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Modeling of nonlinear system based on deep learning framework

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A novel modeling based on deep learning framework which can exactly manifest the characteristics of nonlinear system is proposed in this paper. Specifically, a Deep Reconstruction Model (DRM) is defined integrating with the advantages of the deep learning and Elman neural network (ENN). The parameters of the model are initialized by performing unsupervised pre-training in a layer-wise fashion using restricted Boltzmann machines (RBMs) to provide a faster convergence rate for modeling. ENN can be used to manifest the memory effect of system. To validate the proposed approach, two different nonlinear systems are used for experiments. The first one corresponds to the class-D power amplifier which operates in the ohmic and cutoff regions. According to error of time domain and spectrum, back propagation neural network model improved by RBMs (BP-RBMs) and ENN are compared with different input signals which are the simulated two-tone signal and actual square wave signal. The second system is a permanent magnet synchronous motor servo control system based on fuzzy PID control strategy. In terms of simulated and actual speed curves, BP-RBMs, DRM and ENN models are adopted on comparison, respectively. It is shown by experimental results that the proposed model with fewer parameters and iteration number can reconstruct the nonlinear system accurately and depict the memory effect, the nonlinear distortion and the dynamic performance of system precisely.

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This work was supported in part by the Foundation of Key Laboratory of China’s Education Ministry and A Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions.

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Correspondence to Reza Malekian.

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Jin, X., Shao, J., Zhang, X. et al. Modeling of nonlinear system based on deep learning framework. Nonlinear Dyn 84, 1327–1340 (2016).

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