Nonlinear Wave Modulation Spectroscopy Research Articles

High-efficiency surface defect detection based on laser ultrasonic state space embedding and compressive sensing

Abstract The laser nonlinear wave modulation spectroscopy(LNWMS) technique has gained considerable attention due to its high sensitivity in detecting small surface defects and its ultra-fast scanning speed. This paper proposes a novel method for synthesizing intact wavefield reference, significantly enhancing the accuracy of surface defect imaging. Moreover, considering the potential for parallel processing of the nonlinearity calculation of ultrasonic signals at scanning points, we incorporate compressive sensing technology to accelerate this process. This innovative approach reduces the computational load to 10% of the original, thereby substantially increasing the imaging speed. The paper validates the method’s superior accuracy and efficiency in defect detection through conducting experiments using a high-speed laser ultrasonic scanning system on aluminum plates and turbine blade, and by comparing with local wavenumber estimation, demonstrating the promising potential of this technology for surface defect analysis.

Evaluation of fatigue cracks on rail material based on laser nonlinear wave modulation and adaptive particle swarm optimization - support vector machines

ABSTRACT The evaluation of fatigue cracks is essential for the detection of early damage to railway tracks. Laser nonlinear wave modulation spectroscopy using broadband excitation is an effective method for fatigue crack detection that can solve the problem of frequency combination optimisation. However, due to the complex components of laser nonlinear ultrasonic signals, the evaluation of fatigue cracks using laser nonlinear ultrasonic signals remains a challenge. In this study, wavelet packet decomposition and principal component analysis were used to extract various features of nonlinear ultrasonic signals in the frequency domain, and four new combinations of features were obtained. These new features were used as input for the evaluation model. Finally, a fatigue crack evaluation model based on adaptive particle swarm optimisation-support vector machines was proposed to accurately evaluate fatigue cracks of different lengths. The experiments conducted showed that the fourth new combination of features and evaluation model proposed in this paper can improve the accuracy of evaluating rail fatigue cracks of different lengths, reaching a classification accuracy of 97%.

The effect of stress and saturation on low-frequency nonlinear elasticity in geological materials

Wave propagation in rocks is typically treated in seismology as a purely linear elastic phenomenon; however, evidence for nonlinear elastic behavior in geomaterials has existed for years. The degree of nonlinearity in fractured material is much greater than that in intact material, resulting in signals that are highly sensitive to the state of the fracture (stress, chemistry, fluids). Elastic nonlinearity can cause a propagating wave to distort, resulting in generation of harmonics and multiplication of waves of different frequencies. One way to exploit these behaviors is to propagate waves of differing frequencies through a material and observe nonlinear wave mixing phenomena, a technique referred to in the literature as nonlinear wave modulation spectroscopy (NWMS). I will discuss the use of NWMS for the study of geologic materials at a range of conditions to highlight the frequency, stress, and fluid dependence of nonlinear parameters in rocks. Analysis of various dependencies can provide insight into the mechanisms of nonlinearity and has the potential to provide methods of monitoring the dynamic state of the subsurface.

Broadband nonlinear elastic wave modulation spectroscopy for damage detection in composites

A non-destructive testing procedure is proposed for damage detection in composites using full wavefield measurement obtained using a scanning laser Doppler vibrometer. Vibrations are excited using two low-power piezoelectric actuators leading to nonlinear elastic wave modulation at the defect. One actuator is supplied with a broadband chirp signal and the other actuator is supplied with a single-frequency sine signal. First, a time–frequency filtering method is proposed to extract specific nonlinear components of interest (e.g. second higher harmonic and first modulation sideband) without the need for multiple excitation sequences. Next, damage maps are constructed using broadband bandpower calculation of the filtered nonlinear components. It is demonstrated that the modulation sidebands provide an exclusive imaging of defect nonlinearity, and are not affected by potential source nonlinearity. The proposed damage map construction procedure is applied for various carbon fiber reinforced polymer test specimens with different damage features: (1) coupon with quasi-static indentation damage, (2) coupon with artificial delaminations, (3) bicycle frame with impact damage, and (4) stiffened aircraft panel with partially debonded stiffener. The obtained results indicate the high performance of the developed procedure for detection of various defect types in curved and/or stiffened carbon fiber reinforced polymer components.

