Iterative Inversion Algorithm Research Articles

An Inverse recursive algorithm to retrieve the shape of the inaccessible dielectric objects

A regularized electromagnetic iterative inverse algorithm is formulated and implemented to reconstruct the shape of 2D dielectric objects using the far-field pattern of the scattered field data. To achieve this, an integral operator that maps the unknown boundary of the object onto the far-field pattern of the scattered field is defined and solved for the unknown boundary. The addressed inverse problem has an ill-posed nature and inherits nonlinearity. To overcome these, the proposed solution is linearized via Newton and regularized by Tikhonov in the sense of least squares. Besides, the dominance of the shadow region in the inverse-imaging process is exceeded by considering the superposition of multi-incoming plane waves, leading to less computational cost and a very fast inversion process. Comprehensive numerical analyses are carried out to ascertain the algorithm's feasibility, revealing that it is very efficient and promising.

Design and kinematics of a novel rigid-flexible coupling hybrid robot for aeroengine blades in situ repair

PurposeThis paper aims to present the mechanical design and kinematics of a novel rigid-flexible coupling hybrid robot to develop a promising aeroengine blades in situ repair technology.Design/methodology/approachAccording to requirements analysis, a novel rigid-flexible coupling hybrid robot is proposed by combining a three degrees of freedom (DOF) parallel mechanism with a flexible continuum section. Then the kinematics models of both parallel mechanism and flexible continuum section are derived respectively. Finally, based on equivalent joint method, a two-step numerical iterative inverse kinematics algorithm is proposed for the whole robot: (1) the flexible continuum section is equivalently transformed to a 2-DOF spherical joint, thus the approximate analytical inverse kinematic solution can be obtained; (2) the accurate solution is derived by an iterative derivation of both parallel mechanism and flexible continuum section.FindingsTo verify structure scheme and the proposed kinematics modeling method, numerical simulations and prototype experiments are implemented. The results show that the proposed kinematics algorithm has sufficient accuracy and computational efficiency in the whole available workspace, that is end-effector position error and orientation error are less than 0.2 mm and 0.01° respectively, and computation time is less than 0.22s.Originality/valueA novel rigid-flexible coupling hybrid robot for aeroengine blades in situ repair is designed. A two-step numerical iterative inverse kinematics algorithm is proposed for this unique hybrid robots, which has good accuracy and computational efficiency.

Magnetic surface geometry inversion of Kimberlites in Botswana

AbstractSurface geometry inversion of geophysical data has recently been introduced as an effective approach for generating surface‐based geological models. The models obtained through surface geometry inversion clearly delineate the contacts between distinct rock units, making them easily interpretable by geologists. Surface geometry inversion has shown promising preliminary results in other works, but the practical application of surface geometry inversion on real geophysical data has not been thoroughly investigated. To move towards a better understanding of the practicalities involved, we applied surface geometry inversion to a real magnetic dataset acquired over two kimberlite pipes located in north‐central Botswana. The objective was to assess the effectiveness and limitations of the surface geometry inversion approach in accurately characterizing the subsurface geometry and identifying the boundaries of the kimberlite pipes. We first perform an anomaly separation approach to isolate the magnetic anomalies associated with the kimberlite pipes. A surface geometry inversion algorithm was applied to the original and separated datasets using various initial models and other control parameters. Several tests were performed to investigate the effects that data processing, initial models, and other parameter choices have on the surface geometry inversion results. We successfully recover the geometry, extension and dip of the two kimberlite pipes. We discuss the results of our various tests and provide advice for practitioners interested in applying surface geometry inversion methods to their data. Our work indicates that surface geometry inversion can be used as a complementary approach to voxel inversion, and we propose an iterative surface geometry inversion algorithm as a possible alternative approach to voxel inversion for simple geological scenarios. This work provides valuable insights into the appropriate application of surface geometry inversion on real geophysical datasets.

