Waveform Distortion Research Articles

Special Issue on Modeling and Analysis of Interaction Between Grids and Grid-Connected Power Electronics Converters in Distribution Networks

Increasing penetration of grid-connected renewable energy systems and smart loads based on power electronics converters (such as solar inverters, wind turbines, and variable speed motor drive systems) has been increasing in low- and medium-voltage power networks. High penetration of power electronics converters has the potential to degrade the power quality of grids introducing strong resonances in grids, waveform distortion (e.g., harmonics), transients, or flicker, which pose severe risks to the distribution networks and connected equipment. Especially waveform distortion above and below 2 kHz, as well as fast transients, can cause failures in grid communication, degradation of equipment such as distribution transformers, and losses of energy, and can affect system protection. This further faces the community with challenges in the measurement of voltage and current as well as in maintaining the requirements of the electricity codes and contractual obligations between network operators and users. The automobile industry is going through an incredible transformation from internal combustion engines (ICEs) to all-electric vehicles (EVs). Some European countries have decided to ban all petrol-powered cars in the next 25–40 years. The fast-growing penetration of EVs charger will result in new challenges in distribution networks and connected loads. For example, grid impedance and its variation have a significant impact on grid-connected power converter behavior, interaction, stability, and harmonic emission and immunity. Thus, grid impedance modeling and estimation are required for existing and future analysis of distribution networks with a high number of grid-connected inverters. This Special Issue aimed to emphasize and document the latest research that addresses the abovementioned emerging challenges. In response to the call for articles, the total number of manuscripts received was 53, and 15 articles were accepted for publication. The submitted manuscripts came from 19 different countries, covering most of IEEE regions, i.e., Australia, China, Hong Kong, India, Bangladesh, Iran, Turkey, Finland, Sweden, Denmark, Belgium, France, Germany, the U.K., the United States, Canada, South Africa, Mexico, and Chile. From the accepted articles, all 15 articles address issues directly relevant to this Special Topic. Broadly, the articles can be categorized as follows: control and stability, assessment of frequency-dependent impedance, power quality aspects in distribution networks, and grid distortion impacts on power converters.

A hybrid reference pulse width modulation technique for binary source multilevel inverter

The article presents a seven-level reduced switch asymmetrical multilevel inverter with two different methods of pulse width modulation (PWM) techniques. Phase disposition (PD) PWM and hybrid variable-frequency phase disposition PWM (HVFPD-PWM) are the two different PWM methods for making the quality of output voltage waveform. In the first method, the unipolar sine reference with triangular carriers is used. In the second method, the hybrid unipolar reference (sinusoidal with trapezoidal) is proposed with variable frequency carriers to generate the switching pulses for asymmetric multilevel inverter (MLI). The main objective of this proposed method is to reduce the total harmonic distortion in the output voltage waveforms. A comprehensive comparison of the proposed HVFPD-PWM and the conventional PD-PWM with asymmetrical seven-level inverter is presented to show the enriched performances of the proposed method. The performance and viability of the suggested PWM are evaluated through simulation and experimental results using an asymmetrical seven-level inverter. The total harmonic distortion for the proposed PWM method (16.95%) is significantly reduced as compared with the conventional PWM method (18.01%) at the modulation index of one.

Single-Lane 54-Gbit/s PAM-4/8 Signal Transmissions Using 10G-Class Directly Modulated Lasers Enabled by Low-Complexity Nonlinear Digital Equalization

This work presents the use of a directly modulated laser (DML) in time- and wavelength division multiplexed passive optical networks (TWDM-PONs), in which an EDFA-based booster amplification and an SOA-based pre-amplification are utilized to improve the optical power budget. We experimentally demonstrate the C-band optically amplified data transmissions and compare the performance of the non-return-to-zero on-off keying (NRZ-OOK), four and eight-level pulse amplitude modulation (PAM-4/PAM-8) using a 10-G class DML. With optical amplification, the uplink and downlink power budgets of about 28 dB and 35 dB, respectively, are achieved for the PAM-4 54-Gbit/s signals at the hard-decision forward error correction (HD-FEC) limit of 3.8x10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-3</sup> after transmissions over a 25-km single-mode fiber link. To mitigate waveform distortions caused by the limited bandwidth, nonlinear dynamics, memory effects, and strong laser frequency chirp of the DML, especially during multi-level signal modulations, artificial neural network-based machine learning equalizers and low-complexity Volterra nonlinear equalizers are applied, which operate at the signal baud rate. The bit error ratio performance in conjunction with an enhanced power budget through the use of a low-complexity nonlinear equalizer can justify the validity of using a DML in the next-generation PONs.

