PSI - Issue 38

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Available online at www.sciencedirect.com Fatigue Design (2022) 1– ??

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Fatigue Design (2022) 1– ?? Fatigue Design (2022) 1– ?? Fatigue Design (2022) 1– ?? Fatigue esign (2022) 1– ??

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Procedia Structural Integrity 38 (2022) 342–351 Fatigue Design (2022) 1– ?? www.elsevier.com / locate / procedia www.elsevier.com / locate / procedia Fatigue Design 2021, 9th Edition of the International Conference on Fatigue Design Fatigue esign 2021, 9th dition of the International onference on Fatigue esign .elsevier.co locate procedia f t e I ter ati al fere ce ati e esi / / www.elsevier.com / locate / procedia Fatigue Design 2021, 9th Edition of the International Conference on Fatigue Design Wheel forces estimation with an Augmented and Constrained Extended Kalman Filter applied on a nonlinear multi-body model of a half vehicle Fatigue Design 2021, 9th Edition of the International Conference on Fatigue Design Fatigue Design 2021, 9th Edition of the International Conference on Fatigue Design Wheel forces estimation with an Augment d and Constrained Extended Kalman Filter applied on a nonlinear multi-body model of a half vehicle l f r s sti ti n it t str i li r lti ati e esi , t iti l f r ti ti it t tr i li r lti n d Extended Kalman Filter applied on a nonlinear multi-body Wheel forces estimation with an Augmented and Constrained Extended Kalman Filter applied on a nonlinear multi-body model of a half vehicle Wheel forces estimation with an Augmented and Constrained Extended Kalman Filter applied on a nonlinear multi-body model of a half vehicle A. De´barbouille´ a,b, ∗ , F. Renaud a , Z. Dimitrijevic b , D. Chojnacki c , L. Rota b , J-L. Dion a t l ilt r lie l f lf i l . e´barbouille´ a,b, ∗ , . enaud a , Z. Dimitrijevic b , . hojnacki c , . ota b , J-L. Dion a t l ilt r li l f lf i l . ´ r ille´ ∗ , . , i , D. C ki , . t , A. De´barbouille´ a,b . e a A. De´barbouille´ a,b, ∗ , F. Renaud a , Z. Dimitrijevic b , D. Chojnacki c , L. Rota b , J-L. Dion a A. De´barbouille´ a,b, ∗ , F. Renaud a , Z. Dimitrijevic b , D. Chojnacki c , L. Rota b , J-L. Dion a A. De´barbouille´ a,b, ∗ , F. Renaud a , Z. Dimitrijevic b , D. Chojnacki c , L. Rota b , J-L. Dion a a ISAE-SUPMECA, 3 rue Fernand Hainaut, Saint-Ouen 93407, France b STELLANTIS, Route de Gisy, Ve´lizy-Villacoublay 78140, France c STELLANTIS, Voujeauc urt 25420, France J- . i n a www.elsevier.com / locate / procedia © 2021 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of the scientific committee of the Fatigue Design 2021 Organizers Abstract The design of a vehicle suspension requires the knowledge of wheel loads due to road unevenness. These loads can be identified from measurements acquired during vehicle rolling on roads or tracks. Di ff erent o ff -line methods are used to identify them. Most of these methods use some transfer functions between points of measurements and hypothesis of linear dynamic behaviour of the vehicle. This leads to miss-estimation of end-tail load probability distribution. We propose here an approach based on a nonlinear multi-body model of the half-vehicle and an Augmented and Constrained Extended Kalman Filter for the data fusion with accelerometers, gyrometer, tachometer and GPS measurements. This half vehicle model lies in a 2D plane and allow the description of pitch behavior but not the yaw neither the roll behavior. The specificities of our work are that 1) the Kalman state vector is composed of positions and velocities of each solid in the multi-body system, 2) the state model of the multi-body system is based on the Newmark explicit integration scheme, 3) the road / tracks loads are unknown and 4) the state prediction is constrained by kinematic links between bodies. Finally, this method provides an estimation of wheel center forces for a multi-body car model. Keywords: Numerical twin; Kalman filter; Load identification; 1. Introduction Designing elements of vehicle suspension needs the knowledge of loads due to road unevenness. This knowledge can be obtained via measurements done in vehicle rolling on roads or tracks. They are then identified o ff line using di ff erent methods. Most of these methods use some transfer functions between points of