This article presents an adaptive optimal control method for a semi-active suspension system.The model of the suspension system is built,in which the components of uncertain parameters and exogenous disturbance are de...This article presents an adaptive optimal control method for a semi-active suspension system.The model of the suspension system is built,in which the components of uncertain parameters and exogenous disturbance are described.The adaptive optimal control law consists of the sum of the optimal control component and the adaptive control component.First,the optimal control law is designed for the model of the suspension system after ignoring the components of uncertain parameters and exogenous disturbance caused by the road surface.The optimal control law expresses the desired dynamic characteristics of the suspension system.Next,the adaptive component is designed with the purpose of compensating for the effects caused by uncertain parameters and exogenous disturbance caused by the road surface;the adaptive component has adaptive parameter rules to estimate uncertain parameters and exogenous disturbance.When exogenous disturbances are eliminated,the system responds with an optimal controller designed.By separating theoretically the dynamic of a semi-active suspension system,this solution allows the design of two separate controllers easily and has reduced the computational burden and the use of too many tools,thus allowing for more convenient hardware implementation.The simulation results also show the effectiveness of damping oscillations of the proposed solution in this article.展开更多
To improve the ride quality and enhance the control efficiency of cars’semi-active air suspensions(SASs)under various surfaces of soft and rigid roads,a machine learning(ML)method is proposed based on the optimized r...To improve the ride quality and enhance the control efficiency of cars’semi-active air suspensions(SASs)under various surfaces of soft and rigid roads,a machine learning(ML)method is proposed based on the optimized rules of the fuzzy control(FC)method and car dynamic model for application in SASs.The root-mean-square(RMS)acceleration of the driver’s seat and car’s pitch angle are chosen as the objective functions.The results indicate that a soft surface obviously influences a car’s ride quality,particularly when it is traveling at a high-velocity range of over 72 km/h.Using the ML method,the car’s ride quality is improved as compared to those of FC and without control under different simulation conditions.In particular,compared with those cars without control,the RMS acceleration of the driver’s seat and car’s pitch angle using the ML method are respectively reduced by 30.20% and 19.95% on the soft road and 34.36% and 21.66% on the rigid road.In addition,to optimize the ML efficiency,its learning data need to be updated under all various operating conditions of cars.展开更多
To improve the switching time of the control force in standard sky-hook ON-OFF semi-active control algorithm,a stateadjust coefficient was adopted in the improved ON-OFF( ION-OFF)algorithm. In considering of the ridin...To improve the switching time of the control force in standard sky-hook ON-OFF semi-active control algorithm,a stateadjust coefficient was adopted in the improved ON-OFF( ION-OFF)algorithm. In considering of the riding comfort and the handling stability of vehicle, a comprehensive performance assessment criterion on suspension system was established with the utilization of the corresponding passive suspension system. Several simulations and analyses were conducted on improved ON-OFF semi-active suspension system with the comparison of passive suspension system and ON-OFF semi-active suspension system. The simulation results showed that the optimal comprehensive performance of the improved ON-OFF suspension system could be achieved when the state-adjust coefficient equalled 0. 6 as the vehicle running on C level road with the speed of 10 m/s,and the comprehensive performance was better than ON-OFF suspension system. Conclusions could be drawn from the frequency domain analysis that the performance of riding comfort and handling stability were both improved in the low resonance frequency and the mid-frequency range. The fact could be known that the comprehensive performance of the suspension system was associated with the frequency of the riding road and the sprung mass( SM) with the analysis of affecting factors.展开更多
A systematic and generic procedure for the determination of the reasonable finished state of self-anchored suspension bridges is proposed, the realization of which is mainly through adjustment of the hanger tensions. ...A systematic and generic procedure for the determination of the reasonable finished state of self-anchored suspension bridges is proposed, the realization of which is mainly through adjustment of the hanger tensions. The initial hanger tensions are first obtained through an iterative analysis by combining the girder-tower-only finite element(FE) model with the analytical program for shape finding of the spatial cable system. These initial hanger tensions, together with the corresponding cable coordinates and internal forces, are then included into the FE model of the total bridge system, the nonlinear analysis of which involves the optimization technique. Calculations are repeated until the optimization algorithm converges to the most optimal hanger tensions(i.e. the desired reasonable finished bridge state). The "temperature rigid arm" is introduced to offset the unavoidable initial deformations of the girder and tower, which are due to the huge axial forces originated from the main cable. Moreover, by changing the stiffness coefficient K in the girder-tower-only FE model, the stiffness proportion of the main girder, the tower or the cable subsystem in the whole structural system could be adjusted according to the design intentions. The effectiveness of the proposed method is examined and demonstrated by one simple tutorial example and one self-anchored suspension bridge.展开更多
