Laser Doppler Vibrometer Measurements Research Articles

Using the inverse finite‐element method to harmonise classical modal analysis with fibre‐optic strain data for robust population‐based structural health monitoring

AbstractVibration‐based approaches to structural health monitoring (SHM) gained increasing significance for assessing the behaviour of existing structures because of their non‐intrusive nature and high sensitivity to damage. However, data availability often limits the application of SHM approaches. The population‐based structural health monitoring (PBSHM) theory addresses this challenge, enhancing diagnostic inferences by sharing knowledge across a population of similar structures. In real‐life scenarios, sharing data from distinct structures requires dealing with results obtained with different experimental setups, multiple sensors, input choices and acquisition systems. Therefore, it is crucial to harmonise various features to achieve accurate and reliable results. The present study presents the results of a classic experimental modal analysis (EMA) using scanning laser Doppler vibrometer (SLDV) measurements and a strain‐based EMA conducted using high‐definition distributed fibre‐optic strain sensors. The experimental case study of a laboratory‐scale steel aircraft subjected to specific operating and damage conditions is introduced, allowing for a comprehensive discussion of the features extracted from the two EMA techniques, which can also be generalised to structures within different domains. This research highlights the advantages and limitations of fibre‐optic‐based EMA compared to classic methods, as fibre‐optic strain sensors offer a cost‐effective alternative to accelerometers or SLDV for dynamic testing. Furthermore, the feasibility of employing the inverse finite‐element method (iFEM) in the dynamic domain is investigated. This method can estimate the whole displacement field of a structure from a limited number of strain values, thus harmonising strain measurements with the SLDV measurements. By analysing the features extracted from different EMA techniques within the PBSHM framework, this study contributes to advancing the understanding and application of the PBSHM approach in diverse experimental scenarios, laying the foundation for further investigation of features and adequate methods for sharing damage‐state knowledge across a population of structures.

Laser Doppler Vibrometer measurements of the 3D pressure field for the estimation of the radiation force produced by an acoustic standing-wave levitator

Acoustic levitation devices use powerful ultrasonic standing waves to levitate objects in mid-air. We have created a system and method to measure the full harmonic content of the acoustic field accurately. Our study revealed that levitated particles alter the pressure field in a way that is not immediately apparent from the first harmonic alone, highlighting the importance of precise and non-invasive measurement techniques. Our method uses computational tomography and optical sensing with the acousto-optic effect and a 3 DOF mechanical scanner. Our experiment results in a detailed 3D pressure distribution map for each harmonic of the ultrasonic acoustic field that generates the levitation forces.

Machine Learning approaches to damage detection in composite structures combining experimental and simulation domains

Composite materials are widely used across major industries such as the automotive, aerospace and wind power, due to their excellent mechanical properties. A strong effort is thus put into developing innovative damage detection methodologies, for which Non-Destructive Testing (NDT) techniques can play a vital role as advanced measurement methods. One such technique is Laser Doppler Vibrometry which allows to accurately measure high-frequency vibration behavior with dense grids of points, without mass loading the structure. For data analysis, Machine Learning (ML) techniques have achieved high success on a number of structural applications, and can be leveraged to build automated and reliable damage classifiers. In this work, three methodologies have been developed by combining Laser Doppler Vibrometer (LDV) measurements with ML approaches, for the task of detecting damages on a carbon-fiber reinforced polymer (CFRP) plate. Each damage detection methodology requires pre- and post-processing steps, which were optimized with Bayesian Optimization. Principal Component Analysis (PCA) was also explored to reduce the dimensionality of the data, before classification. Moreover, making use of Finite Element Analysis (FEA), simulation data was generated with the ability of characterizing the high-frequency dynamic behavior of ply-based composite plates. The simulation data enriched the damage detection methodologies in a Transfer Learning (TL) framework. Results are presented for each damage detection methodology, alongside with a comparative overview of the advantages and disadvantages of each method.