Adaptive singular value decomposition for bearing fault diagnosis under strong noise interference

Singular value decomposition (SVD) is an effective tool for analyzing the signals from mechanical systems and for fault diagnosis, which is a non-parametric signal analysis method free from phase shift and waveform distortion. In SVD, the embedding dimension of the Hankel matrix is an important parameter that directly influences the effectiveness of the SVD. However, the embedding dimension is usually determined by experience, which is quite subjective and limits the applicability of SVD. As such, a novel SVD method, named adaptive SVD (ASVD), is proposed in this paper. In ASVD, novel criteria are defined to obtain the specific embedding dimensions for different mechanical signals by means of numerical simulation. A novel phenomenon, that the singular value pairs change periodically with the step size of half-cycle sampling points, is found and it can be used to calculate specific embedding dimension instead of selecting it from a range using experience. Meanwhile, the envelope spectral amplitude ratio index is developed for addressing the issue of excessive decomposition in classic SVD. Lastly, an ASVD-based bearing fault diagnosis method is proposed to adaptively select useful sub-signals and to detect faults. Both simulated signal and experiment signals, collected from different bearing test rigs are used to verify the effectiveness of the proposed method. The results show that the proposed method has a satisfactory ability to eliminate interference noise and detect bearing fault.

Arc Voltage Distortion as a Source of Higher Harmonics Generated by Electric Arc Furnaces

Due to high unit capacities, electric arc furnaces are among the receivers that significantly affect the power system from which they are supplied. Arc furnaces generate a number of disturbances to the power grid, including fast-changing voltage fluctuations causing the phenomenon of flickering light, asymmetry, and deformation of the voltage curve. The main issues discussed in the article are problems related to the distortion of current and voltage waveforms, resulting from the operation of electric arc furnaces. An analysis of the indices characterizing the voltage distortion recorded in the supply network of the arc furnaces is presented. The changes in the range of current and voltage waveform deformation in individual smelting phases in the arc furnace are also presented. Furthermore, the changes in the degree of deformation of the current and voltage waveforms in the individual smelting phases in an arc furnace are presented. A multi-voltage electric arc model used in computer simulations is proposed.

Infrasound single-channel noise reduction: application to detection and localization of explosive volcanism in Alaska using backprojection and array processing

SUMMARY Infrasound sensors are deployed in a variety of spatial configurations and scales for geophysical monitoring, including networks of single sensors and networks of multisensor infrasound arrays. Infrasound signal detection strategies exploiting these data commonly make use of intersensor correlation and coherence (array processing, multichannel correlation); network-based tracking of signal features (e.g. reverse time migration); or a combination of these such as backazimuth cross-bearings for multiple arrays. Single-sensor trace-based denoising techniques offer significant potential to improve all of these various infrasound data processing strategies, but have not previously been investigated in detail. Single-sensor denoising represents a pre-processing step that could reduce the effects of ambient infrasound and wind noise in infrasound signal association and location workflows. We systematically investigate the utility of a range of single-sensor denoising methods for infrasound data processing, including noise gating, non-negative matrix factorization, and data-adaptive Wiener filtering. For the data testbed, we use the relatively dense regional infrasound network in Alaska, which records a high rate of volcanic eruptions with signals varying in power, duration, and waveform and spectral character. We primarily use data from the 2016–2017 Bogoslof volcanic eruption, which included multiple explosions, and synthetics. The Bogoslof volcanic sequence provides an opportunity to investigate regional infrasound detection, association, and location for a set of real sources with varying source spectra subject to anisotropic atmospheric propagation and varying noise levels (both incoherent wind noise and coherent ambient infrasound, primarily microbaroms). We illustrate the advantages and disadvantages of the different denoising methods in categories such as event detection, waveform distortion, the need for manual data labelling, and computational cost. For all approaches, denoising generally performs better for signals with higher signal-to-noise ratios and with less spectral and temporal overlap between signals and noise. Microbaroms are the most globally pervasive and repetitive coherent ambient infrasound noise source, with such noise often referred to as clutter or interference. We find that denoising offers significant potential for microbarom clutter reduction. Single-channel denoising of microbaroms prior to standard array processing enhances both the quantity and bandwidth of detectable volcanic events. We find that reduction of incoherent wind noise is more challenging using the denoising methods we investigate; thus, station hardware (wind noise reduction systems) and site selection remain critical and cannot be replaced by currently available digital denoising methodologies. Overall, we find that adding single-channel denoising as a component in the processing workflow can benefit a variety of infrasound signal detection, association, and location schemes. The denoising methods can also isolate the noise itself, with utility in statistically characterizing ambient infrasound noise.

