Transformation Matrix Research Articles

Boundary scattering in massless AdS3

We study the boundary integrability problem of the massless sector of AdS3 × S3 × T4 string theory. Exploiting the difference-form of the massless scattering theory, we find a very simple and exhaustive list of reflection matrices for all the possible boundary coideal subalgebras — singlet and vector representations, right and left boundary — and check basic properties of our solutions, primarily the boundary Yang-Baxter equation, for all possible combinations of scattering particles.

DMT-OMPA: Innovative applications of an efficient adversarial Marine Predators Algorithm based on dynamic matrix transformation in engineering design optimization

This paper introduces an innovative variant of the Marine Predators Algorithm (MPA), termed the Dynamic Matrix Transformation-based Oppositional Marine Predators Algorithm (DMT-OMPA), aimed at enhancing the efficiency of engineering optimization strategies. Traditional MPAs have several shortcomings, including insufficient solution diversity and coverage in the initialization phase, a tendency to become trapped in local optima, and inadequate search capabilities in the later stages of iteration, all of which negatively impact the algorithm’s efficiency and effectiveness. To address these issues, the DMT-OMPA incorporates oppositional learning mechanisms and dynamic matrix transformation strategies, significantly enhancing global search capabilities and accelerating convergence speed, particularly in handling complex multidimensional optimization problems.Experimental results on the CEC2013 and CEC2017 test suites demonstrate that DMT-OMPA outperforms other recent MPA variants, various classical algorithm variants, and newly proposed algorithms, verifying its advantages in precision and reliability. Furthermore, the application of this algorithm to various real-world engineering problems substantiates its broad applicability and high efficiency. The study’s findings not only deepen our understanding of swarm intelligence optimization algorithms but also provide a new efficient tool for solving complex engineering problems. The results indicate a promising potential for wider application in diverse fields, suggesting that the DMT-OMPA algorithm could become an effective tool for tackling complex optimization problems in the future.

Formulating strain-based quadrilateral membrane finite elements with drilling rotations

Membrane finite elements with drilling degrees of freedom have sparked interest in many research works since they can be conveniently combined with plates to form shell elements. This study presents two non-conforming strain-based four-node quadrilateral membrane elements, SBQ13 and SBQ13E, for static analysis. SBQ13 partially satisfies the equilibrium equations, while SBQ13E completely fulfils the force balance equations. Both elements carry drilling rotations at each node. One difficulty when formulating quadrilateral elements is the singularity in the transformation matrix, which is addressed in this study by utilising the properties of singular matrices. Both quadrilateral elements were tested in several benchmark problems. It has been found that both elements passed the higher-order patch test but failed the constant stress patch test. Nevertheless, SBQ13 produced accurate responses in most numerical tests, but SBQ13E unreasonably overestimated the solution. Solving the eigenvalue problem revealed that the SBQ13E element has a near-zero energy deformation mode, which might explain the anomaly. Although fulfilling equilibrium does not always enhance solution accuracy, it is essential to overcome volumetric locking. Apart from the newly developed elements, this paper presents several new ideas that may apply to strain-based element formulations.

Geometry-independent spline finite element method to analyze two-dimensional heat conduction and elasticity problems

Traditional isogeometric analysis involves redundant geometric calculations and is more complex than the finite element method when imposing boundary conditions. To address this, a geometry-independent spline finite element method is proposed, which integrates the geometric construction techniques of isogeometric analysis and the element construction techniques of finite element method. Firstly, the geometrical precision element is constructed by using non-uniform rational B-spline and B-splines to describe the geometry and the physical field, where a transformation matrix is introduced to construct shape functions with interpolation properties. Secondly, calculation formats for two-dimensional heat conduction and elasticity problems are derived by parameter mapping. Finally, the feasibility and accuracy of the method are verified through several numerical examples. Unlike in isogeometric analysis, in the proposed method, geometry and physics are separated, and the shape functions have interpolation properties, which reduce redundant geometry calculations and allow the boundary conditions to be applied directly to the nodes. The numerical results indicate that the method has a higher convergence rate compared to the original isogeometric analysis.

