Full Matrix Research Articles

Comparative study of advanced image reconstruction algorithms for complex arbitrary components

Accurate ultrasonic imaging and inspection of specimens with non-planar complex surfaces are often challenging from both transducer coupling and imaging perspectives. Several inspection strategies have been developed to inspect such complex interfaced components such as flat arrays with flexible wedges or water-filled chambers with a flexible membrane. In these methods, firstly surface profiles are estimated and then Fermat’s principle or other algorithms are applied to calculate delay laws. The main drawback of these methods is the longer computation time and therefore real time inspection is limited, also a coupling problem due to the complex geometries. Alternative approaches have been developed to compute the ultrasonic beam paths such as the Fast-Marching Method (FMM), Dijkstra’s algorithms, numerical analysis, bisection and root-finding algorithms for the inspection of complex surface components. These algorithms can be applied in two and three-dimensional domains resulting in high computation time. This work presents an experimental comparison of an iterative beamforming method for arbitrary shaped surface profile imaging against both Full Matrix Capture-Total Focusing Method (FMC-TFM) and CIVA simulation on an aluminium calibration block with Side drilled holes (SDHs) at various depths in the range of 15-80 mm. The performance of the iterative beamforming method is evaluated in terms of sensitivity, Signal to Noise Ratio (SNR) and Array Performance Indicators (API). The method provides a 2 dB improved SNR when compared to FMC-TFM.

Ultrasonic sectorial inspection in the presence of temperature gradients

Ultrasonic nondestructive testing is a precise tool for equipment inspections. Among the usual methods, sectorial scanning stands out within contact-based techniques, as it provides broad angular sweeps without the need to physically steer the transducer, and the configuration of the beams hinges on the geometry of the tested objects. However, in high-temperature scenarios (e.g., oil treatment vessels), thermal gradients along the propagation path result in inaccurate sizing of discontinuities, given that the presence of such gradients is responsible for variations in the velocities and distortions of the ultrasonic beams. This paper proposes a method to compensate for these distortions during the sectorial inspection. Optimal linear approximation parameters are determined offline from a controlled Full Matrix Capture (FMC) test, in which the setup consists of a phased array transducer, a high-temperature resistant wedge and an aluminium test block with flaws at known positions. The positions of the flaws are measured on the Total Focusing Method (TFM) reconstructions, and the parametric velocity models for specific instants of heating time are estimated through the minimization of a cost function. Then, focal laws are calculated from the parameters using the ray tracing technique and stored in a text file to be interpreted by the instruments as a native focal law. An online test is proposed for validating the method at the controlled temperature of 70oC. The results show that the positions of the flaws, and the distance between them in the S-scan image, present improved accuracy (with errors reduced by approximately 64%) when the proposed correction is applied.

Total Focusing (TFM) for the Ultrasonic Testing (UT) of drawn arc stud welding

This article describes the results obtained applying ultrasonic testing (UT) with phased arrays (PAUT) using full matrix capture (FMC) and total focusing method (TFM) for the inspection of drawn arc stud welding. Weld studs are usually directly applied on the top of a metal slab using a dedicated welding gun. This procedure involves heating the end tip of the stud using a strong electric arc created by a positive electric current. This welding procedure shall comply to various normative requirements, but on the other side there is not a clear reference to any applicable non-destructive method (NDT) to control the quality of the weld seam. Shear connectors are normally used in concrete/steel composite structures to allow the combined action of the concrete slab and the steel profile thereby increasing both the stiffness and strength of the structure. Flaws in this connection would result in severe bending and cracking of the entire structure. This article proposes an advanced UT method to inspect the weld between shear connections and metal slab using FMC. Data acquired with FMC are processed by TFM algorithms improving image resolution, signal to noise performances and allowing 3D data imaging. The combined use of PAUT searching units and signal processing with high resolution measurement shows a great potential in industrial NDT applied to civil engineering, resulting in a more effective, reliable, and faster inspection methodology than many other methods, such as radiographic testing (RT).

Inspection for non-planar shaped welded joints of pipes using FMC ultrasonic technique

In applying ultrasonic testing (UT) to pipes with welded joints, one of the challenges is about the access limitation of UT probes caused by non-planar weld reinforcement profiles. One way to avoid this problem is to remove weld reinforcement for ensuring the contactability of a probe on welded parts. However, the removing process for flatten weld reinforcement needs extra day per joint and might damage pipes surface. To overcome this issue, we have been developing a proprietary UT method that enables inspection of non-planar welded joints using the Full Matrix Capture (FMC) and the Total Focusing Method (TFM). A specially designed wedge is used between a probe and a welded part in order to extract the weld surface shape from the recorded data. In the TFM, multilayer propagation paths are analyzed with considering refractions at interfaces between the layer and the weld surface. The analysis is based on the Fermat's principle of least time, whereas this is generally known to be a time-consuming process. With the aim of performing real-time scanning in inspection to pipes on weld reinforcement, the shape of the wedge is optimized for welded joints to reduce the calculation time of the multilayer analysis. In this presentation, we will report the developed FMC/TFM technique and, furthermore, the validation results using pipe specimens with weld reinforcement.