measurements. However end tail distribution of the loads are not well estimated with such linear approaches. The method proposed here is based on a twin numerical model of the car (multi-body model of car body and bodies of the ground connection) and a specific Kalman filter Kalman, R. E. (1960) taking into account the nonlinear behavior of the suspension for the data fusion with accelerometers, gyrometer, tachometer and GPS measurements. One can find in E. Risaliti, T. Tamarozzi, B. Cornelis, W. Desmet (2016) a virtual sensing approach for estimating wheel center forces. A simplified multi-body suspension Abstract The design f a v hicle suspension requires the knowledge of wheel loads due to road unevenness. Th se loads can be identified from measurements acquire during vehicle rolling on roads or tracks. Di ff erent o ff -line methods are used to identify them. Most of these methods use some transfer functions between points of measurements and hypothesis of linear dynamic behaviour of the vehicle. This eads to iss-estimation of end-tail load probability distribution. We propose here an approach based on nonli ear multi-body model of the half-vehicle and an Augmented and Constrained Extended Kalman Filter for the data fusion wi accelerometers, gyrometer, tachometer and GPS measurements. This half vehicle model lies in a 2D plane and allow the description of pitch behavior but not the y w neither the roll behavior. The specificities of our work are th 1) the Kalman state vector is co posed of positions and velocities of each solid in the multi-body system, 2) the state model of the multi-body system is based on th Newmark explicit integratio scheme, 3) the road / tracks loads are unknown and 4) the state prediction is c strained by kinematic links between bodies. Finally, thi method provides an estimation of whe l center forces for a multi-body car model. Keywords: Numerical twin; Kalman filter; Load identification; 1. Introduction Desi ning elements of vehicle suspension needs the knowledge of l ads due to road unevenness. This knowledge can be obtained via measurements done in vehicle rolling on roads or tracks. They are th ide tified o ff lin using di ff erent methods. Most of these methods use some transfer functions between points of measure ents. Howev r end tail di tribution of the loads re not well estimated with such linear approaches. The method proposed here is based on a twin numerical mod l of the car (multi-body model of car body and bodies of the ground connection) and a specific Kalman filter K lman, R. E. (1960) taking into account the nonlinear behavior of th suspe sio for the data fusion with accelerometers, gyrometer, tachometer and GPS measurements. One ca find in E. Risaliti, T. Tamarozzi, B. Cornelis, W. Desmet (2016) a virtual sensing approach for estimating wheel center forces. A simplified multi-body suspension Abstract The design of a vehicle suspension requires the knowledge of wheel loads due to road unevenness. These loads can be identified from measurements acquired during vehicle rolling on roads or tracks. Di ff erent o ff -line methods are used to identify them. Most of these methods use some transfer functions between points of measurements and hypothesis of linear dynamic behaviour of the vehicle. This leads to miss-estimation of end-tail load probability distribution. We propose here an approach based on a nonlinear multi-body model of the half-vehicle and an Augmented and Constrained Extended Kalman Filter for the data fusion with accelerometers, gyrometer, tachometer and GPS measurements. This half vehicle model lies in a 2D plane and allow the description of pitch behavior but not the yaw neither the roll behavior. The specificities of our work are that 1) the Kalman state vector is composed of positions and velocities of each solid in the multi-body system, 2) the state model of the multi-body system is based on the Newmark explicit integration scheme, 3) the road / tracks loads are unknown and 4) the state prediction is constrained by kinematic links between bodies. Finally, this method provides an estimation of wheel center forces for a multi-body car model. Keywords: Numerical twin; Kalman filter; Load identification; 1. Introduction Designing elements of vehicle suspension needs the knowledge of loads due to road unevenness. This knowledge can be obtained