Surface crack characterization using laser nonlinear ultrasonics based on the bispectrum

Laser nonlinear wave modulation spectroscopy (LNWMS) has been used to detect nonlinear ultrasonic signatures caused by fatigue cracks in materials. The nonlinear feature extraction from the spectral plot plays a significant role in LNWMS. This paper uses the bispectrum to distinguish harmonically related signals which result from nonlinear interactions and to remove those which do not. A feature called bispectrum damage factor (BDF), which is defined as the ratio of the bispectrum peak difference value of the damage and intact signals to the bispectrum peak value of intact signals at frequencies F 1, F 2, is extracted from the bispectral plot to characterize the crack features. The basic premise of the proposed laser nonlinear wave modulation bispectrum (LNWMBS) is that this BDF value will vary regularly as the level of crack-induced nonlinearity increases. A finite element model and a noncontact laser ultrasonic system have been built for LNWMBS measurement. The simulation results show that the BDF value is sensitive to crack depth and angle, and is insensitive to crack length and detecting position. BDF values of reflected Rayleigh waves are positive and approximately linearly increase with an increase of the crack depths in the range of 0.1 λ ∼ 0.6 λ (λ is the corresponding wavelength of adopted frequency); meanwhile, the values of the transmitted waves are negative and decreasing. The BDF values are larger than the crack angle at 90° when they are less than 90°, which is beneficial for crack detection. The proposed LNWMBS technique has been successfully tested for detecting artificial sub-millimeter surface-breaking cracks in aluminum alloy plates and closed fatigue cracks of torque load simulator connection blocks.

Imaging of barely visible impact damage on a composite panel using nonlinear wave modulation thermography

Thermosonics is a well-established non-destructive evaluation (NDE) technique that uses an infrared camera to visualise material damage by capturing the frictional heating at crack surfaces when the sample under inspection is vibrated. A high power ultrasonic horn is typically used to generate vibrations, which is pressed against the surface of the test component. However, the direct contact between the horn and the surface generates acoustic chaos and high-amplitude vibrations, which can lead to non-reproducible and unreliable measurements and, ultimately, they can harm the structural integrity of components. This paper proposes an alternative to thermosonics, here named as nonlinear wave modulation thermography, for the detection and imaging of material flaws on a damaged carbon fibre composite panel. This material inspection technology combines the concept of nonlinear wave modulation spectroscopy using dual excitation with contact piezoelectric transducers and thermographic equipment. Whilst nonlinear ultrasonic modulation was used to enhance the sensitivity to micro-cracks, an infrared camera was used for defect visualisation. A nonlinear narrow sweep excitation method was employed to experimentally identify the dual excitation frequencies that resulted in high-amplitude damage resonance effects causing frictional heat at crack surfaces. A laser vibrometry system was also used to create a spatial mapping of the amplitude of sidebands. Nonlinear wave modulation thermography has proved to successfully detect barely visible impact damage in composites in a quick and reliable manner, thus overcoming the limitations of traditional optical thermography and thermosonics.

Damage detection using sideband peak count in spectral correlation domain

Nonlinear ultrasonic techniques have been proven to be more sensitive to the presence of an early-stage damage than linear techniques. Among various nonlinear techniques, laser nonlinear wave modulation spectroscopy (LNWMS) utilizes a pulse laser to exert a broadband input and a damage on the target structure exhibits nonlinear wave modulation among various input frequency components. A sideband peak count (SPC) technique in the spectral frequency domain was proposed to estimate the damage-induced nonlinearity. In this study, the SPC operation is conducted in the spectral correlation domain so that noise has less influence on damage detection performance and a higher sensitivity to damage can be achieved. In addition, through spatial comparison of SPC over an inspection area, damage can be detected without relying on the baseline data obtained from a pristine condition. The performance of the proposed technique is validated using a numerical simulation performed on an aluminum plate with a simulated crack, and experiments performed on an aluminum plate with a fatigue crack and a carbon fiber reinforced polymer plate with delamination.

Comparison of various methods of nonlinear signatures extraction

Nonlinear Acoustic NDE (NA NDE) methods are very sensitive to defect presence and currently number on publications on this matter exceed several thousand. Despite intensive research of NA NDE, these methods are still do not widely used in practice and the goal of this presentation is to give review of various methods of nonlinear signatures extraction and to show advantages on some of them in the comparison with the others. The major part of the NA NDE was applied for characterization the tested part as whole. These methods include: High Harmonic Generation, Nonlinear Resonant Ultrasound Spectroscopy (NRUS), Amplitude Dependent Internal Friction, Nonlinear Wave Modulation Spectroscopy (NWMS) or Vibro Acoustic Modulation (VAM), Slow Dynamics Diagnostics (SDD), Nonlinear Reverberation Spectroscopy (NRS) or Nonlinear Impact Resonance Acoustic Spectroscopy (NRAS), Nonlinear Coda Wave Interferometry, Bi Spectral and High Order Statistic Analysis, Subharmonic and Ultraharmonic Methods. The methods that can provide nonlinear imaging and damage localization include: Nonlinear Time Reversal Acoustics (NTRA) or TR NEWS, Nonlinear Harmonic Imaging, Nonlinear Acoustic Tomography, Pulse Modification of Vibro Acoustic Modulation (VAM), Nonlinear Guided Wave Imaging and Tomography, Subharmonic and Ultraharmonic imaging, Nonlinear Structural Intensity.

