振動臺實驗廣泛使用在各領域中，包含測試阻尼器、結構體耐震試驗甚至是隔震墊產品測試，因此如何有效的控制振動臺，使其加速度重現能達到預期，一直是重要且熱門的問題。以往的研究以比例-積分-微分控制器(PID)以及三參數控制器(TVC)為基礎，以內、外迴路控制的方法雖然能提升振動臺加速度的性能，但仍有部分問題有待解決，本研究提出使用深度學習的方式，以長短期記憶(Long Short-Term Memory, LSTM)神經網路為架構，透過大量實驗資料訓練出控制器，以提升振動臺重現地震加速度的表現。此架構又可分為內、外迴路控制方法，在外迴路控制方法中以油壓致動器振動臺進行實驗，以深度學習訓練出LSTM前饋控制器，加裝在原本振動臺TVC控制架構中，由實驗證明，其時間域均方根誤差由原本的52.44%下降到38.91%，而頻率域均方根誤差由原本的35.19%下降到25.63%，並與線性逆轉移函數控制器做比較，雖未能達到其效能，但未來發展的價值與進步的空間很大。內迴路控制方法中以伺服馬達振動臺進行實驗，並分別以空臺及加載試體做為驗證，嘗試以LSTM控制器直接對伺服馬達下達電壓命令，提升了電動振動臺加速度的表現，並結合PID控制器形成NN-PID控制器以解決振動臺飄移的問題。實驗數據顯示在原有的PID控制器改為NN-PID控制器後，空臺試驗的時間域RMSE由97.48%下降到69.77%，而加載試體的時間域RMSE由94.78%下降到78.81%，足以顯示長短期記憶神經網路適用於提升振動臺加速度的表現。

Shake table testing has been widely used in various fields, including damper testing, structural testing and even seismic isolator testing. Therefore, accurately reproducing predefined acceleration time histores has always been an important and challenging problem. Previous studies have proposed various methods of inner and outer loop control based on proportional-integral-derivative (PID) and three-variable control (TVC) methods. Although they can improve the acceleration performance of the shake table, there are numerous problems and shortcomings that need to be solved. Deep learning approach is proposed as an alternative for seismic shake table control in this research. Based on the Long Short-Term Memory (LSTM) neural network, the controller is trained to improve the acceleration performance of the shake table. In the outer loop control method, the shake table testing data are used to train a feedforward controller using LSTM which is installed over the original shake table TVC controller. The experimental results prove that the time domain root-mean-square error (RMSE) is improved from 52.44% to 38.91%, and the frequency domain RMSE is decreased from 35.19% to 25.63%. Although the performance is not better than that of the feedforward controller based on the inverse model principle, it shows the value of future potential development and progress. In the inner loop control method, an AC-motor shake table is adopted and the empty table and the loaded test body are used as verifications. LSTM controller is used to directly generate control voltage commands to the servo motor which improves the acceleration performance of the electric shake table. In addition, by combining the PID controller with the neural network controller, the NN-PID controller is able to solve with the problem of table’s drift. After the original PID controller is changed to the NN-PID controller, the time domain RMSE of the empty table decreases from 97.48% to 69.77%, while the time domain RMSE of the loaded test body decreases from 94.78% to 78.81%, which is sufficient enough to show that the LSTM neural network is suitable for improving the acceleration performance of the seismic shake table.

[1] Chen, P. C., Kek, M. K., Hu, Y. W., and Lai, C. T. (2018). Statistical reference values for control performance assessment of seismic shake table testing. Earthquakes and Structures, 15(6), 595-603.
[2] Yao, J., Dietz, M., Xiao, R., Yu, H., Wang, T., & Yue, D. (2016). An overview of control schemes for hydraulic shaking tables. Journal of Vibration and Control, 22(12), 2807–2823.
[3] Dyke, S. J., Spencer, B. F., Quast, P., and Sain, M. K. (1995). Role of Control-Structure Interaction in Protective System Design. Journal of Engineering Mechanics, ASCE, 121(2): 322-338.
[4] Kiam Heong Ang., Chong, G., and Yun Li. (2005). PID Control System Analysis, Design, and Technology. IEEE Transactions on Control Systems Technology, 13(4), 559-576.
[5] Tagawa, Y., & Kajiwara K. (2007). Controller development for the E-Defense shaking table. Proceedings of the Institution of Mechanical Engineers. Journal of Systems and Control Engineering, 221(2), 171-181.
[6] Stoten, D., & Gómez, E. (2001). Adaptive Control of Shaking Tables Using the Minimal Control Synthesis Algorithm. Philosophical Transactions: Mathematical, Physical and Engineering Sciences, 359(1786), 1697-1723.
[7] Nakata, N. (2010). Acceleration Trajectory Tracking Control for Earthquake Simulators. Engineering Structures, 32(8): 2229-2236.
[8] Yang, T. Y., Li, K, Lin, J. Y., Li, Y., and Zhang, Y. F. (2013). Implementation of Nonlinear Control Algorithm for Shaking Table Tests. Proceedings. 5th International Conference on Advances inExperimental Structural Engineering, Taipei, Taiwan.
[9] R. Bouc. (1971). Mathematical model for hysteresis, Reportto the Centre de Recherches Physiques, 16-25, Marseille, France.
[10] Spencer, Jr. B. F., and Yang, G. (1998). Earthquake Simulator Control by Transfer Function Iteration. Proceedings. 12th Engineering Mechanics Conference, LaJolla, CA. 766-769.
[11] Chen, P. C., Lai, C. T., and Tsai, K. C. (2017). A Control Framework for Uniaxial Shaking Tables Considering Tracking Performance and System Robustness. Structural Control and Health Monitoring, 24(11): e2015.
[12] Lee, S.K., Park, E.C., Min, K.W. and Park, J.H. (2007). Real-time substructuring technique for the shaking table test of upper substructures. Engineering Structures, 29(9):2219-2232.
[13] Li, Q., Qian, J., Zhu, Z., Bao, X., Helwa, M. K., and Schoellig, A. P. (2017). Deep Neural Networks forImproved, Impromptu Trajectory Tracking of Quadrotors. Proceedings, IEEE International Conference on Robotics and Automation (ICRA), Singapore.
[14] Paula, M. D., and Acosta, G. G. (2015). Trajectory Tracking Algorithm for Autonomous Vehicles using Adaptive Reinforcement Learning. Proceedings, OCEANS 2015-MTS/IEEE, Washington.
[15] Chen, P., He, Z., Chen, C., and Xu, J. (2018). Control Strategy of Speed Servo Systems Based on Deep Reinforcement Learning. Algorithms, 11(5), 65.
[16] Selma H. Larbi., Nouredine Bourahla., Hacine Benchoubane., Khireddine Choutri. and Mohammed Badaoui. (2020). Earthquake Ground Motion Matching on a Small Electric Shaking Table Using a Combined NN-PDFF Controller. Shock and Vibration, vol. 2020, Article ID 7260590, 14pages.
[17] 簡楷益 (2020)，應用機器學習於結構主動控制律之設計與驗證，國立臺灣科技大學碩士學位論文，陳沛清指導
[18] Kingma, D.P. and Ba, J.L. (2015). Adam, A method for stochastic optimization. The 3rd International Conference for Learning Representations. San Diego.
[19] Ziegler, J.G., and Nichols, N. B. (1942). Optimum Settings for Automatic Controllers. Transactions of the ASME, 64: 759-768.