Advanced Ultrasonic Inspection of Thick-Section Composite Structures for In-Field Asset Maintenance.

An investigation into the inspection capabilities of in-field advanced ultrasound detection for use on ultra-thick (20 to 100 mm) glass fibre-reinforced polyester composites is presented. Plates were manufactured using custom moulding techniques, such that delamination flaws were created at calibrated depths. The full matrix capture technique with an on-board total focussing method was used to detect flaws scanned by a 0.5 MHz linear array probe. Flaw through-thickness dimensions were altered to assess the threshold for crack face separation at which delaminations could be identified. Furthermore, part thickness and in-plane flaw dimensions were varied to identify the inspection capability limitations of advanced ultrasonics for thick composites. The results presented in this study demonstrate an inverse relationship between the ability to find delaminations and plate thicknesses, with inspections successful at depths up to 74 mm. When the delamination thickness exhibited surface-to-surface contact, the inspection capability was reduced to 35 mm. There was an exponential decay relationship between the accuracy of the flaw depth measurement and plate thickness, likely due to the necessity of low probe frequencies. The effective inspection depth was determined to be in the range of 1 to 20 times the wavelength. It is speculated that the accuracy of measurements could be improved using probes with novel coupling solutions, and detectors with optimised signal processing/filtration algorithms.

Fast hierarchical low-rank view factor matrices for thermal irradiance on planetary surfaces

We present an algorithm for compressing the radiosity view factor model commonly used in radiation heat transfer and computer graphics. We use a format inspired by the hierarchical off-diagonal low rank format, where elements are recursively partitioned using a quadtree or octree and blocks are compressed using a sparse singular value decomposition—the hierarchical matrix is assembled using dynamic programming. The motivating application is time-dependent thermal modeling on vast planetary surfaces, with a focus on permanently shadowed craters which receive energy through indirect irradiance. In this setting, shape models are comprised of a large number of triangular facets which conform to a rough surface. At each time step, a quadratic number of triangle-to-triangle scattered fluxes must be summed; that is, as the sun moves through the sky, we must solve the same view factor system of equations for a potentially unlimited number of time-varying righthand sides. We first conduct numerical experiments with a synthetic spherical cap-shaped crater, where the equilibrium temperature is analytically available. We also test our implementation with triangle meshes of planetary surfaces derived from digital elevation models recovered by orbiting spacecraft. Our results indicate that the compressed view factor matrix can be assembled in quadratic time, which is comparable to the time it takes to assemble the full view matrix itself. Memory requirements during assembly are reduced by a large factor. Finally, for a range of compression tolerances, the size of the compressed view factor matrix and the speed of the resulting matrix vector product both scale linearly (as opposed to quadratically for the full matrix), resulting in orders of magnitude savings in processing time and memory space.

Transport coefficients for ion and solvent coupling. The case of the lithium-ion battery electrolyte.

Transport properties are essential for the understanding and modeling of electrochemical cells, in particular complex systems like lithium-ion batteries. In this study, we demonstrate how a certain degree of freedom in the choice of variables allows us to efficiently determine a complete set of transport properties. We apply the entropy production invariance condition to different sets of electrolyte variables and obtain a general set of formulas. We demonstrate the application of these formulas to an electrolyte typical for lithium-ion batteries, 1M lithium hexafluoro-phosphate in a 1:1 wt. % mixture of ethylene and diethyl carbonates. While simplifications can be introduced, they provide inadequate predictions of conductivity and transport numbers, and we argue that a full matrix of Onsager coefficients is needed for adequate property predictions. Our findings highlight the importance of a complete set of transport coefficients for accurate modeling of complex electrochemical systems and the need for careful consideration of the choice of variables used to determine these properties.