Application of Time Synchronous Averaging in Mitigating UAV Noise and Signal Loss for Continuous Scanning Laser Doppler Vibrometry

The laser Doppler vibrometer (LDV) has been shown to be effective for a wide application of vibration assessments that are well accepted. One of the new avenues for exploring alternative measurement scenarios, mounting LDVs on unmanned aerial vehicles (UAVs) is emerging as a potential avenue for remote and harsh environment measurements. Such configurations grapple with the challenge of the LDV sensor head being sensitive to UAV vibration during flight and signal loss due to tracking error. This study investigates the effectiveness of several Time Synchronous Averaging (TSA) techniques to circumvent these obstacles. Through comprehensive evaluations, all three TSA techniques under investigation demonstrated significant potential in suppressing UAV-induced noise and minimising the effects of signal dropout. Traditional TSA showcased a remarkable sixfold enhancement in signal quality when analysed via the mean square error. However, the study also highlighted that while TSA and Multi-Cycle Time Synchronous Average (MCTSA) elevated signal clarity, there is a trade-off between noise suppression and signal duration. Additionally, the findings emphasise the importance of synchronisation between scanning and target vibration. To achieve optimal results in Continuous Scanning Laser Doppler Vibrometer measurements, there is a need for advanced algorithms capable of estimating target vibration and synchronising scanning in real-time. As the study was rooted in steady-state vibrations, future research should explore transient vibration scenarios, thereby broadening the application scope of TSA techniques in UAV-mounted LDV systems.

Railway sleeper vibration measurement by train‐borne laser Doppler vibrometer and its speed‐dependent characteristics

AbstractA train‐borne laser Doppler vibrometer (LDV) directly measures the dynamic response of railway track components from a moving train, which has the potential to complement existing train‐borne technologies for railway track monitoring. This paper proposes a holistic methodology to characterize train‐borne LDV measurements by combining computer‐aided approaches and real‐life measurements. The focus is on the speed‐dependent characteristics because the train speed affects the intensity of railway sleeper vibrations and the intensity of speckle noise, which further affects the quality and usability of the measured signals. First, numerical models are established and validated to simulate sleeper vibrations and speckle noise separately. Then, a vibration–noise separation method is proposed to effectively extract speckle noise and structural vibrations from LDV signals measured at different speeds. The parameters of the separation method are tuned using simulation signals. The method is then validated using laboratory measurements in a vehicle‐track test rig and applied to field measurements on a railway track in Rotterdam, the Netherlands. Further, the speed‐dependent characteristics of train‐borne LDV measurement are determined by analyzing the competition between sleeper vibrations and speckle noise at different speeds. Simulation and measurement results show that an optimal speed range yields the highest signal‐to‐noise ratio, which varies for different track structures, measurement configurations, and operational conditions. The findings demonstrate the potential of train‐borne LDV for large‐scale rail infrastructure monitoring.

Realistic prediction and engineering of high-Q modes to implement stable Fano resonances in acoustic devices

Quasi-bound states in the continuum (QBICs) coupling into the propagating spectrum manifest themselves as high-quality factor (Q) modes susceptible to perturbations. This poses a challenge in predicting stable Fano resonances for realistic applications. Besides, where and when the maximum field enhancement occurs in real acoustic devices remains elusive. In this work, we theoretically predict and experimentally demonstrate the existence of a Friedrich-Wintgen BIC in an open acoustic cavity. We provide direct evidence for a QBIC by mapping the pressure field inside the cavity using a Laser Doppler Vibrometer (LDV), which provides the missing field enhancement data. Furthermore, we design a symmetry-reduced BIC and achieve field enhancement by a factor of about three compared to the original cavity. LDV measurements are a promising technique for obtaining high-Q modes’ missing field enhancement data. The presented results facilitate the future applications of BICs in acoustics as high-intensity sound sources, filters, and sensors.

A novel demodulation method with a reference signal for operational modal analysis and baseline-free damage detection of a beam under random excitation

