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.     

A NARX damper model for virtual tuning of automotive suspension systems with high-frequency loading

A computationally efficient NARX-type neural network model is developed to characterise highly nonlinear frequency-dependent thermally sensitive hydraulic dampers for use in the virtual tuning of passive suspension systems with high-frequency loading. Three input variables are chosen to account for high-frequency kinematics and temperature variations arising from continuous vehicle operation over non-smooth surfaces such as stone-covered streets, rough or off-road conditions. Two additional input variables are chosen to represent tuneable valve parameters. To assist in the development of the NARX model, a highly accurate but computationally excessive physical damper model [originally proposed by S. Duym and K. Reybrouck, Physical characterization of non-linear shock absorber dynamics, Eur. J. Mech. Eng. M 43(4) (1998), pp. 181–188] is extended to allow for high-frequency input kinematics. Experimental verification of this extended version uses measured damper data obtained from an industrial damper test machine under near-isothermal conditions for fixed valve settings, with input kinematics corresponding to harmonic and random road profiles. The extended model is then used only for simulating data for training and testing the NARX model with specified temperature profiles and different valve parameters, both in isolation and within quarter-car vehicle simulations. A heat generation and dissipation model is also developed and experimentally verified for use within the simulations. Virtual tuning using the quarter-car simulation model then exploits the NARX damper to achieve a compromise between ride and handling under transient thermal conditions with harmonic and random road profiles. For quarter-car simulations, the paper shows that a single tuneable NARX damper makes virtual tuning computationally very attractive.     

基于ARIMA与人工神经网络组合模型的交通流预测

将自回归求和滑动平均(ARIMA)与人工神经网络组合模型用于短时交通流预测。利用ARIMA模型良好的线性拟合能力和人工神经网络强大的非线性关系映射能力,把交通流时间序列看成由线性自相关结构和非线性结构两部分组成,采用ARIMA模型对交通流序列的线性部分进行预测,用人工神经网络模型对其非线性残差部分进行预测。结果表明:组合模型的预测准确性高于各自单独使用时的准确性;组合方法发挥了2种模型各自的优势,是短期交通流预测的有效方法。     

基于小波优化GRU-ARMA模型的空中交通流量短时预测方法

空中交通流量短时预测是空中交通管理的基础,是有效缓解交通拥堵问题的前提。为提高空中交通流量短时预测的精度,减小空中交通管制员的工作压力,提出了基于小波优化GRU-ARMA的空中交通流量短时预测方法。在传统预测方法的基础上,通过小波变换对原始流量数据进行多尺度分解,提取不同频率交通流量的细节特征,对原始流量数据进行预处理。同时,根据小波变换,在低频处将频率细分作为趋势项,高频处将时间细分作为噪声项。其中,趋势项反映了空中交通流量随时间演化的整体趋势性,噪声项反映了随机因素对空中交通流量的综合影响。使用门控循环单元（GRU）神经网络模型预测趋势项,自回归滑动平均模型（ARMA）模型预测噪声项;将趋势项和噪声项的预测值叠加,得到最终的短时流量预测值。误差分析表明,该方法在每个预测点上的误差保持在2%左右,预测效果稳定;而直接采用原始流量数据进行预测的GRU、BiLSTM、CNN-LSTM神经网络模型及单一的ARMA模型,每个点的预测误差在5%~37.14%之间。与GRU、BiLSTM、CNN-LSTM神经网络模型相比,该模型的预测精度分别提高了3.02%,5.39%,5.05%。      

基于Takens理论和SVM的滑坡位移预测

针对滑坡变形时序非线性,数据量少的特点,引入Takens理论,采用支持向量机(SVM)建立其预测模型,建模过程中,比较了由不同核函数获得的SVM模型的性能,同时将SVM与RBF、El-man神经网络模型进行外推7步预测试验比较。结果表明:RBF核函数具有更好的工程实用价值;在有限样本情况下,SVM预测模型具有更好的准确性和泛化性,其7步预测平均误差率控制在5%以内,可见该方法在滑坡变形预测方面极具潜力。     

