Analysis for global characteristics of Lyapunov exponents in vehicle plane motion system
In the field of vehicle system dynamics, it is significant to propose an appropriate quantitative indicator for system stability or dynamics characteristics. Lyapunov exponents method is an excellent quantitative indicator for analysing nonlinear system characteristics. It was used to studied the st...
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| Published in | Scientific reports Vol. 12; no. 1; pp. 9300 - 14 |
|---|---|
| Main Authors | , , , , |
| Format | Journal Article |
| Language | English |
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Nature Publishing Group UK
03.06.2022
Nature Publishing Group Nature Portfolio |
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| Abstract | In the field of vehicle system dynamics, it is significant to propose an appropriate quantitative indicator for system stability or dynamics characteristics. Lyapunov exponents method is an excellent quantitative indicator for analysing nonlinear system characteristics. It was used to studied the stable region of nonlinear vehicle plane motion system. However, the effect of Lyapunov exponents method in revealing the global dynamics characteristics has not been fully studied. Aiming at this key problem, this paper analyses the global characteristics of Lyapunov exponents with different degrees of freedom nonlinear models. The results show that Lyapunov exponents can well reflect the global layer characteristics for vehicle system. However, the value characteristic under different DOF models is not unified. The research and analysis in this paper supplement the quantitative analysis theory for vehicle system dynamics. |
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| AbstractList | In the field of vehicle system dynamics, it is significant to propose an appropriate quantitative indicator for system stability or dynamics characteristics. Lyapunov exponents method is an excellent quantitative indicator for analysing nonlinear system characteristics. It was used to studied the stable region of nonlinear vehicle plane motion system. However, the effect of Lyapunov exponents method in revealing the global dynamics characteristics has not been fully studied. Aiming at this key problem, this paper analyses the global characteristics of Lyapunov exponents with different degrees of freedom nonlinear models. The results show that Lyapunov exponents can well reflect the global layer characteristics for vehicle system. However, the value characteristic under different DOF models is not unified. The research and analysis in this paper supplement the quantitative analysis theory for vehicle system dynamics. Abstract In the field of vehicle system dynamics, it is significant to propose an appropriate quantitative indicator for system stability or dynamics characteristics. Lyapunov exponents method is an excellent quantitative indicator for analysing nonlinear system characteristics. It was used to studied the stable region of nonlinear vehicle plane motion system. However, the effect of Lyapunov exponents method in revealing the global dynamics characteristics has not been fully studied. Aiming at this key problem, this paper analyses the global characteristics of Lyapunov exponents with different degrees of freedom nonlinear models. The results show that Lyapunov exponents can well reflect the global layer characteristics for vehicle system. However, the value characteristic under different DOF models is not unified. The research and analysis in this paper supplement the quantitative analysis theory for vehicle system dynamics. In the field of vehicle system dynamics, it is significant to propose an appropriate quantitative indicator for system stability or dynamics characteristics. Lyapunov exponents method is an excellent quantitative indicator for analysing nonlinear system characteristics. It was used to studied the stable region of nonlinear vehicle plane motion system. However, the effect of Lyapunov exponents method in revealing the global dynamics characteristics has not been fully studied. Aiming at this key problem, this paper analyses the global characteristics