Geometric phase sensing using cross-correlations for structural anomaly detection under broadband and stochastic excitations

We describe the geometric (Berry) phases arising when some quantum systems are driven by control classical parameters but also by outer classical stochastic processes (as, for example, classical noises). The total geometric phase is then divided into an usual geometric phase associated with the control parameters and a second geometric phase associated with the stochastic processes. The geometric structure in which these geometric phases take place is a composite bundle (and not an usual principal bundle), which is explicitly built in this paper. We explain why the composite bundle structure is the more natural framework to study this problem. Finally, we treat a very simple example of a two-level atom driven by a phase modulated laser field with a phase instability described by a Gaussian white noise. In particular, we compute the average geometric phase issued from the noise.

The properties of the geometric phases between three quantum states are\ninvestigated in a high-dimensional Hilbert space using the Majorana\nrepresentation of symmetric quantum states. We found that the geometric phases\nbetween the three quantum states in an N-state quantum system can be\nrepresented by N-1 spherical triangles on the Bloch sphere. The parameter\ndependence of the geometric phase was analyzed based on this picture. We found\nthat the geometric phase exhibits rich nonlinear behavior in a high-dimensional\nHilbert space.\n

A composite lattice structure has been used in an aircraft and a space launcher to reduce the structural weight. Defects can occur during fabrication because of structural complexity and they are mostly invisible as occurring inside a structure. Also, they lead to the deterioration of structural performance and expensive failures. Therefore, non-destructive evaluation (NDE) to detect defects should be conducted not to damage an initially intact part. So far, various NDEs methods have been attempted, however, a standard inspection method has not been proposed for the large and curved lattice structures. In this study, two modified rotational through-transmission (TT) ultrasonic propagation imagers (UPIs) are proposed to inspect a skinless cylindrical lattice structure and a conical lattice structure with skin. In the first case of the skinless cylindrical specimen, there is a problem with the breakdown of the laser Doppler vibrometer (LDV) when an ultrasonic generation beam directly entered the LDV through an empty space of the specimen. For this issue, a wavelength domain beam splitting mechanism was included in the system. A proof-of-concept for the proposed inspection setup was performed using unit cells of the lattice structure, and defects could be visualized. The results were reliable compared with the radiation tomographic results. We also inspected the full-scale skinless lattice structure and visualized its internal defects. Conventional radiographic and visual inspection verified the location to be the same as that obtained using the TT UPI. In the second case of the conic specimen with skin, there is a problem with a change in a stand-off distance due to its shape. The change of the stand-off distance causes a steady decrease in signal-to-noise ratio (SNR), a change in the incident angle of the LDV beam and a change in a time-of-flight (ToF) at a received signal. These make defect visibility worse. For this issue, an additional manual rotational stage was incorporated into the rotational TT UPI to ensure that the sensing beam from the LDV would be perpendicularly incident on the skin surface. First, an appropriate scanning width was determined by measuring the variation in the SNR based on the stand-off distance. Furthermore, a ToF compensation algorithm was used to match the arrival times of signals for conic geometry. Then, the full-scale conical lattice structure with skin was inspected, and de-bonding defect was visualized via ultrasonic wave propagation imaging. As a result, it was possible to quickly inspect a large area of composite lattice structures regardless of the shape condition.

White noise nonlinear system analysis in nuclear magnetic resonance spectroscopy

Non-negative intensity for planar structures under stochastic excitation

Composite layered materials offer many engineering advantages including high strength-to-weight ratio, tailorable material properties, and high fatigue resistance. Detection of small intra-layer delaminations that occur during manufacturing or while in the service environment are critical to ensure that the structure maintains its designed performance. Nondestructive evaluation (NDE) methods, such as ultrasonic testing, can identify hidden defects and damage, but detection can be challenging because the separated layers often remain in physical contact and prevent ultrasonic waves from scattering. Simultaneous multi-frequency excitation has the ability to incite contact acoustic nonlinearities and unique ultrasonic scattering patterns which can be observed within the ultrasonic signatures of the harmonics and mixing frequencies. Acoustic steady-state excitation spatial spectroscopy (ASSESS) is a full-field ultrasonic NDE inspection technique. ASSESS implements a steady-state ultrasonic excitation using a transducer and rapidly measures a structure’s surface velocity response using a laser Doppler vibrometer (LDV). The measurement product is a complex-valued wavefield response mapped to the surface geometry. This research investigates the presence of nonlinear signatures in a dual tone ASSESS measurement of a composite laminate panel with three impact delaminations. From a single measurement, complex velocity wavefield maps are calculated at the two excitation frequencies and additional harmonic and mixing frequencies. Contact acoustic nonlinearity signatures are identified as changes in response amplitude over certain frequencies. Spatial and temporal frequency and image processing methods are applied to individual wavefield images to identify damage locations.

