高速列车载荷反演技术及其运用研究
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摘要
激励随时间变化的关系对工程结构的设计、分析以及使用过程中的可靠性等具有十分重要的影响。对于高速列车而言,轮轨之间的相互作用是决定其运行稳定性的主要因素之一。对轨道来说,随着列车运行速度的提高,轮轨作用载荷急剧恶化,将导致轨道变形的加速,严重影响高速列车行车安全。另外,从评估高速列车动力学特性、各部件之间的振动耦合关系、摩擦磨损性能、耐久性等方面来说,实现对轮轨作用力的实时掌握和分析也是非常必要的。因此,轮轨之间的接触力信息一直是研究人员和工程人员关注的热点课题。
在高速列车的运行中,由于轮轨之间的高速相对运动、结构复杂以及各个方向载荷相互影响等,运行状态下的轮轨激励载荷通常难以测量,因此需要发展一种间接的载荷-时间关系求解方法,即载荷反演法。论文在理论推导的基础上,与工程实际需求紧密结合,主要完成了以下工作：
(1)论文全面总结了国内外有关载荷反演方法最新研究进展,并对载荷反演方法在铁道机车车辆上的发展和运用进行了梳理和详细的总结。从我国机车车辆以及高速列车的现状着手,分析了建立具有广泛应用价值的高精度的运行列车轮轨动载荷反演方法的重要性。
(2)提出了一种基于动态规划的非迭代载荷反演时域方法。从系统的角度建立了结构输入载荷评估的数学模型,通过间接测量的方法,建立结构未知激励载荷与该激励下的结构响应之间的关系,从而得到时域下的输入激励载荷。由于反演模型的非迭代性,方法有效解决了动载荷反演中对初始条件过分依赖的问题,同时避免了载荷反演过程中误差的传递和累积,具有良好的数值稳定性。将Bellman最优化原理引入到目标函数的最小化当中,保证了每个积分步长上得到的反演载荷和响应均能够使目标函数最小,有效地降低了载荷识别过程中无法避免的病态问题对反演结果的影响,得到了与真实载荷非常相近的反演载荷。
(3)系统地对正则化参数的求解方法进行了理论推导和研究,得到了适用于本反演模型的广义交叉验证法计算公式。数学物理反问题在求解过程中,由于原始测量数据受到测量仪器、外界干扰等的影响以及在反演数学模型中受到已知测量数据不足、边界条件取值不当、测量响应的噪声干扰和近似解的不稳定性等因素的影响,导致反演求解过程通常存在不适定性。正则化方法是解决这一不适定性问题的一类有效的方法。将正则化理论引入到载荷反演数学模型当中,基于反演数学模型和广义交叉验证法(GCV法)的原理,推演得到了适用于本反演模型的广义交叉验证法计算公式。利用GCV法和L曲线法对最优正则化参数进行求解,大大减小了计算舍入误差和测量噪声对反演结果的影响,克服了现有载荷反演技术中普遍存在的识别结果波动较大的问题,提高了反演数学模型抗噪声的能力,从而抑制测量噪声导致的反演载荷“漂移”现象。在上述载荷反演数学模型的基础上,本文进一步引入特征值缩减技术,解决了大型结构复杂载荷反演过程中,当待反演载荷数目以及测量响应的数目都比较少时,控制矩阵求解效率低的问题。
(4)开展了载荷反演方法在高速列车上的工程运用研究。将载荷反演数学模型引入到高速列车轮轨接触力反演当中,分别建立了高速客车10自由度垂向随机振动力学模型和17自由度横向随机振动力学模型,首先从SIMPACK动力学仿真的角度对所提出的载荷反演数学模型进行了验证。在运行速度分别为100km/h和250km/h两个速度级下,将SIMPACK动力学仿真输出的轴箱纵向、横向和垂向加速度作为反演数学模型的输入,对轮轨接触力以及脱轨系数进行了预测,从时域和频域两个方面对反演结果与SIMPACK动力学仿真结果进行了对比分析。结果表明,轮轨垂向力和横向力反演结果与仿真结果趋势一致,两种方法得到的接触力相关系数均介于0.5和0.8之间,属于中等程度相关和强相关；对两种方法得到的接触力曲线进行功率谱密度分析表明,反演模型在O.1Hz-500Hz频率范围内,反演结果均令人满意。
(5)利用西南交通大学牵引动力国家重点实验室的滚动振动试验台对反演模型进行了验证。通过24通道的DDS32数采集系统对280km/h运行速度下某高速车车体垂向加速度、构架的垂向加速度以及四个轴箱垂向加速度进行了采集。将任意四个部位的测量加速度作为反演数学模型的输入,对车辆轮轨垂向载荷和其它部位垂向振动加速度进行反演,得到了车辆的轮轨垂向载荷,并获得了与试验值非常吻合的垂向振动加速度。
The relationship between excitation and time is very important for the design and analysis of engineering structures, and also impact on their use of process reliability. For high-speed vehicle, its operational stability is very high decided by the interaction between the wheel and rail in some extent. For the rail, with the improvement of train running speed, the wheel/rail interaction force will be dramatically worse, this would be serious influence the safety of high speed train. In addition, from the evaluation of high speed train dynamics characteristics, the vibration coupling relationship between the components, friction and wear performance, durability and so on, to controlling and analysis the real time of the wheel/rail force is also very necessary. Therefore, how to get the wheel/rail contact force is always a hot topic for researchers and engineers.