On the minimal faithful degree of Rhodes semisimple semigroups

In this paper we compute the minimal degree of a faithful representation by partial transformations of a finite semigroup admitting a faithful completely reducible matrix representation over the field of complex numbers. This includes all inverse semigroups, and hence our results generalize earlier results of Easdown and Schein on the minimal faithful degree of an inverse semigroup. It also includes well-studied monoids like full matrix monoids over finite fields and the monoid of binary relations (i.e., matrices over the Boolean semiring). Our answer reduces the computation to considerations of permutation representations of maximal subgroups that are faithful when restricted to distinguished normal subgroups. This is analogous to (and inspired by) recent results of the second author on the minimal number of irreducible constituents in a faithful completely reducible complex matrix representation of a finite semigroup that admits one. To illustrate what happens when a finite semigroup does not admit a faithful completely reducible representation, we compute the minimal faithful degree of the opposite monoid of the full transformation monoid.

Fabrication, microstructure and mechanical properties of TiAl matrix composite reinforced by submicro/nano-Ti2AlC

In the present work, using pre-alloyed Ti-48Al-2Cr-2Nb powders and graphene nanosheets as raw materials, the TiAl matrix composite reinforced by submicro/nano-Ti2AlC was fabricated via spark plasma sintering and subsequent heat-treatment. The microstructure characterization results have indicated that submicro-Ti2AlC and nano-Ti2AlC exhibit the coherent atomic correspondence with the full lamellar TiAl matrix. Furthermore, The Ti2AlC/TiAl composite has excellent balance relationship of room-temperature compression strength (∼2171 ± 3 MPa) and fracture strain (∼31 ± 1%). The submicro-Ti2AlC could effectively hinder the twin propagation and inhibit the dislocations motion, which is benefit to improve the strength of the Ti2AlC/TiAl composite. In addition, the nano-Ti2AlC could not only cause the dislocation multiplication in γ-TiAl by the activation of pyramidal dislocations, but also induce the formation of deformation twins in γ-TiAl by the basal-plane slip, resulting in the improvement of plastic deformation capacity in the Ti2AlC/TiAl composite.

FMC/TFM Technique Design Using the FMC Beamset in BeamTool

Eclipse Scientific’s BeamTool software has supported Full Matrix Capture/Total Focusing Method (FMC/TFM) technique design through the FMC Beamset since version 9.0 (released in 2017). With the release of BeamTool 10.1, however, the FMC Beamset now includes more sophisticated tooling to help users design FMC/TFM based inspection techniques – these include: Sensitivity, Focal Area and Resolution maps which together allow users to quickly assess how similar reflectors will be imaged (amplitude, shape, size) throughout the chosen region of interest. For each of these focal metrics, the absolute minimum and maximum values are provided along with other helpful derived quantities (amplitude fidelity, maximum sensitivity difference) which allows the influence of probe and wedge parameters to be compared directly. This document details what these new focal metrics are as well as how to use them to optimize FMC/TFM based techniques for various common applications. It is assumed that the reader is familiar with the principles of FMC/TFM and the BeamTool software.

BEYONDPLANCK

We present a Gibbs sampling solution to the mapmaking problem for cosmic microwave background (CMB) measurements that builds on existing destriping methodology. Gibbs sampling breaks the computationally heavy destriping problem into two separate steps: noise filtering and map binning. Considered as two separate steps, both are computationally much cheaper than solving the combined problem. This provides a huge performance benefit as compared to traditional methods and it allows us, for the first time, to bring the destriping baseline length to a single sample. Here, we applied the Gibbs procedure to simulatedPlanck30 GHz data. We find that gaps in the time-ordered data are handled efficiently by filling them in with simulated noise as part of the Gibbs process. The Gibbs procedure yields a chain of map samples, from which we are able to compute the posterior mean as a best-estimate map. The variation in the chain provides information on the correlated residual noise, without the need to construct a full noise covariance matrix. However, if only a single maximum-likelihood frequency map estimate is required, we find that traditional conjugate gradient solvers converge much faster than a Gibbs sampler in terms of the total number of iterations. The conceptual advantages of the Gibbs sampling approach lies in statistically well-defined error propagation and systematic error correction. This methodology thus forms the conceptual basis for the mapmaking algorithm employed in the BEYONDPLANCKframework, which implements the first end-to-end Bayesian analysis pipeline for CMB observations.

