State reconstruction in a nonlinear vehicle suspension system using deep neural networks

Hwanmoo Yong, Joohwan Seo, Jungkyu Kim, Jongeun Choi

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


Modern control synthesis assumes that observability of a dynamic system is satisfied. However, in particular, observability may not be met due to manufacturing cost. To cope with this challenging dilemma, we consider training a neural network with a large dataset that contains prior information of a given nonlinear vehicle dynamics system. In this paper, we proposed and designed a long short-term memory (LSTM)-based neural network to estimate the velocity and position states of a full car’s suspension system using only online data streams from cheap inertial sensory measurements. In the training stage, we collect the input and output data that we want to reconstruct using a nonlinear full car model simulation. An LSTM-based neural network is subsequently trained with the collected data, and it reconstructs the velocity and position states only from the acceleration information inputs in the production stage. Finally, to further enhance the performance via Bayesian filtering, the neural network’s outputs are projected into the vehicle dynamics using the extended Kalman filter. To demonstrate the effectiveness of our approach, we compare the performance of the proposed method against a conventional kinematic Kalman filter. The results show that the proposed method recorded 148.8 times smaller value in terms of the mean squared error (MSE) than that of the benchmark. Furthermore, we analyzed the sensitivity of the proposed neural network with or without gyroscope sensors in the full car model. Then, an illustrative control example for implementing the proposed method is presented. Our approach shows that with only noisy accelerometer and gyroscope sensors, we can successfully reconstruct nearly perfect states in a full car’s nonlinear dynamic system using a well-trained LSTM-based neural network combined with the extended Kalman filter.

Original languageEnglish
Pages (from-to)439-455
Number of pages17
JournalNonlinear Dynamics
Issue number1
Publication statusPublished - 2021 Jul

Bibliographical note

Funding Information:
This work was supported in part by the National Research Foundation of Korea grant funded by the Korea government (Ministry of Science and Information Technology, 2021R1A2B5B01002620) and in part by the Ministry of Culture, Sports and Tourism (MCST) and the Korea Creative Content Agency (KOCCA) thorugh the Culture Technology (CT) Research & Development Program 2019 (R2019020038).

Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer Nature B.V.

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Aerospace Engineering
  • Ocean Engineering
  • Mechanical Engineering
  • Electrical and Electronic Engineering
  • Applied Mathematics


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