A novel demodulation method with a reference signal is developed for operational modal analysis and damage detection of a beam structure under random excitation. The novel demodulation method can process measurements of the beam by a continuously scanning laser Doppler vibrometer (CSLDV) system and measurements of a reference point on the beam by a single-point laser Doppler vibrometer to estimate its modal parameters, such as damped natural frequencies and undamped mode shapes. Damped natural frequencies of the beam are estimated from fast Fourier transforms of measurements of the CSLDV system. A cross-correlation function between a measurement of the CSLDV system and a measurement of a single-point laser Doppler vibrometer is calculated, and the cross-correlation function is multiplied by a sinusoidal signal whose frequency is an estimated damped natural frequency of the beam. The processed cross-correlation function is filtered by a low-pass filter to obtain the undamped mode shape of the beam that corresponds to the estimated damped natural frequency of the beam. Smooth polynomials are used to fit estimated undamped mode shapes, which can be considered as undamped mode shapes of an undamaged beam. Curvatures of estimated undamped mode shapes and polynomials are compared by curvature damage indices to determine the location of a damage in the beam. The novel demodulation method with a reference signal is investigated for baseline-free damage detection from both finite element simulation and experiment. Modal parameters of a finite element model of the damaged beam and a damaged beam specimen, which are under random excitation, are successfully estimated, and locations of damages in the beam model and beam specimen are accurately determined.

Correction of scanning laser Doppler vibrometer measurements when subjected to six degree-of-freedom base motion

Scanning laser Doppler vibrometer (SLDV) measurements are affected by sensor head vibrations as though they are vibrations of the target surface itself. Previous work has established a fully general theoretical analysis which shows that the only measurement required for measurement correction is of the vibration velocity at the incident point on the final steering mirror in the direction of the outgoing laser beam. Two practical—but not quite perfect—options for measurement correction were presented (one more suitable to manufacturer implementation, one more applicable to the vibration engineer end user). In both cases, placement of the correction transducer is critical with correction working for totally arbitrary instrument vibration and scan angle. Experimental validation, employing frequency-domain based processing, has been completed for one degree-of-freedom, on-axis vibration. Simultaneously, advancements in the data processing approach have realised improved correction in practice, especially for lower frequencies and for transient, as opposed to statistically stationary, vibration. In this paper, extension of the experimental validation to six degree-of-freedom instrument vibration is presented for the first time. In combination with the latest data processing approaches, reductions in the measurement error of 29.4 and 28.2 dB for the frequency- and time-domain processing techniques, respectively, are realised.

Experimental measurements of stress in an acoustic black hole using a laser Doppler vibrometer

Acoustic Black Holes (ABHs) make use of modifications to a structure to effectively decrease the structural wavespeed, thus increasing the effect of damping material applied in the ABH taper region, resulting in greater vibration attenuation. The most common way in which this is implemented is by gradually reducing the thickness of the structure over a finite interval, to a very thin tip. The focusing effect of the ABH results in high amplitude vibrations occurring in the thin part of the structure, resulting in high stresses and raising significant concerns about fatigue life. This paper presents an experimental assessment of stress in the taper section of an ABH used to terminate a uniform beam, using laser Doppler vibrometer measurements to avoid the mass loading associated with accelerometers or strain gauges. A calculation of stress using Euler–Bernoulli beam theory is then presented, and the validity of this approach is assessed for a thick damping layer applied to a thin structure. A comparison is then made to predictions from a numerical model, in order to validate the results from the experimental measurements.

Estimating Young’s moduli based on ultrasound and full-waveform inversion

Ultrasound is commonly utilized to determine the dynamic Young’s moduli for estimating material deterioration or quantifying material parameters. This is either done with a resonance frequency analysis or ultrasound for rock or concrete specimens in geophysics or civil engineering. For ultrasound, these are typically cylindrical specimens measured in a through-transmission arrangement. However, this method presents some challenges, such as the need to accurately determine the onset of each wave mode and to calibrate system latency. To overcome these challenges, this study introduces a novel method that utilizes wavefield simulation and full-waveform inversion to estimate p- and s-wave, also called compression and shear wave, velocities. Where the traditional method requires two measurements, this innovative approach requires only one measurement with a single p-wave transducer. The s-wave velocity is estimated considering mode conversions within the specimen. High-fidelity ultrasound simulations are necessary for this approach. For that reason, the spatially distributed excitation of the ultrasound transducer is characterized by a laser Doppler vibrometer measurement. This led to a good estimate of the directivity pattern of the ultrasound transducer. The inverse problem for determining p- and s-wave velocity was solved successfully using a suitable misfit or cost function, the so-called graph-optimal-transport misfit. The specimens for the proof of concept study include six different metals. The precision of the estimated velocities using full-waveform inversion was compared with manual picking. As the simulated and measured waveforms matched well, this study can be seen as a starting point for material parameter determination for more complex geometries and heterogeneous materials using full-waveform inversion.