A novel color image encryption method using Fibonacci transformation and chaotic systems

INTRODUCTION: With the rapid increase in network information data, the protection of image data has become a challenging task, where image encryption technology can play an important role. This paper studies color image encryption algorithms and proposes a novel method for color image encryption to enhance the security and effectiveness of image encryption.OBJECTIVES: The purpose of this study is to effectively integrate different channel information of color images, thereby improving the effect of pixel decomposition based image encryption algorithm. Different indicators are used to analyze the effect of image encryption, and it is also compared with existing image encryption algorithms.METHODS: Initially, through pixel decomposition, the pixel values of the R, G, B channels of the color image, each with a depth of 8 bits, are decomposed into two integers between 0-15 and combined into a new data matrix. Then, multiple rounds of scrambling are performed on the transformed matrix. Next, the Fibonacci transformation matrix is applied to the scanned matrix to further change the values of its elements. Finally, XOR diffusion operation is carried out to obtain the encrypted image.RESULTS: Experimental results show that the proposed method achieves relatively good results in multiple image encryption indicator tests. The algorithm not only inherits the advantages of existing image encryption but also effectively integrates the information of each channel of the color image, providing better security.CONCLUSION: This study further proves the effectiveness of image encryption algorithms based on pixel decomposition and provides a new idea for better color image encryption algorithms, which is expected to be applied to other issues such as information hiding and data protection.

A multi-chamber soft robot for transesophageal echocardiography: continuous kinematic matching control of soft medical robots.

This research investigates designing a continuum soft robot and proposing a kinematic matching control to enable the robot to perform a specified medical task, which in this paper is the transesophageal echocardiography (TEE). A multi-chamber soft robot was designed and fabricated based on the molding of separate layers. The method of transformation matrices was used to develop the kinematic models, and a control method using Jacobian matrices was proposed to manipulate the robot. A prototype was made based on a multi-chamber multi-layer design. The system contains three segments that can be actuated independently to mimic the active bending part of the respective probe. Kinematic models were developed. Negative pressure (vacuum) was used as actuation input. An open-loop controller inspired by a redundancy resolution technique was proposed to make the soft robot tip follow the desired path, i.e.the path of the rigid ultrasound probe. It is concluded that the soft solution can perform the required task as the reachable points of the TEEtip cover the proposed robot workspace and the proposed control can be used for maneuvering in arbitrary trajectories.

Effect of Antiseizure Medication on the Salience Network in Patients with Epilepsy with Generalized Tonic-Clonic Seizures Alone.

This study aimed to investigate the effects of antiepileptic drugs on salience network regions in patients with epilepsy with generalized tonic-clonic seizures alone (EGTCSa). A retrospective observational case-control study was performed on 40 patients diagnosed with epilepsy with EGTCSa and 40 healthy age-matched controls. In LORETA, a voxel-by-voxel analysis between regions from the salience network was performed for both hemispheres, specifically between the anterior cingulate (BA 32 and BA 24) and the sublobar insula (BA 13). Subsequently, a Wilcoxon rank-sum test (the Mann-Whitney U test) was conducted for the equality of medians in the transformation matrix. A comparison was then made between each region of interest as defined by the salience network and the controls. Marked differences were found in the brain regions assessed in patients with EGTCSa treated with valproic acid and carbamazepine compared to the control group; few differences in patients treated with levetiracetam; and no difference was found in the group without treatment compared with those in the control group. These results suggest that ASMs can influence cognitive processes, which provide novel insights toward understanding the neural mechanisms underlying the effects of ASMs administration.

Multiple Sound Scattering by Combinations of Cylindrically Symmetric and Linearly Invariant Anomalies

A number of previous papers have used the coupled-mode method to assess three-dimensional scattering by cylindrically symmetric anomalies (seamounts, hills) or anomalies which are invariant in a horizontal direction (wedges, ridges). This paper makes an extension to combinations of these two anomaly types. The upper and lower depth boundaries of the anomalies may be flat or irregular, and the sound source may be anywhere in the medium. After a discretization of the anomalies of the two types with laterally homogeneous rings and strips, respectively, an adaptation of the coupled-mode method yields the solution of the pertinent Helmholtz equation. The adaptation involves a combination of Fourier-series summations to handle the ring anomalies and adaptive wavenumber integrations to handle the strip structure. For each anomaly, recursively computed reflection matrices relate the expansion coefficients for incoming and outgoing normal modes. Iterative solution of a linear equation system for the amplitudes of the scattered cylindrical waves from the ring anomalies, involving formulas for transformation between plane and cylindrical waves, yields an expansion of the field. Related expansions allow isolation of partial waves, multiply scattered among the anomalies. The paper includes examples from underwater acoustics and atmospheric acoustics.

