# A Review of Signal Processing Techniques for Ultrasonic Guided Wave Testing

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## Abstract

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## 1. Introduction

## 2. Searching Method

## 3. Signal Processing Techniques

#### 3.1. Pipes

#### 3.2. Plates

#### 3.3. Other Structures

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

UGWT | Ultrasonic guided wave testing |

NDT | Non-destructive testing |

SHM | Structural health monitoring |

SNR | Signal-to-noise ratio |

EMD | Empirical mode decomposition |

RAPID | Reconstruction algorithm for the probabilistic inspection of damage |

WT | Wavelet transform |

SSP | Split spectrum |

NLMS | Normalised least mean square |

SDMP | Dispersion based matching pursuit |

CSA | Cross-sectional area |

ESPRIT | Estimation of signal parameters via rotational variant technique |

CFRP | Carbon fibre reinforced polymer |

MLS | Maximum length sequence |

DCNN | Deep convolutional neural network |

WRS | Weight-range selection |

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**Figure 1.**Representation of the conceptual difference between conventional ultrasonic testing (on the

**left**) and guided wave ultrasonic testing (on the

**right**).

**Figure 2.**Articles published in the last 20 years, which were gathered using the keywords “guided wave ultrasonic testing, signal processing”.

**Table 1.**Overview of the signal processing techniques that have been commonly used in ultrasonic guided wave testing.

Technique | Summary | Application | Advantages | Limitations | Ref |
---|---|---|---|---|---|

Adaptive filtering | Functions as a linear filter with a transfer function controlled by parameters and an optimisation technique for adjusting those parameters in each iteration. | Enhances the SNR of Torsional waves generated by defects by reducing the impact of dispersive modes. | Effectively removes noise, such as noise whose power spectrum changes over time. | For lower-order Flexural waves that have closer wave speeds to Torsional waves, the noise is not cancelled. | [28] |

Split spectrum | Determines distinct interferograms for spectral sub-bands, allowing the ionospheric and non-dispersive phase terms to be separated. | Improves SNR by eliminating dispersive modes. | Enables the detection of flaws within coherent noise levels. | Accuracy is achieved when the appropriate filter bank parameters are chosen, as the technique is sensitive to their selection. | [29,30] |

Wavelet transforms | Projects a signal into a set of basis functions named wavelets, which offer localisation in the frequency domain. | Pattern recognition, damage detection and classification. | Better performance than the Fourier based filters, with little to no loss of information. | Improper selection of the mother wavelet significantly affects its usefulness in extracting defect information. | [4,10,17,22,31,32,33,34,35,36] |

Hilbert–Huang transform | Decomposes a signal into so-called intrinsic mode functions along with a trend with empirical mode decomposition (EMD) and obtains instantaneous frequency data using the Hilbert transform. | Defect identification. | Preserves the characteristics of the varying frequency, it is effective in extracting the low-frequency oscillations, and it can be applied to transient data without zero or mean references. | Poorly suited for separating signals when their frequencies are too close. | [4,10,11,35] |

Matching pursuit | Sparse approximation algorithm that finds a sub-optimal solution to the problem of an adaptive approximation of a signal in a redundant set, i.e., dictionary, of functions. | Damage classification. | Good results obtained for wave separation. | Construction of the dictionaries can be not straightforward, the results are highly dependent upon the quality of the dictionary used, and it has high computational complexity. | [6,19,25,26,37] |

Winger-Ville distribution | Computes the Fourier transform of the ambiguity function, which provides a high-resolution representation in both time and frequency for non-stationary signals. | Time–frequency signal analysis leading to high calculation accuracy of the frequency and duration of the modes. | High spectral resolution can be achieved, and it does not suffer from leakage effects. Can be applied to pipes and plates. | Cross-term interference can make it difficult to interpret the signal properties. | [8,9,21,38] |

Reconstruction algorithm for the probabilistic inspection of damage (RAPID) | By comparing the signal difference coefficient of data acquired either before and after damage, or at low and high excitation amplitude, a damage presence probability map can be obtained. | Defect imaging | Construction of an energy pattern that allows identifying the dimension of the failure. | Advanced RAPID tomographic techniques are required to improve the resolution and accuracy of the obtained images with respect to the operating surroundings. Not practical for field evaluation taking into account that two measurements are required. | [39] |

Author | Year | Technique | Summary and Results |
---|---|---|---|

Liu S. [4] | 2021 | Wavelet transform (WT) and empirical mode decomposition (EMD) | The decomposed signal in WT can better preserve defect information and reduce the interference of noise signals, but the signal processed by the EMD is better than that of the WT. |

Chen J. [34] | 2017 | Tone-burst wavelet | Results show that the location of the corroded areas of the pipes could be accurately detected using the calculated group velocity of the guided wave. Comparing the temporal waveforms of the normal pipe with those of the corrosion, flaws were easily observed and detected. |

Rostami J. [6] | 2017 | Sparse representation with dispersion-based matching pursuit | The SDMP with a dispersive dictionary has greatly enhanced the performance of the matching pursuit and guarantees the maximum sparsity. Although the presented SDMP for signal interpretation addresses the inspection of steel pipes, it can be applied to any plate. |