Automated defect recognition (ADR) for monitoring industrial components using neural networks with phased array ultrasonic images

In this paper, we propose a framework to automate the process of defect characterizing for industrial structural component health monitoring by implementing automatic defect recognition (ADR) system. The ADR system consists of a convolutional neural network (CNN) and an edge detection algorithm medial axis transform (MAT). The CNN learns the defect feature space from the training dataset to detect and classify the defect. The MAT algorithm is used upon post-validation of the ADR, and the predicted feature’s edges are extracted to size them. The ADR is trained using the simulation-assisted finite element (FE) simulation datasets consisting of side drilled holes (SDH) and crack defects images. The training datasets are generated by introducing virtual array source aperture (VASA), which is a full matrix capture (FMC) scanning strategy by activating the group of elements in an active aperture with predefined focal laws to form a focused beam at a virtual source in the material. The VASA technique uses multiple virtual sources and active aperture positions in a given transducer, which are determined using the Poisson point process. The ultrasound beam is excited in sequence on each virtual source, and the reflected wave is recoded using all the transducers in the array to create FMC A-scans signals. The total focusing method (TFM) technique is a postprocessing algorithm implemented on the FMC signal to generate an image. A large quantity of training datasets is created for each defect by modeling various FE models with varying defect morphology. To create nearly close to experimental images, the experimental noise is introduced in the simulated images. The three separate ADR systems are trained with individual defects class and combined defects. The effectiveness of the trained ADR system is validated by conducting experiments on the plates with laboratory-made SDH and crack defects, the casting components, and weldments with unknown defect types and sizes. The mAP of ADR training is 82%, and the F1-score on testing image classification is 89%. The ADR system could detect and size the smallest defect is 0.219 mm, which is λ L /5.

Model-independent search for anisotropies in stochastic gravitational-wave backgrounds and application to LIGO-Virgo’s first three observing runs

A stochastic gravitational-wave (GW) background consists of a large number of weak, independent and uncorrelated events of astrophysical or cosmological origin. The GW power on the sky is assumed to contain anisotropies on top of an isotropic component, i.e., the angular monopole. Complementary to the LIGO-Virgo-KAGRA (LVK) searches, we develop an efficient analysis pipeline to compute the maximum-likelihood anisotropic sky maps in stochastic backgrounds directly in the sky pixel domain using data folded over one sidereal day. We invert the full pixel-pixel correlation matrix in map-making of the GW sky, up to an optimal eigenmode cutoff decided systematically using simulations. In addition to modeled mapping, we implement a model-independent method to probe spectral shapes of stochastic backgrounds. Using data from LIGO-Virgo's first three observing runs, we obtain upper limits on anisotropies as well as the isotropic monopole as a limiting case, consistent with the LVK results. We also set constraints on the spectral shape of the stochastic background using this novel model-independent method.

Compressive sensing of ultrasonic array data with full matrix capture in nozzle welds inspection

The phased array ultrasonic technique (PAUT) with full matrix capture (FMC) exhibits the advantages of high imaging accuracy and great defect characterization ability, which play important roles in the nondestructive testing of welded structures. To address the problem of a large amount of signal acquisition, storage, and transmission data in nozzle weld defect monitoring, a PAUT with an FMC data compression method based on compressive sensing (CS) was proposed. To accomplish this, the detection of nozzle welds using PAUT with FMC was performed by simulation and experiment, and the obtained FMC data were compressed and reconstructed. A suitable sparse representation was found dedicated to the FMC data of nozzle welds, and the reconstruction performance was compared between the greedy theory-based orthogonal matching pursuit (OMP) algorithm and the convex optimization theory-based basis pursuit (BP). Also, an empirical mode decomposition (EMD)-based intrinsic mode function (IMF) circular matrix was constructed to provide another idea for the construction of the sensing matrix. Although the experimental results were not able to reach the ideal effect in the simulation, the image was restored accurately with a small number of measured values, and flaw identification could be guaranteed, indicating that the CS algorithm can effectively improve the defect detection efficiency of the phased array.

Generalized result on the global existence of positive solutions for a parabolic reaction diffusion model with a full diffusion matrix

"In this paper, we study the global existence in time of solutions for a parabolic reaction di usion model with a full matrix of di usion coe cients on a bounded domain. The technique used is based on compact semigroup methods and some estimates. Our objective is to show, under appropriate hypotheses, that the proposed model has a global solution with a large choice of nonlinearities."

A robust experimental design for conceptual model discrimination based on information theory

This study introduces firm information gain for model discrimination based on Shannon entropy and worst-case scenario experimental design. Firm information gain is the minimal additional information gained by an experimental design with respect to existing information. Robust experimental design aims to maximize the firm information gain by searching for the least number of new pumping wells and observation wells. Robust experimental design includes a Bayes factor threshold to ensure that new data provide strong evidence for model discrimination. To maximize the firm information gain, a framework is proposed that combines the parallel-sequential genetic algorithm (GA) for parallel computing and the nested quadrature rule for efficiently solving multidimensional integrals. The numerical experiment involves the true model for the purpose of verification. The results show that using a full covariance matrix is imperative to avoid exaggerating firm information gain. Collecting new groundwater data is prioritized over exploring additional pumping wells. Maximizing firm information gain is able to identify the same and true model.