In the high speed train operation, because of the high-speed relative motion between wheel and rail, structure complexity and load influence each other in each direction, it is very difficult to measure the wheel/rail excitation force in running state. So, we need to develop a kind of indirect force-time solution method, namely force inversion method. Based on the basis of theoretical derivation, with the engineering actual demand closely, the main works of this paper are as follows:
(1) The domestic and foreign latest load inversion methods are comprehensively reviewed, and for the first time, we summarize the development and application of the load inversion methods which have been used in railway locomotive vehicles. From the present situation of the locomotive vehicle and high-speed train in our country, the importance of load inversion method for operation train to get high precision wheel/rail contact dynamic force is analyzed.
(2) A non iterative load inversion time domain method which based on the dynamic programming is proposed. From the point of view of system, the structure input force evaluation mathematical model is established, and through the indirect measurement method, the relationship of the unknown excitation load and its response of the structure are also established, then the input excitation load in time domain is gotten. Because of the non iterative property of the inversion model, the initial condition dependence problem is solved effectively in the process of the load inversion. At the same time, the transfer and accumulation of the error are also avoided in the process of the method which makes the result have better numerical stability. Then the Bellman's principle of optimality is used for the minimization of the objective function to estimate the excitation forces, which ensure to get the inverse forces and responses that make the objective function minimum in each time step, and effectively reduce the influence that caused by avoidless the ill-posed in the process of the load inversion, and get the inverse load which is very similar to the real load.
(3) For the first time to systematically deduce and research the regularization parameter solution, and the generalized cross-validation (GCV) method calculation formula which is very suitable for the inversion model is obtained. Because the original measurement data is influenced by measuring instruments and external disturbance, and in the inverse problem of mathematical physics solving process, it often meets such as the insufficiency of known measuring data, improper values of boundary conditions, the noise disturbance of measuring response and the instability of the approximate solution, etc., the inversion solution process usually exists ill-posedness. Regularization method is a kind of effective methods to solve the ill-posedness problem. The regularization theory is introduced into the inversion mathematical model, based on the inversion model and the principle of GCV method, the GCV calculation formula which is very suitable for the inversion model is obtained. The regularization parameter is solved by GCV method and the L-curve method, and the method greatly reduces the influence that due to a calculation rounding measurement error and the signal noise during the load identification process, overcome the large fluctuation which is widespread existing in the current load inversion technology, and improve the anti-noise ability of the inversion mathematical model. At the same time, load drift is inhibited. In the above load inversion mathematical model, this paper further introduces characteristic value reduction technology, which is effectively used in the load inversion process of the large complex structure, especially when there are less number of inversion loads and measuring responses, and the control matrix solution efficiency is very low.
(4) The load inversion method is used in the high-speed train. The load inversion mathematical model is introduced into the high-speed train wheel/rail contact force inversion,10degrees of freedom vertical vibration model and17degrees of freedom horizontal vibration model are established, respectively. First of all, the load inversion mathematical model is verified from the point of the SIMPACK dynamics simulation. Under100km/h and250km/h, longitudinal acceleration, transverse acceleration and vertical acceleration of the axle box from the SIMPACK dynamics simulation are used as the input of the inversion mathematical model, the wheel/rail contact forces and derailment coefficients are identified. From the time domain and frequency domain, inverse results are compared with SIMPACK simulation results. The results indicate that the vertical and horizontal wheel/rail forces had the same trend with SIMPACK simulation results, and in time domain, their correlation coefficients are greater than0.5, belongs to the moderate related and strong correlation. PSD analysis shows that, both in the low frequency range and in the high frequency range, from0.1Hz to500Hz, the PSD of the inverse forces is as the same as the simulation results, the inversion results are satisfactory.
