基于EMD和Cohen核的时—频分析研究及其在轨道不平顺监测中的应用
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摘要
铁路轨道因初始弯曲、运行变形、磨损等原因,会产生垂向、水平以及轨距方向的不平顺。轨道不平顺是车辆振动的主要激振源,将产生车辆沉浮振动、横向滚摆、左右摇摆、侧滚等耦合振动。这种振动又加剧了轮轨磨耗,从而进一步加大轨道的不平顺,影响车辆运行的平稳性和安全性。随着列车运行速度越来越高,轨道不平顺对列车的动力作用更加显著。因此,在高速行车条件下研究轨道的不平顺性问题具有重要意义。
论文在讨论了轨道不平顺研究现状的基础上,分析了高速动车组走行部信号非平稳的特点,针对轨检车需要专门的设备,同时占用营运时间的局限性,对现有的时-频分析方法进行了研究和改进,提出了EMD和Cohen核结合的时-频分析方法,并将此方法应用在轨道不平顺的监测中,得到的结论与利用轨检车得到的轨道不平顺信息一致。该方法对于弥补轨检车的上述不足,进行高速高密度的轨道不平顺监测具有一定价值。
论文主要包含以下工作内容：
(1)对Cohen核中的指数分布进行了算法改进。针对指数分布只适用于模糊函数自分量分布沿ζ和τ轴附近的信号的问题,通过将指数核函数进行坐标旋转,让自模糊函数项尽可能的全部通过指数核函数,而互模糊函数项尽可能的远离该指数核函数。解决了信号在模糊域中不沿ζ和τ轴附近分布时,其指数分布效果差的问题。仿真结果表明,该方法算法简单,易于实现,为抑制指数核的交叉项问题,提供了另一种思路。
(2)对EMD分解中的几个关键问题进行了研究。关于EMD分解的参数指标,提出在利用仿真信号进行数值试验过程中,利用相关系数作为参数指标,是一种比较简便的选择。关于EMD算法的端点延拓,利用数值试验的方法,将通过数学拟合延长两端数据的方法与延长采样时间直接截取两端数据的方法进行比较,并将实际的EMD分解结果与理想分解结果分别作为矩阵,通过计算它们之间的相关系数来衡量EMD的分解效果。仿真结果表明,若左右各截取半个信号周期长度的数据信号,则得到的分解结果优于通过端点延拓方法得到的EMD分解结果,且截取的点数越多,得到的结果越接近理想的分解结果。
(3)基于以上两部分的讨论,提出了经验模态分解法和Cohen类法结合的时-频变换方法,以更好的抑制二次时-频分析的交叉项。该方法从频域上分离为若干个内禀模态函数之和,再将分解后的信号分别进行Cohen类分布。可消除信号内部各IMF之间的交叉项,使总的交叉项项数减少。通过仿真表明,论文提出的方法较Wigner-Ville分布和广义指数核时-频分布能够更好的抑制交叉项,真实的反应信号本身的时-频特性。
(4)将前述的理论应用于轨道不平顺的监测。总结了轴箱信号的特点,通过测量某型动车组在高速运行时轴箱的振动加速度响应,利用提出的改进的时-频分析方法来研究轨道不平顺问题。实验表明,此方法能够有效的扩大轴箱加速度的动态响应范围,得到的结论与利用轨检车得到的轨道不平顺信息一致,从而验证了此方法的正确性。
Track irregularities will be generated in vertical, level and gauge, due to the initial bend, run deformation and wear. Track irregularities are the main source of vehicle vibration. They will cause the coupling vibration of the vehicle in ups and downs, roll placed horizontally, swinging left and right. This vibration intensifies the wheel and rail vibration wear, increasing the track irregularities. With increasing the train speed, researching the track irregularities is more significant.
First, the track irregularities research current situation was summarized, then the non-stationary signals features of EMU running gear was analyzed. To analyze the track irregularities based on the axle-box acceleration, a method based on Empirical Mode Decomposition (EMD) and Cohen's class distribution was advanced. Compared with the result by track inspection car, the consistent results were getting. It indicated that this approach was a good method to compensate some shortage for track inspection vehicle, and it play an important role in the high-speed high-density test track irregularities by means of contact methods.
