Ultrasonic Guided Wave Signal Research Articles

An interpretable TFAFI-1DCNN-LSTM framework for UGW-based pre-stress identification of steel strands

Steel strands serve as the key load-bearing components of pre-stressed bridges, yet the identification of effective pre-stress for steel strands is a challenging task. In this study, a time and frequency adaptive fusion input-one dimensional convolutional neural network-long short-term memory (TFAFI-1DCNN-LSTM) framework was proposed for ultrasonic guided wave (UGW)-based effective pre-stress identification of steel strands. In this framework, the time and frequency domain signals of UGW were input into the network as two parallel branches, CNN and LSTM were utilized to extract spatial and serial-related features, and a trainable weight coefficient was introduced for adaptive fusion of time and frequency domain features. Firstly, ablation studies were conducted to investigate the influence of each key component in the proposed framework on the prediction results. Secondly, deep learning (DL) models of Res Net, Dense Net and Inception Net were introduced as comparisons, and the prediction results based on TFAFI-1DCNN-LSTM were compared with those based on the above DL models. Thirdly, the noise-robustness and performance under a few trainable samples of TFAFI-1DCNN-LSTM were also investigated. Finally, the outputs of various key layers of the proposed framework were subjected to dimensionality reduction and visualization to provide an intuitive demonstration of the feature extraction process, and the inherent mechanisms of the proposed framework were interpreted using local interpretable model-agnostic explanations (LIME). Results show that the architecture of TFAFI-1DCNN-LSTM is reasonably designed and all key components are necessary. The weights of features in time and frequency domain branches are rationally assigned due to the addition of an adaptive weight coefficient. Compared with other DL models, the proposed TFAFI-1DCNN-LSTM exhibits higher pre-stress identification accuracy, excellent noise-robustness, and superior performance under only a few trainable samples. The correlation between features extracted by the network and the pre-stress labels significantly increases with the deepening of the network, and the correlation between input UGW signals and predicted pre-stress values is effectively interpreted utilizing LIME, proving that the architecture of the proposed framework is reasonable and effective, the predicted results are reliable and credible.

Rail Flaw Detection via Kolmogorov Entropy of Chaotic Oscillator Based on Ultrasonic Guided Waves.

Ultrasonic guided wave (UGW) inspection is an emerging non-destructive testing(NDT) technique for rail flaw detection, where weak UGW signals under strong noise backgrounds are difficult to detect. In this study, a UGW signal identification model based on a chaotic oscillator is established. The approach integrates the UGW response into the critical state of the Duffing system to serve as a disturbance control variable. By evaluating the system's motion state before and after introducing the UGW response, identification of UGW signals can be realized. Thus, the parameters defining the critical state of Duffing oscillators are determined by Ke. Moreover, an electromagnetic transducer was specifically devised to enable unidirectional excitation for UGWs targeted at both the rail base and rail head. Experimental studies showed that the proposed methodology effectively detected and located a 0.46 mm notch at the rail base and a 1.78 mm notch at the rail head. Furthermore, Ke was directly proportional to the notch size, which could be used as a quantitative index to characterize the rail flaw.

Sparse reconstruction of ultrasonic guided wave signals of fluid-filled pipes by multistrategy hybrid DBO-OMP using dispersive Hanning-windowed chirplet model

Ultrasonic guided waves (UGWs) in fluid-filled pipes are subject to more severe dispersion and coherent noise than those of vacant pipes, posing significant challenges for defect identification and localization. To this end, a novel sparse signal decomposition method called multistrategy hybrid dung beetle optimization based orthogonal matching pursuit (MHDBO-OMP) using dispersive Hanning-windowed chirplet model was proposed, of which the model not only represents the nonlinear frequency and asymmetric envelope of the dispersive UGW, but also contains the mode and propagation distance information, and this model exhibits better matching and interpretability than the other UGW models. For dispersive perturbed UGW signals with multiple modes and features, MHDBO-OMP achieves high reconstruction accuracy in both signal reconstruction (RES < 0.3) and propagation distance estimation (RES < 3 cm). When applied to experimental UGW signals obtained from water/oil-filled pipes containing cracks and corrosion pits, MHDBO-OMP successfully reconstructs dispersion-compensated signals that solely contain feature signals, and the minimum location error is 0.72 cm while the average location error is 2.65 cm. © 2001 Elsevier Science. All rights reserved.