(5) The rolling and vibrating test-bed in TPL at Southwest Jiaotong University is used to verify the effectiveness of the load inversion mathematical method. Under280km/h, the car body vertical acceleration, two bogie frames accelerations and four axle boxes accelerations are measured using DDS32data acquisition system. Selecting four values in these measurement responses as the input of the inversion mathematical model, the wheel/rail vertical force and other parts of the inversion vertical vibration acceleration are gotten. The inversion vertical vibration acceleration is very close to the test value, at the same time, we also get the vertical contact force of the train.
在高速列车的运行中,由于轮轨之间的高速相对运动、结构复杂以及各个方向载荷相互影响等,运行状态下的轮轨激励载荷通常难以测量,因此需要发展一种间接的载荷-时间关系求解方法,即载荷反演法。论文在理论推导的基础上,与工程实际需求紧密结合,主要完成了以下工作：
(1)论文全面总结了国内外有关载荷反演方法最新研究进展,并对载荷反演方法在铁道机车车辆上的发展和运用进行了梳理和详细的总结。从我国机车车辆以及高速列车的现状着手,分析了建立具有广泛应用价值的高精度的运行列车轮轨动载荷反演方法的重要性。
(2)提出了一种基于动态规划的非迭代载荷反演时域方法。从系统的角度建立了结构输入载荷评估的数学模型,通过间接测量的方法,建立结构未知激励载荷与该激励下的结构响应之间的关系,从而得到时域下的输入激励载荷。由于反演模型的非迭代性,方法有效解决了动载荷反演中对初始条件过分依赖的问题,同时避免了载荷反演过程中误差的传递和累积,具有良好的数值稳定性。将Bellman最优化原理引入到目标函数的最小化当中,保证了每个积分步长上得到的反演载荷和响应均能够使目标函数最小,有效地降低了载荷识别过程中无法避免的病态问题对反演结果的影响,得到了与真实载荷非常相近的反演载荷。
(3)系统地对正则化参数的求解方法进行了理论推导和研究,得到了适用于本反演模型的广义交叉验证法计算公式。数学物理反问题在求解过程中,由于原始测量数据受到测量仪器、外界干扰等的影响以及在反演数学模型中受到已知测量数据不足、边界条件取值不当、测量响应的噪声干扰和近似解的不稳定性等因素的影响,导致反演求解过程通常存在不适定性。正则化方法是解决这一不适定性问题的一类有效的方法。将正则化理论引入到载荷反演数学模型当中,基于反演数学模型和广义交叉验证法(GCV法)的原理,推演得到了适用于本反演模型的广义交叉验证法计算公式。利用GCV法和L曲线法对最优正则化参数进行求解,大大减小了计算舍入误差和测量噪声对反演结果的影响,克服了现有载荷反演技术中普遍存在的识别结果波动较大的问题,提高了反演数学模型抗噪声的能力,从而抑制测量噪声导致的反演载荷“漂移”现象。在上述载荷反演数学模型的基础上,本文进一步引入特征值缩减技术,解决了大型结构复杂载荷反演过程中,当待反演载荷数目以及测量响应的数目都比较少时,控制矩阵求解效率低的问题。
(4)开展了载荷反演方法在高速列车上的工程运用研究。将载荷反演数学模型引入到高速列车轮轨接触力反演当中,分别建立了高速客车10自由度垂向随机振动力学模型和17自由度横向随机振动力学模型,首先从SIMPACK动力学仿真的角度对所提出的载荷反演数学模型进行了验证。在运行速度分别为100km/h和250km/h两个速度级下,将SIMPACK动力学仿真输出的轴箱纵向、横向和垂向加速度作为反演数学模型的输入,对轮轨接触力以及脱轨系数进行了预测,从时域和频域两个方面对反演结果与SIMPACK动力学仿真结果进行了对比分析。结果表明,轮轨垂向力和横向力反演结果与仿真结果趋势一致,两种方法得到的接触力相关系数均介于0.5和0.8之间,属于中等程度相关和强相关；对两种方法得到的接触力曲线进行功率谱密度分析表明,反演模型在O.1Hz-500Hz频率范围内,反演结果均令人满意。
(5)利用西南交通大学牵引动力国家重点实验室的滚动振动试验台对反演模型进行了验证。通过24通道的DDS32数采集系统对280km/h运行速度下某高速车车体垂向加速度、构架的垂向加速度以及四个轴箱垂向加速度进行了采集。将任意四个部位的测量加速度作为反演数学模型的输入,对车辆轮轨垂向载荷和其它部位垂向振动加速度进行反演,得到了车辆的轮轨垂向载荷,并获得了与试验值非常吻合的垂向振动加速度。
The relationship between excitation and time is very important for the design and analysis of engineering structures, and also impact on their use of process reliability. For high-speed vehicle, its operational stability is very high decided by the interaction between the wheel and rail in some extent. For the rail, with the improvement of train running speed, the wheel/rail interaction force will be dramatically worse, this would be serious influence the safety of high speed train. In addition, from the evaluation of high speed train dynamics characteristics, the vibration coupling relationship between the components, friction and wear performance, durability and so on, to controlling and analysis the real time of the wheel/rail force is also very necessary. Therefore, how to get the wheel/rail contact force is always a hot topic for researchers and engineers.
