# Neural Network Based Modeling of Hysteresis in Smart Material Based Sensors

## Abstract

Hysteresis is a nonlinear phenomenon which is involved with dynamics, non-smoothness and multi-valued mapping. It usually exists in elastic materials, smart materials, and energy-storage materials. For describing the characteristic of hysteresis, a basis function based neural network model is proposed in this paper. In this method, the multi-valued mapping of hysteresis is transferred into a one-to-one mapping with an expanded input space involving the input variable and a constructed hysteretic auxiliary function. Thus, the neural network can be employed to approximate the characteristic of hysteresis. Finally, the method is used to the modeling of hysteresis in a smart material based sensor.

## Keywords

Hysteresis Expanded input space Neural network Modeling## Notes

### Acknowledgment

The work presented in this paper has been funded by the National Science Foundation of China under Grants 61671303 and 61571302, the Open Fund of the Key Laboratory of Nano-Devices and Applications, Chinese Academy of Sciences under Grant 18ZS06, the Shanghai Pujiang Program under Grant 18PJ1400100, the Natural Science Foundation of Shanghai under Grant 16ZR1446700, and the project of the Science and Technology Commission of Shanghai under Grant 18070503000.

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