Modelling And Methodology Of Time–frequency Characteristics Mining Of Track Dynamic Detection Data And Assessment Of Track Regularity For High-speed Railway

China has the world’s longest high-speed railway,reaching 36,000 kilometers.The “outline of powerful nation railway advance planning in the new era” clearly indicates that by 2035,China will have about 70,000 kilometers of high-speed railway.Safety and ride comfort are the core issues of railway operation.The high-speed train operation requires the track structure to have higher safety,stability,and regularity.Track irregularities are the main sources of the vehicle/track systems and the important factors of vehicle vibrations and wheel–rail dynamic responses.In addition to affecting the safety,stability,and comfort of train operation,track irregularities also affect the working lives of rolling stocks,tracks,and even infrastructures under the railway.As the train speed increases,the wheel–rail dynamic interactions increase,and the long-term and repeated interactions reduce the reliability of track structure and make the geometric irregularities more serious.Track irregularities are the input function of vehicle dynamics analysis,and play an important role in studying wheel–rail interaction and vehicle/track system dynamics test and simulation.Therefore,we must in-depth study and mine the distribution characteristics of track irregularities in the time–frequency domain.It has important practical significance for determining the types and locations of track defects,assessing track geometry quality,and studying the influence of track irregularities on the wheel–rail systems and even the infrastructures such as route,bridge,and tunnel.Based on the analysis and evaluation of track irregularities in the mileage domain and frequency domain respectively,this dissertation used time–frequency analysis methods to process the track irregularity data,to mine its distribution characteristics and variation rules in the mileage–frequency joint plane and determine the mileage locations and wavelength distributions of track defects.The dissertation analysed the relationships between track irregularities and vehicle responses in the time–frequency domain,and established a comprehensive evaluation method for track irregularities based on vehicle dynamic responses and wavelengths.It can provide technical support for scientific and reasonable formulation of maintenance plans by extracting and grasping the time–frequency distribution characteristics of track irregularities and reasonably evaluating the track geometry quality.It also lays the foundation for the simulation and analysis of vehicle–track coupled systems in the time–frequency domain.In this context,the main research of this dissertation is as follows:(1)Due to the reliability of equipment manufacturing and changes in the external measurement environment,track irregularity data tends to be incomplete,noisy,and inconsistent.Data preprocessing attempts to fill in missing values,smooth out noise while identifying outliers,and correct inconsistencies in order to make the data mining methods more effective and accurate.Data preprocessing of track irregularities was performed on each parameter separately,without considering the correlation and consistency between the irregularity parameters.we proposed the multivariate data synchronization preprocessing system methods,which simultaneously performed data preprocessing such as outlier detection,denoising,detrending,and mileage correction on multiple track irregularity parameters.The multivariate data preprocessing methods,in terms of considered interrelations and maintained the consistency between parameters,were demonstrated via simulations and measured data.(2)Due to the deficiencies in analysis and evaluation of track irregularities in the mileage domain and frequency domain respectively,this dissertation utilized time–frequency signal analysis methods to mine the mileage–frequency distribution characteristics of track irregularities.After theoretically analysing the time–frequency resolutions,advantages and disadvantages of typical time–frequency signal analysis methods,the Hilbert–Huang transform was applied to the track irregularity data.The influence of noise characteristics on noise-assisted empirical mode decomposition(NA-EMD)was demonstrated via simulations,thus we had determined the basic principle of adding noise in NA-EMD.We theoretically deduced the time and frequency resolutions of the discrete Hilbert energy density spectrum,and analysed the influence mechanism of noise on the spectrum.(3)The Hilbert energy density spectrum was proposed to characterise the energy distributions of track irregularities in the time–frequency domain.The mathematical relationships between Hilbert energy density spectrum and standard deviation and power spectral density were theoretically inferred.Standard deviation and power spectral density can be regarded as the projection distributions of Hilbert energy density spectrum in the time and frequency domain respectively.We can detect track defects and evaluate track geometric quality in the mileage–frequency domain via the mileage–frequency–energy density distributions of track irregularities.Therefore,the wavelength distributions and mileage locations of track irregularities can be determined at the same time.Wen can extract the energy distributions within the sensitive wavelength ranges via the energy density spectrum of track irregularity,and summarize the distribution characteristics in the mileage domain.The energy density spectrum of track irregularity was applied to the typical railway line—turnout sections to extract the distribution characteristics of turnout irregularities in the mileage domain,frequency domain,and time–frequency domain respectively.(4)Track irregularities are the main factors that produce vehicle vibrations and wheel–rail dynamic forces,but the influence mechanism of track irregularities on vehicle dynamic responses is not clear.On the basis of traditional time-domain correlation coefficient and frequency-domain coherence,we utilized the multi-scale time-dependent intrinsic correlation(TDIC)method to analyse the interrelations between track irregularities and vehicle dynamic responses on different scales(wavelengths).The TDIC can not only reveal which parameters of track irregularity are the main factors of vehicle accelerations,but also determine the wavelength ranges and mileage locations of these factors.Due to the limitation of frequency-resolution of the TDIC,as well as the non-stationarity of track irregularities and vehicle dynamic responses,this dissertation used the time–frequency coherence anlysis methods based on wavelet transform and Hilbert–Huang transform to analyse the coherence between track irregularities and vehicle dynamic responses in the time–frequency domain.(5)Due to the inadequacy of assessing methods of track geometry quality in mileage domain and frequency domain respectively,such as peak value,standard deviation,and power spectral density,the track energy density index(TEDI)was proposed to assess track geometry quality based on the energy density spectrum of track irregularity.The TEDI combined the wavelength transfer function of track irregularities to vehicle dynamic responses and the energy density spectrum of track irregularity to evaluate the overall track geometry quality of a section track.Due to the correlation between track irregularity parameters,principal component analysis(PCA)was applied on track irregularity data,and the main principal components were selected to comprehensively evaluate track regularity quality,so as to reduce redundant variables in the multi-index comprehensive evaluation.