A dual-loop waveform distortion suppression method for electromagnetic vibrators at low frequencies

The total harmonic distortions (THDs) of output acceleration waveforms from an electromagnetic vibrator are always large due to the nonlinear stiffness, damping and magnetic intensity, which will affect the vibration calibration precision. To suppress THDs of output acceleration waveforms, a dual-loop waveform distortion suppression method based on current and velocity feedback for electromagnetic vibrators at low frequencies is presented. A counter electromotive force compensator is adopted in the current loop to remove the coupling between the current loop and velocity loop, which improves the performance of the current loop. Besides, a damping adjuster is adopted in the velocity loop to increase the damping ratio, which can improve dynamic characteristics and reduce waveform distortions when the multiple working frequencies coincide with the resonant frequency. Finally, the cooperation of the outer velocity loop and the inner current loop reduces THDs of acceleration waveforms effectively. Especially, the vibration velocity for the velocity loop is extracted by a secondary coil instead of commercial sensors, which is coaxially and separately wound around the driving coil of the electromagnetic vibrator. The proposed method is analyzed in simulation and verified by experiments, whose results show that the THDs of output acceleration waveforms are well restrained from 25% before feedback to less than 3% after feedback at low frequencies.

Data-driven reflection imaging based on seismic interferometry

In conventional land seismic exploration, shallow seismic reflections with low fold are usually contaminated by noise and most conventional acquisition geometries struggle to produce sufficient near-offset fold to process shallow seismic reflections based on the velocity model. Deep seismic reflections tend to occur as weak events due to seismic wave absorption and attenuation. To enhance the shallow and deep seismic reflections, we have developed a data-driven reflection imaging method based on seismic interferometry of cross-coherence type, which first retrieves coherent reflections by cross-coherence of full wavefields with zero-offset reflections and then achieves imaging results with high quality by summing all of the crosscorrelations of full wavefields with coherent reflections in a common-midpoint gather. The novel purely data-driven method does not require any velocity information and can flatten noisy interfering reflection events with no waveform distortions. The focusing effects, which represent the stack of all the seismic reflection events, increase the fold of weak seismic reflections and further significantly improve the signal-to-noise ratio of imaging results. In comparison with data-driven reflection imaging methods based on seismic interferometry of crosscorrelation type, our results illustrate that the data-driven reflection imaging method based on seismic interferometry of cross-coherence type can automatically compress the band-limited source signature and make full use of background noise to broaden the bandwidth of reflection signals for achieving imaging results with a higher resolution.

Measurements and modeling of the frequency behavior of residual current devices- from 4 Hz to 40 kHz

Residual current devices (RCDs) are a common means of protection against shock due to indirect contact in low voltage (LV) systems. Due to the increasing penetration of power electronics equipment in LV systems, higher amounts of waveform distortion at a broad range of frequencies, from dc, subharmonics up to hundreds of kHz (supraharmonics), are expected to be present both during normal operation and during faults. The standardization committees and manufacturers have responded to this challenge by proposing different types of RCDs that are expected to function under given conditions of fault current waveform. However, subharmonic and supraharmonic frequency components are not considered in the standards for most of the RCD types. This article studies the effect of these frequency components on RCDs type AC, A, B and F. An assessment is made in terms of two types of RCD failure: blinding and nuisance tripping, for which both magnitude of the current and breaking time is considered. A frequency mapping of the RCDs is performed, and an assessment of these results based on the frequency-dependent response of the human body to currents is performed. Finally, a frequency model for RCDs type A, F and B is developed.