Optimization of steady spin prediction by nonlinear iterative inversion algorithm

PurposeSince the inception of aircraft, the phenomenon of spin has persistently accompanied aircraft, and research into spin has been ongoing. This paper aims to introduce an optimization technique to enhance the traditional geometric method for predicting steady spin, aiming to achieve more precise predictive outcomes.Design/methodology/approachTo begin with, the force and moment equations used for motion analysis are initially presented, followed by the establishment of the motion model. Subsequently, the forward problem is set up, and the equilibrium solutions for the left and right spins of the aircraft are determined using the geometric method under the basic and wingtip configurations, thus solving the forward problem. In the final stage, nonlinear inversion is applied, and the inversion objective function is formulated based on the least squares approach. Through iterative processes, the measured data are interpolated, leading to the acquisition of the accurate equilibrium solution.FindingsThe findings indicate that the utilization of the nonlinear iterative inversion algorithm has effectively optimized the geometric method, yielding favorable outcomes. Postoptimization, the prediction accuracy has been enhanced, and the error has significantly diminished when compared to the preoptimization results.Originality/valueThe nonlinear inversion algorithm is used to refine the steady spin prediction for general aviation aircraft. This approach significantly mitigates the precision issues inherent in the forward problem. As demonstrated through the simulations provided, the application of the nonlinear iterative algorithm to resolve the inversion function yields promising optimization outcomes.

Uniqueness and numerical inversion in bioluminescence tomography with time-dependent boundary measurement

In the paper, an inverse source problem in bioluminescence tomography (BLT) is investigated. BLT is a method of light imaging and offers many advantages such as sensitivity, cost-effectiveness, high signal-to-noise ratio and non-destructivity. It thus has promising prospects for many applications such as cancer diagnosis, drug discovery and development as well as gene therapies. In the literature, BLT is extensively studied based on the (stationary) diffusion approximation (DA) equation, where the distribution of peak sources is reconstructed and no solution uniqueness is guaranteed without proper a priori information. In this work, motivated by solution uniqueness, a novel dynamic coupled DA model is proposed. Theoretical analysis including the well-posedness of the forward problem and the solution uniqueness of the inverse problem are given. Based on the new model, iterative inversion algorithms under the framework of regularizing schemes are introduced and applied to reconstruct the smooth and non-smooth sources. We discretize the regularization functional with the finite element method and give the convergence rate of numerical solutions. Several numerical examples are implemented to validate the effectiveness of the new model and the proposed algorithms.

A Concrete Core Void Imaging Approach and Parameter Analysis of Concrete-Filled Steel Tube Members Using Travel Time Tomography: Multi-Physics Simulations and Experimental Studies.

Concrete-filled steel tube (CFST) members have been widely used in civil engineering due to their advanced mechanical properties. However, internal defects such as the concrete core voids and interface debonding in CFST structures are likely to weaken their load-carrying capacity and stiffness, which affects the safety and serviceability. Visualizing the inner defects of the concrete cores in CFST members is a critical requirement and a challenging task due to the obvious difference in the material mechanical parameters of the concrete core and steel tube in CFST members. In this study, a curved ray theory-based travel time tomography (TTT) with a least square iterative linear inversion algorithm is first introduced to quantitatively identify and visualize the sizes and positions of the concrete core voids in CFST members. Secondly, a numerical investigation of the influence of different parameters on the inversion algorithm for the defect imaging of CFST members, including the effects of the model weighting matrix, weighting factor and grid size on the void's imaging quality and accuracy, is carried out. Finally, an experimental study on six CFST specimens with mimicked concrete core void defects is performed in a laboratory and the mimicked defects are visualized. The results demonstrate that TTT can identify the sizes and positions of the concrete core void defects in CFST members efficiently with the use of optimal parameters.

