An Improved Deep Neural Network Model of Intelligent Vehicle Dynamics via Linear Decreasing Weight Particle Swarm and Invasive Weed Optimization Algorithms
Abstract
:1. Introduction
2. DNN Modeling for Vehicle’s Longitudinal-Lateral Dynamics
2.1. Vehicle Dynamics Data Acquisition
2.2. DNN Model of the Vehicle
3. Optimization Algorithms
3.1. Linear Decreasing Weight Particle Swarm Optimization
3.2. Invasive Weed Optimization
4. Numerical Results and Errors
4.1. Numerical Results
- -
- The predicted results of DNNs, LDWPSO-DNNs, and IWO-DNNs for longitudinal responses can fit the results of the vehicle multibody model well. The absolute percentage errors of less than 1% are observed.
- -
- The absolute percentage errors of LDWPSO-DNNs and IWO-DNNs for lateral and longitudinal-lateral responses are smaller than that of DNNs. The results verify that LDWPSO and IWO algorithms improve the prediction accuracy of the DNN model.
4.2. Error Analysis
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
- Guo, H.; Yin, Z.; Cao, D.; Chen, H.; Lv, C. A Review of Estimation for Vehicle Tire-Road Interactions Toward Automated Driving. IEEE Trans. Syst. Man Cybern. Syst. 2019, 49, 14–30. [Google Scholar] [CrossRef]
- Yang, P.; Zang, M.; Zeng, H.; Guo, X. The interactions between an off-road tire and granular terrain: GPU-based DEM-FEM simulation and experimental validation. Int. J. Mech. Sci. 2020, 179, 105634. [Google Scholar] [CrossRef]
- Pang, H.; Yao, R.; Wang, P.; Xu, Z. Adaptive backstepping robust tracking control for stabilizing lateral dynamics of electric vehicles with uncertain parameters and external disturbances. Control. Eng. Pract. 2021, 110, 104781. [Google Scholar] [CrossRef]
- Ye, Y.; Huang, P.; Sun, Y.; Shi, D. MBSNet: A deep learning model for multibody dynamics simulation and its application to a vehicle-track system. Mech. Syst. Signal Process. 2021, 157, 107716. [Google Scholar] [CrossRef]
- Rodríguez, A.J.; Sanjurjo, E.; Pastorino, R.; Ángel Naya, M. State, parameter and input observers based on multibody models and Kalman filters for vehicle dynamics. Mech. Syst. Signal Process. 2021, 155, 107544. [Google Scholar] [CrossRef]
- Sattar, S.; Li, S.; Chapman, M. Road surface monitoring using smartphone sensors: A review. Sensors 2018, 18, 3845. [Google Scholar] [CrossRef] [Green Version]
- Gat, G.; Franco, Y.; Shmulevich, I. Fast dynamic modeling for off-road track vehicles. J. Terramech. 2020, 92, 1–12. [Google Scholar] [CrossRef]
- Yamashita, H.; Chen, G.; Ruan, Y.; Jayakumar, P.; Sugiyama, H. Parallelized Multiscale Off-Road Vehicle Mobility Simulation Algorithm and Full-Scale Vehicle Validation. J. Comput. Nonlinear Dyn. 2020, 15, 091007. [Google Scholar] [CrossRef]
- Ji, X.; He, X.; Lv, C.; Liu, Y.; Wu, J. A vehicle stability control strategy with adaptive neural network sliding mode theory based on system uncertainty approximation. Veh. Syst. Dyn. 2018, 56, 923–946. [Google Scholar] [CrossRef] [Green Version]
- Xing, Y.; Lv, C. Dynamic state estimation for the advanced brake system of electric vehicles by using deep recurrent neural networks. IEEE Trans. Ind. Electron. 2019, 67, 9536–9547. [Google Scholar] [CrossRef]
- Nguyen, T.; Nguyen-Phuoc, D.Q.; Wong, Y.D. Developing artificial neural networks to estimate real-time onboard bus ride comfort. Neural Comput. Appl. 2021, 33, 5287–5299. [Google Scholar] [CrossRef]