Fatigue crack localization using noncontact laser ultrasonics and state space attractors.

A fatigue crack and its precursor often serves as a source of nonlinear mechanism for ultrasonic waves, and the resulting nonlinear features are often much more sensitive to the fatigue crack than their linear counterparts. Among various nonlinear ultrasonic techniques, the proposed laser nonlinear wave modulation spectroscopy (LNWMS) is unique in that (1) it utilizes a pulse laser to exert a single broadband input instead of conventional two distinctive sinusoidal waves, and (2) a complete noncontact measurement can be realized based on LNWMS. Under a broadband excitation, a nonlinear source exhibits modulations due to interactions among various input frequency components. These modulations are often weak and can be hardly directly detected. In this paper, a damage feature called Bhattacharyya distance is extracted from the ultrasonic time signal corresponding to a pulse laser input and used to quantify the degree of damage-induced nonlinearity and localize the crack. This feature is a measure of a statistical distance used to detect the geometrical changes between state space attractors reconstructed before and after damage formation. It has been successfully used for localizing fatigue cracks in metallic plates.

Baseline-free damage visualization using noncontact laser nonlinear ultrasonics and state space geometrical changes

Damage often causes a structural system to exhibit severe nonlinear behaviors, and the resulting nonlinear features are often much more sensitive to the damage than their linear counterparts. This study develops a laser nonlinear wave modulation spectroscopy (LNWMS) so that certain types of damage can be detected without any sensor placement. The proposed LNWMS utilizes a pulse laser to generate ultrasonic waves and a laser vibrometer for ultrasonic measurement. Under the broadband excitation of the pulse laser, a nonlinear source generates modulations at various frequency values due to interactions among various input frequency components. State space attractors are reconstructed from the ultrasonic responses measured by LNWMS, and a damage feature called Bhattacharyya distance (BD) is computed from the state space attractors to quantify the degree of damage-induced nonlinearity. By computing the BD values over the entire target surface using laser scanning, damage can be localized and visualized without relying on the baseline data obtained from the pristine condition of a target structure. The proposed technique has been successfully used for visualizing fatigue crack in an aluminum plate and delamination and debonding in a glass fiber reinforced polymer wind turbine blade.

Advanced Fatigue Crack Detection Using Nonlinear Self-Sensing Impedance Technique for Automated NDE of Metallic Structures

This article reports the application of a nonlinear impedance technique under a low-frequency vibration to detect contact-type structural defects such as fatigue cracks. If the contact-type damage is developed within the structure due to the low-frequency dynamic load, the vibration can cause a nonlinear fluctuation of the structural impedance because of the contact acoustic nonlinearity (CAN). This nonlinear effect can lead to amplitude modulation and phase modulation of the current flow. The nonlinear characteristics of the structural impedance can be extracted by observing the coupled electromechanical impedance of a piezoelectric active sensor and utilizing nonlinear wave modulation spectroscopy. Experimentally, a low-frequency vibration was applied to a notched coupon at a certain natural frequency by a shaker, so that a nonlinear fatigue crack can be artificially formed at the notch tip. Then, the nonlinear features are extracted based on a self-sensing impedance measurement from a host structure under a low-frequency vibration. The damage metric was established based on the nonlinear fluctuation of the impedance due to the CAN.

Influence of fiber orientation on the inherent acoustic nonlinearity in carbon fiber reinforced composites.

This paper presents the study of non-classical nonlinear response of fiber-reinforced composites. Nonlinear elastic wave methods such as nonlinear resonant ultrasound spectroscopy (NRUS) and nonlinear wave modulation spectroscopy have been used earlier to detect damages in several materials. It was observed that applying these techniques to composites materials becomes difficult due to the significant inherent baseline nonlinearity. Understanding the non-classical nonlinear nature of the composites plays a vital role in implementing nonlinear acoustic techniques for material characterization as well as qualitative nondestructive testing of composites. Since fiber reinforced composites are orthotropic in nature, the baseline response variation with fiber orientation is very important. This work explores the nature of the inherent nonlinearity by performing nonlinear resonant spectroscopy (NRS) in intact unidirectional carbon/epoxy samples with different fiber orientations with respect to major axis of the sample. Factors such as frequency shifts, modal damping ratio, and higher harmonics were analyzed to explore the non-classical nonlinear nature of these materials. Conclusions were drawn based on the experimental observations.

