Multipoint chord reference system for track irregularity: Part II – Numerical analysis

Yuan Wang, Huiyue Tang, Ping Wang, Xiang Liu, Rong Chen

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


This paper proposed a novel approach to measure track irregularity by using a multipoint chord reference (MCR) system. In Part I of this study, the theory and methodology were introduced and the performance in the spatial domain were analyzed through theoretical proofs. The current paper analyzes the performance of an MCR system in the wavelength domain based on numerical approaches regarding two aspects: transfer function (TF) and false track geometry (FTG) in wavelength domain (FWD). To address the short wavelength performance of an MCR system, the minimum measurable wavelength (MMW) was analyzed according to the TF of different MCR systems. The numerical results are consistent with the theoretical value of MMW. Numerical experiments based on Fourier transform were conducted to analyze the FWD for a given MCR system. Critical wavelength (CW) is proposed to quantify the long wavelength performance. Moreover, the influences of the order, configuration, and length of rail on the performance of FWD are considered for different MCR systems. The main results suggest that (1) a higher order leads to better system performance in the wavelength domain, smaller MMW, and larger CW. (2) In addition, the sparse configurations have a significant influence on the FTG for the short wavelengths below 1.5 m. (3) The magnitude of FTG increases rapidly with 1.91 power of the wavelength. (4) The magnitude of FTG for a long wavelength increases with 1.5 power of the rail length, whereas those of short and intermediate wavelengths drop with −0.562 and −0.647 powers of rail length, respectively. (5) CW increases with the increasing order of the MCR system or with the increase in the length of rail to be measured. The MMW, FWD, and CW proposed in this paper are essential tools, which can be used to predict and optimize the performance of an MCR system.

Original languageEnglish (US)
Pages (from-to)194-205
Number of pages12
JournalMeasurement: Journal of the International Measurement Confederation
StatePublished - May 2019

All Science Journal Classification (ASJC) codes

  • Instrumentation
  • Electrical and Electronic Engineering


  • Fourier transform
  • Multipoint chord reference system
  • Numerical simulation
  • Track geometry irregularity
  • Transfer function


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