Iterative Refinement Algorithm Research Articles

An errors-unidentified hand-eye calibration method via robot relocalization and iterative combinatorial refinement

The accuracy of hand-eye calibration is easily affected by robot kinematic error, measurement error, random error, etc., and can be to a certain extent enhanced by the complicated error identification. To address this problem, we propose a novel errors-unidentified hand-eye calibration method. A relocalization-based hand-eye calibration is implemented to overcome the challenge from robot kinematics at first owing to the high robot relocalization accuracy. The tool center point (TCP) coordinates are then obtained based on an iterative reweighted least squares (IRLS) spherical fitting algorithm. An iterative combinatorial refinement algorithm is finally presented to search the solutions in the form of permutation and combination when solving the rigid transformation matrix. Experiments on criterion sphere and blade demonstrate that by converting the hand-eye matrix solving problem into a point set matching problem, the accuracy of the proposed method is enhanced by 60% on average compared with three state-of-the-art hand-eye calibration methods.

Crack Segmentation Extraction and Parameter Calculation of Asphalt Pavement Based on Image Processing.

Crack disease is one of the most serious and common diseases in road detection. Traditional manual methods for measuring crack detection can no longer meet the needs of road crack detection. In previous work, the authors proposed a crack detection method for asphalt pavements based on an improved YOLOv5s model, which is a better model for detecting various types of cracks in asphalt pavements. However, most of the current research on automatic pavement crack detection is still focused on crack identification and location stages, which contributes little to practical engineering applications. Based on the shortcomings of the above work, and in order to improve its contribution to practical engineering applications, this paper proposes a method for segmenting and analyzing asphalt pavement cracks and identifying parameters based on image processing. The first step is to extract the crack profile through image grayscale, histogram equalization, segmented linear transformation, median filtering, Sauvola binarization, and the connected domain threshold method. Then, the magnification between the pixel area and the actual area of the calibration object is calculated. The second step is to extract the skeleton from the crack profile images of asphalt pavement using the Zhang-Suen thinning algorithm, followed by removing the burrs of the crack skeleton image using the connected domain threshold method. The final step is to calculate physical parameters, such as the actual area, width, segments, and length of the crack with images obtained from the crack profile and skeleton. The results show that (1) the method of local thresholding and connected domain thresholding can completely filter noise regions under the premise of retaining detailed crack region information. (2) The Zhang-Suen iterative refinement algorithm is faster in extracting the crack skeleton of asphalt pavement, retaining the foreground features of the image better, while the connected-domain thresholding method is able to eliminate the missed isolated noise. (3) In comparison to the manual calibration method, the crack parameter calculation method proposed in this paper can better complete the calculation of crack length, width, and area within an allowable margin of error. On the basis of this research, a windowing system for asphalt pavement crack detection, WSPCD1.0, was developed. It integrates the research results from this paper, facilitating automated detection and parameter output for asphalt pavement cracks.

RIS-Aided Near-Field Localization Under Phase-Dependent Amplitude Variations

We investigate the problem of reconfigurable intelligent surface (RIS)-aided near-field localization of a user equipment (UE) served by a base station (BS) under phase-dependent amplitude variations at each RIS element. Through a misspecified Cramér-Rao bound (MCRB) analysis and a resulting lower bound (LB) on localization, we show that when the UE is unaware of amplitude variations (i.e., assumes unit-amplitude responses), severe performance penalties can arise, especially at high signal-to-noise ratios (SNRs). Leveraging Jacobi-Anger expansion to decouple range-azimuth-elevation dimensions, we develop a low-complexity approximated mismatched maximum likelihood (AMML) estimator, which is asymptotically tight to the LB. To mitigate performance loss due to model mismatch, we propose to jointly estimate the UE location and the RIS amplitude model parameters. The corresponding Cramér-Rao bound (CRB) is derived, as well as an iterative refinement algorithm, which employs the AMML method as a subroutine and alternatingly updates individual parameters of the RIS amplitude model. Simulation results indicate fast convergence and performance close to the CRB. The proposed method can successfully recover the performance loss of the AMML under a wide range of RIS parameters and effectively calibrate the RIS amplitude model online with the help of a user that has an a-priori unknown location.