Stress wave response in a two-dimensional membrane subjected to hypervelocity impact of a micro-flyer

The stress wave propagation in 2D membrane subjected to hypervelocity impact (HVI) is studied in this paper. A triangular-pulse stress wave model is developed and the complete solution is derived to characterize the far-field stress wave initiated by HVI. The developed model is verified by the explicit dynamics finite element, and the predictive capability for the HVI event is evaluated by the smoothed particle hydrodynamics. Based on this theoretical model, the influences of the system parameters (the time ratio, the pulse width, and the propagation distance) on the dynamic behaviors of the far-field stress wave are analyzed. A waveform distortion phenomenon during the far-field stress wave propagation is observed and the associated distortion criterion is proposed. When the distortion criterion is satisfied, the waveform of the circumferential stress wave is transformed from the normal-triangle shape to the inverted-triangle one, leading to the consequent change of the stress state. It indicates that the waveform distortion phenomenon should be considered when studying the dynamic responses and the related damage behaviors of 2D membranes.

The Errors of Electronic Energy Meters That Measure Energy Consumed by LED Lighting

Various metrological aspects for the correct measurements of electrical energy that is consumed by energy-saving (mainly LED) single phase loads are discussed in this paper. One of the most important problems presented here concerns the question of how strong distortions of the current waveform, introduced by typical LED lighting, affects the operation of electronic energy meters. Measurement results for the energy consumption of different LED lamps used in households in various conditions, alongside comparative results that were obtained by electronic and electromechanical energy meters, were also offered and the appropriate conclusions were then drawn.

Electrical Life Assessment of the Low-Voltage Circuit Breaker (LVCB) Considering Arc Voltage

The low-voltage circuit breaker (LVCB) is commonly utilized in the distribution network. An accurate evaluation of its electrical life is related to the safety and reliability of electric energy output. The traditional arc erosion model only considers the effect of current on contact wear while ignoring the impact of operation conditions (supply voltage and power factor) on electrical life. As a result of the arc voltage, the original circuit topology changes, resulting in an early current zero. At 220–660 V AC supply voltages, arc voltage causes the distortion of the breaking current waveform, and the contact erosion amount (CEA) is smaller than that in the ideal case. This work investigates the effect of arc voltage on breaking current, develops an arc erosion model that includes arc voltage, and compares the CEA curves for various supply voltages and power factors. The electrical life of the LVCB is then simulated using the Monte Carlo approach to determine the distribution of electrical life under various operating situations. The results reveal that the LVCB’s electrical life diminishes as the supply voltage increases under the same power factor; it first declines and then increases as the power factor grows under the same supply voltage. For the combination of two parameters (220 V, 0.95) and (660 V, 0.65), the electrical life difference of the LVCB can reach 21.4%. The method solves the low accuracy problem of the LVCB life assessment under different operation conditions. It improves the efficiency of overhaul and maintenance on the LVCB in power distribution systems.

Learning-based digital back propagation to compensate for fiber nonlinearity considering self-phase and cross-phase modulation for wavelength-division multiplexed systems

We propose a learning-based digital back propagation (LDBP) technique that addresses self-phase modulation (SPM) and cross-phase modulation (XPM) of a wavelength-division multiplexed (WDM) optical signal. The LDBP has a structure defined for each of the individual channels of a WDM signal, and connections between the channels address the XPM to effectively compensate for nonlinear waveform distortion of the signal in long-distance optical transmission systems. We attempt to optimize the limited number of parameters used in the structure such as the dispersion, nonlinear coefficient, and walkoff parameter to compensate for the nonlinear phase shift induced by the XPM. We derive equations to update the parameters through an iterative process based on the stochastic gradient descent algorithm. We verify the effectiveness of the proposed LDBP technique through a transmission experiment that uses an 11-channel WDM, 32-Gbaud, dual-polarization 16 quadrature amplitude modulation (QAM), and probabilistically shaped (PS) 64QAM signals. With the focus on the LDBP with a 1-step/span configuration, we operate the learning process using the received 16QAM signal in the experiment. We confirmed the successful convergence of particular parameters of the model of the transmission line after the developed learning procedure. We apply the LDBP with fixed optimized parameters to the received waveforms of the PS-64QAM signals and compare the performance with some DBPs. We observed that the proposed LDBP technique that considers XPM with 1-step/span configuration exhibits the best performance in compensating for nonlinear waveform distortion. Additionally, the learning process is effective for the case considering both SPM and XPM compared with the case of SPM only. Finally, we investigate the computational complexity of the LDBP and reveal that the total calculation cost is of the same order as that of a conventional DBP considering only SPM with a 2-step/span configuration.