This work presents a novel, non-destructive evaluation (NDE) method for detecting delaminations in fiber metal laminate (FML) plate-like structures. FMLs are rapidly replacing other materials in many aerospace applications because of their superior mechanical properties, including improved tolerance to fatigue, corrosion, and impact damage. However, delaminations can occur deep in the plate, and since access is limited to the composite face during most operations, the ability of traditional NDE techniques to discern these defects is limited. Many researchers have proposed using ultrasonic guided waves to image defects, but the anisotropic nature of wave propagation in FMLs and the subtlety of defects between metal and fiber-reinforced composite layers necessitate a new approach. In contrast to repeated transient excitations proposed in other literature, the method proposed here utilizes the full-field, steady-state response of an FML plate to ultrasonic excitation. Thus, the inspection time is shortened as the delay between measurements is removed, and a higher-energy input improves the signal-to-noise ratio. A 2D scanning laser Doppler vibrometer (LDV) is used to record the measurements at discrete points, while a piezoelectric transducer supplies the ultrasonic excitation. The steady-state response is processed to visualize defects on a pixel-by-pixel basis and locate potential regions of delamination in the FML plate. In this study, the one-dimensional response of a plate-like T800 graphite composite Ti-6Al-4V FML specimen with known areas of delamination is simulated. Two defect-detection features, based on simulated physical phenomena—detrended Hilbert envelope magnitude (DHEM) and low-pass local phase derivative (LLPD)—are subsequently evaluated over a wide range of excitation frequencies, to determine an optimal input for increased precision. Results from these simulations suggest potential guidelines to achieve a rapid and reliable NDE method for delamination detection in FML structures.KeywordsUltrasonic inspectionFiber metal laminate (FML)Composite-overwrapped pressure vessel (COPV)Acoustic wavenumber spectroscopy (AWS)Laser Doppler vibrometer (LDV)

In this work, a magneto-acousto-electrial tomography (MAET) method based on laser-generated ultrasound excitation was proposed for high-spatial-resolution images of the impedance of conductive media. Optically generated ultrasound is reported with broad bandwidth and insensitive to electromagnetic interference (EMI). Composite films were used as the optoacoustic sources, which composed of candle soot (CS) and elastomeric polymers. To characterize the laser-generated ultrasonic waves, laser Doppler vibrometer was adopted as the detecting device making the system totally optical while maintaining millimeter-level resolution and detective depths of several centimeter. Photoacoustic waves were then introduced to a sample of different conductivity distribution by laser-generated ultrasound transmitter at one point and detected by a pair of electrodes on the surface of the sample. Due to the absence of EMI between acoustic excitation and magnetic field, the combination of non-electronic ultrasound generator and low-cost, non-invasive MAET have shown its great capacity for effective early tumor assessment.

There is much interest in detecting a target and optical communications from an airborne platform to a platform submerged under water. Accurate detection and communications between underwater and aerial platforms would increase the capabilities of surface, subsurface, and air, manned and unmanned vehicles engaged in oversea and undersea activities. The technique introduced in this paper involves a Laser Doppler Vibrometer (LDV) for acousto-optic sensing for detecting acoustic information propagated towards the water surface from a submerged platform inside a 12 gallon water tank. The LDV probes and penetrates the water surface from an aerial platform to detect air-water surface interface vibrations caused by an amplifier to a speaker generating a signal generated from underneath the water surface (varied water depth from 1” to 8”), ranging between 50Hz to 5kHz. As a comparison tool, a hydrophone was used simultaneously inside the water tank for recording the acoustic signature of the signal generated between 50Hz to 5kHz. For a signal generated by a submerged platform, the LDV can detect the signal. The LDV detects the signal via surface perturbations caused by the impinging acoustic pressure field; proving a technique of transmitting/sending information/messages from a submerged platform acoustically to the surface of the water and optically receiving the information/message using the LDV, via the Doppler Effect, allowing the LDV to become a high sensitivity optical-acoustic device. The technique developed has much potential usage in commercial oceanography applications. The present work is focused on the reception of acoustic information from an object located underwater.

We introduce a method, topological acoustic sensing, which exploits changes in the geometric phase of acoustic waves to sense defects in some structure or environment. This method is illustrated in two cases of perturbations taking the form of (1) a mass defect located on an array of coupled acoustic waveguides, and (2) a small subwavelength object on a flat surface submerged under water. We represent the state of the acoustic field in the unperturbed and perturbed cases as multidimensional vectors. The change in geometric phase is obtained by calculating the angle between those vectors. This angle represents a rotation of the state vector of the wave due to scattering by the perturbation. By exploiting sharp topological features spanned by the acoustic field multidimensional state vector, we show that this geometric phase sensing modality can have higher sensitivity than magnitude-based sensing approaches.