Min-Deviation-Flow in Bi-directed Graphs for T-Mesh Quantization

Subdividing non-conforming T-mesh layouts into conforming quadrangular meshes is a core component of state-of-the-art (re-)meshing methods. Typically, the required constrained assignment of integer lengths to T-Mesh edges is left to generic branch-and-cut solvers, greedy heuristics, or a combination of the two. This either does not scale well with input complexity or delivers suboptimal result quality. We introduce the Minimum-Deviation-Flow Problem in bi-directed networks (Bi-MDF) and demonstrate its use in modeling and efficiently solving a variety of T-Mesh quantization problems. We develop a fast approximate solver as well as an iterative refinement algorithm based on matching in graphs that solves Bi-MDF exactly. Compared to the state-of-the-art QuadWild [Pietroni et al. 2021] implementation on the authors' 300 dataset, our exact solver finishes after only 0.49% (total 17.06s) of their runtime (3491s) and achieves 11% lower energy while an approximation is computed after 0.09% (3.19s) of their runtime at the cost of 24% increased energy. A novel half-arc-based T-Mesh quantization formulation extends the feasible solution space to include previously unattainable quad meshes. The Bi-MDF problem is more general than our application in layout quantization, potentially enabling similar speedups for other optimization problems that fit into the scheme, such as quad mesh refinement.

Acceleration of iterative refinement for singular value decomposition

We propose fast numerical algorithms to improve the accuracy of singular vectors for a real matrix. Recently, Ogita and Aishima proposed an iterative refinement algorithm for singular value decomposition that is constructed with highly accurate matrix multiplications carried out six times per iteration. The algorithm runs for the problem that has no multiple and clustered singular values. In this study, we show that the same algorithm can be run with highly accurate matrix multiplications carried out five times. Also, we proposed four algorithms constructed with highly accurate matrix multiplications, two algorithms with the multiplications carried out four times, and the other two with the multiplications carried out five times. These algorithms adopt the idea of a mixed-precision iterative refinement method for linear systems. Numerical experiments demonstrate speed-up and quadratic convergence of the proposed algorithms. As a result, the fastest algorithm is 1.7 and 1.4 times faster than the Ogita-Aishima algorithm per iteration on a CPU and GPU, respectively.

An aerial ammunition ad hoc network collaborative localization algorithm based on relative ranging and velocity measurement in a highly-dynamic topographic structure

In the internet of battlefield things, ammunition is becoming networked and intelligent, which depends on location information. Therefore, this paper focuses on the self-organized network collaborative localization of munitions with an aerial three-dimensional (3D) highly-dynamic topographic structure under a satellite denied environment. As for aerial networked munitions, the measurement of munitions is objectively incomplete due to the degenerated and interrupted link of munitions. For this reason, a cluster-oriented collaborative localization method is put forward in this paper. Multidimensional scaling (MDS) was first integrated with a trilateration localization method (TLM) to construct a relative localization algorithm for determining the relative location of a mobile cluster network. The information related to relative velocity was then combined into a collaborative localization framework to devise a TLM-vMDS algorithm. Finally, an iterative refinement algorithm based on scaling by majorizing a complicated function (SMACOF) was employed to effectively eliminate the influence of incomplete link observation on localization accuracy. Compared with the currently available advanced algorithms, the proposed TLM-vMDS algorithm achieves higher localization accuracy and faster convergence for a cluster of extensively networked munitions, and also offers better numerical stability and robustness for high-speed motion models.

Double shear layer evolution on the non-uniform computational mesh

This paper considers the problem of a thin shear layer evolution at Reynolds number rmRe = 400000 using the novel Compact Accurately Boundary Adjusting high-Resolution Technique (CABARET). The study is focused on the effect of the specific mesh refinement in the high shear rate areas on the flow properties under the influence of the developing instability. The original sequence of computational meshes (2562, 5122, 10242, 20482 cells) is modified using an iterative refinement algorithm based on the hyperbolic tangent. The properties of the solutions obtained are discussed in terms of the initial momentum thickness and the initial vorticity thickness, viscous and dilatational dissipation rates and also integral enstrophy. The growth rate for the most unstable mode depending on the mesh resolution is considered. In conclusion the accuracy of calculated mesh functions is estimated via L 1, L 2, L ∞ norms.

Iterative refinement algorithm for efficient velocities and accelerations solutions in closed-loop multibody dynamics

To simulate closed-loop multibody systems in effective and accurate way, the semi-recursive formulations can be used together with optimal numerical integrators. Although numerous contributions have been reported in this field, there still exists a demand to improve the computation efficiency for the faster-than-real-time simulation and hardware-in-the-loop control applications. This paper presents an iterative refinement algorithm to accelerate the numerical integration process of a semi-recursive multibody formulation. By reusing the constraint Jacobian matrix factorization and generalized mass matrix factorization, respectively, the presented algorithm is introduced to enhance the solution of dependent relative velocities and independent relative accelerations. The introduced procedure consists of three steps; initial guess determination, iterative refinement process and termination criteria. The iterative refinement process is designed to find an accurate numerical solution, which contains residual computing, solution increment computing and solution updating. For higher efficiency, the initial guess can be re-determined to repeat the iterative refinement process. Three closed-loop multibody systems with increasing complexity are taken as numerical examples to verify the accuracy and efficiency of the presented iterative refinement algorithm. The results highlight more than 15% efficiency gain. The algorithm also can be implemented in other numerical integrators and multibody formulations.