Localization of travelling and standing waves in a circular membrane coupled to a continuous viscoelastic support

We present an analytical approach for realizing the localization of travelling and standing waves in a circular membrane by means of an interior, continuous, ring-type viscoelastic support when the membrane is subjected to harmonic boundary excitation. This work is a continuation of the wave separation dynamics induced by nonclassical damping in one-dimensional elastic continua. For a two-dimensional azimuthally symmetric configuration, a necessary and sufficient condition is established to realize wave localization, leading to uniformly distributed spring stiffness and damping coefficients for the interior support. A rotating wave localization pattern can also be realized by applying a circumferentially moving boundary excitation. The desired results are shown to depend strongly on the excitation frequency, the circumferential wavenumber, and the radius of the continuous support. For a weakly eccentric configuration with uniformly distributed boundary excitation, non-uniform required distributions of the support properties can be obtained analytically. However, waveform distortion will occur for either non-uniformly distributed boundary excitation with weak support eccentricity or highly eccentric coupling, such that the parameter values of the support have zero crossings on the nodal diameters of the membrane and thus lose physical meaning. The results presented in this work are expected to be useful in the design of mechanical and acoustic systems to localize energy to a sonic bullet by means of the continuous distribution of damping.

High-Performance Five-Phase Axial Flux Permanent Magnet Generator for Small-Scale Vertical Axis Wind Turbine

Commonly, electrical energy is generated by using non-renewable energy such as natural gas, coal, and oil. As electrical energy is a basic asset for the development of a region, its utilization is increasing every year, which causes the existence of non-renewable energy to decrease every year. This issue is becoming a serious concern all over the world, which encourages every country to harness energy from renewable energy. Wind energy is a promising candidate for generating electricity today. In wind turbine generation, a three-phase generator is usually used. Along with the rapid development of power electronic devices and efforts to improve generator performances, the use of a multiphase system is considered important for harnessing energy from the wind more efficiently. In this study, a five-phase system is proposed to upgrade the output power and power density of the most qualified AFPMG in the previous study. The Taguchi optimization method is employed to obtain the lowest total harmonic distortion (THD) of the on-load voltage waveform. In addition to the Taguchi method, an Artificial Neural Network (ANN) is also employed to compare the results from the Taguchi method and the results are proven to have an excellent relationship. The data processed for Taguchi and ANN methods are strongly helped by using the finite element method from the Ansys Maxwell software. The performances of the proposed five-phase axial flux permanent magnet generator (FP-AFPMG) show good improvement, especially in THD, ripple torque, and ripple in the rectified voltage.

Wind Power System for Grid-connection Based on PMSG and PI Controlling under Variable Wind Speed

Wind power is an important part of sustainable energy development and plays a pivotal role in the background of the ‘Dual Carbon’ goal. In this paper, a wind power grid-connected model based on Permanent Magnetic Synchronous Generator(PMSG) is proposed. The pitch angle of the wind turbine and the waveform of the grid-side currents are controlled by the PI controller in order to realize the tracking of the power frequency and phase of the grid voltages, and eventually achieve the purpose of grid-connection. By utilizing MATLAB/Simulink, the simulation results reveal that the final output currents’ frequency and phase meet the requirements of grid-connection, and the Total Harmonic Distortion(THD) of the current waveform is less than 2%, which represents a high power quality. It can provide reference for efficient and convenient grid-connection of wind power generation.

Low-Frequency-Drop of Electroabsorption Modulated Lasers and the Improvement With Partially Corrugated Grating Based DFB Lasers

Electroabsorption modulated lasers (EMLs) is sensitive to the residual facet reflection (RFR), which can cause a low-frequency drop (LFD) in the modulation response. The LFD may result in output waveform distortion, especially for high-data rate and multi-level modulation. We verify by simulation and experiments that the effect of LFD on the EML performance and propose to use LFD as one of the key performance indices for qualifying EMLs in high-speed optical transceivers. LFD can be suppressed by incorporating partial-corrugated-grating (PCG) in the laser section. With PCG-DFB structure, the EMLs can maintain high single-mode yield (SMY) and an excellent quality factor even with a strong modulator reflection from EAM section. This provides the robustness in applying the PCG-DFB to achieve a flat intensity modulation response or to enhance the output waveform under large signal modulation. By designing the PCG-EML to have about 60% of grating region, it can reach >80% of SMY and improve the average Q-value from the reduced LFD in the modulation response. The PCG-EML with reduced LFD can enhance the eye-opening through reduced waveform undershoot and overshoot for transmitting 56-Gbaud/s or beyond PAM-4 signals.

