Track Health Monitoring Using Wavelets

2010 ◽  
Author(s):  
Brad M. Hopkins ◽  
Saied Taheri
Keyword(s):  
Signal Processing ◽  
Fourier Transform ◽  
Defect Detection ◽  
Health Monitoring ◽  
Finite Energy ◽  
Detection Algorithm ◽  
Transient Signal ◽  
Vertical Acceleration ◽  
Typical Day ◽  
The Fourier Transform

This paper presents a defect detection algorithm for rail health monitoring that could potentially be used with limited bogie. Current wheel and track monitoring requires expensive track instrumentation and/or time consuming operation of railway monitoring vehicles. The proposed health monitoring algorithm can potentially be used with a portable data acquisition system that can be relocated from train to train to monitor and diagnose the conditions of the track as a train is driven during typical day-to-day operation. The algorithm processes the data using wavelets and is able to locate defects and provide information that may help to distinguish between various types of rail defects. In recent years, wavelets have been used extensively in signal processing because of their ability to analyze a signal simultaneously in the time and frequency domains. The Fourier transform has been used traditionally in signal processing to locate dominant frequencies in a signal, but it is unable to provide time localization of those frequencies. Unlike the Fourier transform, the wavelet transform uses a set of basis functions with finite energy, which is advantageous for detecting the irregular events that may show up in a transient signal. The wavelets used in the proposed signal processing routine were chosen for optimal signal decomposition through consideration of the signals that are likely to be generated from common rail and wheel defects, including rail cracks, squats, corrugation, and, wheel out-of-rounds. A sample accelerometer signal was generated from information found in existing literature and was then processed using the proposed defect detection algorithm. Results show the potential of this algorithm to locate and diagnose defects from limited bogie vertical acceleration data. This study is intended to present a proof-of-concept for the proposed defect detection algorithm, providing a basis for which a more comprehensive defect detection and diagnosis algorithm can be developed.

Broken Rail Prediction and Detection Using Wavelets and Artificial Neural Networks

2011 ◽  
Author(s):  
Brad M. Hopkins ◽  
Saied Taheri
Keyword(s):  
Neural Networks ◽  
Defect Detection ◽  
Classification Algorithm ◽  
Vertical Acceleration ◽  
Acceleration Signal ◽  
Acceleration Data ◽  
Frequency Domains ◽  
Artificial Neural ◽  
The Fourier Transform ◽  
Signal Processing Methods

Current track health monitoring requires time consuming use of railway monitoring vehicles. This paper presents a rail defect detection and classification algorithm that could potentially be used with bogie side frame vertical acceleration data from a data acquisition system located onboard a train car during daily operation. The algorithm uses wavelets to process the vertical acceleration data and detect irregularities in the signal. Wavelets have proven themselves to be useful in event detection and other applications where localization is needed in both the time and frequency domains. Traditional signal processing methods may use the Fourier transform which is limited to localization only in the frequency domain. Wavelets provide a solution for recognizing rail defects and determining their location. The wavelet-processed data is fed into an artificial neural network for defect classification. Neural networks can be a powerful tool in pattern recognition and classification because of their ability to be taught. The network in this algorithm has been trained to recognize impending breaks and breaks in a rail from the original vertical acceleration signal and the first four scales of the wavelet transformed signal. This paper presents an offline analysis of a set of collected data using the proposed defect detection and classification algorithm.

Discrete Time, Discrete Frequency

2021 ◽  
pp. 106-155
Author(s):  
Victor Lazzarini
Keyword(s):  
Signal Processing ◽  
Fourier Transform ◽  
Discrete Time ◽  
Time Domain ◽  
Continuous Time ◽  
Time Varying ◽  
Discrete Frequency ◽  
The Fourier Transform ◽  
Definition Of ◽  
The Time Domain

This chapter is dedicated to exploring a form of the Fourier transform that can be applied to digital waveforms, the discrete Fourier transform (DFT). The theory is introduced and discussed as a modification to the continuous-time transform, alongside the concept of windowing in the time domain. The fast Fourier transform is explored as an efficient algorithm for the computation of the DFT. The operation of discrete-time convolution is presented as a straight application of the DFT in musical signal processing. The chapter closes with a detailed look at time-varying convolution, which extends the principles developed earlier. The conclusion expands the definition of spectrum once more.