Non-uniform refinement: adaptive regularization improves single-particle cryo-EM reconstruction.

Cryogenic electron microscopy (cryo-EM) is widely used to study biological macromolecules that comprise regions with disorder, flexibility or partial occupancy. For example, membrane proteins are often kept in solution with detergent micelles and lipid nanodiscs that are locally disordered. Such spatial variability negatively impacts computational three-dimensional (3D) reconstruction with existing iterative refinement algorithms that assume rigidity. We introduce non-uniform refinement, an algorithm based on cross-validation optimization, which automatically regularizes 3D density maps during refinement to account for spatial variability. Unlike common shift-invariant regularizers, non-uniform refinement systematically removes noise from disordered regions, while retaining signal useful for aligning particle images, yielding dramatically improved resolution and 3D map quality in many cases. We obtain high-resolution reconstructions for multiple membrane proteins as small as 100 kDa, demonstrating increased effectiveness of cryo-EM for this class of targets critical in structural biology and drug discovery. Non-uniform refinement is implemented in the cryoSPARC software package.

AIR: Iterative refinement acceleration using arbitrary dynamic precision

The increased degree of concurrent operations by lower precision arithmetic enables high performance for iterative refinement. Most of related work present statically defined mixed precision arithmetic approaches, while adapting a level of arithmetic precision dynamically in a loop with one-bit granularity can further improve the performance. This paper presents Arbitrary Dynamic Precision Iterative Refinement algorithm (AIR) that minimizes the total significand bit-width to solve iterative refinement. AIR detects the number of cancellation bits dynamically per iteration and uses the information to provide the least sufficient significand bit-width for the next iteration. We prove that AIR is a backward stable algorithm and can bring up to 2−3× speedups over a mixed precision iterative refinement depending on the characteristics of hardware. Our software demonstration shows that AIR requires only 83% of the significand bits required by mixed precision iterative refinement that solve linear systems for double precision accuracy for backward error with 32 × 32 standard normally distributed matrices.

New Research Results of Algorithms for Analysis of Changing Electric Circuits

New research results in the field of accelerated analysis of linear and linearizable electrical circuits with variable elements are presented. The considered algorithms are based on a new modification of Gaussian elim-ination for solution of systems of linear equations. The researches was directed on a systematic thorough study of the phenomenon of quasi-stabilization of the error discovered by the authors during multiple repeated cir-cuit analyzes. The Sherman-Morrison algorithm and the iterative refinement algorithm are considered as alter-natives. To control the results of numerical experiments, the representation of floating-point numbers in the bi-nary128 format of the IEEE 754 standard is used. A method for the machine formation of mathematical models of circuits with an unlimited number of elements is proposed.

Technique of Informative Features Selection in Geoacoustic Emission Signals

Studies of geoacoustic emission in a seismically active region in Kamchatka show that geoacoustic signals produce pronounced pulse anomalies during the earthquake preparation and post-seismic relaxation of the local stresses field at the observation point. The qualitative selection of such anomalies is complicated by a strong distortion and weakening of the signal amplitude. A review of existing acoustic emission analysis methods shows that most often researchers turn to the analysis of more accessible to study statistical properties and energy of signals. The distinctive features of the approach proposed by the authors are the extraction of informative features based on the analysis of time and frequency-time structures of geoacoustic signals and the description of various forms of recognizable pulses by a limited pattern set. This study opens up new ideas to develop methods for detecting anomalous behavior of geoacoustic signals, including anomalies before earthquakes.
 The paper describes a technique of information extraction from geoacoustic emission pulse streams of sound frequency range. A geoacoustic pulse mathematical model, reflecting the signal generation process from a variety of elementary sources, is presented. A solution to the problem of detection of geoacoustic signal informative features is presented by the means of description of signal fragments by the matrixes of local extrema amplitude ratios and of interval ratios between them. The result of applying the developed algorithm to describe automatically the structure of the detected pulses and to form a pattern set is shown. The patterns characterize the features of geoacoustic emission signals observed at IKIR FEB RAS field stations. A technique of reduction of the detected pulse set dimensions is presented. It allows us to find patterns similar in structure. A solution to the problem of processing of a large data flow by unifying pulses description and their systematization is proposed. A method to identify a geoacoustic emission pulse model using sparse approximation schemes is suggested. An algorithmic solution of the problem of reducing the computational complexity of the matching pursuit method is described. It is to include an iterative refinement algorithm for the solution at each step in the method. The results of the research allowed the authors to create a tool to investigate the dynamic properties of geoacoustic emission signal in order to develop earthquake prediction detectors.

