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Combined recurrent neural networks and particle-swarm optimization for sideslip-angle estimation based on a vehicle multibody dynamics model

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Abstract

The active safety system of a vehicle typically relies on real-time monitoring of the sideslip angle and other critical signals, such as the yaw rate. The vehicle sideslip angle cannot be measured directly due to the high cost and impracticality of sensor networks. The vehicle sideslip can be estimated using kinematic, dynamic, or machine-learning models and available vehicle states. This paper combines recurrent neural networks and the particle-swarm optimization (PSO) algorithm to estimate the vehicle sideslip angle accurately. First, a vehicle-dynamics model is constructed to conduct dynamics simulations of vehicles under various driving conditions and road environments for data collection. Secondly, the obtained vehicle states, including velocity, acceleration, yaw rate, and steering, are used to develop machine-learning models that estimate the vehicle sideslip angle. Two machine-learning models are proposed using the long short-term memory neural network (LSTM) and the bidirectional long short-term memory neural network (BiLSTM). Thirdly, the PSO algorithm is employed to optimize the hyperparameters of the LSTM and BilLSTM models for enhanced estimation precision. The Gaussian noise is added to the datasets to evaluate the robustness of the estimation models. The results indicate that the estimation models are capable of accurately predicting the vehicle’s sideslip angle. The \(R^{2}\) values of the results are mostly greater than 0.96. The PSO algorithm can improve estimation precision, and the PSO-LSTM model performs the best.

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References

  1. Al-qaness, M.A.A., Ewees, A., Abualigah, L., Alrassas, A., Elsayed Abd Elaziz, M.: Evaluating the applications of dendritic neuron model with metaheuristic optimization algorithms for crude-oil-production forecasting. Entropy 24, 1674 (2022)

    Article  ADS  PubMed  PubMed Central  Google Scholar 

  2. Al-qaness, M.A.A., Ewees, A., Elsayed Abd Elaziz, M., Samak, A.: Wind power forecasting using optimized dendritic neural model based on seagull optimization algorithm and aquila optimizer. Energies 15(24), 9261 (2022)

    Article  Google Scholar 

  3. Al-qaness, M.A.A., Ewees, A., Alrassas, A., Dahou, A., Elsayed Abd Elaziz, M.: Predicting CO2 trapping in deep saline aquifers using optimized long short-term memory. Environ. Sci. Pollut. Res. Int. 30(12), 33780–33794 (2023)

    Article  CAS  PubMed  Google Scholar 

  4. Azimi, M., Moradi, S.: Robust optimal solution for a smart rigid–flexible system control during multimode operational mission via actuators in combination. Multibody Syst. Dyn. 52, 1–25 (2021)

    Article  MathSciNet  Google Scholar 

  5. Blanco, J.L., Moreno, J.L., Gimenez, A.: Multibody dynamic systems as Bayesian networks: applications to robust state estimation of mechanisms. Multibody Syst. Dyn. 34, 103–128 (2015)

    Article  MathSciNet  Google Scholar 

  6. Boada, B., Boada, M., Diaz, V.: Vehicle sideslip angle measurement based on sensor data fusion using an integrated ANFIS and an unscented Kalman filter algorithm. Mech. Syst. Signal Process. 72(73), 832–845 (2016)

    Article  ADS  Google Scholar 

  7. Boada, B., Boada, M., Diaz, V.: A robust observer based on energy-to-peak filtering in combination with neural networks for parameter varying systems and its application to vehicle roll angle estimation. Mechatronics 50, 196–204 (2018)

    Article  Google Scholar 

  8. Bonfitto, A., Feraco, S., Tonoli, A., Amati, N.: Combined regression and classification artificial neural networks for sideslip angle estimation and road condition identification. Veh. Syst. Dyn. 58, 1–22 (2019)

    Google Scholar 

  9. Callejo, A., Pan, Y., Ricón, J., Kovecses, J., García de Jalón, J.: Comparison of semirecursive and subsystem synthesis algorithms for the efficient simulation of multibody systems. J. Comput. Nonlinear Dyn. 12, 011020 (2017)

    Article  Google Scholar 

  10. Chen, L., Chen, T., Xu, X., Cai, Y., Jiang, H., Sun, X.: Sideslip angle estimation of in-wheel motor drive electric vehicles by cascaded multi-Kalman filters and modified tire model. Metrol. Meas. Syst. 26, 185–208 (2019)