Reparation with moving least squares sampling and extraction of body sizes of beef cattle from unilateral point clouds

Body measurements of beef cattle at various growth stages are crucial for assessing breeding quality. To decrease the stress responses of live cattle during measurement, noncontact body size measurement using a deep sensor is conducted. After directly obtaining the point cloud data (PCD) of a unilateral surface, novel point cloud repair and body measurement are proposed. The PCD of beef cattle are first preprocessed using Euclidean clustering, conditional filtering, and Random Sample Consensus. To merge the unilateral PCD into the entire contour, a Euclidean transformation matrix and moving least squares are applied. To address holes caused by stitching due to camera angle restrictions, various upsampling techniques based on least squares deformation are investigated to repair holes in different surfaces with varying growth stages. Finally, polynomial fitting is chosen to be in accordance with the feature point distribution of the body height (BH), chest girth (CG), back height (AH), waist height (WH), ischial tuberosity, and shoulder end of beef cattle. Using the formulas of Euclidean distance and cubic B–spline curve fitting, the values of BH, AH, WH, CG, and body length are obtained and then compared with manual measurement data. The predicted values of the five body sizes of 100 beef cattle had a mean absolute error and mean absolute percentage error of 7.77 cm and 5.42 %, respectively. The largest absolute error was 12.05 cm, and the smallest absolute error was 4.12 cm. A series of PCD processing and repair methods provides a new method for the noncontact automated measurement of beef cattle. This approach promotes more effective practices in livestock welfare and trait assessment compared with traditional management.

Q-discretization of the Kostant–Toda equation and its asymptotic analysis

Abstract The famous Toda equation is an integrable system related to similarity transformations of tridiagonal matrices. The discrete Toda equation, which is a time-discretization of the Toda equation, is essentially the recursion formula of the quotient-difference (qd) algorithm for computing eigenvalues of tridiagonal matrices. Another time-discretization of the Toda equation is the $q$-discrete Toda equation, which is derived by replacing standard derivatives with the so-called $q$-derivatives that involves a parameter $q$ such that $0<q<1$. In a prior work, we related the $q$-discrete Toda equation to implicit-shift $LR$ transformations (which are similarity transformations) of tridiagonal matrices. Furthermore, we developed the determinantal solution to clarify the convergence as discrete-time goes to infinity. In this paper, we propose an extension of the $q$-discrete Toda equation as a time-discretization of the Kostant–Toda equation and then show the convergence as discrete-time goes to infinity from the perspective of implicit-shift $LR$ transformations of Hessenberg matrices. We also present numerical examples to verify the convergence as discrete-time goes to infinity in the proposed $q$-discrete Kostant–Toda equation.

Nonnegative low multi‐rank third‐order tensor approximation via transformation

AbstractThe main aim of this paper is to develop a new algorithm for computing a nonnegative low multi‐rank tensor approximation for a nonnegative tensor. In the literature, there are several nonnegative tensor factorizations or decompositions, and their approaches are to enforce the nonnegativity constraints in the factors of tensor factorizations or decompositions. In this paper, we study nonnegativity constraints in tensor entries directly, and a low rank approximation for the transformed tensor by using discrete Fourier transformation matrix, discrete cosine transformation matrix, or unitary transformation matrix. This strategy is particularly useful in imaging science as nonnegative pixels appear in tensor entries and a low rank structure can be obtained in the transformation domain. We propose an alternating projections algorithm for computing such a nonnegative low multi‐rank tensor approximation. The convergence of the proposed projection method is established. Numerical examples for multidimensional images are presented to demonstrate that the performance of the proposed method is better than that of nonnegative low Tucker rank tensor approximation and the other nonnegative tensor factorizations and decompositions.

Cultural relics fragment assembly based on fracture surface contour features

Addressing the issue of registration deviations caused by local fragment loss and shape diversity during the process of cultural relics fragment assembly, this paper proposes a method for assembling cultural relics fragments based on the contour features of fracture surfaces. Initially, the curvature of discrete point clouds is calculated using the quartic surface method and the Weingarten matrix, and curvature discontinuity points are identified using a proportional method as a candidate feature point set. Subsequently, the angle difference between a point and its neighboring points’ directed segments is defined as a neighborhood feature parameter, which further optimizes the feature point set and selects the optimal matching set. Then the 4-points congruent sets (4PCS) algorithm is utilized for the initial registration of the fragments, and the unit quaternion method is employed to calculate the rigid body transformation matrix during the iteration process. Finally, corresponding point pairs are determined by the intersection of a point’s normal with a set of points, improving the iterative closest point (ICP) algorithm to achieve precise assembly of the fragments. The experimental results show that, compared to other assembly algorithms, the proposed method is more accurate in feature point extraction, robust, and effectively enhances the accuracy and efficiency of fragment assembly.

