NARX Neural Network Modelling of Hydraulic Suspension Dampers for Steady-state and Variable Temperature Operation

Summary Two NARX-type neural networks are developed for modelling nonlinear dynamic characteristics of passive twin-tube hydraulic dampers used in vehicle suspension systems. Quasi-isothermal and variable temperature NARX models are rigorously tested and compared with a state-of-the-art physical model proposed by Duym and Reybrouck (1998) and Duym (2000). Measured damper data, generated under isothermal and temperature varying conditions, is used for NARX training, physical model calibration, and predictive comparisons. Test kinematics include high amplitude sinusoidal displacements up to 14 Hz, and realistic random road profiles. The NARX models are trained via 'teacher forcing' and the feedforward backpropagation algorithm using both 'Early Stopping' and Bayesian Regularisation. Stable network design is also examined using the minimum posterior prediction error as the criterion for selecting a good network from a small number of tests. Calibration of the physical model proves highly complicated owing to considerable nonlinearity-in-the-parameters, requiring use of Sequential Quadratic Programming with an implicitly nonlinear constraint. The paper shows that NARX neural network modelling is vastly superior in terms of calibration efficiency, and prediction times, whilst offering roughly similar, if not better, model accuracy.     

NARX Neural Network Modelling of Hydraulic Suspension Dampers for Steady-state and Variable Temperature Operation

Summary Two NARX-type neural networks are developed for modelling nonlinear dynamic characteristics of passive twin-tube hydraulic dampers used in vehicle suspension systems. Quasi-isothermal and variable temperature NARX models are rigorously tested and compared with a state-of-the-art physical model proposed by Duym and Reybrouck (1998) and Duym (2000). Measured damper data, generated under isothermal and temperature varying conditions, is used for NARX training, physical model calibration, and predictive comparisons. Test kinematics include high amplitude sinusoidal displacements up to 14 Hz, and realistic random road profiles. The NARX models are trained via ‘teacher forcing’ and the feedforward backpropagation algorithm using both ‘Early Stopping’ and Bayesian Regularisation. Stable network design is also examined using the minimum posterior prediction error as the criterion for selecting a good network from a small number of tests. Calibration of the physical model proves highly complicated owing to considerable nonlinearity-in-the-parameters, requiring use of Sequential Quadratic Programming with an implicitly nonlinear constraint. The paper shows that NARX neural network modelling is vastly superior in terms of calibration efficiency, and prediction times, whilst offering roughly similar, if not better, model accuracy.     

Adaptive neuron control using an integrated error approach with application to active suspensions

This paper proposes a new neuron control strategy for an active vehicle suspension system, with the emphasis on the study of multivariable and uncertain suspension characteristics. The novelty of this strategy is in the use of integrated error, which consists of multiple output errors in the regulated plant. By combining the integrated error approach with the traditional neuron control (TNC), integrated error neuron control (IENC) is presented. It provides a direct control to the multiple outputs of the control plant simultaneously. Taking a quarter-car model as an example, the proposed control strategy is applied and comparative simulations are carried out with various vehicle parameters and road input conditions. Simulation results prove the effectiveness and robustness of the proposed IENC method. In addition, the newly proposed neuron scheme provides a simple yet efficient new possibility for the control of a class of uncertain multivariable systems similar to an active vehicle suspension.     

汽车半主动悬架的模型参考自适应控制

在1／4车辆动力学模型的基础上，基于李雅普诺夫稳定性理论，以天棚阻尼半主动悬架为参考模型，设计了半主动悬架模型参考自适应控制器。自适应控制器包括可调前置控制器和状态反馈控制器两个部分。推导了自适应控制律与相应的约束条件。仿真结果表明：该控制器对于模型参数的不确定性具有良好的鲁棒特性。自适应控制器不仅明显降低了车身加速度，提高了平顺性，同时也使汽车的行驶安全性获得了改善，悬架动变形稍有增大。     

Energy-harvesting potential of automobile suspension

This study is aimed quantify dissipated power in a damper of automobile suspension to predict energy harvesting potential of a passenger car more accurately. Field measurements of power dissipation in a regenerative damper are still rare. The novelty is in using the broad database of real road profiles, a 9 degrees-of-freedom full-car model with real parameters, and a tyre-enveloping contact model. Results were presented as a function of road surface type, velocity and road roughness characterised by International Roughness Index. Results were calculated for 1600 test sections of a total length about 253.5?km. Root mean square of a dissipated power was calculated from 19 to 46?W for all four suspension dampers and velocity 60?km/h and from 24 to 58?W for velocity 90?km/h. Results were compared for a full-car model with a tyre-enveloping road contact, full-car and quarter-car models with a tyre–road point contact. Mean difference among three models in calculated power was a few per cent.     