    Article  CAS  Google Scholar 

  11. Chen, X., Li, S., Li, L., Zhao, W., Cheng, S.: Longitudinal-lateral-cooperative estimation algorithm for vehicle dynamics states based on adaptive-square-root-cubature-Kalman-filter and similarity-principle. Mech. Syst. Signal Process. 176, 109162 (2022)

    Article  Google Scholar 

  12. Chindamo, D., Lenzo, B., Gadola, M.: On the vehicle sideslip angle estimation: a literature review of methods, models, and innovations. Appl. Sci. 8(3), 355 (2018)

    Article  Google Scholar 

  13. Coronel-Escamilla, A., Torres, F., Gómez-Aguilar, J., Escobar Jiménez, R., Guerrero-Ramírez, G.: On the trajectory tracking control for an scara robot manipulator in a fractional model driven by induction motors with pso tuning. Multibody Syst. Dyn. 40, 1–21 (2018)

    MathSciNet  Google Scholar 

  14. Ewees, A.A., Al-qaness, M.A., Abualigah, L., Elaziz, M.A.: Hbo-lstm: optimized long short term memory with heap-based optimizer for wind power forecasting. Energy Convers. Manag. 268, 116022 (2022)

    Article  Google Scholar 

  15. García de Jalón, J., Álvarez, E., de Ribera, F., Rodríguez, I., Funes, F.: A fast and simple semi-recursive formulation for multi-rigid-body systems. In: Ambrósio, J. (ed.) Advances in Computational Multibody Systems. Computational Methods in Applied Sciences, vol. 2, Chap. 1, pp. 1–23. Springer, Dordrecht (2005)

    Google Scholar 

  16. Guo, H., Cao, D., Chen, H., Lv, C., Wang, H., Yang, S.: Vehicle dynamic state estimation: state of the art schemes and perspectives. IEEE/CAA J. Autom. Sin. 5(2), 418–431 (2018)

    Article  Google Scholar 

  17. Guo, J., Luo, Y., Li, K., Dai, Y.: Coordinated path-following and direct yaw-moment control of autonomous electric vehicles with sideslip angle estimation. Mech. Syst. Signal Process. 105, 183–199 (2018)

    Article  ADS  Google Scholar 

  18. Han, B.L., Zhao, R., Luo, Q.S., Xu, F., Zhao, J.H.: Static gait optimization method for quadruped robot based on particle swarm optimization algorithm. Beijing Ligong Daxue Xuebao/Trans. Beijing Inst. Technol. 37, 461–465 (2017)

    Google Scholar 

  19. Hashemi, A., Orzechowski, G., Mikkola, A., McPhee, J.: Multibody dynamics and control using machine learning. Multibody Syst. Dyn. 58, 397–431 (2023)

    Article  MathSciNet  Google Scholar 

  20. He, L., Pan, Y., He, Y., Li, Z., Krolczyk, G., Du, H.: Control strategy for vibration suppression of a vehicle multibody system on a bumpy road. Mech. Mach. Theory 174, 104891 (2022)

    Article  Google Scholar 

  21. Hidalgo, A.F., García de Jalón, J.: Real-time dynamic simulations of large road vehicles using dense, sparse, and parallelization techniques. J. Comput. Nonlinear Dyn. 10(3), 031005 (2015)

    Article  Google Scholar 

  22. Jalali, S., Ahmadian, S., Khodayar, M., Khosravi, A., Ghasemi, V., Shafie-khah, M., Nahavandi, S., Catalão, J.: Towards novel deep neuroevolution models: chaotic Levy grasshopper optimization for short-term wind speed forecasting. Eng. Comput. 38, 1787–1811 (2022)

    Article  Google Scholar 

  23. Khan, T.A., Ling, S.H.: A novel hybrid gravitational search particle swarm optimization algorithm. Eng. Appl. Artif. Intell. 102, 104263 (2021)

    Article  Google Scholar 

  24. Kim, D., Min, K., Kim, H., Huh, K.: Vehicle sideslip angle estimation using deep ensemble-based adaptive Kalman filter. Mech. Syst. Signal Process. 144, 106862 (2020)

    Article  Google Scholar 

  25. Li, L., Jia, G., Ran, X., Song, J., Wu, K.: A variable structure extended Kalman filter for vehicle sideslip angle estimation on a low friction road. Veh. Syst. Dyn. 52(2), 280–308 (2014)