Two degrees of freedom PID multi-controllers to design a mathematical driver model: experimental validation and robustness tests

This paper proposes a mathematical driver model based on PID multi-controllers having two degrees of freedom. Each PID controller making up this model is synthesised by the Ziegler–Nichols oscillation method, using the linear time invariant models which are obtained around their nominal operating points. Different PID controllers are combined using nonlinear optimisation and the H _∞ constraint. To demonstrate its robustness, it was tested on two models: a linear parameter variant model and a nonlinear four-wheel model. It was also tested in situations of high dynamic demand. The driver model showed good performance, stability and trajectory tracking. The performance tests were carried out using experimental data acquired by a Laboratory Peugeot 307 developed by INRETS-MA. This driver model was developed for an application known as ‘Itinerary Rupture DIagnosis’ (DIARI), which aims to evaluate the physical limits of a vehicle negotiating a bend. DIARI requires a tool to determine the steering commands to be applied to a vehicle model, making extrapolations with respect to speed.     

基于时间序列相似性搜索的交通流短时预测方法

为了进一步提高交通流短时预测的效果,在分析现有预测模型存在问题的基础上,设计了1种基于时间序列相似性搜索的交通流短时多步预测方法.利用界标模型对交通流时间序列数据进行模式表示,在历史数据库中搜索与当前交通流时间序列相似度较高的历史时间序列,进而确定与预测时刻相对应的历史数据,利用回声状态网络模型实现交通流的短时多步预测.采用某特大城市快速路5 min采样间隔的交通流量数据进行实验验证和对比分析.实验结果表明,回声状态网络模型的预测精度分别比ARIMA模型和BP神经网络模型提高了6.25%和3.85%,以时间序列相似性搜索结果作为模型输入数据能够进一步提高交通流短时预测的精度.      

非线性耦合模型在桥梁桩基沉降预测中的应用研究

通过对桥梁桩基的沉降预测,能有效地评价和判断桥梁的稳定性,为现场施工提供一定的指导依据。同时,系统性的预测方法能有效提高预测精度,因此,将灰色模型和BP神经网络进行耦合,建立了桥梁桩基沉降的初步预测模型,再利用马尔科夫链建立误差修正模型,实现桥梁桩基沉降的分阶段预测。该模型发挥了灰色模型“累加生成”灰色序列的优点,增加了沉降数据的规律性,又充分利用了BP神经网络和马尔科夫链的非线性预测能力,具有系统性强、全面性高等优点。同时,利用2个实例进行验证,结果表明实测值和预测值较吻合。其中,实例1平均相对误差为1.37%,实例2的平均相对误差为1.39%,两实例的预测结果差异不大,具有较高的预测精度,验证了所提预测模型的有效性。     

基于支持向量机的交通事故组合预测方法研究

对灰色理论、神经网络和支持向量机的预测模型进行了研究,对灰色理论、神经网络和支持向量机3种预测方法进行了线性组合、神经网络组合和支持向量机的组合预测.以1995～2004年某公路路段的交通事故次数为例,与单一预测方法结果、线性组合预测和神经网络组合预测进行对比,认为支持向量机组合预测方法比较精确.     

基于GA、RBF和改进Cao方法的空中交通流预测方法

针对传统空中交通流量预测方法精度不足、时效性差的问题,考虑空中交通流量时间序列的混沌特征,在相空间重构理论的基础上,研究了结合遗传算法（GA）、径向基（RBF）神经网络与改进Cao方法的空中交通流量预测方法。为降低传统Cao方法人为参数选择引入的误差,提高相空间重构精度,通过判定虚假邻近点,以及迭代比较嵌入维度离差和可接受偏差,确定重构相空间嵌入维度值的选择标准,进而得到重构后的空中交通流量时间序列数据;为提升径向基神经网络预测精度并降低参数误差,使用遗传算法优化RBF神经网络的中心矢量、加权系数和输出层阈值,再通过最优系数标定后的神经网络对重构后的时间序列进行预测;利用实际空中交通流量数据进行仿真以验证方法的有效性,并结合最大Lyapunov指数和预测结果分析了预测的时效性以及时间尺度对精度影响。结果显示：(1)改进后的预测方法具有更好的非线性拟合能力,提高了交通流量时间序列的预测精度;(2)以5 min时间间隔预测为例,相比传统RBF神经网络,改进方法的平均绝对误差、均方误差以及平均绝对百分比误差分别降低了19.44%、34.78%和27.21%;(3)相比反向传播（BP）神经网络...     