Inverse neuro-fuzzy MR damper model and its application in vibration control of vehicle suspension system

In this paper, a magneto-rheological (MR) damper-based semi-active controller for vehicle suspension is developed. This system consists of a linear quadratic Gauss (LQG) controller as the system controller and an adaptive neuro-fuzzy inference system (ANFIS) inverse model as the damper controller. First, a modified Bouc–Wen model is proposed to characterise the forward dynamic characteristics of the MR damper based on the experimental data. Then, an inverse MR damper model is built using ANFIS technique to determine the input current so as to gain the desired damping force. Finally, a quarter-car suspension model together with the MR damper is set up, and a semi-active controller composed of the LQG controller and the ANFIS inverse model is designed. Simulation results demonstrate that the desired force can be accurately tracked using the ANFIS technique and the semi-active controller can achieve competitive performance as that of active suspension.     

车辆悬架的最优自适应与自校正控制

本文研究了车辆主动悬架自适应与自校正控制的策略与算法。     

Generalized magnetorheological (MR) damper model and its application in semi-active control of vehicle suspension system

In this paper, analytical characterization of the magneto-rheological (MR) damper is done using a new modified algebraic model. Algebraic model is also more preferable because of its low computational expenses compared to differential Bouc-Wen’s model which is highly computationally demanding. This model along with the obtained model parameters is used as a semi-active suspension device in a quarter car model and the stationary response of the vehicle traversing on a rough road is obtained. The control part consists of two nested controllers. One of them is the system controller which generates the desired damping force and the other is the damper controller which adjusts the voltage level to MR damper so as to track the desired damping force. For the system controller a model reference skyhook Sliding Mode Controller (SMC) is used and for the damper controller a continuous state algorithm is built to determine the input voltage so as to gain the desired damping force. The analytical model is subsequently used in the quarter car vehicle model and the vehicular responses are studied. A simulation study is performed to prove the effectiveness and robustness of the semi-active control approach. Results show that the semi-active controller can achieve compatible performance as that of active suspension controller except for a little deterioration.     

虚拟试车场技术预报载货汽车底盘耐久性研究

针对载货汽车开发过程中传统耐久性试验周期长、费用高的缺点,以某耐久性试车场道路为输入条件,应用虚拟试车场技术(VPG)建立了整车虚拟仿真模型.模拟分析载货汽车底盘动应力响应,并与相同路况下的实车试验测试结果进行了对比研究.结果表明,测试结果与VPG模拟结果在时域与频域上的趋势基本一致.在此基础上,运用疲劳分析软件FEMFAT4.7实现了对载货汽车底盘耐久性的有效预报.     

面向动态避障的智能汽车滚动时域路径规划

为解决城市低速条件下智能汽车在避障过程中的路径规划问题，提出面向动态避障的智能汽车滚动时域路径规划方法。首先，划分车道可行区域，利用3次拉格朗日插值法拟合车道边界，并根据"车-路"的相对位置关系将车道区域进一步划分为车道间区域与车道内区域两部分。其次，以区域虚拟力场进行动态交通场景模拟，包括在障碍车周身沿车道方向的虚拟矩形区域斥力场，行驶目标位置的虚拟引力场和车道保持虚拟区域引力场3个部分，然后结合划分的车道区域确定各虚拟力场的作用区域。再次，建立主车动力学与运动学模型，障碍车运动学预测模型，把主车与障碍车无碰撞，主车行驶在车道内区域，趋向目标位置以及保证车辆稳定性作为优化目标，综合车辆模型的控制输入、状态变量等动力学约束条件，构建多目标的滚动时域控制器用于车辆避障路径规划，求解获得前轮转角作为控制量。最后，利用MATLAB和veDYNA软件对提出的路径规划控制系统分别在静态障碍和动态障碍工况下进行联合仿真。研究结果表明：该方法能够很好地解决躲避静态障碍和低速动态障碍车的问题，控制车辆驶向目标位置，并且在避障过程中满足车辆的动力学约束，同时又不会与道路边界发生碰撞，保证了车辆的安全性和稳定性。     