Implementing new computational methods for the study of JCT and SC inner wall basement membrane biomechanics and hydrodynamics

PurposeThe conventional aqueous outflow pathway, which includes the trabecular meshwork (TM), juxtacanalicular tissue (JCT), and the inner wall endothelium of Schlemm's canal (SC), regulates intraocular pressure (IOP) by controlling the aqueous humor outflow resistance. Despite its importance, our understanding of the biomechanics and hydrodynamics within this region remains limited. Fluid-structure interaction (FSI) offers a way to estimate the biomechanical properties of the JCT and SC under various loading and boundary conditions, providing valuable insights that are beyond the reach of current imaging techniques. MethodsIn this study, a normal human eye was fixed at a pressure of 7 mm Hg, and two radial wedges of the TM tissues, which included the SC inner wall basement membrane and JCT, were dissected, processed, and imaged using 3D serial block-face scanning electron microscopy (SBF-SEM). Four different sets of images were used to create 3D finite element (FE) models of the JCT and inner wall endothelial cells of SC with their basement membrane. The outer JCT portion was carefully removed as the outflow resistance is not in that region, leaving only the SCE inner wall and a few µm of the tissue, which does contain the resistance. An inverse iterative FE algorithm was then utilized to calculate the unloaded geometry of the JCT/SC complex at an aqueous humor pressure of 0 mm Hg. Then in the model, the intertrabecular spaces, pores, and giant vacuole contents were replaced by aqueous humor, and FSI was employed to pressurize the JCT/SC complex from 0 to 15 mm Hg. ResultsIn the JCT/SC complex, the shear stress of the aqueous humor is not evenly distributed. Areas proximal to the inner wall of SC experience larger stresses, reaching up to 10 Pa, while those closer to the JCT undergo lower stresses, approximately 4 Pa. Within this complex, giant vacuoles with or without I-pore behave differently. Those without I-pores experience a more significant strain, around 14%, compared to those with I-pores, where the strain is roughly 9%. ConclusionsThe distribution of aqueous humor wall shear stress is not uniform within the JCT/SC complex, which may contribute to our understanding of the underlying selective mechanisms in the pathway.

Dexterous obstacle-avoidance motion control of Rope Driven Snake Manipulator based on the bionic path following

The RDSM (Rope Driven Snake Manipulator) is a hyper-redundant robot operating in narrow and confined environments, such as aerospace, nuclear industry and etc. Inspired from the bionic following motion, an obstacle-avoidance control method of the RDSM in uncharted environments is proposed without the information of global obstacles. First, the kinematic model of a 17-DOF RDSM is established considering the mapping among the joint angle, rope length and end posture. Then, the motion path and inverse kinematic iterative algorithm of the RDSM in multi-obstacle environments is deduced using the piecewise Bézier curves. The motion control method of the RDSM is designed based on the model reference adaptive control, guaranteeing the joint error and end posture error asymptotically stable. Finally, the proposed obstacle avoidance method is verified with the simulation and experiment. As the result shown, the RDSM avoids obstacles on a path with a minimum curvature radius of 1/8 arm length, and the motion control precision of the end posture is within ±2.5mm/±0.5∘.

A third-order iterative algorithm for inversion of cumulative central beta distribution

A third-order iterative algorithm for inversion of cumulative central beta distribution

Structure Guided Multiparameter Waveform Inversion With Attenuation Compensation in Viscoacoustic Medium

Full waveform inversion (FWI) has been proved as an effective method for subsurface parameter estimation by iteratively reducing the residual between the predictions and the observations. In recent years, FWI has been widely used due to the increasing computing power. However, seismic waves usually suffer from energy dissipation and phase distortion during their propagation in the anelastic medium, which will decelerate the convergence rate of FWI and make the inversion processing even more time-consuming. In this letter, we propose a structure guided FWI method with attenuation compensation to estimate velocity model and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</i> model simultaneously. We refer to the proposed method as SGQFWI. With the help of a fractional decoupled viscoacoustic equation, we introduce the attenuation compensation mechanism into full waveform inversion iterative algorithm, which can effectively compensate the deep weak amplitude, so as to obtain a more accurate inversion gradient and improve the accuracy and efficiency of inversion. Additionally, the structure regularization is added to model update, which helps to retrieve local detailed information more efficiently. Benefit from the incorporation of the priori structure constraint and attenuation compensation, this method has the ability to invert velocity and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</i> model with improved efficiency and resolution. Synthetic and field data examples are adopted to further verify the effectiveness of the proposed method.