Quantitative monitoring of icing on CFRP laminate with guided wave combining forward modeling and inverse characterization

Aircraft icing is one of the critical factors for flight safety. Timely and accurate monitoring of in-flight ice accretion is essential for flight systems to take immediate and effective action to significantly improve the efficiency of subsequent de-icing processes and ensure flight safety. Since carbon fiber reinforced polymer (CFRP) are now widely used in the aviation industry, the study of ice accretion on the surfaces of CFRP with anisotropic properties is of great importance. In this work, a three-dimensional frequency domain finite element model for icing CFRP laminate is first established, via which the mechanism of mode conversion of ultrasonic guided waves (UGWs) at different ice layer thicknesses is quantitatively analyzed. Then, the time-domain finite element simulation was performed, from which the time–frequency domain spectrogram of the acquired UGW signal is obtained by short-time Fourier transform (STFT). The extracted frequency–time-of-flight (ToF) curve of the signal via STFT shows high agreement with the theoretical results, which confirms the influence of icing on UGW propagation. Finally, numerous experiments with bonded lead zirconate titanate wafers to excite and acquire UGWs are conducted with different ice layer thicknesses and lengths on CFRP. The extracted frequency–ToF curves of UGW signals are used as input to a two-layer feedforward artificial neural network (ANN) to accurately evaluate the length and thickness of the ice layer. The high reliability of this method with ANN is confirmed, which shows the potential of the proposed UGW-based method for quantitative monitoring of icing length and thickness on aircraft CFRP laminate.

Research on Ultrasonic Guided Wave Technology for the Rail Fatigue Cracks Based on PCA-adaboost.M2 Algorithm

Abstract As a key equipment in high-speed railway operation, rails inevitably produce various fatigue cracks during long-term service, which are major safety hazards in the railway transportation. In order to achieve intelligent detection of the rail fatigue cracks, the PCA-adaboost.M2 algorithm based on ultrasonic guided waves is proposed for the classification and identification of rail fatigue cracks. First, a rail fatigue crack detection system based on an ultrasonic guided wave was established to obtain ultrasonic guided wave signals at different depths of the rail fatigue cracks. Then, five time–frequency domain features of the ultrasonic guided wave (the maximum, the mean, the variance, the center of gravity frequency, and the frequency variance) were extracted, and the five main components of the ultrasonic guided wave were extracted by the principal component analysis (PCA) method and are used for classification and recognition of the adaboost and the adaboost.M2 algorithm, separately. The experimental results show that the ultrasonic guided wave based on the PCA-adaboost.M2 algorithm proposed has good performance in quantitative detection of the rail fatigue crack depth. The ultrasonic guided wave based on the PCA-adaboost.M2 algorithm proposed in this paper provides a method for detecting the rail fatigue crack depth.

Three-dimensional fatigue crack quantification using densely connected convolutional network-assisted ultrasonic guided waves

Linear and nonlinear ultrasonic guided wave (UGW)-based methods are available for fatigue crack detection and quantification. However, linear methods usually fail to detect undersized cracks, while nonlinear methods struggle to assess cracks once they have extended to a certain degree. The fusion of linear and nonlinear UGW features offers a new opportunity to enhance evaluation precision and effectiveness, yet it necessitates highly complex modeling. Motivated by this, a regression model is proposed based on the famed densely connected convolutional network, DenseNet, for three-dimensional (3D) fatigue crack quantification in both crack initiation and growth stages. Via the continuous wavelet transform (CWT), the spectra of UGW signals embracing both linear and nonlinear features of UGW are obtained. Subsequently, DenseNet is adopted to extract implicit features of spectra images. Finally, the last fully connected layer of DenseNet is modified as a regression layer to estimate the length and depth of 3D fatigue cracks. A dataset comprising 500 UGW signals is created for validating the proposed model. The results demonstrate that the model can characterize the length and depth of 3D cracks in both initiation and growth stages, establishing it as a promising proof-of-concept for the deep learning-based quantification of 3D fatigue cracks.

Reconstruction of Water-Filled Pipe Ultrasonic Guided Wave Signals in the Distance Domain by Orthogonal Matching Pursuit Based on Dispersion and Multi-Mode.

