Circular Sensor Array Research Articles

Structural Health Monitoring Using Lamb Wave Reflections and Total Focusing Method for Image Reconstruction

This investigation aimed to adapt the total focusing method (TFM) algorithm (originated from the synthetic aperture focusing technique in digital signal processing) to accommodate a circular array of piezoelectric sensors (PZT) and characterise defects using guided wave signals for the development of a structural health monitoring system. This research presents the initial results of a broader study focusing on the development of a structural health monitoring (SHM) guided wave system for advance carbon fibre reinforced plastic (CFRP) composite materials. The current material investigated was an isotropic (aluminium) square plate with 16 transducers operating successively as emitter or sensor in pitch and catch configuration enabling the collection of 240 signals per assessment. The Lamb wave signals collected were tuned on the symmetric fundamental mode with a wavelength of 17 mm, by setting the excitation frequency to 300 kHz. The initial condition for the imaging system, such as wave speed and transducer position, were determined with post processing of the baseline signals through a method involving the identification of the waves reflected from the free edge of the plate. The imaging algorithm was adapted to accommodate multiple transmitting transducers in random positions. A circular defect of 10 mm in diameter was drilled in the plate, which is similar to the delamination size introduced by a low velocity impact event in a composite plate. Images were obtained by applying the TFM to the baseline signals, Test 1 data (corresponding to the signals obtained after introduction of the defect) and to the data derived from the subtraction of the baseline to the Test 1 signals. The result shows that despite the damage diameter being 40 % smaller than the wavelength, the image (of the subtracted baseline data) demonstrated that the system can locate where the waves were reflected from the defect boundary. In other words, the contour of the damaged area was highlighted enabling its size and position to be determined.

Three-dimensional underwater target localization with circular vector sensor array in strong reverberation environment

As reverberation can be regarded as an output of time-varying stochastic filtering of the emitted signal, it always leads to high false alarm in shallow water. In this case, some methods have been used to suppress reverberation such as empirical mode decomposition filter, match filter, etc. However, a strong correlation between transmitted signal and reverberation restricts the performance of these methods. In this paper,a novel method based on a circular vector sensor array is proposed to detect and locate multiple targets, respectively, in a strong reverberation environment by using the difference of the Doppler shift distribution between reverberation and target echo. First, spherical harmonic decomposition and beamforming are used to process the wideband signal and generate multiple beams which contain spatial information of interested region. Then, fractional Fourier transform is adopted to get Doppler shift distribution and localization information of reverberation and target echo. Multiple targets can be detected and located separately by estimating variance fluctuation associated with the reflections in different beams. Simulation result shows that this method performs efficiently and reliably in server reverberation environment without any prior information.

Design of Tunnel Magnetoresistive-Based Circular MFL Sensor Array for the Detection of Flaws in Steel Wire Rope

Tunnel magnetoresistive (TMR) devices have superior performances in weak magnetic field detection. In this study, TMR devices were first employed to form a circular magnetic flux leakage (MFL) sensor for slight wire rope flaw detection. Two versions of this tailor-made circular TMR-based sensor array were presented for the inspection of wire ropes with the diameters of 14 mm and 40 mm, respectively. Helmholtz-like coils or a ferrite magnet-based magnetizer was selected to provide the proper magnetic field, in order to meet the technical requirements of the TMR devices. The coefficient of variance in the flaw detection performance of the sensor array elements was experimentally estimated at 4.05%. Both versions of the MFL sensor array were able to detect multiple single-broken wire flaws in the wire ropes. The accurate axial and circumferential positions of these broken wire flaws were estimated from the MFL scanning image results. In addition, the proposed TMR-based sensor array was applied to detect the MFL signal induced by slight surface wear defects. A mutual correlation analysis method was used to distinguish the signals caused by the lift-off fluctuation from the MFL scanning image results. The MFL sensor arrays presented in this study provide inspiration for the designing of tailor-made TMR-based circular sensor arrays for cylindrical ferromagnetic structural inspections.

Robust high-order superdirectivity of circular sensor arrays.

This paper presents a detailed study of the high-order superdirectivity of circular sensor arrays, which is aimed at completing the authors' recently proposed analytical superdirectivity model. From the limit expression of the maximum directivity factor, it is shown that the circular arrays possess good potential for directivity improvement. It is found that the sensitivity function used as a robustness measurement can also be accurately decomposed into a series of closed-form sensitivity functions of eigenbeams, similar to the optimal beampattern and its corresponding directivity factor. Moreover, the performance of eigenbeams can be regarded as an indicator of error sensitivity, and the robustness constraint parameters can be estimated easily. Two specific approaches are proposed for obtaining robust superdirectivity on the basis of robustness analyses, and their performance is demonstrated experimentally.