of Lyapunov exponents with different degrees of freedom nonlinear models. The results show that Lyapunov exponents can well reflect the global layer characteristics for vehicle system. However, the value characteristic under different DOF models is not unified. The research and analysis in this paper supplement the quantitative analysis theory for vehicle system dynamics.In the field of vehicle system dynamics, it is significant to propose an appropriate quantitative indicator for system stability or dynamics characteristics. Lyapunov exponents method is an excellent quantitative indicator for analysing nonlinear system characteristics. It was used to studied the stable region of nonlinear vehicle plane motion system. However, the effect of Lyapunov exponents method in revealing the global dynamics characteristics has not been fully studied. Aiming at this key problem, this paper analyses the global characteristics of Lyapunov exponents with different degrees of freedom nonlinear models. The results show that Lyapunov exponents can well reflect the global layer characteristics for vehicle system. However, the value characteristic under different DOF models is not unified. The research and analysis in this paper supplement the quantitative analysis theory for vehicle system dynamics. |
| ArticleNumber | 9300 |
| Author | Meng, Fanyu Zhang, Boshi Bai, Minghui Lin, Nan Shi, Shuming |
| Author_xml | – sequence: 1 givenname: Fanyu surname: Meng fullname: Meng, Fanyu organization: College of Transportation, Jilin University – sequence: 2 givenname: Shuming surname: Shi fullname: Shi, Shuming organization: College of Transportation, Jilin University – sequence: 3 givenname: Boshi surname: Zhang fullname: Zhang, Boshi organization: College of Transportation, Jilin University – sequence: 4 givenname: Minghui surname: Bai fullname: Bai, Minghui organization: College of Transportation, Jilin University – sequence: 5 givenname: Nan surname: Lin fullname: Lin, Nan email: linnan@jlu.edu.cn organization: College of Transportation, Jilin University |
| BackLink | https://www.ncbi.nlm.nih.gov/pubmed/35665768$$D View this record in MEDLINE/PubMed |
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| Cites_doi | 10.1080/00423114.2012.657653 10.1080/00423114.2018.1467019 10.1109/87.668041 10.4050/JAHS.61.022003 10.1080/00423114.2021.1988115 10.1007/s42154-018-0019-7 10.1201/9780429492563 10.1016/j.ast.2015.10.015 10.1080/00423119208969994 10.1007/s12239-010-0042-0 10.1016/0167-2789(85)90011-9 10.1080/00423110802007779 10.1504/IJVD.2002.002032 10.1109/TAC.1985.1104057 10.1080/00423110600828285 10.1007/s11071-009-9535-7 10.1201/9780203913567 10.1007/978-3-662-11585-5 10.1080/00423114.2013.771785 10.1177/09544070211043358 |
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| References | OnoEHosoeSTuanHDDoiSIBifurcation in vehicle dynamics and robust front wheel steering controlIEEE Trans. Control Syst. Technol.1998641242010.1109/87.668041 PacejkaHBBakkerEThe magic formula tyre modelVeh. Syst. Dyn.19922111810.1080/00423119208969994 YangCWuQOn stability analysis via Lyapunov exponents calculated from a time series using nonlinear mapping—a case studyNonlinear Dyn.201059239257258528910.1007/s11071-009-9535-7 Nguyen, V. Vehicle handling, stability, and bifurcaiton analysis for nonlinear vehicle models, MSc Thesis, University of Maryland, College Park, Maryland, USA, (2005). KarnoppDVehicle Stability2004CRC Press10.1201/9780203913567 MasaratiPTamerAThe real schur decomposition estimates lyapunov characteristic exponents with multiplicity greater than oneProc. Inst. Mech. Eng. Part K J. Multi-body Dyn.2016230568578 ShiSMengFBaiMLinNThe stability analysis using Lyapunov exponents for high-DOF nonlinear vehicle plane motionProc. Inst. Mech. Eng. Part D-J. Automob. Eng.202110.1177/09544070211043358 ShenSWangJShiPPremierGNonlinear dynamics and stability analysis of vehicle plane motionsVeh. Syst. Dyn.200745153510.1080/00423110600828285 SadriSWuCStability analysis of a nonlinear vehicle model in plane motion using the concept of Lyapunov exponentsVeh. Syst. Dyn.2013519069242013VSD....51..906S10.1080/00423114.2013.771785 WolfASwiftJBSwinneyHLVastanoJADetermining