A Fast Globally Convergent Particle Swarm Optimization for Defect Profile Inversion Using MFL Detector

For the problem of defect inversion in magnetic flux leakage technology, a fast, globally convergent particle swarm optimization algorithm based on the finite-element forward model is introduced as an inverse iterative algorithm in this paper. Two aspects of the traditional particle swarm optimization algorithm have been improved: self-adaptive inertia weight and speed updating strategy. For the inertia weight, it can be adaptively adjusted according to the particle position. The speed update strategy mainly uses the best experience positions of other particles in a randomly selected population to realize the algorithm’s learning. At the same time, the learning factor of the position variable is designed to change with the number of iteration steps. The particle with a good position is added to jump out of the local minimum and accelerate the optimization process. Through the comparison experiment, the improved particle swarm optimization algorithm has a faster convergence speed compared with other traditional particle swarm optimization algorithms. It is more difficult for it to fall into the local minimum value and it is more easily converted to a higher precision.

Uniqueness and numerical inversion in the time-domain fluorescence diffuse optical tomography

This work considers the time-domain fluorescence diffuse optical tomography (FDOT). We recover the distribution of fluorophores in biological tissue by the boundary measurements. With the Laplace transform and the knowledge of complex analysis, we build the uniqueness theorem of this inverse problem. After that, the numerical inversions are considered. We introduce an iterative inversion algorithm under the framework of regularizing scheme, then give several numerical examples in three-dimensional space illustrating the performance of the proposed inversion schemes.

Application of Generative Adversarial Network-Based Inversion Algorithm in Imaging 2-D Lossy Biaxial Anisotropic Scatterer

An effective quasi-real-time inversion algorithm based on the super-resolution generative adversarial network (SR-GAN) is proposed to quantitatively image the 2-D biaxial anisotropic scatterers. The SR-GAN was originally proposed for the purpose of super-resolution image reconstruction, which exactly fits the need for inverse problem. In addition, Visual Geometry Group (VGG) loss is introduced to extract the high-level features of the object instead of the low-level pixel-wise error measures. The angle-dependent reconstruction effect due to the dipole radiation as in the traditional inversion methods is effectively resolved by the machine learning method. Numerical results using both synthetic data and experimental data are given to validate the effectiveness of the proposed method. Both the imaging quality and resolution are greatly improved by the proposed SR-GAN algorithm, compared to the traditional iterative inversion algorithm. In addition, the computational time is reduced significantly and the quasi-real-time imaging is finally realized, which promises a potential real-time application of the inverse scattering method.

Full-waveform inversion of ultrasonic echo signals to evaluate grouting quality of tendon ducts in post-tensioned concrete structures

Reliable techniques for non-destructive evaluation of reinforced and prestressed concrete structures are of utmost importance for the maintenance of aging infrastructure. A particular area of interest is the evaluation of grouting quality within tendon ducts in post-tensioned concrete. Detecting voids and water-filled cavities in plastic or metal ducts is challenging, especially at greater depths or in the vicinity of rebar. Conventional non-destructive inspection methods based on elastic waves, such as impact-echo or ultrasonic pulse echo method using synthetic aperture focusing and/or signal phase analysis, often lack sensitivity to those defects and/or rely on manual and subjective interpretation of the complex data. To overcome these problems, we present a synthetic feasibility study based on full-waveform inversion for reliable ultrasonic non-destructive testing. Full-waveform inversion is a powerful imaging technique that infers tomographic reconstructions of the material properties from ultrasound measurements. The method is widely used for geophysical applications based on seismic waves and has recently gained increasing attention for ultrasonic inspection applications. Using digital twins, we demonstrate the effect of voids and water inclusions on simulated ultrasonic echo signals. This information can be used in an iterative inversion algorithm to create a 3-D quantitative model of the specimen’s interior. We showcase in several numerical examples that even under uncertainties regarding aggregate size distribution and location of the rebar, full-waveform inversion can reveal defects related to the tendon ducts, which enables a robust and automated assessment of the grouting quality.