This paper presents a novel modified particle swarm optimization algorithm (MPSO) for both offline and online parametric identification of dynamic models. The MPSO is applied for identifying a suspension system introd...This paper presents a novel modified particle swarm optimization algorithm (MPSO) for both offline and online parametric identification of dynamic models. The MPSO is applied for identifying a suspension system introduced by a quarter-car model. A novel mutation mechanism is employed in MPSO to enhance global search ability and increase convergence speed of basic PSO (BPSO) algorithm. MPSO optimization is used to find the optimum values of parameters by minimizing the sum of squares error. The performance of the MPSO is compared with other optimization methods including BPSO and Genetic Algorithm (GA) in offline parameter identification. The simulating results show that this algorithm not only has advantage of convergence property over BPSO and GA, but also can avoid the premature convergence problem effectively. The MPSO algorithm is also improved to detect and determine the variation of parameters. This novel algorithm is successfully applied for online parameter identification of suspension system.展开更多
Ride and handling are two paramount factors in design and development of vehicle suspension systems. Conflicting trends in ride and handling characteristics propel engineers toward employing multi-objective optimizati...Ride and handling are two paramount factors in design and development of vehicle suspension systems. Conflicting trends in ride and handling characteristics propel engineers toward employing multi-objective optimization methods capable of providing the best trade-off designs compromising both criteria simultaneously. Although many studies have been performed on multi-objective optimization of vehicle suspension system, only a few of them have used probabilistic approaches considering effects of uncertainties in the design. However, it has been proved that optimum point obtained from deterministic optimization without taking into account the effects of uncertainties may lead to high-risk points instead of optimum ones. In this work, reliability-based robust multi-objective optimization of a 5 degree of freedom （5-DOF） vehicle suspension system is performed using method of non-dominated sorting genetic algorithm-II （NSGA-II） in conjunction with Monte Carlo simulation （MCS） to obtain best designs considering both comfort and handling. Road profile is modeled as a random function using power spectral density （PSD） which is in better accordance with reality. To accommodate the robust approach, the variance of all objective functions is also considered to be minimized. Also, to take into account the reliability criterion, a reliability-based constraint is considered in the optimization. A deterministic optimization has also been performed to compare the results with probabilistic study and some other deterministic studies in the literature. In addition, sensitivity analysis has been performed to reveal the effects of different design variables on objective functions. To introduce the best trade-off points from the obtained Pareto fronts, TOPSIS method has been employed. Results show that optimum design point obtained from probabilistic optimization in this work provides better performance while demonstrating very good reliability and robustness. However, other optimum points from deterministic optimizations violate the regarded constraints in the presence of uncertainties.展开更多
In this paper,we have formulated mathematical models to optimize the bouncing transmissibility of the sprung mass of the half car system with passengers’seat suspensions considering different road conditions.The corr...In this paper,we have formulated mathematical models to optimize the bouncing transmissibility of the sprung mass of the half car system with passengers’seat suspensions considering different road conditions.The corresponding problem has been solved with the help of advanced real coded Genetic Algorithm(GA).The nonlinearity of suspension spring and damper,which are the most important characteristics of the suspension,has been taken into account in order to validate the model to real applications.The nonlinear cubic polynomial has been used to describe the spring characteristic and a quadratic polynomial has been used to describe the damper characteristic.The coefficients of each polynomial represent the design parameters of the suspension system and are to be determined.To find these parameters we have formulated a nonlinear optimization problem in which the bouncing transmissibility of the sprung mass at the center of mass has been minimized with respect to technological constraints and the constraints which satisfy the performance as per ISO 2631 standards.The advanced real coded GA has been used to solve this problem in time domain and the results obtained have been compared to those obtained using the existing design parameters.The objective function and the constraints have been evaluated by simulating the vehicle model over two roads with multiple bumps at uniform velocity.展开更多
基金supported in part by the Thai Nguyen University of Technology,Vietnam.