via measurements done in vehicle rolling on roads or tracks. They are then identified o ff line using di ff erent methods. Most of these methods use some transfer f ctions between points of measur t . However end tail distribution of the loads are not well estimated with such linear approaches. The method proposed here is base o a twin numerical model of the car (multi-body model of car body and bodies of th ground connection) and a specific Kalman filter Kalman, R. E. (1960) taking into account the nonlinear behavior of he suspensi f r t e d ta fusion with accelerometers, gyro eter, tach met r a GPS measurem nts. One can find in E. Risaliti, T. Tamarozzi, B. Cornelis, W. Desm t (2016) a virtual sensing approach for estimating wheel center forces. A simplified multi-body suspens on ∗ alexandre.debarbouille@stelantis.com Abstract The design of a vehicle suspension requires the knowledge of wheel loads due to road unevenness. These loads can be identified fro measurements acquired during vehicle rolling on roads or tracks. Di ff erent o ff -line methods are used to identify them. ost of these methods use some transfer functions between points of measurements and hypothesis of linear dyna ic behaviour of the vehicle. This leads to miss-estimation of end-tail load probability distribution. e propose here an approach based on a nonlinear multi-body model of the half-vehicle and an Augmented and Constrained Extended Kalman Filter for the data fusion with accelero eters, gyro eter, tachometer and GPS measurements. This half vehicle model lies in a 2D plane and allow the description of pitch behavior but not the yaw neither the roll behavior. The specificiti s of our work are that 1) the Kalman state vector is co posed of positions and velocities of each solid in the multi-body system, 2) the state model of the multi-body system is based on the Newmark explicit integration scheme, 3) the road / tracks loads are unknown and 4) the state prediction is constrained by kinematic links between bodies. Finally, this method provides an estimation of wheel center forces for a multi-body car model. Keywords: Numerical twin; Kalman filter; Load identification; 1. Introduction esigning ele ents of vehicle suspension needs the kno ledge of loads due to road evenness. This kno ledge can be obtained via easure ents done in vehicle rolling on roads or tracks. They are then identified o ff line using di ff erent ethods. ost of these ethods use so e transfer functions bet een points of easure ents. o ever end tail distribution of the loads are not ell esti ated ith such linear approaches. The ethod proposed here is based on a t in nu erical odel of the car ( ulti-body odel of car body a bodies of the ground connection) and a specific al an filter al an, R. E. (1960) taking into account the nonlinear behavior of the suspension for the data fusion ith accelero eters, gyro eter, tacho eter and PS easure ents. ne can find in E. Risaliti, T. Ta arozzi, B. Cornelis, . es et (2016) a virtual sensing approach for esti ating heel center forces. si plified ulti-body suspension bstract The design of a vehicle suspension requires the kno ledge of heel loads due to road unevenness. These loads can be identified fro easure ents acquired during vehicle rolling on roads or tracks. i er nt o -line ethods are used to identify the . ost of these ethods use so e transfer functions bet een points of easure ents and hypothesis of linear dyna ic behaviour of the vehicle. This leads to iss-esti ation of end-tail load probability distribution. e propose here an appro ch based on a nonlinear ulti-body odel of the half-vehicle and n ug ented and onstrained Extended al an Filter for the data fusion ith accelero eters, gyro eter, tacho eter and PS easure ents. This half vehicle odel lies in a 2 plane and allo the description of pitch behavior but not the ya neither the roll behavior. T of our ork are that 1) the al an state vector is co posed of positions and velocities of eac solid in the ulti-body syste , 2) t ed on the e ark explicit integration sche e, 3) the road tracks loads are unkno n and 4) the state prediction is inks bet een bodies. Finally, this ethod provides an esti ation of el center forces for a ulti-body car odel. K r; Load identificatio 1. Introduction esigning el ents of v hicle suspension needs the kno ledge of loads due to road uneve