Wind-field identification for parafoils based on deep Q-learning iterative inversion

Powered parafoils are flexible aircraft with high load capacities and low costs and are often used in long-term surveillance and airdrop missions. As a flexible aircraft, powered parafoil flights are easily affected by winds. However, wind-field identification is difficult for low-to-medium speed unmanned aerial vehicles (UAV), which makes it challenging for UAVs such as powered parafoils to perform targeted wind compensation. To observe and compensate for this, we must accurately identify the wind field for the powered parafoil. In this study, we designed a deep Q-learning iterative inversion (DQII) algorithm for wind-field identification to concretely analyze wind-field identification through model inversion. Using a deep Q-learning (DQ) inverting dynamic model, a powered parafoil can identify the wind field within 2 s. In addition, iterative chaotic particle swarm optimization was performed based on DQ inversion, which achieved a high-precision wind-field identification effect. Simulation experiments showed that, compared with the traditional dead reckoning (DR) algorithm, DQII can reduce the error by 80%–90%. In a powered parafoil homing experiment, DQII achieved a wind-field identification effect that was significantly better than that of the DR algorithm.

Gravity‐Derived Antarctic Crustal Thickness Based on the Gauss‐FFT Method

AbstractThe information on crustal thickness in Antarctica can provide significant constraints on its crustal deformation and tectonic evolution. To generate reliable images of crustal features, we investigate the model of Moho depth and crustal thickness beneath Antarctica by applying the Bott‐Parker's formulas based on the Gauss‐fast Fourier transform method through a comprehensive analysis of gravity data, ice and sediment thicknesses and bedrock elevation, combined with seismic constraints. Tests with synthetic data indicate that the iterative inversion algorithm can yield a highly accurate Moho topography. Ultimately, inverted crustal thickness reveals a more detailed crustal image by clearly identifying more tectonic elements at different scales than previous results and correlates well with major tectonic provinces. Airy isostasy and flexural isostasy models are used to assess the crustal isostatic compensation. The distinctive negative isostatic anomalies are observed in the Transantarctic Mountains and the East Antarctic areas of the great escarpment in the Dronning Maud Land and Aurora and Wilkes Subglacial Basin, indicating that the low density of the uppermost mantle and lithospheric strength may play important roles in compensating for their elevations. Variations in crustal thickness in interior East Antarctica are analyzed; the thickened crust from Dronning Maud Land to the Gamburtsev Subglacial Mountains may be associated with the collision of continental blocks and is interpreted as the fossil sutures. We compare the relationship between the Moho and Curie interfaces and find that the uppermost mantle is magnetized in some areas of East Antarctica, which may indicate preserved Precambrian cratonic roots.

Enhancing Finite Element-Based Photoacoustic Tomography by Localized Reconstruction Method

Iterative reconstruction algorithm based on finite element (FE) modeling is a powerful approach in photoacoustic tomography (PAT). However, an iterative inverse algorithm using conventional FE meshing of the entire imaging zone is computationally demanding, which hinders this powerful tool in applications where quick image acquisition and/or a large image matrix is needed. To address this challenge, parallel computing techniques are proposed and implemented in the field. Here, we present an alternative approach for 2D PAT, which locoregionally reconstructs the region of interest (ROI) instead of the full imaging zone. Our simulated and phantom experimental results demonstrate that this ROI reconstruction algorithm can produce almost the same image quality as the conventional full zone-based reconstruction algorithm; however, the computation time can be significantly reduced without any additional hardware cost by more than two orders of magnitude (100-fold). This algorithm is further applied and validated in an in vivo study. The major vessel structures in a rat’s brain can be imaged clearly using our ROI-based approach, coupled with a mesh of 11,801 nodes. This novel algorithm can also be parallelized using MPI or GPU acceleration techniques to further enhance the reconstruction performance of FE-based PAT.