基于BP神经网络的阿拉套山隧道围岩物理力学参数反演分析

为研究高寒地区设置中心深埋水沟单线铁路隧道的围岩力学参数问题,以兰新铁路新建博州支线阿拉套山隧道为工程背景,基于FLAC3D数值模拟软件联合MATLAB中的神经网络工具箱构建BP神经网络算法,建立隧道开挖位移正演和反演模型,对围岩物理力学参数作反演分析。通过对中心水沟开挖前的拱顶和拱腰监测数据做拟合分析,发现隧道变形已趋于稳定,反演过程不需考虑中心水沟开挖对围岩的二次扰动。以水沟开挖前的拱顶沉降值和拱腰收敛值作为输入函数,以围岩的体积弹性模量K、剪切弹性模量G、黏聚力c、内摩擦角φ、重度γ作为输出函数训练神经网络模型,利用训练好的模型进行所需参数的反演分析。将反演参数代入FLAC3D正演模型计算后,提取中心水沟开挖前的拱顶沉降值和拱腰收敛值,与中心深埋水沟开挖前的实际监控量测值相比较为接近。结果证明,围岩物理力学参数的反演较为合理,对于变形的预测较为准确,可为隧道后期工程的施工和优化设计提供参考。     

融合深度反残差与注意力机制的山区高速公路事故严重程度预测模型

山区高速公路事故严重程度预测对保障交通安全具有重大意义。针对现有事故严重程度预测模型存在准确率低、泛化性差等问题,考虑到深度卷积神经网络可以高效处理图像问题,为此将事故影响因素图像化,提出一种融合深度反残差与注意力机制的山区高速公路事故严重程度预测模型。该模型首先采用相关性分析确定影响交通事故严重程度的因素,依据严重程度与影响因素将事故划分为财产损失、轻伤事故、重伤事故和死亡事故4类;然后将影响因素处理成图片的形式,进而将事故严重程度预测问题转化为图像的分类问题,随之构建基于反残差与注意力机制的山区高速公路事故严重程度预测模型,其中：基于深度可分离卷积的反残差结构可以以较少训练参数获取较高的准确率,基于软阈值的注意力机制作为一种非线性层可以忽略与事故严重程度无关的信息,Mish激活函数可以确保更好的信息流入神经网络。结果表明：在山区高速公路交通安全事故严重程度评估中,相比于传统的机器学习模型,所提出的模型识别准确率具有明显的提高,且测试准确率为85%左右,满足山区高速公路安全评估的实际预测需求。     

基于灰色BP神经网络组合模型的基坑变形预测研究

为了使得基坑变形预测在“少样本”“贫信息”的情况下依然能够得出精度较高的结果,在传统的灰色GM(1,1)模型和BP神经网络模型的基础上,进行了灰色BP神经网络组合模型的研究。通过总结2传统模型的原理和算法,归纳各自的优缺点,分析2模型在本质原理上的关系,提出了构建组合模型的方法。利用广州市轨道交通三号线燕塘站的监测数据,对灰色GM(1,1)模型、BP神经网络模型和灰色BP神经网络组合模型分别进行了检验,肯定了组合模型的优越性。     

Efficient empirical modelling of a high-performance shock absorber for vehicle dynamics studies

This paper develops an intuitive empirical nonlinear dynamic shock absorber model for simulation studies. Unlike other existing dynamic shock absorber models, it does not suffer from the complexity of modelling complex physical behaviour, or the inefficiencies of unstructured black-box modelling. The model consists of an algebraic backbone, which is a function of velocity alone, and a nonlinear low-pass filter, which has been designed based on the observation that the damper can respond more quickly at higher velocities. Due to the simplicity of the model, it can be fitted with data and evaluated quickly. The model was fitted using shock dynamometer test data using a random shock position command. The completed model is then validated using random, sine wave, and bump test data. This analysis shows the strengths and weaknesses of the model and suggests areas for future development.     