    Article  ADS  Google Scholar 

  26. Li, M., Si, W., Ren, Q., Song, L., Liu, H.: An integrated method for evaluating and predicting long-term operation safety of concrete dams considering lag effect. Eng. Comput. 37, 2505–2519 (2021)

    Article  Google Scholar 

  27. Liao, Y.W., Borrelli, F.: An adaptive approach to real-time estimation of vehicle sideslip, road bank angles, and sensor bias. IEEE Trans. Veh. Technol. 68(8), 7443–7454 (2019)

    Article  Google Scholar 

  28. Liu, J., Wang, Z., Zhang, L., Walker, P.: Sideslip angle estimation of ground vehicles: a comparative study. IET Control Theory Appl. 14(20), 3490–3505 (2020)

    Article  Google Scholar 

  29. Melzi, S., Sabbioni, E.: On the vehicle sideslip angle estimation through neural networks: numerical and experimental results. Mech. Syst. Signal Process. 25(6), 2005–2019 (2011)

    Article  ADS  Google Scholar 

  30. Min, C., Pan, Y., Dai, W., Kawsar, I., Li, Z., Wang, G.: Trajectory optimization of an electric vehicle with minimum energy consumption using inverse dynamics model and servo constraints. Mech. Mach. Theory 181, 105185 (2023)

    Article  Google Scholar 

  31. Nguyen, H., Bui, X.N., Hieu, T., Nguyen, H., Nguyen Dinh, A., Thi Thu Hoa, L., Lê, Q.: Prediction of ground vibration intensity in mine blasting using the novel hybrid MARS–PSO–MLP model. Eng. Comput. 38, 4007–4025 (2022)

    Article  Google Scholar 

  32. Nie, X., Min, C., Pan, Y., Li, Z., Krolczyk, G.: An improved deep neural network model of intelligent vehicle dynamics via linear decreasing weight particle swarm and invasive weed optimization algorithms. Sensors 22, 4676 (2022)

    Article  ADS  PubMed  PubMed Central  Google Scholar 

  33. 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 22, 2013 (2022)

    Article  ADS  PubMed  PubMed Central  Google Scholar 

  34. Pan, Y., Callejo, A., Bueno, J.L., Wehage, R.A., García de Jalón, J.: Efficient and accurate modeling of rigid rods. Multibody Syst. Dyn. 40(1), 23–42 (2017)

    Article  MathSciNet  Google Scholar 

  35. Pan, Y., He, Y., Mikkola, A.: Accurate real-time truck simulation via semirecursive formulation and Adams–Bashforth–Moulton algorithm. Acta Mech. Sin. 35, 641–652 (2019)

    Article  ADS  MathSciNet  Google Scholar 

  36. Pan, Y., Dai, W., Xiong, Y., Xiang, S., Mikkola, A.: Tree-topology-oriented modeling for the real-time simulation of sedan vehicle dynamics using independent coordinates and the rod-removal technique. Mech. Mach. Theory 143, 103626 (2020)

    Article  Google Scholar 

  37. Pan, Y., Huang, L., Dai, W., Zhao, J., Yu, X., Mikkola, A.: Rod-removal technique for flexible-rods in the framework of semi-recursive multibody formulation. Mech. Mach. Theory 169, 104625 (2022)

    Article  Google Scholar 

  38. Pan, Y., Sun, Y., Min, C., Li, Z., Gardoni, P.: Maneuver-based deep learning parameter identification of vehicle suspensions subjected to performance degradation. Veh. Syst. Dyn. 61, 1–17 (2022)

    Google Scholar 

  39. Pan, Y., Sun, Y., Li, Z., Gardoni, P.: Machine learning approaches to estimate suspension parameters for performance degradation assessment using accurate dynamic simulations. Reliab. Eng. Syst. Saf. 230, 108950 (2023)

    Article  Google Scholar 

  40. Park, G.: Vehicle sideslip angle estimation based on interacting multiple model Kalman filter using low-cost sensor fusion. IEEE Trans. Veh. Technol. 71(6), 6088–6099 (2022)

    Article  Google Scholar 

  41. Rahman, M.A., Venayagamoorthy, G.K.: A hybrid method for power system state estimation using cellular computational network. Eng. Appl. Artif. Intell. 64, 140–151 (2017)

    Article  Google Scholar 

  42. Rajamani, R., Phanomchoeng, G., Piyabongkarn, D., Lew, J.Y.: Algorithms for real-time estimation of individual wheel tire-road friction coefficients. IEEE/ASME Trans. Mechatron. 17(6), 1183–1195 (2012)