Ultrasonic guided waves (UGWs) in water-filled pipes are subject to more severe dispersion and attenuation than vacant pipes, posing significant challenges for defect identification and localization. To this end, a novel sparse signal decomposition method called orthogonal matching pursuit based on dispersion and multi-mode (DMOMP) was proposed, which utilizes the second-order asymptotic solution of dispersion curves and the conversion characteristics of asymmetric UGWs in the defect contact stage to reconstruct the dispersive signals and converts the time-domain dispersive signals to distance-domain non-dispersive signals by dispersion compensated time-distance mapping. The synthesized simulation results indicate that DMOMP not only exhibits higher reconstruction accuracy compared to OMP, but also reveals more accurate and stable mode recognition and localization compared to DOMP, which only considers the dispersion under perturbation and noise. In addition, the UGW testing experimental results of water-filled pipes verify the effectiveness of DMOMP, the localization accuracies of three feature signals (defct 1, defct 2 and end echo) with DMOMP are 99.10%, 98.72% and 98.36%, respectively, and the average localization accuracy of DMOMP is as high as 98.73%.

Stress measurement of aero-engine thin-walled catheter based on ultrasonic guided wave.

A pipeline system made of catheters is used for liquid-gas transportation in aero-engines. It is important to measure the residual stresses, such as the assembly stress in this system, as they influence performance and lifetime. Compared to other testing techniques, ultrasonic measurement methods based on acoustic-elastic effects can better solve problems. For the above requirements, this paper researches an aero-engine thin-wall catheter's assembly stress measurement method based on ultrasonic guided waves's acoustic, elastic effect. The propagation and dispersion characteristics of guided ultrasonic waves in the catheter were studied. Then, the excitation frequency, guided wave mode, and single-mode excitation mode of the simulation model were determined. Next, a finite element simulation model was established for simulation experiments. In order to reduce the influence of sampling rate and working environment noise on the measurement accuracy of assembly stress, the ultrasonic guided wave signal was processed by the wavelet threshold method. A good noise reduction effect was obtained by determining the wavelet base and the number of decomposition layers. Finally, an experimental platform was built to measure the assembly stress of thin-walled catheters. The maximum measurement error of the assembly stress of a thin-walled catheter was 21.1 MPa, which verified the feasibility of the measurement method. This study provides a promising method for accurately measuring the assembly stress of thin-walled catheters in aero-engines.

Deep learning-based corrosion-like defect localization technique for high-voltage cable aluminum sheaths using guided waves

High-voltage cable accessories are important parts of a power system and are needed to ensure the reliability of electrical connections. However, their aluminum sheaths are prone to corrosion under complex working conditions, which has a detrimental effect on the normal operation of the electric system. Ultrasonic guided wave detection is a promising non-destructive testing method suited to detecting aluminum sheath corrosion in complex high-voltage cable accessory structures. However, current ultrasonic guided wave detection methods still require manual extraction of the signal features and have a high reliance on professional knowledge. This paper proposes a deep learning-based corrosion-like defect localization technique for high-voltage cable aluminum sheaths using guided waves. First, the original ultrasonic guided wave signals of corrosion defects at different locations are obtained using an ultrasonic guided wave detection platform. Then, the original signals are input into a variable auto-encoder (VAE) network to obtain a low-dimensional representation for automatic feature extraction. Finally, the low-dimensional representation is input into a gated recurrent unit (GRU) based recurrent network for corrosion defect localization. In the feature extraction stage, the VAE can automatically extract the effective features and avoid the interference of noisy signals. In the defect localization stage, the GRU can accurately identify the location of corrosion defects. The experimental results indicate that the VAE-GRU method is capable of accurately identifying corrosion defects based on the original signals.

Analysis and application of weak guided wave signal detection based on double Duffing oscillators

In this study, a double chaotic detection system was proposed to identify the weak defect echo signal caused by small defects during ultrasonic guided wave (UGW) nondestructive testing of pipelines. By identifying the amplitude and time of flight (ToF) of defect echoes, minor defects in early damage identification of pipelines were quantitatively detected. First, the Duffing oscillator detection system parameters were determined using the displacement bifurcation diagram and a Poincare map. Thereafter, the UGW signal was added to the driving force of the Duffing system. The influence characteristics of UGWs on Duffing systems were deduced in detail, and the identification method of the UGW amplitude was obtained. Two Duffing chaotic systems with specific frequencies were constructed, and the ToF of the UGW was determined from the compensation phase. Simulation and experimental results showed that this method could identify the size and ToF of UGWs simultaneously. Even when the signal-to-noise ratio (SNR) was −20 dB, the identification error of the amplitude was only 8 %, which indicated that the detection result was acceptable. Pipeline defects identified using this method, in which the identification error of the defect size was below 7 %, and the defect location identification error was below 6 %, indicated that the method could effectively improve the sensitivity of UGWs in the detection of small defects in a pipeline. This provided a guarantee for early damage identification of a pipeline.