基于GRA-SSA-Elman的隧洞TBM掘进适应性评价

为准确评价隧洞施工TBM掘进适应性，保障TBM安全、高效施工，提出一种基于灰色关联分析（GRA）与麻雀搜索算法（SSA）优化Elman神经网络的TBM掘进适应性预测模型。首先，从地质条件、掘进参数、不良地质、施工组织4个方面综合考虑，初步选取13个主要影响因素，建立隧洞TBM掘进适应性评价指标体系； 然后，利用GRA分析指标与掘进适应性间的关联性，引入SSA优化Elman神经网络，提高模型性能，并采用留一交叉验证法验证模型的准确性及可靠性，使得模型最接近原始数据分布特征； 最后，结合北疆水利工程某标段中待测样本对模型预测效果进行验证，同时与Elman、PSO-Elman、BP神经网络模型预测结果及现场实际结果对比分析。结果表明： SSA-Elman模型预测结果与实际工程结果吻合度较高，该模型能够正确、有效地对TBM掘进适应性进行预测评价，且具有合理性和可操作性，可为隧洞TBM适应性评价提供一种新方法。     

基于BP神经网络预测正庚烷-乙醇混合燃料自燃温度

正庚烷-乙醇混合燃料的自燃温度对研究反应控制压燃(RCCI)具有重要的参考意义。采用BP神经网络预测正庚烷-乙醇混合燃料自燃温度,该神经网络模型以正庚烷掺混比、当量比和进气压力为输入,自燃温度为输出,单层隐含层有16个节点时迭代过程均方误差和训练状态梯度均最小。研究结果表明:对神经网络模型训练、验证、测试的线性系数和全局线性系数R分别为0.997 78,0.997 9,0.994 92和0.997 33,预测精度较高;验证了该神经网络模型对正庚烷掺混比、当量比和进气压力变化的泛化能力,预测值与试验值的误差均在允许范围内,因此本模型得到的预测值与试验值具有良好的一致性。     

Calibration efficiency improvement of rule-based energy management system for a plug-in hybrid electric vehicle

This paper presents a calibration method of a rule-based energy management strategy designed for a plug-in hybrid electric vehicle, which aims to find the optimal set of control parameters to compromise within the conflicting calibration requirements (e.g. emissions and economy). A comprehensive evaluating indicator covering emissions and economy performance is constructed by the method of radar chart. Moreover, a radial basis functions (RBFs) neural network model is proposed to establish a precise model within the control parameters and the comprehensive evaluation indicator. The best set of control parameters under offline calibration is gained by the multi-island genetic algorithm. Finally, the offline calibration results are compared with the experimental results using a chassis dynamometer. The comparison results validate the effectiveness of the proposed offline calibrating approach, which is based on the radar chart method and the RBF neural network model on vehicle performance improvement and calibrating efficiency.     

Modeling retroreflectivity degradation of traffic signs using artificial neural networks