An inversion algorithm for P-functions with applications to multi-energy CT

Multi-energy computed tomography (ME-CT) is an x-ray transmission imaging technique that uses the energy dependence of x-ray photon attenuation to determine the elemental composition of an object of interest. Mathematically, forward ME-CT measurements are modeled by a nonlinear integral transform. In this paper, local conditions for global invertibility of the ME-CT transform are studied, and explicit stability estimates quantifying the error propagation from measurements to reconstructions are provided. Motivated from the inverse problem of image reconstruction in ME-CT, an iterative inversion algorithm for the so-called P-functions is proposed. Numerical simulations for ME-CT, in two and three materials settings with an equal number of energy measurements, confirm the theoretical predictions.

A Reconstruction Scheme Using an Average Conductivity Element for Pitting Corrosion Defects in Steam Generator Tubes From Eddy Current Testing Signals

Pitting corrosion is a typical defect in steam generator tubes of nuclear power plants (NPPs) which may cause leak of coolant water in the first circulation loop of an NPP. Different from a crack, the pitting defect has small hole-like geometrical feature, which makes the conventional inversion scheme for crack profile reconstruction using eddy current testing (ECT) signals unsuitable. In this article, a numerical scheme to reconstruct the pitting corrosion defect from ECT signals is proposed and validated, including a new efficient ECT signal forward solver and an iterative inversion algorithm. For efficient calculation of the ECT signals due to a pitting hole, defect model based on a finite element of average conductivity is proposed. The model is validated by comparing its results with those of the conventional finite element method and boundary element method (FEM-BEM) hybrid code of $A$ – $\phi $ formulation using a detailed mesh for a flat-bottom hole. To reconstruct the defect profile such as the depth and diameter, the particle swarm optimization algorithm was adopted to solve the inversion problem iteratively. Finally, ECT experiments were conducted for test piece tubes with artificial pitting defects of different sizes and the defect profile parameters were reconstructed from the measured ECT signals with the proposed numerical schemes. Both the depths and the diameters of the artificial pitting defects, i.e., flat-bottom holes, were properly reconstructed referring to the true defect sizes.

High surface accuracy and pretension design for mesh antennas based on dynamic relaxation method

Cable truss structures are widely used in large satellite antennas with ultrahigh electromagnetic performance. The electromagnetic performance is directly determined by the mesh reflector's surface accuracy, which triggers research on the pretension design. In this paper, a novel pretension design method for both high surface accuracy and uniform tension distribution is proposed based on the dynamic relaxation (DR) method. In this approach, members of the cable network are regarded as string elements with 3 degrees of freedom to resist the axial tensile force, and members of the supporting truss are regarded as Euler-Bernoulli beams with 6 degrees of freedom to resist the axial and transverse forces and the bending and torsion moments. The DR method is adopted to find the static equilibrium of the whole mesh antenna, including both the cable mesh and the supporting truss. Thus, the deformation of the cables and rods and their interactive effects are fully captured. Then, to find an expected high-precision mesh surface with a uniform tension distribution, the inverse iteration algorithm (IIA) is adopted to adjust the original cable lengths of the cable network in each DR calculation cycle until the convergence criterion is met. Finally, this approach is effectively applied to the pretension design of symmetric and asymmetric mesh antennas, and the results indicate that the method is effective in obtaining both high surface accuracy and uniform tension distribution with high computational efficiency.