Broadband pattern synthesis for circular sensor arrays.

The solutions of pattern synthesis are derived for circular sensor arrays based on the criterion of minimizing the mean square error between the desired and synthesized beampatterns. Specifically, the optimal weighting vector, the output beam, and the minimum mean square error are all expressed in closed-form exactly when the desired beampattern is properly formulated. These results provide a more effective and convenient scheme for designing practical frequency-invariant beamformers. Simulations and experimental results demonstrate the performance of the proposed approach.

Moving Defect Localization of Wheel-Bearings with Particle Filter and MUSIC

To solve the problem of moving defect localization for wheel-bearings, a novel algorithm based on particle filter and multiple signal classification (MUSIC) is proposed in this paper. It introduces two-dimensional circular sensor array to measure acoustic signals of defective bearings. By through of MUSIC, the direction-of-arrivals (DOAs) of defective signal are firstly estimated. After the motion trajectory was calculated by particle filter and DOAs, the defect was located by reference sound source. The experimental results show that the radius and phase errors of proposed method are less than 2mm and 5 degrees.

Location of partial discharge in transformer oil using circular array of ultrasonic sensors

Partial discharge (PD) in transformer oil is one of the major causes of electrical insulation failures in oil transformers. An accurate location of PD provides important information required for detection and elimination of insulation defects. To improve accuracy of PD location, a new location method is proposed in this paper based on using circular array of ultrasonic sensors (CAUS) and implemented as follows. First, the fast independent component analysis (FastICA) algorithm is used to de-noise PD signal obtained by CAUS. Second, the total least square (TLS) algorithm is used to transform the wide-band signal obtained by CAUS to the narrowband one. Third, the mode excitation algorithm and the fast direction of arrival (FastDOA) algorithm are combined together to find three different directions of arrival (DOA) of the signal from PD to CAUS. Next, using the azimuth and pitch angles of these three DOAs, the PD location is determined in the center of a sphere whose surface tangents to these three DOAs in three different planes. Finally, the improved genetic algorithm is used to obtain accurate coordinates of the PD source. An experimental system of PD-location has been developed, which consists of (i) CAUS made of 8 sensors evenly placed along a circle, and a single sensor placed in the center of the circle, (ii) classic three-capacitance PD model, (iii) 16-channel synchronous data collector, (iv) oil tank, and (v) computer. The preliminary experimental results show that the accuracy of PD location after denoising is better than that before de-noising.

Theoretical and Practical Solutions for High-Order Superdirectivity of Circular Sensor Arrays

An analytical and closed-form optimal solution expressed in elementary functions for superdirectivity of a circular sensor array is proposed in this paper. By utilizing the circulant property of the data covariance matrix for circular sensor arrays, such solutions are derived to accurately calculate the optimal beamforming vector, optimal beam pattern, corresponding directivity factor, and eigenbeams. Based on these solutions, it is proved that such array possesses several important properties which facilitate an eigenbeam decomposition and synthesis approach for practical implementations. Experiments conducted result in superdirective beams which contain zeroth- to fifth- and sixth-order eigenbeams. As a typical result, the superdirective beam which contains zeroth- to fifth-order eigenbeams has a 28 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">°</sup> beamwidth and a 12-dB directivity index with a small circular array radius of 0.267 wavelength.

Resolution and robustness to noise of the sensitivity-based method for microwave imaging with data acquired on cylindrical surfaces

The spatial resolution limit of a Jacobian-based microwave imaging algorithm and its robustness to noise are evaluated. The focus here is on tomographic systems where the wideband data are acquired with a vertically scanned circular sensor array and at each scanning step a 2D image is reconstructed in the plane of the sensor array. The theoretical resolution is obtained as one-half of the maximum-frequency wavelength with far-zone data and about two-thirds of the array radius with near-zone data. Validation examples are given using analytical electromagnetic models. The algorithm is shown to be robust to noise when the response data are corrupted by Gaussian white noise.

Flow Measurement of Biomass and Blended Biomass Fuels in Pneumatic Conveying Pipelines Using Electrostatic Sensor-Arrays

Key parameters such as particle velocity, concentration of solid particles, and stability of pulverized fuel flow in fuel injection pipelines are useful to power plant operators to detect fuel supply problems at an early stage. This paper presents the use of a novel multichannel instrumentation system with circular and arc-shaped electrostatic sensor arrays for the online continuous measurement of “mean” and “local” characteristics of blended biomass flow. Experimental tests were conducted on a pneumatic conveying test rig under various flow conditions on both horizontal and vertical pipes. The biomass fuels tested include willow, wood, and bark. A ground grain (flour) was used to replicate a biomass of finer particles. The results suggest that, due to the physical differences between the constituent biomass fuels, the characteristics of the flow depend on the proportion of larger biomass particles in the blend. It is found that pure flour particles travel faster and carry more electrostatic charge than those of larger biomass particles. As more biomass particles are added to the flow, the overall velocity of the flow slows down, the electrostatic charge level decreases, and the flow becomes less stable compared to the pure flour flow. Particles in the vertical pipe are found to be more evenly distributed, and the particle velocity profile across the pipe cross section is more regular when compared to those in the horizontal pipe.