    Article  Google Scholar 

  43. Schwerin, R.V.: Multibody System Simulation, Numerical Methods, Algorithms and Software. Springer, Berlin (1999)

    Book  Google Scholar 

  44. Sieberg, P.M., Blume, S., Reicherts, S., Maas, N., Schramm, D.: Hybrid state estimation – a contribution towards reliability enhancement of artificial neural network estimators. IEEE Trans. Intell. Transp. Syst. 23(7), 6337–6346 (2022)

    Article  Google Scholar 

  45. Strano, S., Terzo, M.: Constrained nonlinear filter for vehicle sideslip angle estimation withno a priori knowledge of tyre characteristics. Control Eng. Pract. 71, 10–17 (2018)

    Article  Google Scholar 

  46. Tuerxun, W., Xu, C., Guo, H., Guo, L., Zeng, N., Gao, Y.: A wind power forecasting model using lstm optimized by the modified bald eagle search algorithm. Energies 15, 2031 (2022)

    Article  Google Scholar 

  47. Wang, H., Liu, B., Qiao, J.: Advanced high-speed lane keeping system of autonomous vehicle with sideslip angle estimation. Machines 10(4), 257 (2022)

    Article  Google Scholar 

  48. Wrobel, K., Doroz, R., Porwik, P., Naruniec, J., Kowalski, M.: Using a probabilistic neural network for lip-based biometric verification. Eng. Appl. Artif. Intell. 64, 112–127 (2017)

    Article  Google Scholar 

  49. Xia, X., Xiong, L., Lu, Y., Gao, L., Yu, Z.: Vehicle sideslip angle estimation: fusion of vehicle kinematics and dynamics. Int. J. Veh. Des. 87, 73–94 (2021)

    Article  Google Scholar 

  50. Xia, X., Hashemi, E., Xiong, L., Khajepour, A.: Autonomous vehicle kinematics and dynamics synthesis for sideslip angle estimation based on consensus Kalman filter. IEEE Trans. Control Syst. Technol. 31(1), 179–192 (2023)

    Article  Google Scholar 

  51. Zeng, J., Roy, B., Kumar, D., Mohammed, A., Jahed Armaghani, D., Zhou, J., Mohamad, E.: Proposing several hybrid pso-extreme learning machine techniques to predict tbm performance. Eng. Comput. 38, 3811–3827 (2022)

    Article  Google Scholar 

  52. Zhang, B., Du, H., Lam, J., Zhang, N., Li, W.: A novel observer design for simultaneous estimation of vehicle steering angle and sideslip angle. IEEE Trans. Ind. Electron. 63(7), 4357–4366 (2016)

    Article  ADS  Google Scholar 

  53. Zhang, Q., Jing, H., Liu, Z., Jiang, Y., Gu, M.: A novel PWA lateral dynamics modeling method and switched T-S observer design for vehicle sideslip angle estimation. IEEE Trans. Ind. Electron. 69(2), 1847–1857 (2022)

    Article  Google Scholar 

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Funding

This work was funded by the National Natural Science Foundation of China (No. 12072050).

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Authors and Affiliations

  1. College of Mechanical and Vehicle Engineering, Chongqing University, Chongqing, 400044, China

    Yu Sun, Yongjun Pan & Ibna Kawsar

  2. Exeter Small-Scale Robotics Laboratory, Engineering Department, University of Exeter, Exeter, EX4 4QF, UK

    Gengxiang Wang

  3. Pen-Tung Sah Institute of Micro-Nano Science and Technology, Xiamen University, Xiamen, 361102, China

    Liang Hou

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  1. Yu Sun
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  2. Yongjun Pan
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  4. Gengxiang Wang
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Contributions

Yu Sun: Software, Formal analysis, Data curation, Investigation, Writing-Original draft preparation. Yongjun Pan: Conceptualization, Methodology, Writing-Reviewing and Editing, Supervision, Funding acquisition. Ibna Kawsar: Writing-Reviewing and Editing, Validation. Gengxiang Wang: Formal analysis, Data curation, Validation. Liang Hou: Methodology, Writing-Reviewing and Editing.

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Correspondence to Yongjun Pan.

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Sun, Y., Pan, Y., Kawsar, I. et al. Combined recurrent neural networks and particle-swarm optimization for sideslip-angle estimation based on a vehicle multibody dynamics model. Multibody Syst Dyn (2024). https://doi.org/10.1007/s11044-024-09973-5

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