基于半主动自适应悬架系统的整车道路友好性研究

为了提高车辆的道路友好性与平顺性,设计了以磁流变减振器为控制对象的整车自适应模糊控制半主动悬架系统。在试验测试和理论分析的基础上,建立了基于磁流变减振器的整车半主动悬架模型及其状态方程,并用该模型对自适应模糊控制方法进行了研究。模型的输入采用B级和C级路面谱;道路友好性评价指标采用动载荷系数和动载荷应力因子;使用MATLAB/Simulink建立基于2个自适应模块的模糊控制器控制系统,模糊控制器的输入均采用车身与车桥的相对速度和相对加速度。仿真结果表明:与被动悬架相比,在B级和C级路面、不同速度下,半主动自适应悬架动载荷系数均降低30%左右,动载荷应力因子均降低40%以上,同时也提高了车辆的运行平顺性和稳定性。     

Road roughness estimation based on discrete Kalman filter with unknown input

ABSTRACT

The road roughness acts as a disturbance input to the vehicle dynamics, and causes undesirable vibrations associated with the ride and handing characteristics. Furthermore, the accurate measurement of road roughness plays a key role in better understanding a vehicle dynamic behaviour and active suspension control systems. However, the direct measurement by laser profilometer or other distance sensors are not trivial due to technical and economic issues. This study proposes a new road roughness estimation method by using the discrete Kalman filter with unknown input (DKF-UI). This algorithm is built on a quarter-car model and uses the measurements of the wheel stroke (suspension deflection), and the acceleration of the sprung mass and unsprung mass. The estimation results are compared to the measurements by laser profilometer in-vehicle test.     

基于整车在环仿真的自动驾驶汽车室内快速测试平台

整车在环仿真测试方法可以安全、高效地验证复杂环境和极端工况等场景下自动驾驶汽车性能的有效性,基于此研发一种基于整车在环仿真的自动驾驶汽车室内快速测试平台,该平台由前轴可旋转式转鼓试验台、试验台测控子系统、虚拟场景自动生成子系统、虚拟传感器模拟子系统、驾驶模拟器、自动驾驶汽车和测试结果自动分析评价子系统组成。通过在试验台滚筒上独立加载转矩模拟车辆行驶阻力,可动态模拟不同的路面附着系数,同时利用坡度、侧倾和转向随动机构可模拟车辆俯仰角、侧倾角和航向角3个自由度;采用虚拟现实技术柔性集成车辆动力学模型、传感器仿真、复杂道路交通环境及测试用例仿真,模拟多种道路交通场景,并通过传感器仿真及数据融合等技术快速测试自动驾驶汽车智能感知与行为决策等性能指标。将自动驾驶汽车、虚拟仿真场景和试验台耦合构建一个闭环系统,完成了多项关键技术研发,包括：多自由度高动态试验台结构设计、虚拟测试场景自动重构方法和传感器数据模拟及注入方法,可满足在各种场景下测试自动驾驶汽车整车性能的需求。此外,为验证快速测试平台的有效性,以U-turn轨迹跟踪控制为研究实例,基于简化的车辆运动学模型和模型预测控制算法,在平台上搭建U-turn场景并对自动驾驶汽车的轨迹跟踪控制算法性能进行大量测试。结果表明：自动驾驶汽车室内快速测试平台可以真实地模拟汽车在道路上的运行工况,自动驾驶汽车在虚拟场景中的轨迹跟踪效果良好,与参考轨迹的偏差小于8%,证明了该测试平台检测方法的有效性。     

汽车平顺性时域仿真分析

采用虚拟试验场技术进行了汽车行驶平顺性的时域仿真。建立了面向汽车平顺性分析的整车刚弹耦合有限元模型,同时建立了脉冲输入路面模型和随机输入路面模型。采用1/3倍频带分布加速度均方根值方法及总加权方法对试验车辆的平顺性进行了评价。试验结果表明,运用虚拟试验场技术能够真实地反映汽车的行驶平顺性,仿真分析结果可靠。     

Vehicle Dynamic Analysis and Evaluation of Continuously Controlled Semi-Active Suspensions Using Hardware-in-the-loop Simulation

A semi-active suspension system with continuously variable damper is greatly expected to be used mainly in the future as a high-performance suspension system due to its cost-effectiveness, light weight, and low energy consumption. In this paper, to develop a suitable control logic for the semi-active suspension system, the hardware-in-the-loop simulation is performed for the experimental continuously variable damper combined with a quarter-car model, and the simulation results are compared for passive, on/off controlled, and continuously controlled dampers in the aspects of ride comfort and driving safety, assuming each damper to be installed on the vehicle.     