Resolution Enhancement Method of L(0,2) Ultrasonic Guided Wave Signal Based on Variational Mode Decomposition, Wavelet Transform and Improved Split Spectrum Processing

Pipeline systems are prone to defects due to the harsh service conditions, which may induce catastrophic failure if found not in time. Ultrasonic guided wave (UGW) testing provides a convenient option for pipeline detection, showing high-efficiency, non-contact, long-distance and large-scale capabilities. To address the problem that UGW signals suffer from poor signal resolution that is mainly related to the coherent noise caused by the dispersion, multi-mode and mode conversion, an advanced signal processing method called VWISSP, based on variational mode decomposition (VMD), wavelet transform (WT), and improved split spectrum processing (ISSP) was proposed, of which SSP was improved by replacing the Gaussian filter bank with cosine filters of constant frequency-to-bandwidth and frequency-to-filter spacing ratios. Compared with ISSP, VWISSP shows better higher accuracy and resolution processing effects to noisy multi-defect UGW signals, which is manifested through the improvement of both the signal-to-noise ratio gain and the defect-to-noise gain. Only feature signals (defects and pipe end) are retained, whereas noise signals are eliminated completely.

Estimating dispersion relations of ultrasonic guided waves in bone using a modified matrix pencil algorithm

Guided wave ultrasound technology is well recognized for non-destructive testing. The technology is increasingly applied in bone characterization and imaging to evaluate bone strength and fracture risk. Cortical bone with porous microstructure induces substantial dispersion and attenuation effects on ultrasonic guided waves (UGW). Estimating frequency-dependent propagation characteristics of co-excited wave modes is significant to studying UGW propagation and developing wave-based approaches. This work implements a modified matrix pencil method to simultaneously compute modal wavenumber and attenuation coefficient from dispersive bone UGW signals with improved convergence rate and noise reduction ability. The dispersion estimation is formulated as a matrix pencil or generalized eigenvalue problem with Loewner matrices. The extracted eigenvalues are estimated complex wavevectors, in which the wavenumber and attenuation can be deduced from the real and imaginary components respectively. The performance of the proposed algorithm is demonstrated with low signal-to-noise-ratio synthetic and experimental datasets acquired using axial-transmission measurement settings. The computed dispersive features are validated via comparison with the theoretically calculated dispersion curves by semi-analytical finite-element simulation. The dispersive wave properties are accurately reconstructed in a computationally efficient manner and can be further utilized for bone parametric analyses and subsequently clinical bone health assessment.

Evaluation of the Transverse Crack Depth of Rail Bottoms Based on the Ultrasonic Guided Waves of Piezoelectric Sensor Arrays.

A method based on the high-frequency ultrasonic guided waves (UGWs) of a piezoelectric sensor array is proposed to monitor the depth of transverse cracks in rail bottoms. Selecting high-frequency UGWs with a center frequency of 350 kHz can enable the monitoring of cracks with a depth of 3.3 mm. The method of arranging piezoelectric sensor arrays on the upper surface and side of the rail bottom is simulated and analyzed, which allows the comprehensive monitoring of transverse cracks at different depths in the rail bottom. The multi-value domain features of the UGW signals are further extracted, and a back propagation neural network (BPNN) is used to establish the evaluation model of the transverse crack depth for the rail bottom. The optimal evaluation model of multi-path combination is reconstructed with the minimum value of the root mean square error (RMSE) as the evaluation standard. After testing and comparison, it was found that each metric of the reconstructed model is significantly better than each individual path; the RMSE is reduced to 0.3762; the coefficient of determination R2 reached 0.9932; the number of individual evaluation values with a relative error of less than 10% and 5% accounted for 100% and 87.50% of the total number of evaluations, respectively.