Lyapunov exponents from a time seriesPhys. D19851628531780570610.1016/0167-2789(85)90011-90585.58037 MitschkeMWallentowitzHDynamik der Kraftfahrzeuge19721Springer10.1007/978-3-662-11585-5 MengFDissipation of energy analysis approach for vehicle plane motion stabilityVeh. Syst. Dyn.202110.1080/00423114.2021.1988115 BealCEBoydCCoupled lateral-longitudinal vehicle dynamics and control design with three-dimensional state portraitsVeh. Syst. Dyn.2019572863132019VSD....57..286B10.1080/00423114.2018.1467019 StrogatzSHNonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering2018CRC Press10.1201/9780429492563 InagakiSKushiroIYamamotoMAnalysis on vehicle stability in critical cornering using phase-plane methodJSAE Rev.19952216 RamasubramanianKSriramMSA comparative study of computation of Lyapunov spectra with different algorithmsPhys. D Nonlinear Phenomena20002217447990947.34041 AbeMVehicle Handling Dynamics: Theory and Application2015Butterworth-Heinemann YamamotoMKoibuchiKFukadaYInagakiSVehicle stability control in limit cornering by active brakeTrans. Soc. Automotive Eng. Japan199628323323 TamerAMasaratiPStability of nonlinear, time-dependent rotorcraft systems using lyapunov characteristic exponentsJ. Am. Helicop. Soc.20166111210.4050/JAHS.61.022003 PacejkaHTire and Vehicle Dynamics2005Elsevier MasaratiPEstimation of Lyapunov exponents from multibody dynamics in differential-algebraic formProc. Inst. Mech. Eng. Part K J. Multi-body Dyn.20132272333 LiuLShiSShenSChuJVehicle planar motion stability study for tyres working in extremely nonlinear regionChin. J. Mech. Eng.20101852 KoYSongCVehicle modeling with nonlinear tires for vehicle stability analysisInt. J. Automot. Technol.20101133934410.1007/s12239-010-0042-0 GenesioRTartagliaMVicinoAOn the estimation of asymptotic stability regions: State of the art and new proposalsIEEE Trans. Autom. Control19853074775579420810.1109/TAC.1985.1104057 MuYLiLShiSModified tire-slip-angle model for chaotic vehicle steering motionAutomot. Innov.2018117718610.1007/s42154-018-0019-7 HoriuchiSEvaluation of chassis control method through optimisation-based controllability region computationVeh. Syst. Dyn.20125019312012VSD....50S..19H10.1080/00423114.2012.657653 TamerAMasaratiPSensitivity of lyapunov exponents in design optimization of nonlinear dampersJ. Comput. Nonlinear Dyn.2019142 Catino, B., Santini, S. & Di Bernardo, M. in 42nd IEEE International Conference on Decision and Control. 2252–2257 (IEEE). HoriuchiSOkadaKNohtomiSAnalysis of accelerating and braking stability using constrained bifurcation and continuation methodsVeh. Syst. Dyn.20084658559710.1080/00423110802007779 KoYELeeJMEstimation of the stability region of a vehicle in plane motion using a topological approachInt. J. Veh. Des.20023018119210.1504/IJVD.2002.002032 MasaratiPTamerASensitivity of trajectory stability estimated by Lyapunov characteristic exponentsAerosp. Sci. Technol.20154750151010.1016/j.ast.2015.10.015 P Masarati (13411_CR20) 2015; 47 K Ramasubramanian (13411_CR28) 2000; 2 H Pacejka (13411_CR23) 2005 C Yang (13411_CR26) 2010; 59 M Abe (13411_CR1) 2015 R Genesio (13411_CR15) 1985; 30 A Wolf (13411_CR27) 1985; 16 P Masarati (13411_CR30) 2016; 230 Y Mu (13411_CR25) 2018; 1 S Sadri (13411_CR16) 2013; 51 S Shi (13411_CR17) 2021 HB Pacejka (13411_CR24) 1992; 21 L Liu (13411_CR14) 2010; 185 M Mitschke (13411_CR3) 1972 E Ono (13411_CR6) 1998; 6 A Tamer (13411_CR21) 2019; 14 S Horiuchi (13411_CR11) 2008; 46 S Inagaki (13411_CR4) 1995; 2 YE Ko (13411_CR12) 2002; 30 D Karnopp (13411_CR2) 2004 13411_CR8 A Tamer (13411_CR19) 2016; 61 P Masarati (13411_CR22) 2013; 227 S Horiuchi (13411_CR10) 2012; 50 CE Beal (13411_CR29) 2019; 57 13411_CR7 M Yamamoto (13411_CR5) 1996; 28 SH Strogatz (13411_CR31) 2018 F Meng (13411_CR18) 2021 Y Ko (13411_CR13) 2010; 11 S Shen (13411_CR9) 2007; 45 |