Low-Rank Tensor Completion Based on Self-Adaptive Learnable Transforms.

The tensor nuclear norm (TNN), defined as the sum of nuclear norms of frontal slices of the tensor in a frequency domain, has been found useful in solving low-rank tensor recovery problems. Existing TNN-based methods use either fixed or data-independent transformations, which may not be the optimal choices for the given tensors. As the consequence, these methods cannot exploit the potential low-rank structure of tensor data adaptively. In this article, we propose a framework called self-adaptive learnable transform (SALT) to learn a transformation matrix from the given tensor. Specifically, SALT aims to learn a lossless transformation that induces a lower average-rank tensor, where the Schatten- p quasi-norm is used as the rank proxy. Then, because SALT is less sensitive to the orientation, we generalize SALT to other dimensions of tensor (SALTS), namely, learning three self-adaptive transformation matrices simultaneously from given tensor. SALTS is able to adaptively exploit the potential low-rank structures in all directions. We provide a unified optimization framework based on alternating direction multiplier method for SALTS model and theoretically prove the weak convergence property of the proposed algorithm. Experimental results in hyperspectral image (HSI), color video, magnetic resonance imaging (MRI), and COIL-20 datasets show that SALTS is much more accurate in tensor completion than existing methods. The demo code can be found at https://faculty.uestc.edu.cn/gaobin/zh_CN/lwcg/153392/list/index.htm.

2-D DOA Estimation of Coherent Signals Using the Dual-Size Spreading Array

Abstract We introduce a novel approach for high-precision estimation of two-dimensional (2-D) Direction-of-Arrival (DOA) under conditions of coherent interference. This study innovatively devises an antenna configuration, termed the Dual-Size Spreading Array, specifically tailored to estimate DOAs in such environments. The method involves integrating a subarray with the primary array to create a Dual-Size Extended Array structure. This integration allows for a transformation of the covariance matrix into a new form, where its rank solely depends on the number of impinging waves. Both the subarray and primary array must have a scale no less than the number of incoming wavefronts. This proposed technique not only amplifies the effective aperture but also significantly reduces the computational intricacy associated with DOA estimation procedures. The efficacy of our methodology has been substantiated through simulation results, which demonstrate that it outperforms the conventional spatial smoothing techniques. Moreover, we provide several practical guidelines designed to enhance estimation accuracy while concurrently minimizing computational demands. In summary, this research presents an advanced solution that effectively addresses challenges in 2D DOA estimation under coherent scenarios, achieving improved performance and computational efficiency compared to existing methods.

A knowledge-data integration framework for rolling element bearing RUL prediction across its life cycle

Prediction of Remaining Useful Life (RUL) for Rolling Element Bearings (REB) has attracted widespread attention from academia and industry. However, there are still several bottlenecks, including the effective utilization of multi-sensor data, the interpretability of prediction models, and the prediction across the entire life cycle, which limit prediction accuracy. In view of that, we propose a knowledge-based explainable life-cycle RUL prediction framework. First, considering the feature fusion of fast-changing signals, the Pearson correlation coefficient matrix and feature transformation objective function are incorporated to an Improved Graph Convolutional Autoencoder. Furthermore, to integrate the multi-source signals, a Cascaded Multi-head Self-attention Autoencoder with Characteristic Guidance is proposed to construct health indicators. Then, the whole life cycle of REB is divided into different stages based on the Continuous Gradient Recognition with Outlier Detection. With the development of Measurement-based Correction Life Formula and Bidirectional Recursive Gated Dual Attention Unit, accurate life-cycle RUL prediction is achieved. Data from self-designed test rig and PHM 2012 Prognostic challenge datasets are analyzed with the proposed framework and five existing prediction models. Compared with the strongest prediction model among the five, the proposed framework demonstrates significant improvements. For the data from self-designed test rig, there is a 1.66 % enhancement in Corrected Cumulative Relative Accuracy (CCRA) and a 49.00 % improvement in Coefficient of Determination (R2). For the PHM 2012 datasets, there is a 4.04 % increase in CCRA and a 120.72 % boost in R2.