Optimized ultrasonic total focusing imaging of diverse and multiple defects in crossply CFRP: Floquet wave theory, numerical simulation, and experimental validation

Carbon fiber reinforced polymers (CFRPs) with large thickness (≥20 mm) are being extensively used for aerospace structures, and are prone to the manufacturing and in-service defects due to the complexity and difficulty of manufacturing. This study addresses an intensive interrogation of multi-parameter optimization towards a high-quality ultrasonic total focusing method (TFM) imaging for diverse and multiple defects in crossply CFRP. Firstly, material parameters of unidirectional laminate are inversely constructed based on Christoffel equation by inputting the experimentally measured wave speed, based on which the wave speed and homogenization region for the crossply CFRP are obtained with the Floquet wave theory. Then, the wave propagation at crossply CFRP with preset side drilled holes (SDHs) at depths of 4 mm and 12 mm is modelled, from which the full matrix data are extracted for TFM imaging using multiple parameter optimization, including wave velocity correction, propagation restriction angle, and wave central frequency. With the proposed signal-to-noise ratio as the criterion of TFM imaging quality, the combined parameters for optimized imaging are sorted out, which are strongly related to the feature of propagating and non-propagating waves calculated with the Floquet wave homogenization theory. A further experimental validation is performed to image multiple SDHs and delamination with size over 2 mm and depths covering 2.5 mm to 17.5 mm. This systematic analysis of parameter optimization for TFM imaging in thick CFRP sets up the foundation for the TFM towards a real engineering application of CFRP detection.

Perception and memory retrieval states are reflected in distributed patterns of background functional connectivity

The same visual input can serve as the target of perception or as a trigger for memory retrieval depending on whether cognitive processing is externally oriented (perception) or internally oriented (memory retrieval). While numerous human neuroimaging studies have characterized how visual stimuli are differentially processed during perception versus memory retrieval, perception and memory retrieval may also be associated with distinct neural states that are independent of stimulus-evoked neural activity. Here, we combined human fMRI with full correlation matrix analysis (FCMA) to reveal potential differences in "background" functional connectivity across perception and memory retrieval states. We found that perception and retrieval states could be discriminated with high accuracy based on patterns of connectivity across (1) the control network, (2) the default mode network (DMN), and (3) retrosplenial cortex (RSC). In particular, clusters in the control network increased connectivity with each other during the perception state, whereas clusters in the DMN were more strongly coupled during the retrieval state. Interestingly, RSC switched its coupling between networks as the cognitive state shifted from retrieval to perception. Finally, we show that background connectivity (1) was fully independent from stimulus-related variance in the signal and, further, (2) captured distinct aspects of cognitive states compared to traditional classification of stimulus-evoked responses. Together, our results reveal that perception and memory retrieval are associated with sustained cognitive states that manifest as distinct patterns of connectivity among large-scale brain networks.

Exhaustive study on post effect processing of 3D image based on nonlinear digital watermarking algorithm

Abstract In this work, an exhaustive study on post effect processing of three-dimensional (3D) image is carried to solve the problem of nonlinear digital watermarking algorithm. First, through the feature space decomposition method of the host image, the embedded watermark is constructed with the full row or column rank of the matrix, and then the public key is constructed by using the existence of the unitary matrix of the full row rank and column rank matrix, so that the algorithm can embed and extract the watermark in an asymmetric way. Watermark extraction correlation coefficient (ρ) value is 1. When the deformation amplitude of the model is slight and the noise intensity is σ = 0.0001, the watermark can be extracted successfully, and the watermark extraction correlation coefficient (ρ) is 0.92. In addition, the security of the algorithm is analyzed from many angles, the theoretical analysis is given, and verified by the experimental results. The proposed 3D watermarking methods are used to examine the information capacity of various 3D meshes. The 3D watermarking methods’ resistance to noise perturbation and object cropping is also investigated.

Total retardance measurements based on the complex Fourier coefficients for the rotating polarizer analyzer system

We propose a demodulation algorithm based on the calculus of the complex Fourier coefficients; we used a dual rotating polarizer-analyzer polarimeter to show the feasibility of our proposal. Our demodulation algorithm considers the frequency response obtained by the system, and its possible to calculate the total retardation, fast axis orientation and ellipticity of a sample. Our proposal does not require recovering the full Mueller matrix from getting those parameters. In addition, as the proposal does not use retarders for the measurement, the system presents potential applications for multi-wavelength measurements on phase retardation samples. We show experimental results showing the capabilities of our proposal in characterizing a polarization retardance sample.