文摘This article presents an adaptive optimal control method for a semi-active suspension system.The model of the suspension system is built,in which the components of uncertain parameters and exogenous disturbance are described.The adaptive optimal control law consists of the sum of the optimal control component and the adaptive control component.First,the optimal control law is designed for the model of the suspension system after ignoring the components of uncertain parameters and exogenous disturbance caused by the road surface.The optimal control law expresses the desired dynamic characteristics of the suspension system.Next,the adaptive component is designed with the purpose of compensating for the effects caused by uncertain parameters and exogenous disturbance caused by the road surface;the adaptive component has adaptive parameter rules to estimate uncertain parameters and exogenous disturbance.When exogenous disturbances are eliminated,the system responds with an optimal controller designed.By separating theoretically the dynamic of a semi-active suspension system,this solution allows the design of two separate controllers easily and has reduced the computational burden and the use of too many tools,thus allowing for more convenient hardware implementation.The simulation results also show the effectiveness of damping oscillations of the proposed solution in this article.
基金The National Key Research and Development Plan(No.2019YFB2006402)Talent Introduction Fund Project of Hubei Polytechnic University(No.17xjz01R)Key Scientific Research Project of Hubei Polytechnic University(No.22xjz02A)。
文摘To improve the ride quality and enhance the control efficiency of cars’semi-active air suspensions(SASs)under various surfaces of soft and rigid roads,a machine learning(ML)method is proposed based on the optimized rules of the fuzzy control(FC)method and car dynamic model for application in SASs.The root-mean-square(RMS)acceleration of the driver’s seat and car’s pitch angle are chosen as the objective functions.The results indicate that a soft surface obviously influences a car’s ride quality,particularly when it is traveling at a high-velocity range of over 72 km/h.Using the ML method,the car’s ride quality is improved as compared to those of FC and without control under different simulation conditions.In particular,compared with those cars without control,the RMS acceleration of the driver’s seat and car’s pitch angle using the ML method are respectively reduced by 30.20% and 19.95% on the soft road and 34.36% and 21.66% on the rigid road.In addition,to optimize the ML efficiency,its learning data need to be updated under all various operating conditions of cars.
基金Military Scientific Project,China(No.2013ZB06)Innovation Engineering Project of General Armament Department,China(No.2015YY04)
文摘To improve the switching time of the control force in standard sky-hook ON-OFF semi-active control algorithm,a stateadjust coefficient was adopted in the improved ON-OFF( ION-OFF)algorithm. In considering of the riding comfort and the handling stability of vehicle, a comprehensive performance assessment criterion on suspension system was established with the utilization of the corresponding passive suspension system. Several simulations and analyses were conducted on improved ON-OFF semi-active suspension system with the comparison of passive suspension system and ON-OFF semi-active suspension system. The simulation results showed that the optimal comprehensive performance of the improved ON-OFF suspension system could be achieved when the state-adjust coefficient equalled 0. 6 as the vehicle running on C level road with the speed of 10 m/s,and the comprehensive performance was better than ON-OFF suspension system. Conclusions could be drawn from the frequency domain analysis that the performance of riding comfort and handling stability were both improved in the low resonance frequency and the mid-frequency range. The fact could be known that the comprehensive performance of the suspension system was associated with the frequency of the riding road and the sprung mass( SM) with the analysis of affecting factors.