Analytical solutions for optimal ride comfort and tyre grip for passive vehicle suspensions

The paper derives analytical solutions for the global optimum of the ride comfort and tyre grip performance measures for a quarter-car vehicle model optimised both individually and in combination. The solutions are derived for six simple suspension networks comprising one or two springs, one damper and possibly one inerter. The solutions are functions of four vehicle parameters: the sprung mass, the unsprung mass, the tyre stiffness and the static stiffness, of the suspension.     

Optimisation of active suspension control inputs for improved vehicle ride performance

A collocation-type control variable optimisation method is used in the paper to analyse to which extent the fully active suspension (FAS) can improve the vehicle ride comfort while preserving the wheel holding ability. The method is first applied for a cosine-shaped bump road disturbance of different heights, and for both quarter-car and full 10 degree-of-freedom vehicle models. A nonlinear anti-wheel hop constraint is considered, and the influence of bump preview time period is analysed. The analysis is then extended to the case of square- or cosine-shaped pothole with different lengths, and the quarter-car model. In this case, the cost function is extended with FAS energy consumption and wheel damage resilience costs. The FAS action is found to be such to provide a wheel hop over the pothole, in order to avoid or minimise the damage at the pothole trailing edge. In the case of long pothole, when the FAS cannot provide the wheel hop, the wheel is travelling over the pothole bottom and then hops over the pothole trailing edge. The numerical optimisation results are accompanied by a simplified algebraic analysis.     

基于电子地图信息的车辆主动转向仿真

以驾驶员预瞄点处的横向偏移最小为目标，以道路曲率输入的车辆运动模型为基础，分析了车辆进行主动转向所需要的道路环境信息，并研究了利用电子地图及车辆定位传感器得到这些信息的方法。利用设计的转向控制器进行了恒定道路曲率及基于电子地图数据的实际道路信息输入下的主动转向仿真。仿真结果表明，利用电子地图提供的信息能够在投入较低成本的条件下进行主动转向，使车辆在道路曲率变化的情况下沿预定道路行驶并有着较小的侧向加速度；从而提高车辆在弯曲道路行驶的安全性、舒适性。     

Analysis and optimisation of objective vehicle dynamics testing in winter conditions

Objective testing of vehicle handling in winter conditions has not been implemented yet because of its low repeatability and its low signal-to-noise ratio. Enabling this testing, by identifying robust manoeuvres and metrics, was the aim of this study. This has been achieved by using both experimental data, gathered with steering-robot tests on ice, and simulation models of different complexities. Simple bicycle models with brush and MF-tyre models were built, both optimally parameterised against the experimental data. The brush model presented a better balance in complexity performance. This model was also implemented in a Kalman filter to reduce measurement noise; however, a simpler low-pass filter showed almost similar results at lower cost. A more advanced full vehicle model was built in VI-CarRealTime, based on kinematics and compliance data, damper measurements, and real tyre measurements in winter conditions. This model offered better results and was therefore chosen to optimise the initial manoeuvres through test design and simulations. A sensitivity analysis (ANOVA) of the experimental data allowed one to classify the robustness of the metrics. Finally, to validate the results, the proposed and the initial manoeuvres were tested back to back in a new winter campaign.     

Pro-active optimal control for semi-active vehicle suspension based on sensitivity updates

This article suggests a strategy to control semi-active suspensions of vehicles in a pro-active way to adapt to future road profiles. The control strategy aims to maximise comfort while maintaining good handling properties. It employs suitably defined optimal control problems in combination with a parametric sensitivity analysis. The optimal control techniques are used to optimise the time-dependent damper coefficients in an electro-rheological damper for given nominal road profiles. The parametric sensitivity analysis is used to adapt the computed nominal optimal controls to perturbed road profiles in real time. The method is particularly useful for events with a low excitation frequency such as ramps, bumps, or potholes. For high-frequency excitations standard controllers are preferable; so we propose a switched open–closed-loop controller design. Various examples demonstrate the performance of the approach.