Traffic signs are vital for communicating guidance, rules, warning, and other highway agency information for safe and efficient navigation through transportation networks. Signs must be clearly detectable, readable, and understandable to fulfill their intended purpose. Poor sign visibility, particularly during nighttime, is the leading cause of fatalities worldwide. Sign retroreflectivity is one of the key measures to evaluate sign visibility conditions. It gradually deteriorates over time with sign aging, exposure, and other environmental conditions necessitating periodic sign maintenance or, ultimately, replacement when the sign retro values fall below the minimum prescribed standards. In literature, studies have mostly used traditional statistical regression models to model sign retroreflectivity as a function of available explanatory variables. Further, these studies have proposed separate retro degradation prediction models for different sign sheeting grades and colors that limit their applications for other scenarios. To fill the research gap, this study compared the performance of the linear regression method with three different architecture of the neural network namely, Feed-Forward Neural Network (FFNN), Cascade Forward Neuran Network (CFNN), and Elman neural networkNeural Network (ELMNN) for signs retro prediction with an aim to optimize sign maintenance and replacement activities and to enhance road safety. All the Neural Network models were employed with varying combinations of training algorithms, activation functions, and model parameters. Sign retro data for 539 in-service signs along selected sections of two expressways (M-1 and M-2) near the capital city of Islamabad in Pakistan were collected through portable handheld retroreflectometer GR3. Data on other sign attributes like sign ages (0, 2, 5, and 10 years), sign orientation, observation angle, sign sheeting brand, grade, and color were also acquired. Feature-based sensitivity analysis was conducted to identify the relative importance and ranking of input predictor variables. Model prediction results expressed in terms of various statistical evaluation metrics root mean square error (RMSE), mean absolute percent error (MAPE), RMSE-observation standard deviation satio (RSR), coefficient of determination (R²), Willmott's index of agreement (WIA), Nash-Sutcliffe efficiency (NSEC), and percent bias (PBIAS) showed that all the NN models outperformed the regression technique. Comparing the NN models, ELMNN architecture with 21 neurons in the hidden layer for ‘tansig’ activation function and ‘trainlm’ training algorithm yielded better retro-prediction performance. Feature sensitivity analysis revealed that variables sign age, sheeting brand, color, and observation angle were the most sensitive variables in predicting the retro output. Findings of this study can guide the transport agencies and decision-makers for effective policy implications and sign management practices.     

The simulation of in-plane tyre modal behaviour: a broad modal range comparison between analytical and discretised modelling approaches

In-plane tyre modal behaviour determines the response of tyres to ride excitations and braking/traction manoeuvres. In many studies, the interest is limited to relatively low frequencies and a detailed investigation into the ability of models to accurately simulate higher-order responses is unnecessary. In cases where an in-plane model is to be used for the generation of the contact deformation and stresses, or where modal reduction methods are implemented, a detailed knowledge of the modal response is desirable. The present work forms a study on the ability of a number of frequently used modelling approaches to generate realistic modal data throughout a wide frequency range. The analytical ring on elastic foundation model is used as a benchmark throughout the paper. Its predictions are compared with those of two discretised models, namely a truss- and a beam-based model. The sensitivity of the ring’s response to a number of physical parameters is discussed. The results are used to inform the comparison between the analytical ring and the discretised models, providing explanations for any discrepancies observed. The limited applicability of the truss model is pointed out, while the accuracy of the beam-based model is enhanced by a circumferential inextensible string element. Both the ring and the enhanced beam models are further improved with the addition of a nonlinear string-based sidewall that accounts for the change in sidewall stiffness with inflation pressure. The findings may offer a reference when setting up in-plane models, including the stage of planning modal tests for parameter identification.     

Hybrid modelling and damping collaborative optimisation of Five-suspensions for coupling driver-seat-cab system

For the complex structure and vibration characteristics of coupling driver-seat-cab system of trucks, there is no damping optimisation theory for its suspensions at present, which seriously restricts the improvement of vehicle ride comfort. Thus, in this paper, the seat suspension was regarded as ‘the fifth suspension’ of cab, the ‘Five-suspensions’ for this system was proposed. Based on this, using the mechanism modelling method, a 4 degree-of-freedom coupling driver-seat-cab system model was presented; then, by the tested cab suspensions excitation and seat acceleration response, its parameters identification mathematical model was established. Based on this, taking optimal ride comfort as target, its damping collaborative optimisation mathematical model was built. Combining the tested signals and a simulation model with the mathematical models of parameters identification and damping collaborative optimisation, a complete flow of hybrid modelling and damping collaborative optimisation of Five-suspensions was presented. With a practical example of seat and cab system, the damping parameters were optimised and validated by simulation and bench test. The results show that the model and method proposed are correct and reliable, providing a valuable reference for the design of seat suspension and cab suspensions.