Mahal H. [5] | 2019 | Sliding moving window | Three different pipes with defects sizes of 4, 3 and 2% cross-sectional area (CSA) material loss were evaluated. Results demonstrate the capability of this algorithm in detecting Torsional waves with low SNR without requiring any change in the excitation sequence. |

Pedram S. [29] | 2018 | Split-spectrum processing | Both techniques achieved the greatest SNR without distorting the relative amplitudes of the signal of interest, where an improvement of up to 38.9 dB was observed. SSP shows good potential to increase the inspection range from a single test location as it significantly reduces the level of coherent noise. |

Pedram S. [30] | 2020 | Split-spectrum processing | SSP algorithm is shown to have great potential to decrease the background noise entirely by minimising the effect of undesired wave modes throughout the signal’s trace, whereas the traditional method was not able to achieve this. Good results were obtained for coated pipes. |

Mahal H. [45] | 2018 | Axisymmetric wave detection algorithm | An axisymmetric wave detection algorithm was designed, which was validated by laboratory trials on real-pipe data with two defects at different locations with varying CSA sizes. |

Mahal H. [28] | 2019 | Adaptive leaky NLMS filter | The results demonstrated the capability of this algorithm for enhancing the SNR of the defect. The results proved that the model parameters can be chosen using a finite element method model, but it will not result in the maximum gain. |

Majhi S. [49] | 2019 | Modified S-Transform | A novel time–frequency spectrum was developed to monitor the mode conversions in relation to the progress of corrosion. K-means clustering is used to quantify the variation in signal strengths with the progress of corrosion. The proposed technique was able to obtain the variation in the distribution of the spectral contribution from higher-order to lower-order modes. |

Author | Year | Technique | Summary and Results |
---|---|---|---|

Da Y. [32] | 2017 | Wavelet transform in time and wavenumber domains | Wavenumber-domain WT operation gives a better denoising effect than direct time-domain WT denoising. Using the former, one can perform the inverse flaw reconstruction by reflected signals with an SNR as high as −5 dB. |

Xu C. [67] | 2018 | Dispersion compensation method based on compressed sensing | The method can compensate both single-mode and multi-mode dispersive guided waves effectively, based on the accurate dispersion curves and every dispersive wave packet to the waveform of the excitation as well, and achieve better performance than the time-distance mapping method. |

Wu J. [21] | 2017 | Smoothed Pseudo Wigner–Ville distribution and Vold–Kalman filter order tracking | The results of the simulation signal and the experimental signal reveal that the presented algorithm succeeds in decomposing the multi-component signal into mono components. Further research needs to be undertaken to validate the feasibility of locating defects by the algorithm. |

Chen Q. [53] | 2021 | Estimation of signal parameters via rotation invariant technique (ESPRIT) and particle swarm optimisation algorithm | The root mean squared errors between the estimated and theoretical dispersion curves calculated by the inversed model parameters for simulation, steel, aluminium and composite experiments are: 0.027, 0.032, 0.033 and 0.102 rad/m. |

Sabeti S. [54] | 2020 | Spatio-temporal sparse wavenumber analysis | The results indicate the possibility of accurate reconstruction (correlation coefficient of around 0.9) for sampling rates above 60% of the spatio-temporal Nyquist critical sampling rate. |

Rizvi S. [38] | 2021 | Autoregressive model based on Burg’s maximum entropy method to modify the kernel of the discrete Wigner–Ville distribution | The proposed method precisely estimated the distance between two closely spaced notches in a metallic plate from different simulated noisy signals with a maximum uncertainty of 5%. |

Bagheri A. [56] | 2016 | Artificial neural network | The non-contact inspection system and the signal processing technique enable the classification of the plate health with a success rate of > 75 %. |

Wang G. [37] | 2019 | Matching pursuit algorithm of Gabor function | The first iterative compensation of the proposed method can achieve compensation within the temperature range greater than 7 °C, and the compensation within the temperature range greater than 18 °C can be achieved after three iterations. |

Jia H. [57] | 2020 | Baseline-free method based on the mode conversion and the reciprocity principle | In the case of 1.0 mm depth, which performed with a strong mode conversion ability, four obvious wave packets were observed. The result shows that the method could accurately localise both defects. |

Douglass A. [58] | 2018 | Temperature compensation method based on dynamic time warping | For frequencies above 200 kHz and temperature differences above 25 °C, the correlation coefficients were consistently greater than 0.75, while the scale transform showed correlation coefficients below 0.35. Correlation coefficients are consistent above 0.75, while the scale transform’s correlation coefficient dropped to 0.45 with as little as 0.4 ms of data. |

He J. [60] | 2019 | Reverse-time migration (RTM) imaging | A reverse-time migration (RTM) imaging algorithm was combined with a numerical simulator: the three-dimensional elastodynamic finite integration technique (EFIT), in order to provide multi-mode damage imaging. The results represent the damage location and size but do not provide detailed information on different modes. |