Harmonic Distortion of Blood Pressure Waveform as a Measure of Arterial Stiffness.

Aging and disease alter the composition and elastic properties of the aortic wall resulting in shape changes in blood pressure waveform (BPW). Here, we propose a new index, harmonic distortion (HD), to characterize BPW and its relationship with other in vitro and in vivo measures. Using a Fourier transform of the BPW, HD is calculated as the ratio of energy above the fundamental frequency to that at the fundamental frequency. Male mice fed either a normal diet (ND) or a high fat, high sucrose (HFHS) diet for 2–10 months were used to study BPWs in diet-induced metabolic syndrome. BPWs were recorded for 20 s hourly for 24 h, using radiotelemetry. Pulse wave velocity (PWV), an in vivo measure of arterial stiffness, was measured in the abdominal aorta via ultrasound sonography. Common carotid arteries were excised from a subset of mice to determine the tangent modulus using biaxial tension-inflation test. Over a 24-h period, both HD and systolic blood pressure (SBP) show a large variability, however HD linearly decreases with increasing SBP. HD is also linearly related to tangent modulus and PWV with slopes significantly different between the two diet groups. Overall, our study suggests that HD is sensitive to changes in blood pressure and arterial stiffness and has a potential to be used as a noninvasive measure of arterial stiffness in aging and disease.

Spectral Kurtosis Based Methodology for the Identification of Stationary Load Signatures in Electrical Signals from a Sustainable Building

The increasing use of nonlinear loads in the power grid introduces some unwanted effects, such as harmonic and interharmonic contamination. Since the existence of spectral contamination causes waveform distortion that may be harmful to the loads that are connected to the grid, it is important to identify the frequency components that are related to specific loads in order to determine how relevant their contribution is to the waveform distortion levels. Due to the diversity of frequency components that are merged in an electrical signal, it is a challenging task to discriminate the relevant frequencies from those that are not. Therefore, it is necessary to develop techniques that allow performing this selection in an efficient way. This paper proposes the use of spectral kurtosis for the identification of stationary frequency components in electrical signals along the day in a sustainable building. Then, the behavior of the identified frequencies is analyzed to determine which of the loads connected to the grid are introducing them. Experimentation is performed in a sustainable building where, besides the loads associated with the normal operation of the building, there are several power electronics equipment that is used for the electric generation process from renewable sources. Results prove that using the proposed methodology it is possible to detect the behavior of specific loads, such as office equipment and air conditioning.

Diffuse Ultrasonic Wave-Based Damage Detection of Railway Tracks Using PZT/FBG Hybrid Sensing System

Damage detection of railway tracks is vital to ensure normal operation and safety of the rail transit system. Piezoelectric sensors, which are widely utilized to receive ultrasonic wave, may be disturbed in the railway system due to strong electromagnetic interference (EMI). In this work, a hybrid ultrasonic sensing system is proposed and validated by utilizing a lead-zirconate-titanate (PZT) actuator and a fiber Bragg grating (FBG) sensor to evaluate damage conditions of the railway tracks. The conventional ultrasonic guided wave-based method utilizing direct wave to detect damages is limited by the complex data analysis procedure and low sensitivity to incipient damage. Diffuse ultrasonic wave (DUW), referring to later arrival wave packets, is chosen in this study to evaluate structural conditions of railway tracks due to its high sensitivity, wider sensing range, and easy implementation. Damages with different sizes and locations are introduced on the railway track to validate the sensitivity and sensing range of the proposed method. Two damage indices are defined from the perspective of energy attenuation and waveform distortion. The experimental results demonstrate that the DUW signals received by the hybrid sensing system could be used for damage detection of the railway tracks and the waveform-distortion-based index is more efficient than the energy-based index.