Dynamic Measuring Method of Laser Beam Incident Angle for Laser Doppler Vibrometer

Accurately measuring the incident angle of the laser Doppler vibrometer (LDV) laser beam is crucial for calculating the accurate dynamic response of a target. Nonetheless, conventional measuring methods may encounter limitations due to spatial constraints. To address this issue, a novel high-precision dynamic measuring method is proposed based on the measuring principle of LDV. Furthermore, a compact dynamic measuring device is constructed to facilitate this method. The proposed method involves the simulation of various tangential velocities utilizing a high precision rotating disk system. Subsequently, the laser beam incident angle is computed based on the projection relationship established between the average value of LDV measurements and the simulated velocities. To validate the feasibility of the dynamic measuring method and the correctness of the obtained incident angle, the paper compares this angle with that obtained through a conventional laser beam measuring method and device. This paper analyzes four key factors that may affect the angle measuring results theoretically and experimentally: environmental noise, laser spot position error, roll angle, and pitch angle of the rotating disk. The results indicate that the laser spot position error and the pitch angle of the rotating disk are more influential than the other two factors. Corresponding optimization measures are also proposed to improve the measuring accuracy.

Acoustic frequency analysis of the vibrational resonant frequencies of Special Nuclear Material containment

The increase of the resonant frequencies of a Magnox containment package that have been detected by an electromagnetic acoustic transducer and a microphone, are the result of an increase in internal pressure of the package. Therefore, it is possible to infer an internal pressure measurement of the Magnox package by measuring the shift of different resonant frequencies. A model of the Magnox package has been constructed to predict the acoustic vibrational resonant frequencies of the package wall and the corresponding mode shapes. Laser Doppler vibrometer measurements of the Magnox package wall have confirmed the presence of the predicted mode shapes and the resonant frequencies at which they occur have been reasonably estimated by the model.

Low-cost piezo-MEMS speaker technology

In this paper, we are reporting low-cost piezo-MEMS speakers based on an SOI-free process. The speaker membrane is made of a 1.5 μm thick polyimide passive layer, obviating the need for SOI wafers. The custom-made PZT solution for depositing 1 μm sol-gel PZT thin films has further reduced fabrication costs. The membranes are realized by a backside Deep Reactive Ion etching (DRIE) on the silicon wafer. Laser doppler vibrometer (LDV) characterization has shown the resonance frequency of a single speaker element with a diameter of 2.5 mm to be 30 kHz with a sensitivity of 100 mm/s/V, whereas sensitivity at 4 kHz is around 1.2 mm/S/V. The speaker element can produce around 70–90 dB in-ear Sound Pressure Level (SPL) response in audible frequencies (100 Hz – 10 kHz) at 5 V excitation as shown by a simulation in an ear-coupler which is in line with the LDV measurements. Moreover, on average, the fabricated 4 × 4 arrays have shown a 10 dB higher SPL than a single-speaker element as measured by a microphone.

Interpretation of bimodal interference in and optimized operational modal analysis for long-range continuously scanning laser Doppler vibrometer measurements with a beam under white noise excitation

This paper explains the phenomenon of a dominant frequency in the spectrum of a raw response measured by a long-range continuously scanning laser Doppler vibrometer (LCSLDV) system being symmetrically shifted into two sharp peaks. This phenomenon is referred to as bimodal interference in this work, which gradually becomes obvious when the scanning length is greater than 0.5 m. Bimodal interference is significant because it makes natural frequencies unable to be estimated in LCSLDV measurements and this paper analyzes its nature. Natural frequencies and mode shapes of a structure under white noise excitation can be estimated by analysis of its responses measured by the LCSLDV system. The effect of bimodal interference has been ignored in previous LCSLDV and continuously scanning laser Doppler vibrometer (CLSDV) measurement studies, but its appearance makes the value of the dominant frequency not to be accurately identified. By deducing mathematical interpretation of bimodal interference with analysis of incidence and reflection of a continuously scanning laser beam in a tiny time interval and comparing experimental results with 21 groups of different conditions, it is concluded that bimodal interference is caused by signal coupling between the scanning frequency of the mirror and the vibration frequency of the measured structure. There is a positive correlation between the scanning frequency and the magnitude of the symmetric frequency shifts centered at the dominant frequency generated by bimodal interference. In experimental results of LCSLDV measurements with a distance of 60 m, the frequency shift ratio compared to the dominant frequency can be reduced to 0.06% when the scanning frequency is lower than 0.01 Hz. In this case, bimodal interference is not noticeable in the spectrum. The experiment was carried out on a cantilever beam machined based on a prescribed design. Modal parameters of the cantilever beam estimated by white noise excitation were successfully estimated by the LCSLDV system with a distance of 60 m. The maximum difference between the first four natural frequencies of the cantilever beam from the finite element model and the LCSLDV system was 2.97% and the minimum difference was 1.1%.