A Lamb Wave Based Method for the Assessment of Faults in Aluminium Plates

The location and assessment of the damage severity are important steps in structure health monitoring systems. This paper presents a method for locating and assessing the severity of damages in aluminum plates using a Lamb wave approach through a circular array of sensors and a centered actuator. The signals measured by the sensors were processed using the discrete wavelet transform and Hilbert transform to obtain the envelope of these signals. The location and the damage index were obtained from the analysis of the first Lamb wave package peak. The experimental results showed the effectiveness of this method in damage location and in the assessment of the evolution of its severity.

Ultrasonic Lamb wave based monitoring of corrosion type of damage in plate using a circular array of piezoelectric transducers

In this paper we propose a concept and report experimental results based on a circular array of Piezoelectric Wafer Active Sensors (PWASs) for rapid localization and parametric identification of corrosion type damage in metallic plates. Implementation of this circular array of PWASs combines the use of ultrasonic Lamb wave propagation technique and an algorithm based on symmetry breaking in the signal pattern to locate and monitor the growth of a corrosion pit on a metallic plate. Wavelet time-frequency maps of the sensor signals are employed to obtain an insight regarding the effect of corrosion growth on the Lamb wave transmission in time-frequency scale. We present here a method to eliminate the time scale, which helps in identifying easily the signature of damage in the measured signals. The proposed method becomes useful in determining the approximate location of the damage with respect to the location of three neighboring sensors in the circular array. A cumulative damage index is computed from the wavelet coefficients for varying damage sizes and the results appear promising. Damage index is plotted against the damage parameters for frequency sweep of the excitation signal (a windowed sine signal). Results of corrosion damage are compared with circular holes of various sizes to demonstrate the applicability of present method to different types of damage.

Optimally overlapped ultrasonic sensor ring design for minimal positional uncertainty in obstacle detection

This paper presents the optimal overlapping arrangement of a circular array of ultrasonic sensors for minimal positional uncertainty in obstacle detection. First, it is shown that beam overlap among three adjacent ultrasonic sensors leads to significant reduction of positional uncertainty. Second, the positional uncertainty of an overlapped ultrasonic sensor ring is compared to a single ultrasonic sensor in terms of a collision-free region with obstacles. Third, the optimal design index for an overlapped ultrasonic sensor ring is defined as the area closest between the non-overlapped and overlapped sensing sub-zones. Fourth, using commercial low directivity ultrasonic sensors, an optimally overlapped ultrasonic sensor ring is given along with its prototype installed on top of a mobile robot. Finally, experimental results are given to demonstrate the validity and performance of our overlapped ultrasonic sensor ring prototype.

Rapid localization of damage using a circular sensor array and Lamb wave based triangulation

A damage detection and imaging methodology based on symmetry of neighborhood sensor path and similarity of signal patterns with respect to radial paths in a circular array of sensors has been developed. It uses information regarding Lamb wave propagation along with a triangulation scheme to rapidly locate and quantify the severity of damage without using all of the sensor data. In a plate like structure, such a scheme can be effectively employed besides full field imaging of wave scattering pattern from the damage, if present in the plate. This new scheme is validated experimentally. Hole and corrosion type damages have been detected and quantified using the proposed scheme successfully. A wavelet based cumulative damage index has been studied which shows monotonic sensitivity against the severity of the damage, which is most desired in a Structural Health Monitoring system.

Lamb Wave Based Monitoring of Plate-Stiffener Deboding using a Circular Array of Piezoelectric Sensors

Abstract In this paper we propose an efficient way of localization and parametric identification of metallic plate-stiffener debonding. A concept and experimental results based on a circular array of Piezoelectric Wafer Active Sensors (PWASs) is presented. Implementation of this circular array of PWASs combines the Lamb wave technique and symmetry breaking in the signal pattern to monitor the growth of a debonding of a stiffener on a metallic plate. Wavelet time-frequency maps of the sensor signals are employed and a damage index is plotted against the damage parameters for frequency sweep of the excitation signal (a windowed sine signal). Wavelet coefficient in time gives an insight regarding the effect of debonding growth on the Lamb wave transmission in time-frequency scale. We present here a method to eliminate the time scale effect which helps in identifying easily the signature of damage in the measured signals including the reflection from the boundary of the plate. The proposed method becomes useful in determining the approximate location of the damage with respect to the location of three neighboring sensors in the circular array. A cumulative damage index is computed for varying damage sizes and the results appear promising.