In the high speed train operation, because of the high-speed relative motion between wheel and rail, structure complexity and load influence each other in each direction, it is very difficult to measure the wheel/rail excitation force in running state. So, we need to develop a kind of indirect force-time solution method, namely force inversion method. Based on the basis of theoretical derivation, with the engineering actual demand closely, the main works of this paper are as follows:
(1) The domestic and foreign latest load inversion methods are comprehensively reviewed, and for the first time, we summarize the development and application of the load inversion methods which have been used in railway locomotive vehicles. From the present situation of the locomotive vehicle and high-speed train in our country, the importance of load inversion method for operation train to get high precision wheel/rail contact dynamic force is analyzed.
(2) A non iterative load inversion time domain method which based on the dynamic programming is proposed. From the point of view of system, the structure input force evaluation mathematical model is established, and through the indirect measurement method, the relationship of the unknown excitation load and its response of the structure are also established, then the input excitation load in time domain is gotten. Because of the non iterative property of the inversion model, the initial condition dependence problem is solved effectively in the process of the load inversion. At the same time, the transfer and accumulation of the error are also avoided in the process of the method which makes the result have better numerical stability. Then the Bellman's principle of optimality is used for the minimization of the objective function to estimate the excitation forces, which ensure to get the inverse forces and responses that make the objective function minimum in each time step, and effectively reduce the influence that caused by avoidless the ill-posed in the process of the load inversion, and get the inverse load which is very similar to the real load.
(3) For the first time to systematically deduce and research the regularization parameter solution, and the generalized cross-validation (GCV) method calculation formula which is very suitable for the inversion model is obtained. Because the original measurement data is influenced by measuring instruments and external disturbance, and in the inverse problem of mathematical physics solving process, it often meets such as the insufficiency of known measuring data, improper values of boundary conditions, the noise disturbance of measuring response and the instability of the approximate solution, etc., the inversion solution process usually exists ill-posedness. Regularization method is a kind of effective methods to solve the ill-posedness problem. The regularization theory is introduced into the inversion mathematical model, based on the inversion model and the principle of GCV method, the GCV calculation formula which is very suitable for the inversion model is obtained. The regularization parameter is solved by GCV method and the L-curve method, and the method greatly reduces the influence that due to a calculation rounding measurement error and the signal noise during the load identification process, overcome the large fluctuation which is widespread existing in the current load inversion technology, and improve the anti-noise ability of the inversion mathematical model. At the same time, load drift is inhibited. In the above load inversion mathematical model, this paper further introduces characteristic value reduction technology, which is effectively used in the load inversion process of the large complex structure, especially when there are less number of inversion loads and measuring responses, and the control matrix solution efficiency is very low.
(4) The load inversion method is used in the high-speed train. The load inversion mathematical model is introduced into the high-speed train wheel/rail contact force inversion,10degrees of freedom vertical vibration model and17degrees of freedom horizontal vibration model are established, respectively. First of all, the load inversion mathematical model is verified from the point of the SIMPACK dynamics simulation. Under100km/h and250km/h, longitudinal acceleration, transverse acceleration and vertical acceleration of the axle box from the SIMPACK dynamics simulation are used as the input of the inversion mathematical model, the wheel/rail contact forces and derailment coefficients are identified. From the time domain and frequency domain, inverse results are compared with SIMPACK simulation results. The results indicate that the vertical and horizontal wheel/rail forces had the same trend with SIMPACK simulation results, and in time domain, their correlation coefficients are greater than0.5, belongs to the moderate related and strong correlation. PSD analysis shows that, both in the low frequency range and in the high frequency range, from0.1Hz to500Hz, the PSD of the inverse forces is as the same as the simulation results, the inversion results are satisfactory.
(5) The rolling and vibrating test-bed in TPL at Southwest Jiaotong University is used to verify the effectiveness of the load inversion mathematical method. Under280km/h, the car body vertical acceleration, two bogie frames accelerations and four axle boxes accelerations are measured using DDS32data acquisition system. Selecting four values in these measurement responses as the input of the inversion mathematical model, the wheel/rail vertical force and other parts of the inversion vertical vibration acceleration are gotten. The inversion vertical vibration acceleration is very close to the test value, at the same time, we also get the vertical contact force of the train.
引文
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