The properties of generalized offset linear canonical Hilbert transform and its applications

2017 ◽  
Vol 15 (04) ◽  
pp. 1750031 ◽  
Author(s):  
Shuiqing Xu ◽  
Li Feng ◽  
Yi Chai ◽  
Youqiang Hu ◽  
Lei Huang
Keyword(s):  
Signal Processing ◽  
Fourier Transform ◽  
Hilbert Transform ◽  
Analytic Signal ◽  
Linear Canonical Transform ◽  
Single Sideband ◽  
Generalized Hilbert Transform ◽  
Offset Linear Canonical Transform ◽  
The Fourier Transform ◽  
The Hilbert Transform

The Hilbert transform is tightly associated with the Fourier transform. As the offset linear canonical transform (OLCT) has been shown to be useful and powerful in signal processing and optics, the concept of generalized Hilbert transform associated with the OLCT has been proposed in the literature. However, some basic results for the generalized Hilbert transform still remain unknown. Therefore, in this paper, theories and properties of the generalized Hilbert transform have been considered. First, we introduce some basic properties of the generalized Hilbert transform. Then, an important theorem for the generalized analytic signal is presented. Subsequently, the generalized Bedrosian theorem for the generalized Hilbert transform is formulated. In addition, a generalized secure single-sideband (SSB) modulation system is also presented. Finally, the simulations are carried out to verify the validity and correctness of the proposed results.

scholarly journals Time-frequency tools of signal processing for EISCAT data analysis

1996 ◽  
Vol 14 (12) ◽  
pp. 1513-1525
Author(s):  
J. Lilensten ◽  
P. O. Amblard
Keyword(s):  
Signal Processing ◽  
Fourier Transform ◽  
Data Analysis ◽  
Gravity Waves ◽  
Velocity Measurements ◽  
Time Frequency ◽  
Synthetic Signal ◽  
Stationary Analysis ◽  
The Fourier Transform ◽  
Short Time

Abstract. We demonstrate the usefulness of some signal-processing tools for the EISCAT data analysis. These tools are somewhat less classical than the familiar periodogram, squared modulus of the Fourier transform, and therefore not as commonly used in our community. The first is a stationary analysis, "Thomson's estimate'' of the power spectrum. The other two belong to time-frequency analysis: the short-time Fourier transform with the spectrogram, and the wavelet analysis via the scalogram. Because of the highly non-stationary character of our geophysical signals, the latter two tools are better suited for this analysis. Their results are compared with both a synthetic signal and EISCAT ion-velocity measurements. We show that they help to discriminate patterns such as gravity waves from noise.

Introduction to the use of wavelet multiresolution analysis for intelligent structural health monitoring

2004 ◽  
Vol 31 (5) ◽  
pp. 719-731 ◽  
Author(s):  
M.M Reda Taha ◽  
A Noureldin ◽  
A Osman ◽  
N El-Sheimy
Keyword(s):  
Neural Networks ◽  
Signal Processing ◽  
Structural Health Monitoring ◽  
Health Monitoring ◽  
Multiresolution Analysis ◽  
Prestressed Concrete ◽  
Digital Signal ◽  
Detection Algorithm ◽  
Structural Health ◽  
Wavelet Multiresolution Analysis

This paper suggests the use of wavelet multiresolution analysis (WMRA) as a reliable tool for digital signal processing in structural health monitoring (SHM) systems. A damage occurrence detection algorithm using WMRA augmented with artificial neural networks (ANN) is described. The suggested algorithm allows intelligent monitoring of structures in real time. The probability of damage occurrence is determined by evaluating the wavelet norm index (WNI) representing the energy of a signal describing the change in the system dynamics due to damage. An example application of the proposed algorithm is presented using a finite element simulated structural dynamics of a prestressed concrete bridge. The new algorithm showed very promising results.Key words: structural health monitoring, neural networks, wavelet analysis, signal processing, damage detection.