A rail defect detection system based on laser Doppler vibrometer measurements

This paper aims at introducing a non-contact rail damage detection system based on laser Doppler vibrometer (LDV) measurements. Specifically, the system consists of two LDVs mounted on a rail car, to record the waves induced on the rail head by random rail-wheel interaction forces.The developed damage detection framework associated with the system is based on a multivariate analysis that combines damage features which are based on the relative change in amplitude of the LDV signals that are caused by both reflected and transmitted waves. In this study, the damage detection system is introduced and validated through field tests which were carried out at the Transportation Technology Center (TTC) in Pueblo, CO. In these tests, a rail car installed with the damage detection system traveled over a track that consisted of a discontinuity in the rail (i.e., welded joint) at different speeds up to 48 km/h (30mph). Results show that the proposed system can identify the rail segment in which the propagating waves on the rail head are affected by the presence of the welded joint.

Experimental characterization of a shape optimized acoustic lens: Application to compact speakerphone design

This work presents the shape optimization and subsequent experimental validation of an acoustic lens with application to a compact loudspeaker, such as found in commercial speakerphones. The shape optimization framework is based on a combined lumped parameter and boundary element method model using free form deformation geometry parameterization. To test the optimized design, the loudspeaker lens is three-dimensionally printed and experimentally characterized under anechoic conditions on a finite baffle with respect to its off-axis frequency response. The overall tendencies of the frequency responses agree well between measurement and simulations within the optimization frequency range and at low frequencies. The optimization process is applied to a model including acoustic lumped parameter approximations. The shortcomings of the assumptions made in the model are revealed by laser Doppler vibrometer measurements of the loudspeaker driver and modelling of the mechanical vibrations of the lens.

Finite element modelling of the human middle ear using synchrotron-radiation phase-contrast imaging

Finite element (FE) models of the middle ear often lack accurate geometry of soft tissue structures, such as the suspensory ligaments, as they can be difficult to discern using conventional imaging modalities, such as computed tomography. Synchrotron-radiation phase-contrast imaging (SR-PCI) is a non-destructive imaging modality that has been shown to produce excellent visualization of soft tissue structures without the need for extensive sample preparation. The objectives of the investigation were to firstly use SR-PCI to create and evaluate a biomechanical FE model of the human middle ear that includes all soft tissue structures, and secondly, to investigate how modelling assumptions and simplifications of ligament representations affect the simulated biomechanical response of the FE model. The FE model included the suspensory ligaments, ossicular chain, tympanic membrane, the incudostapedial and incudomalleal joints, and the ear canal. Frequency responses obtained from the SR-PCI-based FE model agreed well with published laser doppler vibrometer measurements on cadaveric samples. Revised models with exclusion of the superior malleal ligament (SML), simplification of the SML, and modification of the stapedial annular ligament were studied, as these revised models represented modelling assumptions that have been made in literature.

3D-printed custom ossicular prosthesis - methodology of design and LDV measurements in a cadaver study.

