R., Kalita, J.,

Sinha, N. and Goswami, A.K. Fast transverse-RLS

algorithm based power system harmonic estimation",

2014 International Conference on Information Communication

and Embedded Systems, Chennai, India,

pp. 1253-1257 (2015).

29. Garanayak, P., Panda, G. and Ray, P.K. Harmonic

estimation using RLS algorithm and elimination with

improved current control technique based SAPF in a

distribution network", International Journal of Electrical

Power and Energy Systems, 73(12), pp. 209-217

(2015).

30. Ray, P.K. and Subudhi, B. BFO optimized RLS

algorithm for power system harmonics estimation",

Applied Soft Computing Journal, 12(8), pp. 1965-1977

(2012).

Volume 25, Issue 1

Transactions on Mechanical Engineering (B)

January and February 2018Pages 299-310