This dissertation included the following research contents:
(1) The algorithm in exponential kernel was improved. In traditional way, time-frequency representation method using exponential kernel is only suitable in the condition that self-variable is along theξandτaxis. An improved time-frequency representation method was proposed to solve this problem. Using coordinates rotations, Self-terms in fuzzy function can as far as possible all pass the exponential kernels function, and the cross-terms in fuzzy function can far away from the exponential kernels function. This approach was testified affected through a chirp signal and the simulation result proved that this method cans repression the interference satisfactorily, and an ideal time-frequency analysis result can be acquired.
(2) Several key issues in EMD were studies. In EMD, to suppress the ending effect, extending the data near the two end points was used by mathematics fitting usually. In practice, extending the sampling-time can also extend the end points and suppress the ending effect. Comparison has been made among the data extending method between the Mathematics fitting and terminal intercept near the two end points. To test the effect of EMD, the correlation coefficient between the practical results and ideal results were calculated. As a result of simulation and numerical experiment, it is shown that:if the signal intercept around half the length of data signals, better results can be obtained than endpoint extending. More the interception of points approximates more ending effect can be effectively restrained.
(3) To minimize the cross-term interference in quadratic time-frequency distribution, a method based on EMD and Cohen class distribution was advanced. For the method, at first, the time-domain signal was separated into multiple intrinsic mode functions (IMFs) using EMD, then the Cohen class distributions of the IMFs were calculated. At last a sum of all Cohen class distributions was acquired. By this way, the cross terms between IMFs can be restrained. So the general cross-term interference was restrained in theory. This approach was testified effected through three typical simulation signals and the result was consistent with the theory. Compared with Wigner-Ville distribution, and Cohen class distributions; it indicates that this approach can repression the interference satisfactorily, and the time-frequency analysis result is a better reflection of signal.
(4) The theory aforementioned was applied in track irregularity monitoring. To minimize the cross-term interference, a method based on EMD and Cohen's class distribution was advanced. For the method, at first, the time-domain signal was separated into multiple IMFs using EMD, then the Cohen's class distributions of the IMFs were calculated. And a sum of all Cohen's class distributions was acquired. This approach was testified effected through three typical simulation signals and the result was consistent with the theory. At last this approach was applied to analyze the track irregularities based on the axle-box acceleration. Compared with the result by track inspection car, the Consistent results were getting. It indicated that this approach was a good can compensate some shortage for track inspection vehicle, and it plays an important role in the high-speed high-density test track irregularities.
论文在讨论了轨道不平顺研究现状的基础上,分析了高速动车组走行部信号非平稳的特点,针对轨检车需要专门的设备,同时占用营运时间的局限性,对现有的时-频分析方法进行了研究和改进,提出了EMD和Cohen核结合的时-频分析方法,并将此方法应用在轨道不平顺的监测中,得到的结论与利用轨检车得到的轨道不平顺信息一致。该方法对于弥补轨检车的上述不足,进行高速高密度的轨道不平顺监测具有一定价值。
论文主要包含以下工作内容：
(1)对Cohen核中的指数分布进行了算法改进。针对指数分布只适用于模糊函数自分量分布沿ζ和τ轴附近的信号的问题,通过将指数核函数进行坐标旋转,让自模糊函数项尽可能的全部通过指数核函数,而互模糊函数项尽可能的远离该指数核函数。解决了信号在模糊域中不沿ζ和τ轴附近分布时,其指数分布效果差的问题。仿真结果表明,该方法算法简单,易于实现,为抑制指数核的交叉项问题,提供了另一种思路。
(2)对EMD分解中的几个关键问题进行了研究。关于EMD分解的参数指标,提出在利用仿真信号进行数值试验过程中,利用相关系数作为参数指标,是一种比较简便的选择。关于EMD算法的端点延拓,利用数值试验的方法,将通过数学拟合延长两端数据的方法与延长采样时间直接截取两端数据的方法进行比较,并将实际的EMD分解结果与理想分解结果分别作为矩阵,通过计算它们之间的相关系数来衡量EMD的分解效果。仿真结果表明,若左右各截取半个信号周期长度的数据信号,则得到的分解结果优于通过端点延拓方法得到的EMD分解结果,且截取的点数越多,得到的结果越接近理想的分解结果。
(3)基于以上两部分的讨论,提出了经验模态分解法和Cohen类法结合的时-频变换方法,以更好的抑制二次时-频分析的交叉项。该方法从频域上分离为若干个内禀模态函数之和,再将分解后的信号分别进行Cohen类分布。可消除信号内部各IMF之间的交叉项,使总的交叉项项数减少。通过仿真表明,论文提出的方法较Wigner-Ville分布和广义指数核时-频分布能够更好的抑制交叉项,真实的反应信号本身的时-频特性。
(4)将前述的理论应用于轨道不平顺的监测。总结了轴箱信号的特点,通过测量某型动车组在高速运行时轴箱的振动加速度响应,利用提出的改进的时-频分析方法来研究轨道不平顺问题。实验表明,此方法能够有效的扩大轴箱加速度的动态响应范围,得到的结论与利用轨检车得到的轨道不平顺信息一致,从而验证了此方法的正确性。