scholarly journals Proper Definitions and Demonstration of Dirichlet Conditions

2021 ◽  
Author(s):  
Pushpendra Singh ◽  
Amit Singhal ◽  
Binish Fatimah ◽  
Anubha Gupta ◽  
Shiv Dutt Joshi
Keyword(s):  
Signal Processing ◽  
Fourier Transform ◽  
Fourier Series ◽  
Finite Number ◽  
Large Body ◽  
Dirichlet Condition ◽  
Countable Number ◽  
Dirichlet Conditions ◽  
Time Period ◽  
The Fourier Transform

<div>Fourier theory is the backbone of the area of Signal Processing (SP) and Communication Engineering. However, Fourier series (FS) or Fourier transform (FT) do not exist for some signals that fail to fulfill a predefined set of Dirichlet conditions (DCs). We note a subtle gap in the explanation of these conditions as available in the popular signal processing literature. They lack a certain degree of explanation essential for the proper understanding of the same. For example, </div><div>the original second Dirichlet condition is the requirement of bounded variations over one time period for the convergence of Fourier Series, where there can be at most infinite but countable number of maxima and minima, and at most infinite but countable number of discontinuities of finite magnitude. However, a large body of the literature replaces this statement with the requirements of finite number of maxima and minima over one time period, and finite number of discontinuities. The latter incorrectly disqualifies some signals from having valid FS representation. Similar problem holds in the description of DCs for the Fourier transform. Likewise, while it is easy to relate the first DC with the finite value of FS or FT coefficients, it is hard to relate the second and third DCs as specified in the signal processing literature with the Fourier representation as to how the failure to satisfy these conditions disqualifies those signals from having valid FS or FT representation. <br></div><div><br></div>

Extension of Lamb Waves Defect Location Techniques to the Case of Low Power Excitation by Compressing Chirped Interrogating Pulses

2013 ◽  
Vol 569-570 ◽  
pp. 940-947
Author(s):  
Luca de Marchi ◽  
Nicola Testoni ◽  
Alessandro Perelli ◽  
Alessandro Marzani
Keyword(s):  
Signal Processing ◽  
Structural Health Monitoring ◽  
Low Power ◽  
Defect Detection ◽  
Health Monitoring ◽  
Lamb Waves ◽  
Signal Processing Algorithm ◽  
Imaging Algorithm ◽  
Passive Networks ◽  
Time Waveform

In this work a signal processing algorithm for Lamb waves based defect detection/localization procedures is proposed. In particular, the proposed signal processing allows active-passive networks of piezosensors to use chirp shaped pulses in actuation, instead of classically applied spiky pulses. Thus, defect detection/localization can be achieved by using low power voltages in actuation. Basically, the proposed processing is capable to compensate the acquired time-waveforms from the dispersion due to the traveled distance as well as to compress the additional pulse spreading due to the chirp actuation. A processed time-waveform is thus directly transformed into a distance of propagation. Next, the compensated and compressed signals are exploited to feed an imaging algorithm aimed at providing the position of the defect on the plate. As a result, an automatic detection procedure to locate defect-induced reflections is demonstrated and successfully tested by analyzing experimental Lamb waves propagating in an aluminum plate. The proposed method is suitable for defect detection and can be easily implemented in real applications for structural health monitoring.

A note on 2-D Hartley transform

Geophysics ◽  
1994 ◽  
Vol 59 (7) ◽  
pp. 1150-1155 ◽  
Author(s):  
N. L. Mohan ◽  
L. Anand Babu
Keyword(s):  
Signal Processing ◽  
Fourier Transform ◽  
Fast Fourier Transform ◽  
Seismic Signal ◽  
Clear Definition ◽  
Hartley Transform ◽  
The Fourier Transform ◽  
Definition Of ◽  
Seismic Signal Processing

In recent years the application of the Hartley transform, originally introduced by Hartley (1942), has gained importance in seismic signal processing and interpretation (Saatcilar et al., 1990, 1992). The Hartley transform is similar to the Fourier transform but is computationally much faster than even the fast Fourier transform (Bracewell, 1983; Bracewell et al., 1986; Sorensen et al., 1985; Pei and Wu, 1985; Duhamel and Vetterli, 1987; Zhou, 1992). Surprisingly, we have not seen a clear definition of the 2-D Hartley transform in the published literature.

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