- Tuncali, C.E.; Fainekos, G.; Prokhorov, D.; Ito, H.; Kapinski, J. Requirements-Driven Test Generation for Autonomous Vehicles With Machine Learning Components. IEEE Trans. Intell. Veh. 2020, 5, 265–280. [Google Scholar] [CrossRef] [Green Version]
- Singh, P.; Chaudhury, S.; Panigrahi, B.K. Hybrid MPSO-CNN: Multi-level Particle Swarm optimized hyperparameters of Convolutional Neural Network. Swarm Evol. Comput. 2021, 63, 100863. [Google Scholar] [CrossRef]
- Rutherford, S.J.; Cole, D.J. Modelling nonlinear vehicle dynamics with neural networks. Int. J. Veh. Des. 2010, 53, 260–287. [Google Scholar] [CrossRef]
- Kim, D.; Min, K.; Kim, H.; Huh, K. Vehicle sideslip angle estimation using deep ensemble-based adaptive Kalman filter. Mech. Syst. Signal Process. 2020, 144, 106862. [Google Scholar] [CrossRef]
- Devineau, G.; Polack, P.; Altché, F.; Moutarde, F. Coupled longitudinal and lateral control of a vehicle using deep learning. In Proceedings of the 2018 21st International Conference on Intelligent Transportation Systems (ITSC), Maui, HI, USA, 4–7 November 2018; pp. 642–649. [Google Scholar]
- Melzi, S.; Sabbioni, E. On the vehicle sideslip angle estimation through neural networks: Numerical and experimental results. Mech. Syst. Signal Process. 2011, 25, 2005–2019. [Google Scholar] [CrossRef]
- Ji, X.; He, X.; Lv, C.; Liu, Y.; Wu, J. Adaptive-neural-network-based robust lateral motion control for autonomous vehicle at driving limits. Control. Eng. Pract. 2018, 76, 41–53. [Google Scholar] [CrossRef]
- Acosta, M.; Kanarachos, S. Teaching a vehicle to autonomously drift: A data-based approach using neural networks. Knowl.-Based Syst. 2018, 153, 12–28. [Google Scholar] [CrossRef]
- Da Lio, M.; Bortoluzzi, D.; Rosati Papini, G.P. Modelling longitudinal vehicle dynamics with neural networks. Veh. Syst. Dyn. 2020, 58, 1675–1693. [Google Scholar] [CrossRef] [Green Version]
- El-Nagar, A.M.; El-Bardini, M. Hardware-in-the-loop simulation of interval type-2 fuzzy PD controller for uncertain nonlinear system using low cost microcontroller. Appl. Math. Model. 2016, 40, 2346–2355. [Google Scholar] [CrossRef]
- Dai, X.; Ke, C.; Quan, Q.; Cai, K.Y. RFlySim: Automatic test platform for UAV autopilot systems with FPGA-based hardware-in-the-loop simulations. Aerosp. Sci. Technol. 2021, 114, 106727. [Google Scholar] [CrossRef]
- Pan, Y.; Nie, X.; Li, Z.; Gu, S. Data-driven vehicle modeling of longitudinal dynamics based on a multibody model and deep neural networks. Measurement 2021, 180, 109541. [Google Scholar] [CrossRef]
- Arai, R.; Imakura, A.; Sakurai, T. An improvement of the nonlinear semi-NMF based method by considering bias vectors and regularization for deep neural networks. Int. J. Mach. Learn. Comput. 2018, 8, 191–197. [Google Scholar] [CrossRef] [Green Version]
- Jatoth, C.; Gangadharan, G.; Fiore, U. Optimal fitness aware cloud service composition using modified invasive weed optimization. Swarm Evol. Comput. 2019, 44, 1073–1091. [Google Scholar] [CrossRef]
- Xin, J.; Li, S.; Sheng, J.; Zhang, Y.; Cui, Y. Application of Improved Particle Swarm Optimization for Navigation of Unmanned Surface Vehicles. Sensors 2019, 19, 3096. [Google Scholar] [CrossRef] [Green Version]