Fatigue Crack Localization Using Laser Nonlinear Wave Modulation Spectroscopy (LNWMS)

Nonlinear features of ultrasonic waves are more sensitive to the presence of a fatigue crack than their linear counterparts are. For this reason, the use of nonlinear ultrasonic techniques to detect a fatigue crack at its early stage has been widely investigated. Of the different proposed techniques, laser nonlinear wave modulation spectroscopy (LNWMS) is unique because a pulse laser is used to exert a single broadband input and a noncontact measurement can be performed. Broadband excitation causes a nonlinear source to exhibit modulation at multiple spectral peaks owing to interactions among various input frequency components. A feature called maximum sideband peak count difference (MSPCD), which is extracted from the spectral plot, measures the degree of crackinduced material nonlinearity. First, the ratios of spectral peaks whose amplitudes are above a moving threshold to the total number of peaks are computed for spectral signals obtained from the pristine and the current state of a target structure. Then, the difference of these ratios are computed as a function of the moving threshold. Finally, the MSPCD is defined as the maximum difference between these ratios. The basic premise is that the MSPCD will increase as the nonlinearity of the material increases. This technique has been used successfully for localizing fatigue cracks in metallic plates.

Nonlinear wave structural health monitoring method using an active nonlinear piezoceramic sensor for matrix cracking detection in composites

A structural health monitoring methodology, based on nonlinear wave modulation spectroscopy, is presented and aims to detect matrix cracks in composites. Experiments were conducted on cross-ply carbon/epoxy strips containing matrix cracks, induced via three-point bending. Damage in all tested specimens was categorized according to the acoustic emission hits recorded during loading. The nonlinear ultrasonics methodology is applied via an active nonlinear acousto-ultrasonic piezoelectric sensor, enabling low-cost and wide-frequency operational bandwidth. This active sensor configuration involves two piezoceramic wafer actuators, one excited with a low- and the other with a high-frequency signal, and a piezoceramic sensor, all permanently bonded on the tested structure. The sensitivity of the nonlinear active sensor response at specific high carrier frequencies is depicted and damage indices are proposed. The experimental results illustrate the effectiveness of the nonlinear ultrasonic wave mixing method in matrix crack detection, as well as the potential of the new active sensor for permanent structural health monitoring.

Noncontact detection of fatigue cracks by laser nonlinear wave modulation spectroscopy (LNWMS)

Nonlinear wave modulation spectroscopy (NWMS) has been used to detect nonlinear ultrasonic signatures produced by fatigue cracks in materials. It is done by generating ultrasonic waves at two different frequencies and measuring their modulation. A proper choice of two distinct frequencies for a given structure plays a significant role in NWMS. This paper, instead of using input signals at two distinct frequencies, takes only one broadband pulse signal as the driving input, which can be generated by a laser beam. With a broadband excitation, material nonlinearity exhibits modulation at multiple peaks in a spectral plot due to interactions among various input frequency components of the broadband input. A feature called sideband peak count (SPC), which is defined as the ratio of the number of sideband (modulation) peaks over a moving threshold to the total peak number in the specified frequency band, is extracted from the spectral plot to measure the degree of material nonlinearity. The basic premise of the proposed laser nonlinear wave modulation spectroscopy (LNWMS) is that this SPC value will rise as the level of material nonlinearity increases. A noncontact laser ultrasonic system has been built for LNWMS measurement by integrating and synchronizing a Q-switched Nd:YAG laser for ultrasonic wave generation and a laser Doppler vibrometer for ultrasonic wave detection. The proposed LNWMS technique has been successfully tested for detecting fatigue cracks in metallic plates and aircraft fitting-lugs having complex geometries.