基金Project(20133204120015) supported by Specialized Research Fund for the Doctoral Program of Higher Education of ChinaProject(12KJB560003) supported by the Natural Science Foundation of the Higher Education Institution of Jiangsu Province,China
文摘A systematic and generic procedure for the determination of the reasonable finished state of self-anchored suspension bridges is proposed, the realization of which is mainly through adjustment of the hanger tensions. The initial hanger tensions are first obtained through an iterative analysis by combining the girder-tower-only finite element(FE) model with the analytical program for shape finding of the spatial cable system. These initial hanger tensions, together with the corresponding cable coordinates and internal forces, are then included into the FE model of the total bridge system, the nonlinear analysis of which involves the optimization technique. Calculations are repeated until the optimization algorithm converges to the most optimal hanger tensions(i.e. the desired reasonable finished bridge state). The "temperature rigid arm" is introduced to offset the unavoidable initial deformations of the girder and tower, which are due to the huge axial forces originated from the main cable. Moreover, by changing the stiffness coefficient K in the girder-tower-only FE model, the stiffness proportion of the main girder, the tower or the cable subsystem in the whole structural system could be adjusted according to the design intentions. The effectiveness of the proposed method is examined and demonstrated by one simple tutorial example and one self-anchored suspension bridge.
文摘This paper presents a novel modified particle swarm optimization algorithm (MPSO) for both offline and online parametric identification of dynamic models. The MPSO is applied for identifying a suspension system introduced by a quarter-car model. A novel mutation mechanism is employed in MPSO to enhance global search ability and increase convergence speed of basic PSO (BPSO) algorithm. MPSO optimization is used to find the optimum values of parameters by minimizing the sum of squares error. The performance of the MPSO is compared with other optimization methods including BPSO and Genetic Algorithm (GA) in offline parameter identification. The simulating results show that this algorithm not only has advantage of convergence property over BPSO and GA, but also can avoid the premature convergence problem effectively. The MPSO algorithm is also improved to detect and determine the variation of parameters. This novel algorithm is successfully applied for online parameter identification of suspension system.
文摘Ride and handling are two paramount factors in design and development of vehicle suspension systems. Conflicting trends in ride and handling characteristics propel engineers toward employing multi-objective optimization methods capable of providing the best trade-off designs compromising both criteria simultaneously. Although many studies have been performed on multi-objective optimization of vehicle suspension system, only a few of them have used probabilistic approaches considering effects of uncertainties in the design. However, it has been proved that optimum point obtained from deterministic optimization without taking into account the effects of uncertainties may lead to high-risk points instead of optimum ones. In this work, reliability-based robust multi-objective optimization of a 5 degree of freedom （5-DOF） vehicle suspension system is performed using method of non-dominated sorting genetic algorithm-II （NSGA-II） in conjunction with Monte Carlo simulation （MCS） to obtain best designs considering both comfort and handling. Road profile is modeled as a random function using power spectral density （PSD） which is in better accordance with reality. To accommodate the robust approach, the variance of all objective functions is also considered to be minimized. Also, to take into account the reliability criterion, a reliability-based constraint is considered in the optimization. A deterministic optimization has also been performed to compare the results with probabilistic study and some other deterministic studies in the literature. In addition, sensitivity analysis has been performed to reveal the effects of different design variables on objective functions. To introduce the best trade-off points from the obtained Pareto fronts, TOPSIS method has been employed. Results show that optimum design point obtained from probabilistic optimization in this work provides better performance while demonstrating very good reliability and robustness. However, other optimum points from deterministic optimizations violate the regarded constraints in the presence of uncertainties.
文摘In this paper,we have formulated mathematical models to optimize the bouncing transmissibility of the sprung mass of the half car system with passengers’seat suspensions considering different road conditions.The corresponding problem has been solved with the help of advanced real coded Genetic Algorithm(GA).The nonlinearity of suspension spring and damper,which are the most important characteristics of the suspension,has been taken into account in order to validate the model to real applications.The nonlinear cubic polynomial has been used to describe the spring characteristic and a quadratic polynomial has been used to describe the damper characteristic.The coefficients of each polynomial represent the design parameters of the suspension system and are to be determined.To find these parameters we have formulated a nonlinear optimization problem in which the bouncing transmissibility of the sprung mass at the center of mass has been minimized with respect to technological constraints and the constraints which satisfy the performance as per ISO 2631 standards.The advanced real coded GA has been used to solve this problem in time domain and the results obtained have been compared to those obtained using the existing design parameters.The objective function and the constraints have been evaluated by simulating the vehicle model over two roads with multiple bumps at uniform velocity.