A new winding structure with low common‐mode current in input series output parallel planar transformer LLC converter

AbstractMHz switches and integrated magnetic planar transformers (PT) promote the high density and miniaturization of DC/DC converters. The parasitic parameters of the PT at high frequency significantly affect the performance of converters, resulting in severe electromagnetic interference (EMI) problems. Firstly, this paper proposes a new common‐mode (CM)‐suppression winding structure for the input series output parallel (ISOP) matrix transformer LLC converter. The sources and conduction principle of CM noise are analyzed. Furthermore, this optimization based on winding shape and position is simple and feasible, suppressing the CM noise significantly. Compared with conventional multilayer winding structure, this optimization increases the current‐carrying area by 2.8%–5.9%, effectively improving the primary current distribution. In addition, the proposed structure makes the best planar windings in footprint with expanded windings, bringing the simplest layout in the primary winding. Finally, a 1 MHz 400 V/12 V 300 W LLC converter is constructed to verify the effect of this winding structure. The results show that a 40% reduction in CM current can be achieved while maintaining the current balance.

Damage Detection in External Tendons of Post-Tensioned Bridges

This study investigates damage detection in the tendons of post-tensioned segmental box girder bridges, focusing on the vibration-based technique and its application in conjunction with the Precursor Transformation Matrix (PTM). Due to the critical role of bridge tendons in structural integrity, efficient and timely detection methods are essential. The methodology combines theoretical modeling with Finite Element Method (FEM) simulations and empirical data collection to evaluate the PTM’s effectiveness in identifying tendon damage. Key results indicate that the PTM, when paired with vibration analysis, enhances the identification and localization of damage, proving to be a robust method in structural health monitoring. This approach not only speeds up damage detection but also potentially lowers maintenance costs by pinpointing specific damage sites, thereby preventing widespread structural failures. The findings offer a promising tool for ensuring the longevity and safety of post-tensioned bridges.

Research on a Support-Free Five-Degree-of-Freedom Additive Manufacturing Method.

When using traditional 3D printing equipment to manufacture overhang models, it is often necessary to generate support structures to assist in the printing of parts. The post-processing operation of removing the support structures after printing is time-consuming and wastes material. In order to solve the above problems, a support-free five-degree-of-freedom additive manufacturing (SFAM) method is proposed. Through the homogeneous coordinate transformation matrix, the forward and inverse kinematics equations of the five-degree-of-freedom additive manufacturing device (FAMD) are established, and the joint variables of each axis are solved to realize the five-axis linkage of the additive manufacturing (AM) device. In this research work, initially, the layered curve is obtained through the structural lines of the overhang model, and a continuous path planning of the infill area is performed on it, and further, the part printing experiments are conducted on the FAMD. Compared with the traditional three-axis additive manufacturing (TTAM) method, the SFAM method shortens the printing time by 23.58% and saves printing materials by 33.06%. The experimental results show that the SFAM method realizes the support-free printing of overhang models, which not only improves the accuracy of the parts but also the manufacturing efficiency of the parts.

Straight-Beam Approach for Vibration Analysis of Horizontal Curved Beams

This paper investigates the use of straight-beam elements to simulate the vibration of curved beams that is mathematically more challenging. First, analytical solutions of the out-of-plane and in-plane dynamic responses of the curved beam are derived for reference. Then, for the straight beam approach, the elastic stiffness matrix, consistent mass matrix, consistent nodal loads, and transformation matrix are derived and included in a procedure for computing the dynamic responses of the curved beam. The effectiveness of the straight beam approach in analyzing the free vibration and forced vibration (induced by moving vehicle) of the curved beam is validated, with the results compared with the theoretical solutions and those by Abaqus. It can be concluded that the straight beam approach is a simple and efficient means for analyzing the out-of-plane and in-plane vibrations of curved beams with high precision.

A Retina-inspired Sampling Method for Coding and Compression for Enhancement Image Based on Discrete Double Density Wavelet Transformer

The retina, a layer of light-sensitive tissue on the inner surface of the eye, is what allows for vision. That propose to design and analytically examine an image quantizer coding that is inspired by the way the retina manages and compresses visual features based on past studies. Retina-inspired coding is a new cipher algorithm which is very promising. Comparing the Double-Density Discrete Wavelet Transform (DDDWT) to earlier traditional approaches, it is more difficult but also produces excellent results. This efficient coding is credited to a streamlined account that, by the way, deals with 2-D and 3-D pictures, transformation matrices, and the conversion of the number DDWT as if via matrix multiplication. Naturally, this code makes a lot of interesting points of view available. In this proposal, we'll try to show how various theoretical model extensions can be applied to applications in video surveillance, information technology, and neuroscience. Therefore, that believe that using a multidisciplinary approach will help system achieve objectives. This strategy would apply signal processing methods with data from neurophysiology. There are hoping that our efforts will result in some innovative new coding algorithms. The proposed codes will be implemented in MATLAB for ease of experimentation. To implement this code more successfully, a low-level programming language is required. Index Terms— DDDWT, Retina-inspired, Coding.