- Nie, X.; Min, C.; Pan, Y.; Li, K.; Li, Z. Deep-neural-network-based modelling of longitudinal-lateral dynamics to predict the vehicle states for autonomous driving. Sensors 2022, 22, 2013. [Google Scholar] [CrossRef] [PubMed]
- Rodríguez, J.I.; Jiménez, J.M.; Funes, F.J.; de Jalón, J.G. Recursive and residual algorithms for the efficient numerical integration of multi-body systems. Multibody Syst. Dyn. 2004, 11, 295–320. [Google Scholar] [CrossRef]
- de García Jalón, J.; Álvarez, E.; De Ribera, F.; Rodríguez, I.; Funes, F. A fast and simple semi-recursive formulation for multi-rigid-body systems. In Advances in Computational Multibody Systems; Springer: Berlin, Germany, 2005; pp. 1–23. [Google Scholar]
- Pan, Y.; Callejo, A.; Bueno, J.L.; Wehage, R.A.; de Jalón, J.G. Efficient and accurate modeling of rigid rods. Multibody Syst. Dyn. 2017, 40, 23–42. [Google Scholar] [CrossRef] [Green Version]
- Laulusa, A.; Bauchau, O.A. Review of Classical Approaches for Constraint Enforcement in Multibody Systems. J. Comput. Nonlinear Dyn. 2007, 3, 011004. [Google Scholar] [CrossRef] [Green Version]
- Pan, Y.; Dai, W.; Huang, L.; Li, Z.; Mikkola, A. Iterative refinement algorithm for efficient velocities and accelerations solutions in closed-loop multibody dynamics. Mech. Syst. Signal Process. 2021, 152, 107463. [Google Scholar] [CrossRef]
- He, L.; Pan, Y.; He, Y.; Li, Z.; Królczyk, G.; Du, H. Control strategy for vibration suppression of a vehicle multibody system on a bumpy road. Mech. Mach. Theory 2022, 174, 104891. [Google Scholar] [CrossRef]
- Pan, Y.; Xiang, S.; He, Y.; Zhao, J.; Mikkola, A. The validation of a semi-recursive vehicle dynamics model for a real-time simulation. Mech. Mach. Theory 2020, 151, 103907. [Google Scholar] [CrossRef]
- Elen, A.; Avuçlu, E. Standardized Variable Distances: A distance-based machine learning method. Appl. Soft Comput. 2021, 98, 106855. [Google Scholar] [CrossRef]
- Kim, T.Y.; Cho, S.B. Optimizing CNN-LSTM neural networks with PSO for anomalous query access control. Neurocomputing 2021, 456, 666–677. [Google Scholar] [CrossRef]
- Parcham, E.; Ilbeygi, M.; Amini, M. CBCapsNet: A novel writer-independent offline signature verification model using a CNN-based architecture and Capsule Neural Networks. Expert Syst. Appl. 2021, 185, 115649. [Google Scholar] [CrossRef]
- Chang, Z.; Zhang, Y.; Chen, W. Electricity price prediction based on hybrid model of adam optimized LSTM neural network and wavelet transform. Energy 2019, 187, 115804. [Google Scholar] [CrossRef]
- Khan, A.H.; Cao, X.; Li, S.; Katsikis, V.N.; Liao, L. BAS-ADAM: An ADAM based approach to improve the performance of beetle antennae search optimizer. IEEE/CAA J. Autom. Sin. 2020, 7, 461–471. [Google Scholar] [CrossRef]
- Zhang, P.; Li, H.; Ha, Q.; Yin, Z.Y.; Chen, R.P. Reinforcement learning based optimizer for improvement of predicting tunneling-induced ground responses. Adv. Eng. Inform. 2020, 45, 101097. [Google Scholar] [CrossRef]
- Amer, N.H.; Hudha, K.; Zamzuri, H.; Aparow, V.R.; Kadir, Z.A.; Abidin, A.F.Z. Hardware-in-the-loop simulation of trajectory following control for a light armoured vehicle optimised with particle swarm optimisation. Int. J. Heavy Veh. Syst. 2019, 26, 663–691. [Google Scholar] [CrossRef]