ness. his kno ledge can be ob ained via ea ure ents done in ve icle rolling on roads or tr cks. hey are then identified o line using di erent ethods. ost of these eth ds use so e transfer functions bet een points of easure ents. o ver end tail distribution of the loads are not ell esti ated ith such linear approaches. he thod proposed here is ba ed on a t in nu erical del of the car ( ulti-body odel of car body and bodies of the ground conne tion) and a specific al an filter al an, . . (1960) taking into account the nonlinear behavior of the suspension for the dat fusion ith accelero eters, gyro eter, tacho eter and PS easure ents. ne can find in . isaliti, . a arozzi, . ornelis, . es et (2016) a virtual sensing pp oach for esti ating heel center forces. si plified ulti-body suspension Abstract T to s be id e ff ff ed t of p os l d E l t h T d i y t s / b r 1. k g o t i e e o n p n e on a t a m l n n in o a t e i irtual se ing approac Abstract The des gn of a v hicle susp nsion requires the knowledge of wheel loads due to road un venness. These loads can be identified from measurements acquire d ring vehicle rolling on roads or tracks. Di ff erent o ff -line methods are used to identify them. Most of these methods use some transfer functions between points of measurements and hyp thesis of li ear dyna ic beh viour of the vehicle. This eads t iss-estimation of end-tail lo d probability distribution. We propos here an pproach based on nonli ear multi-body model of t e half-vehicle and an Augmented and Co str ined Extend d Kalman Filter f the dat fusion wi accelerom ters, gyr eter, tachometer and GPS measurem nts. Th s half vehic e m el lies in a 2D plane and allow the description of p tch behavior but no the ya neith r the roll be av r. T e specificities f our work r th 1) the Kalman state vec or is co posed of positions and velocities of each solid in th multi-body ystem, 2) the state model of the multi-body system is based on th Newmark explicit integratio scheme, 3) the road / tracks loads are u known and 4) t state p ediction is constrained by kinematic links between bodies. Finally, this method provides an estimation of wheel center forces for a multi-body car model. Keywords: Numerical twin; Kalman filter; Load identification; 1. Introductio Desi ning ele nts of vehicle suspension needs the knowledge of l a s due to ro d unevenness. This knowledge can e obtained via measurements done in v hicle r lling on roads or tracks. They are th n de tified o ff lin using di ff er nt methods. Most of these methods use some transfer functions betwe n points of measure ents. Howev r end tail distributio of the loads re not well estimated with such linear approaches. The method roposed here is based o a twin numerical model of the car (multi-body odel of car b dy and bodies of the ground connection) and a specific Kalman filter K lman, R. E. (1960) taking into account the nonlinear behavior of th suspension for the data fusion with accelerometers, gyrometer, tachometer and GPS measurements. One can find in E. Risaliti, T. Tamarozzi, B. Cornelis, W. Desmet (2016) a virtual sensing approach for estimating wheel center forces. A simplified multi-body suspension (20 a ISAE-SUPMECA, 3 rue Fernand Hainaut, Saint-Ouen 93407, France b STELLANTIS, Route de Gisy, Ve´lizy-Villacoublay 78140, France c STELLANTIS, Voujeaucourt 25420, France a ISAE-SUPMECA, 3 rue Fernand Hainaut, Saint-Ouen 93407, France b STELLANTIS, Route de Gisy, Ve´lizy-Villacoublay 78140, France c STELLANTIS, Voujeaucourt 25420, France a ISAE-SUPMECA, 3 rue Fernand Hainaut, Saint-Ouen 93407, France b STELLANTIS, Route de Gisy, Ve´lizy-Villacoublay 78140, France c STELLANTIS, Voujeaucourt 25420, France a ue Fernan b , Ve´lizy-Villacoublay 781 ance ELLANT ouje u ISAE-SUPMECA, 3 rue Fernand Hainaut, Saint-Ouen 9 b L I , Route d , l c a ISAE-SUPMECA, 3 rue Fernand Hainaut, Saint-Oue 93407, France b STELLANTIS, Route de Gisy, Ve´lizy-Villacoublay 78140, France c STELLANTIS, Voujeaucourt 25420, France

∗ alexandre.debarbouille@stelantis.com ∗ alexandre.debarbouille stelantis.com ∗ alexandre.debarbouille stelantis.co

2452-3216 © 2021 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of the scientific committee of the Fatigue Design 2021 Organizers 10.1016/j.prostr.2022.03.035 ∗ alexandre.debarbouille@stelantis.com ∗ alexandre.debarbouille@stelantis.com