| References_xml | – reference: HoriuchiSEvaluation of chassis control method through optimisation-based controllability region computationVeh. Syst. Dyn.20125019312012VSD....50S..19H10.1080/00423114.2012.657653 – reference: TamerAMasaratiPStability of nonlinear, time-dependent rotorcraft systems using lyapunov characteristic exponentsJ. Am. Helicop. Soc.20166111210.4050/JAHS.61.022003 – reference: LiuLShiSShenSChuJVehicle planar motion stability study for tyres working in extremely nonlinear regionChin. J. Mech. Eng.20101852 – reference: KarnoppDVehicle Stability2004CRC Press10.1201/9780203913567 – reference: TamerAMasaratiPSensitivity of lyapunov exponents in design optimization of nonlinear dampersJ. Comput. Nonlinear Dyn.2019142 – reference: WolfASwiftJBSwinneyHLVastanoJADetermining Lyapunov exponents from a time seriesPhys. D19851628531780570610.1016/0167-2789(85)90011-90585.58037 – reference: PacejkaHTire and Vehicle Dynamics2005Elsevier – reference: YangCWuQOn stability analysis via Lyapunov exponents calculated from a time series using nonlinear mapping—a case studyNonlinear Dyn.201059239257258528910.1007/s11071-009-9535-7 – reference: YamamotoMKoibuchiKFukadaYInagakiSVehicle stability control in limit cornering by active brakeTrans. Soc. Automotive Eng. Japan199628323323 – reference: HoriuchiSOkadaKNohtomiSAnalysis of accelerating and braking stability using constrained bifurcation and continuation methodsVeh. Syst. Dyn.20084658559710.1080/00423110802007779 – reference: MasaratiPEstimation of Lyapunov exponents from multibody dynamics in differential-algebraic formProc. Inst. Mech. Eng. Part K J. Multi-body Dyn.20132272333 – reference: InagakiSKushiroIYamamotoMAnalysis on vehicle stability in critical cornering using phase-plane methodJSAE Rev.19952216 – reference: MasaratiPTamerAThe real schur decomposition estimates lyapunov characteristic exponents with multiplicity greater than oneProc. Inst. Mech. Eng. Part K J. Multi-body Dyn.2016230568578 – reference: SadriSWuCStability analysis of a nonlinear vehicle model in plane motion using the concept of Lyapunov exponentsVeh. Syst. Dyn.2013519069242013VSD....51..906S10.1080/00423114.2013.771785 – reference: StrogatzSHNonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering2018CRC Press10.1201/9780429492563 – reference: PacejkaHBBakkerEThe magic formula tyre modelVeh. Syst. Dyn.19922111810.1080/00423119208969994 – reference: KoYSongCVehicle modeling with nonlinear tires for vehicle stability analysisInt. J. Automot. Technol.20101133934410.1007/s12239-010-0042-0 – reference: AbeMVehicle Handling Dynamics: Theory and Application2015Butterworth-Heinemann – reference: Nguyen, V. Vehicle handling, stability, and bifurcaiton analysis for nonlinear vehicle models, MSc Thesis, University of Maryland, College Park, Maryland, USA, (2005). – reference: MitschkeMWallentowitzHDynamik der Kraftfahrzeuge19721Springer10.1007/978-3-662-11585-5 – reference: MengFDissipation of energy analysis approach for vehicle plane motion stabilityVeh. Syst. Dyn.202110.1080/00423114.2021.1988115 – reference: OnoEHosoeSTuanHDDoiSIBifurcation in vehicle dynamics and robust front wheel steering controlIEEE Trans. Control Syst. Technol.1998641242010.1109/87.668041 – reference: Catino, B., Santini, S. & Di Bernardo, M. in 42nd IEEE International Conference on Decision and Control. 2252–2257 (IEEE). – reference: GenesioRTartagliaMVicinoAOn the estimation of asymptotic stability regions: State of the art and new proposalsIEEE Trans. Autom. Control19853074775579420810.1109/TAC.1985.1104057 – reference: MasaratiPTamerASensitivity of trajectory stability estimated by Lyapunov characteristic exponentsAerosp. Sci. Technol.20154750151010.1016/j.ast.2015.10.015 – reference: RamasubramanianKSriramMSA comparative study of computation of Lyapunov spectra with different algorithmsPhys. D Nonlinear Phenomena20002217447990947.34041 – reference: BealCEBoydCCoupled lateral-longitudinal vehicle dynamics and control design with three-dimensional state portraitsVeh. Syst. Dyn.2019572863132019VSD....57..286B10.1080/00423114.2018.1467019 – reference: KoYELeeJMEstimation of the stability region of a vehicle in plane motion using a topological approachInt. J. Veh. Des.20023018119210.1504/IJVD.2002.002032 – reference: ShenSWangJShiPPremierGNonlinear dynamics and stability analysis of vehicle plane motionsVeh. Syst. 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| Title | Analysis for global characteristics of Lyapunov exponents in vehicle plane motion system |
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