- Guo, X.; Ji, M.; Zhao, Z.; Wen, D.; Zhang, W. Global path planning and multi-objective path control for unmanned surface vehicle based on modified particle swarm optimization (PSO) algorithm. Ocean. Eng. 2020, 216, 107693. [Google Scholar] [CrossRef]
- Le, T.L.; Lin, C.M.; Huynh, T.T. Self-evolving type-2 fuzzy brain emotional learning control design for chaotic systems using PSO. Appl. Soft Comput. 2018, 73, 418–433. [Google Scholar] [CrossRef]
Parameter | Value |
---|---|
Vehicle mass | 1155 kg |
Wheelbase | 2.8 m |
Centroid height | 0.5373 m |
Tire rolling radius | 0.4673 kg |
Stiffness of front absorber | 40,000 N/m |
Stiffness of rear absorber | 35,000 N/m |
Damping of front absorber | 1800 N/(m/s) |
Damping of rear absorber | 1800 N/(m/s) |
Distance from centroid to front axle | 0.7209 m |
Distance from centroid to rear axle | 2.0791 m |
Final Longitudinal Distance | MAE (m) | MAPE (%) | RMSE (m) | |
---|---|---|---|---|
DNN | 0.107476 | 0.078521 | 0.135354 | 0.999990 |
LDWPSO-DNN | 0.071606 | 0.049622 | 0.138596 | 0.999990 |
IWO-DNN | 0.062153 | 0.048728 | 0.135021 | 0.999990 |
Final Lateral Distance | MAE (m) | MAPE (%) | RMSE (m) | |
---|---|---|---|---|
DNN | 0.002647 | 9.346083 | 0.006920 | 0.998541 |
LDWPSO-DNN | 0.002158 | 4.741057 | 0.003724 | 0.999577 |
IWO-DNN | 0.001912 | 3.201640 | 0.003467 | 0.999634 |
Final Longitudinal Velocity | MAE (m/s) | MAPE (%) | RMSE (m/s) | |
---|---|---|---|---|
DNN | 0.013769 | 0.050521 | 0.018431 | 0.999996 |
LDWPSO-DNN | 0.009383 | 0.032383 | 0.015797 | 0.999997 |
IWO-DNN | 0.007688 | 0.025955 | 0.015518 | 0.999997 |
Final Lateral Velocity | MAE (m/s) | MAPE (%) | RMSE (m/s) | |
---|---|---|---|---|
DNN | 0.000524 | 7.754304 | 0.001778 | 0.996591 |
LDWPSO-DNN | 0.000341 | 4.861110 | 0.000791 | 0.999325 |
IWO-DNN | 0.000290 | 3.255596 | 0.000848 | 0.999224 |
Yaw Angle | MAE (rad) | MAPE (%) | RMSE (rad) | |
---|---|---|---|---|
DNN | 0.000014 | 6.804836 | 0.000040 | 0.998480 |
LDWPSO-DNN | 0.000010 | 3.879418 | 0.000026 | 0.999348 |
IWO-DNN | 0.000008 | 3.176424 | 0.000016 | 0.999734 |
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |
© 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
Share and Cite
Nie, X.; Min, C.; Pan, Y.; Li, Z.; Królczyk, G. An Improved Deep Neural Network Model of Intelligent Vehicle Dynamics via Linear Decreasing Weight Particle Swarm and Invasive Weed Optimization Algorithms. Sensors 2022, 22, 4676. https://doi.org/10.3390/s22134676
Nie X, Min C, Pan Y, Li Z, Królczyk G. An Improved Deep Neural Network Model of Intelligent Vehicle Dynamics via Linear Decreasing Weight Particle Swarm and Invasive Weed Optimization Algorithms. Sensors. 2022; 22(13):4676. https://doi.org/10.3390/s22134676
Chicago/Turabian StyleNie, Xiaobo, Chuan Min, Yongjun Pan, Zhixiong Li, and Grzegorz Królczyk. 2022. "An Improved Deep Neural Network Model of Intelligent Vehicle Dynamics via Linear Decreasing Weight Particle Swarm and Invasive Weed Optimization Algorithms" Sensors 22, no. 13: 4676. https://doi.org/10.3390/s22134676
APA StyleNie, X., Min, C., Pan, Y., Li, Z., & Królczyk, G. (2022). An Improved Deep Neural Network Model of Intelligent Vehicle Dynamics via Linear Decreasing Weight Particle Swarm and Invasive Weed Optimization Algorithms. Sensors, 22(13), 4676. https://doi.org/10.3390/s22134676