\r\nsystems are discussed. Specially, for linear system with single-input

\r\nsingle-output, it could be modeled with shallow neural network.

\r\nThen, gradient based optimization algorithms are used for searching

\r\nthe proper coefficients. Besides, method with normal equation and

\r\nsecond order gradient descent are proposed to accelerate the modeling

\r\nprocess, and ways of better gradient estimation are discussed. It

\r\nshows that the mathematical essence of the learning objective is

\r\nmaximum likelihood with noises under Gaussian distribution. For

\r\nconventional gradient descent, the mini-batch learning and gradient

\r\nwith momentum contribute to faster convergence and enhance model

\r\nability. Lastly, experimental results proved the effectiveness of second

\r\norder gradient descent algorithm, and indicated that optimization with

\r\nnormal equation was the most suitable for linear dynamic models.","references":"[1] J. P. Xiang, \u201cDynamic properties of force transducer,\u201d Process\r\nAutomation instrumentation, no. 6, pp. 12\u201321+102, 1981.\r\n[2] A. Simpkins, \u201cSystem identification: Theory for the user, 2nd edition,\u201d\r\nIEEE Robotics Automation Magazine, vol. 19, no. 2, pp. 95\u201396, June\r\n2012.\r\n[3] K. J. Xu and M. Yin, \u201cA dynamic modeling method based on flann for\r\nwrist force sensor,\u201d Chinese Journal of Scientific Instrument, vol. 21,\r\nno. 1, pp. 92\u201394, 2000.\r\n[4] S. P. Tian, P. P. Jiang, and G. Z. Yan, \u201cApplication o-f recurrent neural\r\nnetwork to dynamic modeling of sensors,\u201d Chinese Journal of Scientific\r\nInstrument, vol. 25, no. 5, pp. 574\u2013576, 2004. [5] X. D. Wang, C. J. Zhang, and H. R. Zhang, \u201cSensor dynamic\r\nmodeling using least square support vector machines,\u201d Chinese Journal\r\nof Scientific Instrument, vol. 27, no. 7, pp. 730\u2013733, 2006.\r\n[6] D. H. Wu, W. Zhao, S. L. Huang, and S. K. He, \u201cResearch on improved\r\nflann for sensor dynamic modeling,\u201d Chinese Journal of Scientific\r\nInstrument, no. 2, pp. 362\u2013367, 2009.\r\n[7] W. J. Yang, \u201cResearch on dynamic characteristics and compensation\r\ntechnology of pressure sensors,\u201d Master\u2019s thesis, North University of\r\nChina, Shanxi, 2017.\r\n[8] T. Dab\u00b4oczi, \u201cUncertainty of signal reconstruction in the case of jittery\r\nand noisy measurements,\u201d IEEE Transactions on Instrumentation and\r\nMeasurement, vol. 47, no. 5, pp. 1062\u20131066, 1998.\r\n[9] J. Brignell, \u201cSoftware techniques for sensor compensation,\u201d Sensors and\r\nActuators A: Physical, vol. 25, no. 1-3, pp. 29\u201335, 1990.\r\n[10] M. A. Nielsen, Neural Networks and Deep Learning. Determination\r\nPress, 2015.\r\n[11] S. P. Tian, Y. Zhao, W. H. Yu, and Z. W. Wang, \u201cNonlinear\r\ncompensation of sensors based on bp neural network,\u201d Journal of Test\r\nand Measurement Technology, vol. 21, no. 1, pp. 84\u201389, 2007.\r\n[12] She Ping Tian, \u201cNonlinear dynamic compensation of sensors based\r\non recurrent neural network model,\u201d Journal of Shanghai Jiao Tong\r\nUniversity, vol. 37, no. 1, pp. 13\u201316, 2003.\r\n[13] H. M. Huang, \u201cDynamical compensation method for weighting sensor\r\nbased on flann,\u201d Transducer and Microsystem Technologies, vol. 25,\r\nno. 8, pp. 25\u201328, 2006.\r\n[14] L. Q. Hou, W. G. Tong, and T. X. He, \u201cNonlinear errors correcting\r\nmethod of sensors based on rbf neural network,\u201d Journal of Transducer\r\nTechnology, vol. 17, no. 4, pp. 643\u2013646, 2004.\r\n[15] Y. LeCun, B. Boser, J. S. Denker, D. Henderson, R. E. Howard,\r\nW. Hubbard, and L. D. Jackel, \u201cBackpropagation applied to handwritten\r\nzip code recognition,\u201d Neural computation, vol. 1, no. 4, pp. 541\u2013551,\r\n1989.\r\n[16] H. Li, Statistical learning method. Beijing: Tsing Hua University Press,\r\n2012.\r\n[17] D. H.Wu, \u201cDynamic compensating method for transducer based on flann\r\ninverse system constructed by ls-svm,\u201d Journal of Data Acquisition and\r\nProcessing, vol. 22, no. 3, pp. 378\u2013383, 2007.\r\n[18] I. Goodfellow, Y. Bengio, and A. Courville, Deep Learning. MIT Press,\r\n2016.\r\n[19] N. Qian, \u201cOn the momentum term in gradient descent learning\r\nalgorithms,\u201d Neural Networks, vol. 12, no. 1, pp. 145\u2013151, 1 1999.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 143, 2018"}