Track irregularities will be generated in vertical, level and gauge, due to the initial bend, run deformation and wear. Track irregularities are the main source of vehicle vibration. They will cause the coupling vibration of the vehicle in ups and downs, roll placed horizontally, swinging left and right. This vibration intensifies the wheel and rail vibration wear, increasing the track irregularities. With increasing the train speed, researching the track irregularities is more significant.
First, the track irregularities research current situation was summarized, then the non-stationary signals features of EMU running gear was analyzed. To analyze the track irregularities based on the axle-box acceleration, a method based on Empirical Mode Decomposition (EMD) and Cohen's class distribution was advanced. Compared with the result by track inspection car, the consistent results were getting. It indicated that this approach was a good method to compensate some shortage for track inspection vehicle, and it play an important role in the high-speed high-density test track irregularities by means of contact methods.
This dissertation included the following research contents:
(1) The algorithm in exponential kernel was improved. In traditional way, time-frequency representation method using exponential kernel is only suitable in the condition that self-variable is along theξandτaxis. An improved time-frequency representation method was proposed to solve this problem. Using coordinates rotations, Self-terms in fuzzy function can as far as possible all pass the exponential kernels function, and the cross-terms in fuzzy function can far away from the exponential kernels function. This approach was testified affected through a chirp signal and the simulation result proved that this method cans repression the interference satisfactorily, and an ideal time-frequency analysis result can be acquired.
(2) Several key issues in EMD were studies. In EMD, to suppress the ending effect, extending the data near the two end points was used by mathematics fitting usually. In practice, extending the sampling-time can also extend the end points and suppress the ending effect. Comparison has been made among the data extending method between the Mathematics fitting and terminal intercept near the two end points. To test the effect of EMD, the correlation coefficient between the practical results and ideal results were calculated. As a result of simulation and numerical experiment, it is shown that:if the signal intercept around half the length of data signals, better results can be obtained than endpoint extending. More the interception of points approximates more ending effect can be effectively restrained.
(3) To minimize the cross-term interference in quadratic time-frequency distribution, a method based on EMD and Cohen class distribution was advanced. For the method, at first, the time-domain signal was separated into multiple intrinsic mode functions (IMFs) using EMD, then the Cohen class distributions of the IMFs were calculated. At last a sum of all Cohen class distributions was acquired. By this way, the cross terms between IMFs can be restrained. So the general cross-term interference was restrained in theory. This approach was testified effected through three typical simulation signals and the result was consistent with the theory. Compared with Wigner-Ville distribution, and Cohen class distributions; it indicates that this approach can repression the interference satisfactorily, and the time-frequency analysis result is a better reflection of signal.
(4) The theory aforementioned was applied in track irregularity monitoring. To minimize the cross-term interference, a method based on EMD and Cohen's class distribution was advanced. For the method, at first, the time-domain signal was separated into multiple IMFs using EMD, then the Cohen's class distributions of the IMFs were calculated. And a sum of all Cohen's class distributions was acquired. This approach was testified effected through three typical simulation signals and the result was consistent with the theory. At last this approach was applied to analyze the track irregularities based on the axle-box acceleration. Compared with the result by track inspection car, the Consistent results were getting. It indicated that this approach was a good can compensate some shortage for track inspection vehicle, and it plays an important role in the high-speed high-density test track irregularities.
引文
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