Hierarchical Adaptive Control System of a Manipulator Based on the Synthesis of a Neural Network of Fuzzy Inference and an Iterative Refinement Algorithm

The main aim of this work is to develop an adaptive control system for a kinematically redundant multilink industrial manipulator. Proposed solution allows to construct a unified real-time control system with the ability to control the accuracy of calculations. In order to achieve the required accuracy of the calculations and the performance of the control system, we propose an algorithm that is based on the so-called hybrid method for finding the solution of the inverse kinematics (IK) problem, including the adaptive neural network and fuzzy inference system with subsequent iterative refinement of numerical solution by the Newton --- Raphson method. The influence of the training sample size on the quality of the obtained initial approximation for the neural network part of the algorithm is described in the paper. The results of experimental studies of the developed hybrid algorithm are presented in comparison with the iterative and neural network methods for three-, five- and eight-link manipulator structures. Paper presents the main steps of the control system synthesis for kinematically redundant industrial manipulator, including the description for developed algorithms for finding an IK solution of multilink structures. The structure of a multi-level hierarchical manipulator control system, based on a programmable logic controller and electric stepping motors with the possibility of integration into the production system at various levels, is presented.

Polarization studies of rotating radio transients

ABSTRACT We study the polarization properties of 22 known rotating radio transients (RRATs) with the 64-m Parkes radio telescope and present the Faraday rotation measures (RMs) for the 17 with linearly polarized flux exceeding the off-pulse noise by 3σ. Each RM was estimated using a brute-force search over trial RMs that spanned the maximum measurable range $\pm 1.18 \times 10^5 \, \mathrm{rad \, m^2}$ (in steps of 1 $\mathrm{rad \, m^2}$), followed by an iterative refinement algorithm. The measured RRAT RMs are in the range |RM| 1–950 rad m−2 with an average linear polarization fraction of 40 per cent. Individual single pulses are observed to be up to 100 per cent linearly polarized. The RMs of the RRATs and the corresponding inferred average magnetic fields (parallel to the line of sight and weighted by the free electron density) are observed to be consistent with the Galactic plane pulsar population. Faraday rotation analyses are typically performed on accumulated pulsar data, for which hundreds to thousands of pulses have been integrated, rather than on individual pulses. Therefore, we verified the iterative refinement algorithm by performing Monte Carlo simulations of artificial single pulses over a wide range of S/N and RM. At and above an S/N of 17 in linearly polarized flux, the iterative refinement recovers the simulated RM value 100 per cent of the time with a typical mean uncertainty of 5 rad m−2. The method described and validated here has also been successfully used to determine reliable RMs of several fast radio bursts (FRBs) discovered at Parkes.

Assessing the best edit in perturbation-based iterative refinement algorithms to compute the median string

Different pattern recognition techniques such as clustering, k-nearest neighbors classification or instance reduction algorithms require prototypes to represent pattern classes. In many applications, strings are used to encode instances, for example, in contour representations or in biological data such as DNA, RNA and protein sequences. Median strings have been used as representatives of a set of strings in different domains. Finding the median string is an NP-Complete problem for several formulations. Alternatively, heuristic approaches that iteratively refine an initial coarse solution by applying edit operations have been proposed. We propose here a novel algorithm that outperforms state of the art heuristic approximations to the median string in terms of convergence speed by estimating the effect of a perturbation in the minimization of the expressions that define the median strings. We present comparative experiments to validate these results.

Adaptive algorithm for sparse signal recovery

The development of compressive sensing in recent years has given much attention to sparse signal recovery. In sparse signal recovery, spike and slab priors are playing a key role in inducing sparsity. The use of such priors, however, results in non-convex and mixed integer programming problems. Most of the existing algorithms to solve non-convex and mixed integer programming problems involve either simplifying assumptions, relaxations or high computational expenses. In this paper, we propose a new adaptive alternating direction method of multipliers (AADMM) algorithm to directly solve the suggested non-convex and mixed integer programming problem. The algorithm is based on the one-to-one mapping property of the support and non-zero element of the signal. At each step of the algorithm, we update the support by either adding an index to it or removing an index from it and use the alternating direction method of multipliers to recover the signal corresponding to the updated support. Moreover, as opposed to the competing “adaptive sparsity matching pursuit” and “alternating direction method of multipliers” methods our algorithm can solve non-convex problems directly. Experiments on synthetic data and real-world images demonstrated that the proposed AADMM algorithm provides superior performance and is computationally cheaper than the recently developed iterative convex refinement (ICR) and adaptive matching pursuit (AMP) algorithms.