Lee Y. [39] | 2021 | Reconstruction algorithm for probabilistic inspection of damage (RAPID) | Location possibility was confirmed through the application of the anti-symmetric mode, and that quantitative imaging was very difficult in the bending stress dominant mode. The more accurate quantitative visualisation of defects was achieved when imaging was performed through this mode. |

Xu C. [62] | 2019 | Weighted sparse reconstruction-based anomaly imaging method | Results for carbon fiber-reinforced polymer (CFRP) plate with an additional mass show that the weights constructed from the correlation coefficients between the scattering signal and the atoms of the dictionary are appropriate and accurate. |

Zhang H. [63] | 2018 | Reverse time migration method | Numerical results demonstrate that the pre-processing of mode separation helps to effectively remove the artefacts resulting from the multi-mode interference in the imaging process. |

Lugovtsova Y. [65] | 2021 | Wavenumber mapping | The approaches used deliver an accurate estimate of the in-plane size of the large delamination at the interface but only a rough estimate of its depth. None of the wavenumber mapping techniques used in the study can quantify every delamination between CFRP plies caused by the impact, which is the case for conventional UT. This may be solved by using higher frequencies or more advanced signal processing techniques. |

Arcos Jiménez A. [36] | 2019 | Wavelet transform and supervised learning classifiers | Results show that the combination of the k-nearest neighbours algorithm with the principal component analysis technique provides the best results for the detection and diagnosis of mud in the developed experiments. The classifier that detects and identifies mud in all cases is the ensemble subspace discriminant model for E-1. Fuzzy k-nearest neighbours is the best classifier for E-2. |

Tiwari K. [66] | 2018 | Wavelet transform | The discrete wavelet transform, along with the amplitude detection technique, was applied on experimental B-scans to locate and size the defects with a significant accuracy: the percentage error was less than 12%. |

Gómez Muñoz C. [31] | 2018 | Wavelet transforms | The envelope of the filtered signal from wavelet transforms is completed based on the Hilbert Transform, and the pattern recognition is achieved by autocorrelations of the Hilbert transform. The approach detects the ISO 12494 cases of un-frozen, frozen without ice, and frozen with ice in wind turbines. |

Tiwari K. [35] | 2017 | Wavelet transform, Hilbert–Huang transform | The size of defects having diameters of 15 and 25 mm at the −3 dB threshold level was measured as 9 mm with a percentage error of 40% and 34.5 mm with a percentage error of 38%. The location of defects at the −3 dB threshold level from the start point of scanning was also calculated as 29 mm (for the defect of 15 mm), with a percentage error of 37.5%, and 405.5 mm (for the defect of 25 mm) with an error of 2%. |

Author | Year | Technique | Summary and Results |
---|---|---|---|

He C. [33] | 2008 | Multi-level discrete wavelet decomposition and single branch reconstruction | The Daubechies wavelet of order 40 is used as the mother wavelet for the decomposition. This wavelet denoise method improves the SNR. |

Legg M. [68] | 2015 | Dispersion curve compensation | Attenuation and dispersion compensation was then performed for a broadband maximum length sequence (MLS) excitation signal. It was found that an increase in terms of SNR between 4 and 8 dB was observed relative to the dispersed signal. The main benefit was the increased ability to resolve the individual echoes from closely spaced structures: the end of the cable and an adjacent cut. |

Ji Q. [69] | 2021 | Singular value decomposition and support vector regression | Results show that the fundamental mode dispersion curve offset on the high-frequency part and cut-off frequency increases as the boundary constraints enhance, demonstrating the capability of the proposed support vector regression method for evaluating the stress level in the strands. |

Tran D. [70] | 2020 | Discrete convolutional neural network | The DCNN and wave propagation imaging produced the highest R2 score and lowest MSE score: 0.91 and 1.55, respectively. |

Liew C. [71] | 2008 | Series combined network with the integration of a weight-range selection | The system was able to achieve average predictions accurate to 2.5 and 7.8% of the original training range sizes for the damage location and depth, while the WRS provided up to 13.9% improvement compared to equivalent conventional neural networks. |

Ju. T. [72] | 2022 | Nonlinear response of multi-mode guided wave ultrasonic signals | Experimental results are consistent with numerical simulations, indicating that the proposed method can be implemented for semi-quantitative detection or early warning indication of microstructural defects in complex, large-area structures. |

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**MDPI and ACS Style**

Diogo, A.R.; Moreira, B.; Gouveia, C.A.J.; Tavares, J.M.R.S.
A Review of Signal Processing Techniques for Ultrasonic Guided Wave Testing. *Metals* **2022**, *12*, 936.
https://doi.org/10.3390/met12060936

**AMA Style**

Diogo AR, Moreira B, Gouveia CAJ, Tavares JMRS.
A Review of Signal Processing Techniques for Ultrasonic Guided Wave Testing. *Metals*. 2022; 12(6):936.
https://doi.org/10.3390/met12060936

**Chicago/Turabian Style**

Diogo, Ana Rita, Bruno Moreira, Carlos A. J. Gouveia, and João Manuel R. S. Tavares.
2022. "A Review of Signal Processing Techniques for Ultrasonic Guided Wave Testing" *Metals* 12, no. 6: 936.
https://doi.org/10.3390/met12060936