In tympanoplasty, surgical reconstruction of the tympanic membrane and ossicular chain is well-established; however, its hearing results still require improvement. Custom 3D printing of individualized ossicular prostheses seems to be an attractive solution for optimal prosthesis adjustment and better hearing results. The aim was to design a custom ossicular prosthesis using a 3D printing method based on Cone-beam Computed Tomography (CBCT) scans and assess the acoustic conduction properties of such prosthesis. A cadaver fresh frozen temporal bone was used. Based on CBCT images, a new incus prosthesis was designed and 3D printed. Next, canal wall-up tympanoplasty was performed. The intact ossicular chain and reconstructed 3D-printed prosthesis chain movements/vibrations were measured with Laser Doppler Vibrometer (LDV) system and analyzed in detail. The CBCT scans provided enough information about the anatomical structures. For frequencies 500 and 1000 Hz and 80 dB SPL sound intensity, collected velocities were higher for the intact ossicular chain than the 3D-printed ossicular prosthesis. The intensity thresholds for movement at 500 and 1000 Hz were lower in the intact ossicular chain than in the 3D-printed ossicular prosthesis. At 2000 Hz, there was the same intensity threshold value in the two measured circumstances. It is possible to design a custom individually fitted ossicular prosthesis using a 3D printing method based on CBCT scans. The acoustic conduction properties of such 3D-printed prosthesis showed differences in movability pattern between the intact and reconstructed ossicular chain. More data are needed to analyze the acoustic properties of such designed prostheses in detail. The results of our experiment showed the 3D-printed prosthesis presents the potential to be an interesting option for conductive hearing loss treatment caused by chronic otitis media and the ossicular chain defects.

Polar Coordinate for Damage Imaging of Adhesively Bonded Plates Using Ultrasonic Guided Waves and Laser Doppler Vibrometer Measurements

Wavefield measurements by a scanning laser Doppler vibrometer are generally carried out in a cartesian coordinate. As a piezoelectric transducer generates Lamb waves following radial paths, the use of a polar coordinate can be a suitable alternative to the use of a cartesian coordinate. Therefore, in the proposed method, using a single transducer placed on the center of the specimen, the measured wavefields are transformed into polar coordinates, making several identical radial line inspections from the center in a direction of incident waves. Taking advantage of the properties of the polar coordinates, a signal processing technique is proposed through a frequency-wavenumber filtering process in these coordinates. In this technique, by using proper filters, unwanted wave modes of the incident wave along with all reflected waves are filtered out. In addition, the conventional features of RMS and Euclidean distance are adapted for the polar coordinate system to image the bonded plate. The proposed signal processing and damage imaging are first introduced through a numerical simulation. Then, the performance of the proposed technique is presented by experimental measurements of two specimens including adhesively bonded carbon fiber-reinforced plastic composite plates and bonded aluminum plates.

Middle Ear Function Changes due to the Combined Effect of Pressure along with Fluid in Middle Ear Pressure Regulation- A Review

The pressure changes in Middle Ear (ME) are due to the effect of both fluid and pressure, which can be detected by tympanometry. In this review article, the mathematical and formal model of regulation of ME pressure is discussed. The air pressure in the ME chamber and the surrounding environment are the same. The auditory tube is a common connection between the ME chamber and the nasopharynx. The main functional role of the auditory tube is the ventilation of ME. When a person breathes air through an auditory tube, it enters into the ME and ventilates it. The ossicles in the ME collect sound from the tympanic membrane and transfer it to the inner ear, which requires proper ventilation of the ME. The auditory tube maintains ME pressure, the same as the external auditory canal and outside pressure. If an auditory tube is blocked, it leads to failure to ventilate ME, leading to changes in ME pressure. Swallowing and yawning allow the passive opening of the auditory tube and thus results in air flow out of the chamber. Easy and passive air exchange is allowed from the ME to the pharynx if, the pressure in the ME is higher than in the surrounding environment. ME pressure is highly variable and can change in many conditions. ME pressures increase when the body rotates from a vertical to a horizontal position because it increases the effusion of the ME mucosa due to an increase in hydrostatic pressure, which leads to an increase in the perfusion rate. Therefore, pressure increases in the case of sleeping and drowsiness. Regulation of ME pressure is a physiological process in which pressure between ME and the surrounding environment is maintained at equilibrium. The mechanism of pressure regulation is possible because of the complex sensory neural reflex pathway. A laser doppler vibrometer measures displacement of the tympanic membrane in response to sound and ME compliance is calculated by tympanometry. The movement of the tympanic membrane reduces due to the combined effect of fluid and pressure on the ME. The ME functions are altered due to the negative pressure of the fluid rather than the positive pressure.