Assessing the applicability of the spatial autocorrelation method: A theoretical approach

We present a rigorous theoretical framework that allows one to assess the range of applicability of the spatial autocorrelation (SPAC) method, a technique of microtremor exploration that is widely used to infer phase velocities of Rayleigh waves using vertical‐motion records from a circular array of seismic sensors. The magnitude of systematic errors (biases) that depend on the number of seismic sensors deployed around the circle, and the magnitude of systematic errors that arise from the presence of incoherent noise, are both evaluated analytically, and their general properties are discussed. The relationship between the magnitude of stochastic errors, inherent in the analysis results, and the duration of measurement (or to put it more accurately, the data's degree of freedom) is also elucidated. The validity of our theory is corroborated by checks against the results of both real data analysis and numerical experiments, and an example is given of how the theory can be adapted to account for practical situations encountered in the field. Discussions on the range of applicability of the SPAC method, which have heretofore often fallen back on empirical observations, have now obtained a theoretical ground on which to stand, providing a basis for strategies to make maximal use of the SPAC method's capabilities.

Beyond the SPAC Method: Exploiting the Wealth of Circular-Array Methods for Microtremor Exploration

We explore the wealth of alternative methods for inferring phase velocities of Rayleigh waves using vertical-component seismograms of microtremors from a circular array of seismic sensors, which are formulable along the extension of the popularly used spatial autocorrelation (SPAC) method. Four such methods are illustrated here: the centerless circular-array (CCA) method, the Henstridge methods of the zeroth and first orders (the H0 and H1 methods, respectively), and what we tentatively call the fifth (V) method. Different methods of phase velocity estimation have different wavelength ranges of good resolution. Implementation to field data from two sites reveals that the traditional SPAC method and the H0 method are both capable of producing reasonable estimates of Rayleigh-wave phase velocities within a relatively narrow range on the short-wavelength side, whereas the H1 method is valid in a relatively narrow range on the long-wavelength side. The CCA and V methods both remain valid over a very broad range of wavelengths, the upper limit extending as far up as several 10s of times the array radius. Use of a noise-compensation technique can further prolong the maximum resolvable wavelength of the CCA method. We also illustrate the field performance of circle phase methods, which give, without recourse to the conventional frequency-wavenumber analysis, estimates for the principal arrival directions of Rayleigh waves on the basis of circular-array seismograms of microtremors.

2-D spatial-spectrum estimation for wide-band sources based on interpolated circular arrays

In array signal processing, 2-D spatial-spectrum estimation is required to determine DOA of multiple signals. The circular array of sensors is found to possess several nice properties for DOA estimation of wide-band sources. C. U. Padmini, et al. (1994) had suggested that the frequency-direction ambiguity in azimuth estimation of wide-band signals received by a uniform linear array (ULA) can be avoided by using a circular array, even without the use of any delay elements. In 2-D spatial-spectrum estimation for wide-band signals, the authors find that it is impossible to avoid the ambiguity in source frequency-elevation angle pairs using a circular array. In this paper, interpolated circular arrays are used to perform 2-D spatial-spectrum estimation for wide-band sources. In the estimation, a large aperture circular array (r > λmin/2) is found to possess superior resolution capability and robustness.

Diffraction tomographic imaging with a circular array

A new approach of imaging an object profile from the scattered wavefield, which is measured using a large (far field approximation) circular array of sensors surrounding the object, is described. It is shown that the measured field is itself proportional to the Fourier transform of the object. Consequently, as compared to the existing methods, such as back propagation method for a linear array, our method overcomes the well known effects of the finite window in numerical evaluation of the Fourier transform of the measured scattered field. This results into improved reconstruction. >

Investigation of Bubbly Flow by Ultrasonic Tomography

AbstractComputerized tomography (CT) means reconstruction of pictures from projections taken at different angles. This method is well known in fields such as medical diagnostics and nondestructive testing. The application of CT to gas/liquid flow measurement results in a non‐intrusive method for measuring the spatial distribution of the gas phase in a cross‐section of the flow. In our application the projection data are obtained from measurement of the extinction along a set of ultrasonic rays in this cross‐section, using piezo‐ceramic ultrasonic transducers. The transducers are arranged in a circular sensor array which is directly integrated in the pipe wall of the flow; instead of mechanical rotation, the sensors are sequentially switched.