Noncontact fatigue crack detection using nonlinear wave modulation spectroscopy

Nonlinear wave modulation spectroscopy (NWMS) has been used to evaluate nonlinear acoustic signature of fatigue cracks in materials and thus to get an idea about the degree of material nonlinearity. It is done by generating ultrasonic waves at two different frequencies and measuring their modulation. The choice of two distinct frequencies plays a significant role in NWMS for different structures. In this paper, instead of using signals at two distinct frequencies, only one broadband pulse signal is used as the driving signal, which can be generated by a laser beam. This driving signal generates multi-frequency responses as different resonance frequency modes and/or Lamb wave modes, generated in a plate-like structure. Nonlinear wave modulation occurs among these frequencies when material nonlinearity exists. It increases the sideband energy and the number of peaks in the spectral plots. These two features, namely sideband energy ratio (SER) and sideband peak number (SPN), are extracted from the spectral plots to measure the material nonlinearity caused by fatigue cracks. The noncontact laser system has been built for NWMS measurement by integrating and synchronizing a Q-switched Nd:YAG laser for ultrasonic wave generation and a laser Doppler vibrometer for ultrasonic wave detection. The proposed modified NWMS technique with the noncontact laser system has been successfully used for the identification of metallic plates with fatigue cracks.

Crack detection in long rod by impact wave modulation method

Engineering Research and Development Center (ERDC) in Vicksburg, MS, is interested in methods of microcracks detection in extended length and conducted test of applications of nonlinear wave modulation spectroscopy (NWMS). This is one of the simplest methods of nonlinear acoustic NDE. It is based on measurements of the modulation of a high frequency wave by a low frequency vibration. NWMS can detect the crack presence but cannot localize cracks. We present modification of NMWS method based on the modulation of by ultrasound by short pulse produced by impact. This method allows crack and damage localization using time delay of the impact produced pulse and modulated part of high frequency wave. The feasibility test was conducted for 60 ft long steel trunnion rod with an imitated crack. The continuous wave ultrasound with the frequency about 50 kHz was modulated by the longitudinal impulse produced by the hammer impact. Time delay between the impact and the received modulated ultrasonic wave allowed finding of the distance to the crack. Propagation speed of the modulated wave was lower than the speed of the hammer impulse as it is followed from the theory describing frequency dispersion of the waves in rods. [The project is funded by the Navigation Research Program at ERDC.]

Theoretical investigation of nonlinear ultrasonic wave modulation spectroscopy at crack interface

This paper studies theoretical results of a nonlinear ultrasonic method based on interaction of two elastic waves of different frequencies. A virtual Nonlinear Wave Modulation Spectroscopy experiment is performed in the vicinity of a crack described by a model combining classical and hysteretic nonlinearity. Quasistatic response to two frequency excitation was computed and harmonic and intermodulation components were studied. The influence of driving signal parameters and nonlinear parameters on the response is thoroughly discussed. A general way of hysteretic response description based on scaling properties is explained. In case of the combined nonlinear model, an analysis of nonlinear spectral components is performed in complex plane. Based on the complex interaction of classical and hysteretic parts, a method of their separation is proposed.

106 非定常低周波振動を用いた非線形波動変調現象に基づく損傷位置の推定(セッション2 同定技術)

This study concerns damage localization method based on nonlinear elastic wave modulation spectroscopy. When fragments of a contact-type damage is rupping and crapping in synchronization with the low-frequency vibration, a high-frequency wave which propagates through the damage may undergo amplitude and phase modulation at the damage location because the scatter characteristics of high -frequency waves in the vicinity of the damage may fluctuate in synchronization with the low-frequency vibration because of the contact acoustic nonlinearity. Since thi modulation propagates through the structure with the group velocity, it may be possible to estimate damage location by measurering the modulation and performing an inverse analysis based on the wave propagation model. In this paper a mathematical model of the phase modulation propagation on a Timoshenko beam is constructed, and by considering the damage as a source of the modulation wave, a localization algorithm which utilizes the time difference between the demodulated waves measured by sensor arrays located at both sides of the damage is proposed, and examind experimentally.

Delamination detection in composites using wave modulation spectroscopy with a novel active nonlinear acousto-ultrasonic piezoelectric sensor

A novel structural health monitoring (SHM) methodology, based on nonlinear wave modulation spectroscopy, is presented for the detection of delamination cracks in composites. The basic element is a novel active nonlinear acousto-ultrasonic piezoelectric sensor enabling low-cost and wide-frequency operational bandwidth. The active sensor configuration involves two piezoceramic wafer actuators, each one excited with a low- and high-frequency signal respectively, and a piezoceramic sensor, all permanently bonded on the tested structure. Experiments are conducted on two sets of composite strips containing delamination cracks of different sizes. Measured results illustrate first the efficiency of the nonlinear ultrasonics methodology to detect delamination cracks, as well as, the potential and benefits of the new active sensor. The sensitivity of the active sensor response to the crack size and the applied high-frequency carrier signals at the actuators, vary at various frequency and voltage levels indicating the appropriate testing setup. Additionally repeatability of proposed SHM methodology is studied.