A Pipe Ultrasonic Guided Wave Signal Generation Network Suitable for Data Enhancement in Deep Learning: US-WGAN

A network ultrasonic Wasserstein generative adversarial network (US-WGAN), which can generate ultrasonic guided wave signals, is proposed herein to solve the problem of insufficient datasets for pipe ultrasonic nondestructive testing based on deep neural networks. This network was trained with pre-enhanced and US-WGAN-enhanced datasets with 3000 epochs; the ultrasound signals generated by the US-WGAN were proved to be of high quality (peak signal-to-noise ratio scores in the range of 30–50 dB) and belong to the same population distribution as the original dataset. To verify the effectiveness of the US-WGAN, a fully connected neural network with seven layers was established, and the performances of the network after data enhancement using the US-WGAN and popular virtual defects were verified for the same network parameters and structures. The results show that adoption of the US-WGAN effectively suppresses the overfitting phenomenon while training the network and increases the dataset size, thereby improving the training and testing accuracies (&gt;97%). Additionally, we noted that a simple, fully connected shallow neural network was sufficient for achieving high-accuracy defect classification using the US-WGAN data enhancement method.

State Characterization of Lithium-Ion Battery Based on Ultrasonic Guided Wave Scanning

Accurate state characterization of batteries is conducive to ensuring the safety, reliability, and efficiency of their work. In recent years, ultrasonic non-destructive testing technology has been gradually applied to battery state estimation. In this paper, research on the state characterization of lithium-ion batteries based on ultrasonic guided wave (UGW) scanning is carried out. The laser Doppler vibrometer (LDV) and the X-Y stage are used to obtain the surface scanning UGW signal and the line scanning UGW signal of lithium-ion batteries under different states of charge and different aging degrees. The propagation law of UGWs in the battery is analyzed by surface scanning signals, then the energy spectrum of the signals is calculated, showing that the aging of the battery attenuates the transmission energy of UGWs. The “point” parameters are extracted from the scanning point signals. On this basis, the “line” parameters composed of line scanning multi-point signals are extracted. By analyzing the changing law of parameters during the charge–discharge process of batteries, several characteristic parameters that can be used to characterize the battery state of charge and state of health are obtained. The method has good consistency in the state characterization of the three batteries and provides a new approach for non-destructive testing and evaluation of battery states.

Split-Spectrum Processing with Raised Cosine Filters of Constant Frequency-to-Bandwidth Ratio for L(0,2) Ultrasonic Guided Wave Testing in a Pipeline

Ultrasonic guided wave (UGW) nondestructive testing suffers from poor signal interpretation accuracy caused by the coherent noise that is related to dispersion, multi-mode and mode conversion. In order to split the L(0,2) UGW from the coherent noise, split-spectrum processing with raised cosine filters of constant frequency-to-bandwidth ratio (FBR-RC-SSP) is proposed. With the advantages of time domain resolution and frequency domain split, FBR-RC-SSP is studied based on time-frequency analysis using the chirplet transform, and the effects of filter parameters on signal-to-noise ratio gain (SNRG) and defect-to-coherent noise gain (DCRG) are explained. The excellent effects of eliminating the coherent noise and improving the signal resolution in FBR-RC-SSP are reported by the validation of synthesized, simulated and experimental UGW signals, of which the average SNRG and DCRG are 22.92% and 23.71% higher than those of traditional SSP using Gaussian filters, and it has the potential to locate and characterize defects in further UGW testing research.

Ultrasonic unilateral double-position excitation lamb wave defect detection and quantification method for ground electrode of transmission tower

The power transmission tower’s ground electrode defect will affect its normal current dispersion function and threaten the power system’s safe and stable operation and even personal safety. Aiming at the problem that the buried grounding grid is difficult to be detected, this paper proposes a method for identifying the ground electrode defects of transmission towers based on single-side multi-point excited ultrasonic guided waves. The geometric model, ultrasonic excitation model, and physical model are established, and the feasibility of ultrasonic guided wave detection is verified through the simulation and experiment. In actual inspection, it is equally important to determine the specific location of the defect. Therefore, a multi-point excitation method is proposed to determine the defect’s actual position by combining the ultrasonic guided wave signals at different excitation positions. Besides, the precise quantification of flat steel grounding electrode defects is achieved through the feature extraction-neural network method. Field test results show that, compared with the commercial double-sided excitation transducer, the single-sided excitation transducer proposed in this paper has a lower defect quantization error in defect quantification. The average quantization error is reduced by approximately 76%.