Modal analysis using camera-based heterodyne interferometry and acoustic excitation

Acoustic landmine detection (ALD) is a technique for the detection of buried landmines including non-metal mines. An important issue in ALD is the acoustic excitation of the soil. Laser excitation is promising for complete standoff detection using lasers for excitation and monitoring. Acoustic excitation is a more common technique that gives good results but requires an acoustic source close to the measured area. In a field test in 2002 both techniques were compared side by side. A number of buried landmines were measured using both types of excitation. Various types of landmines were used, both anti-tank and anti-personnel, which were buried at various depths in different soil types with varying humidity. Two Laser Doppler Vibrometer (LDV) systems of two different wavelengths for the different approaches were used, one based on a He-Ne laser at 0.633 μm with acoustic excitation and one on an erbium fiber laser at 1.54 μm in the case of laser excitation. The acoustic excitation gives a good contrast between the buried mine and the surrounding soil at certain frequencies. Laser excitation gives a pulse response that is more difficult to interpret but is potentially a faster technique. In both cases buried mines could be detected.

Fibre metal laminates (FML) represent an innovative class of advanced composite materials that integrate the mechanical properties of both metals and fibre‐reinforced composites (FRP). Combining the strength and ductility of metals with the lightweight and high stiffness of FRP and FMLs have emerged as new material compositions for applications in chemical, nuclear, automobile, and aerospace engineering disciplines. Structural health monitoring (SHM) using guided ultrasonic waves (GUW) is the state‐of‐the‐art for non‐destructive testing of thin‐walled structures. When applied to FML, SHM plays a crucial role in monitoring the integrity over time and detecting potential damage such as delamination, fibre breakage, or other structural anomalies. In SHM with GUW, a wave‐field is emitted by actuators. This wave‐field can be affected by damage in the structure, thereby changing its propagation characteristics. Sensors monitor the interaction between damage and GUW, which can be utilized to locate and classify the damage and ascertain the overall health state of the structure. In this study, an advanced integration of measurement hardware, that is, sensors and actuators, within the laminate structure is investigated. Sensor integration into FML allows for improved and more sophisticated monitoring capabilities in comparison to measuring techniques like laser vibrometers, which are limited to measuring displacements on the surface of the structure. However, the integration of sensors and actuators yields the technical difficulty of distorting the wave‐fields and may result in an over‐ or underestimation of the damage. Similar to damage, the distortion of the wave‐field is caused by the changes in acoustic impedance resulting from different material properties. In a previous study, incorporating a functionally graded artificial interphase through acoustic impedance matching between the sensor and host material showed notable and significant outcomes. The current contribution extends the prior graded artificial interphase for an isotropic homogeneous material to an FML structure. This paper presents a comprehensive numerical simulation study on a two‐dimensional model of FML with integrated sensors. The interphases are designed based on impedance matching, which improves signal transmission and reduces disturbing reflections. The conducted investigations hold for several interphase configurations for a wide frequency range. The optimised integration of sensors demonstrates promising results for enhancing the reliability and accuracy of SHM systems. This research serves as a foundation for further experimental validation and the development of advanced sensor‐integrated FML structures with improved monitoring capabilities.

The Majorana's stellar representation, which represents the evolution of a quantum state with the trajectories of the Majorana stars on a Bloch sphere, provides an intuitive way to study a physical system with a high dimensional projective Hilbert space. In this Letter, we study the Berry phase by these stars and their loops on the Bloch sphere. It is shown that the Berry phase of a general spin state can be expressed by an elegant formula with the solid angles of Majorana star loops. Furthermore, these results can be used to a general state with arbitrary dimensions. To demonstrate our theory, we study a two mode interacting boson system. Finally, the relation between stars' correlations and quantum entanglement is discussed.

Several experiments have been carried out to investigate the mechanical vibrations generated by an organ pipe. Measurements were made by using Laser Doppler Vibrometry. It is a not-invasive optical measurement technique which allows to detect pipe-wall vibrations. The mechanical vibration field is compared with the acoustic field. Namely, we study the behaviour of these fields when they are excited by different levels of pressure. Strong analogies have been evidenced by using techniques in time e frequency domain supporting the assumption that the pipe is not a passive resonator. The challenge is to understand the complex mechanism of coupling between modes of air and eigen-modes of pipe that produces the sound. Here, we present, in first approximation, a low dimensional dynamical system which describes the main characteristics of pipe-wall vibrations. What is interesting is that the same low dimensional dynamical system is able to reproduce also the recorded acoustic field, implying that wall vibrations and acoustic pressure field are strictly related one to each other.