Energy-Efficient Iterative Refinement Using Dynamic Precision

Mixed precision is a promising approach to save energy in iterative refinement algorithms since it obtains speed-up without necessitating additional cores and parallelization. However, conventional mixed precision methods utilize statically defined precision in a loop, thus hindering further speed-up and energy savings. We overcome this problem by proposing novel methods which allow iterative refinement to utilize variable precision arithmetic dynamically in a loop (i.e., a trans-precision approach). Our methods restructure a numeric algorithm dynamically according to runtime numeric behavior and remove unnecessary accuracy checks. We implemented our methods by extending one conventional mixed precision iterative refinement algorithm on an Intel Xeon E5-2650 2GHz core with MKL 2017 and XBLAS 1.0. Our dynamic precision approach demonstrates 2.0-2.6× speed-up and 1.8-2.4× energy savings compared with mixed precision iterative refinement when double precision solution accuracy is required for forward error and with matrix dimensions ranging from 4K to 32K.

EmClarity: software for high-resolution cryo-electron tomography and subtomogram averaging.

Macromolecular complexes are intrinsically flexible and often challenging to purify for structure determination by single particle cryoEM. Such complexes may be studied using cryo-electron tomography combined with sub-tomogram alignment and classification, which in exceptional cases reaches sub-nanometer resolution, yielding insight into structure-function relationships. Extending this approach to specimens that exhibit conformational or compositional heterogeneity, and that may be present at low abundance, remains challenging. To address this challenge, we developed emClarity (https://github.com/bHimes/emClarity/wiki), a GPU-accelerated image processing package, which features an iterative tomographic tilt-series refinement algorithm using sub-tomograms as fiducial markers and a 3D-samping function compensated, multi-scale Principle Component Analysis classification method. We demonstrate substantial improvements in the resolution of maps and in the separation of different functional states of macromolecular complexes, compared to those generated using current state-of-the-art software.

A Novel Variational Meshless Method With Radial Basis Functions for Waveguide Eigenvalue Problems

A novel variational meshless method is presented to calculate a large number of modes of a homogeneous waveguide with an arbitrary shape. The proposed technique is based on the variational principle combined with the meshless method using radial basis functions (RBFs). Compared with the more traditional point-matching meshless method with RBFs, the proposed technique leads to a well-conditioned matrix problem, and no preconditioning is needed. An iterative refinement algorithm is also presented, which generates automatically new collocation points and locally defined shape parameters for the RBFs, until a prescribed convergence is reached. As proved through many examples, including waveguides with sharp corners, the variational meshless method permits to calculate a large number of waveguide modes with high precision in a very short computing time.

Методика построения гибридной нейросистемы реального времени для решения обратной задачи кинематики избыточного манипулятора

Solution of the inverse kinematics (IK) problem with the aid of neural networks is considered. The control system for a multi-link redundant manipulator is synthesized. The configuration of a control system on the basis of servo drives is presented. The proposed control system is based on an algorithm involving a new hybrid method for solving the IK problem. This method combines the ANFIS adaptive neural fuzzy inference network and an iterative refinement algorithm (according to the Newton-Raphson method). Thus, the proposed algorithm combines the advantages of the neural network and iterative approaches, namely, high precision and high response speed. The required coordinates (link rotation angles) for the inverse problem are calculated in the neural network (ANFIS), after which they are refined by the iteration method. Hence, a much fewer number of iterations have to be carried out in the numerical method, and, accordingly, much shorter time is taken to execute the algorithm. The developed algorithm ensures a controlled accuracy of calculations with due regard of its application in real-time control systems. The developed control system is universal in nature and can be used for manipulators having different design parameters. For investigating the control system synthesized proceeding from the developed method for solving the IK problem, a three-link manipulator design was considered. The mathematical description used for constructing the manipulator’s operating space and for training the control system neural network is presented. The results from experimental investigations of applying the hybrid algorithm for calculating the link and actuator coordinates are given. The method was investigated in the Matlab environment. The results of the performed experiments allowed a conclusion to be drawn about the possibility of using the developed method in real-time control systems. To solve the problem of shaping the operating spaces of certain types of manipulators, a graphical interface was developed using the Matlab GUI. The application includes features for adjusting the design parameters (the mechanical structure and accuracy). As an example, the workspaces of both planar and spatial manipulator designs with the specified parameters are taken.