A novel laser-based duffing oscillator system to identify weak ultrasonic guided wave signals related to rail defects

Laser-generated Rayleigh wave is a promising candidate for noncontact and remote inspection of railway as it can inspect in line-to-line fashion. Attribute to the recent advancement of optical design, wavelength of the laser generated-Rayleigh wave can be controlled at desired frequency band. By adjusting the wavelength of the Rayleigh wave, detection of defect occurred at different depths in rail become possible. Internal and subsurface defects that occur beneath the surface of railhead usually only reflect very small portion of wave energy hence accurate determination of their presences becomes challenging. Besides, such reflected-defect signal is usually contaminated with strong random noise which further hinder identification of weak reflected-defect signal. This study presents a novel method for detection of surface, subsurface and internal defects in railhead using laser-generated Rayleigh wave and chaotic oscillator. The use of laser-generated Rayleigh wave provides a fast mean to assess the health condition of railhead without the need to physically mounting sensor on the specimen. The use of chaotic oscillator can accurately reveal wave signal that is related to defect occurred in railhead. The effectiveness of the proposed method has been verified using numerical simulation model. Three rail specimens were machined with internal, subsurface and surface-breaking defects, respectively. Experimental results revealed that the proposed method can accurately and reliably reveal the presence of reflected-defect signal under strong random noise conditions. The present study also shows that the proposed system is promising in revealing hazardous defects occurred on rai

Research on Coded Excitation Using Kasami Sequence in the Long Rail Detection Based on UGW

For a broken rail detection system based on ultrasonic guided waves (UGW), the multimodal and dispersion characteristics of UGW degrade signal-to-noise ratio (SNR) and range resolution. To improve the SNR of the received signals and range resolution, the coded excitation based on Kasami sequences is presented in this work. Utilizing a PSpice model of piezoelectric ultrasonic transducers, as well as conducting field tests based on the pitch–catch mechanism, it is shown that encoded UGW signals can increase the SNRG (the gain of SNR) by 6.29 dB. The main lobe width of the coded excitation is mainly determined by the number of carrier cycles and the carrier waveform, and the size of the side lobes is mainly determined by the number of coding bits. To quickly identify the corresponding transmissions at the receivers, a peak detection algorithm is shown. It is based on bandpass filter, triangle filter and Hilbert transform. Its accuracy and effectiveness are validated by using some field tests under different distances. It can be concluded that the shown adaptive peak algorithm has strong robustness and immunity to noise.

Physics-based modelling and simulation of reverberating reflections in ultrasonic guided wave inspections applied to welded rail tracks

The development of ultrasonic guided wave monitoring systems has become increasingly important as they have demonstrated the ability to detect damage in structures. An example of such a system is the Ultrasonic Broken Rail Detection system which uses pitch-catch piezoelectric transducers permanently attached to the rail to excite and receive ultrasonic guided wave signals. Changes in signals can provide a reliable indication of damage growth in the rail and ultimately reduce broken rails and derailments. However, the challenge during system development is obtaining monitoring data containing damage signatures as damaged sections of rail are immediately replaced when detected. Laboratory damage experiments are also not plausible due to end reflections from short rail sections dominating the response. Modelling and simulation thus become increasingly important to enable the simulation of unavailable damage scenarios for the upgradation of existing (or development of new reliable) guided wave-based monitoring systems.Two numerical procedures to model and simulate guided wave inspections encompassing the excitation, propagation and scattering from discontinuities in 1D waveguides are presented and applied to the inspection of the web of a welded rail. The major contribution highlighted by these procedures is the ability to simulate complex back and forth reverberating reflections. These reflections occur between various reflectors such as welds and other discontinuities such as damage. The two methods are different but complementary. The first one, which is based on a simple manual simulation of finite reverberating reflections, is useful for interpreting the results to understand how different reflections interact, especially where they overlap. The second method accounts for the scattering by all defects or discontinuities arbitrarily positioned in the waveguide. It offers a more accurate approximation of the simulated inspection since it accounts for infinite reflections.The simulation results obtained from the two modelling procedures are validated using a field experiment from a damage-free rail containing welds and holes as discontinuities. The results show that it would be possible to simulate inspections for unavailable damage scenarios. The paper is concluded with a thorough analysis of the inspection measurement using the first method.