Transformation Matrix Research Articles

Prognostic value of synthetized right-side precordial leads in arrhythmogenic right ventricular cardiomyopathy: data from nordic, dutch, and canadian ARVC registers

Abstract Background T-wave inversion (TWI) in standard ECG leads is a proven risk marker for life-threatening ventricular arrhythmias (VA) in arrhythmogenic right ventricular cardiomyopathy (ARVC). Right-sided precordial leads (RSPL), which may be more sensitive for detection of the arrhythmogenic substrate, are rarely recorded and understudied in this context. Computerized ECG signal-processing allows synthesis of right-sided precordial ECG leads derived from standard 12-lead ECG. Objective We aimed to assess the value of TWI in RSPL, synthetized from the standard 12-lead ECG, for prediction of VA risk in ARVC patients with subtle ECG phenotypes. Methods Patients with definite ARVC by TFC2010 and no history of sustained VA prior to diagnosis from the Nordic, Canadian and Dutch ARVC registries were included. Patients with major repolarization criterion or complete right bundle branch block (RBBB) were excluded. RSPL (V3R-V6R) were derived from digitally recorded eight linearly independent leads (I, II and precordial V1 to V6) of the standard ECG using a linear ECG transformation matrix. The matrix was previously developed based on a library of body surface potential maps from a mixed group of healthy subjects and patients with cardiac diseases using multivariate linear regression and QRS-T data obtained from averaged beats of the right-sided-precordial leads and the basis leads. TWI exceeding 0.1 mV in any of the synthetized leads was tested for its ability to predict sustained VA, defined as either sustained ventricular tachycardia, appropriate ICD shock, aborted cardiac arrest, or sudden cardiac death. In a similar manner, the value of TWI in any of the inferior leads III, aVF or II was assessed. Hazard ratio was calculated using Cox regression analysis adjusted for age, sex, and proband status. Results In total, 144 patients without prior VA history were identified. After exclusion of patients with major repolarization criterion (n=37) and RBBB (n=11), 96 patients comprised the study group (mean age 40±16, 42% female, 41% probands, 48% ICD carriers). Fifty-nine patients (62%) had TWI in one or more synthetized RSPL and 33 patients (34%) had TWI in any of the inferior leads. During 10 years of follow-up, 11 patients (12%) developed VA. Kaplan-Meier curve analysis showed significant association between the presence of TWI in at least one of the RSPL and the risk of VA, which remained an independent predictor in the adjusted Cox regression analysis (HR 10.6, 95%CI 1.3-84.4, p=0.026). TWI in any of the inferior leads was not associated with the risk of VA in this cohort (HR 1.2 95%CI 0.26-5.42). Conclusions Synthetized right-sided precordial leads appear to contain information potentially useful for refining risk stratification of primary prevention ARVC patients with a subtle ECG phenotype, in whom traditional repolarization markers, such as major repolarization criterion or TWI in inferior leads, are not informative.

Approximation of Doublewalsh–Fourier Series by Means of the Matrix Transform

Approximation of Doublewalsh–Fourier Series by Means of the Matrix Transform

Dynamics of a knuckle crane carrying a load subjected to wind pressure

AbstractThe paper presents the authors’ model of a knuckle crane offshore type that takes into account the flexibility of boom and drives, which is used to analyze the effect of constant wind pressure or cyclical gusts on the dynamics of the crane and the load. The mathematical model of the crane is derived using a formalism of joint coordinates, homogeneous transformation matrices, and Lagrange equations. Using this model, the influence of wind pressure on the torques and forces in the crane drives and on the accuracy of load positioning is investigated. The results show that the influence of wind on the accuracy of load positioning should not be assessed by limiting the observation to the movement of its gravity center but by observing the movement of characteristic points, the corners of the load. Root mean squared (RMS) indicators are used to quantitatively assess this impact on the driving torque and forces, and appropriate indicators are proposed to assess the accuracy of load positioning.

MAGIC SQUARES OF PERFECT SQUARES AND PELL NUMBERS

Order three magic squares of distinct squared integers are studied. We show that such a magic square is not possible if the smallest entry is the square of a prime number, or unity. A method for generating all arithmetic progressions of three squared integers whose smallest term is the square of a prime or unity is presented via a set of linear transformation matrices involving the Pell numbers.

CRTF-MoeICP: A robust coarse-to-fine reflector-based LiDAR indoor positioning algorithm

The reflector-based Light Detection and Ranging (LiDAR) positioning method is susceptible to environmental interferences, resulting in instability. This instability not only reduces movement accuracy but also poses safety hazards. To solve the above problems in the application of LiDAR sensors in the field of indoor positioning, we propose a Coarse Registration algorithm based on the Triangular Feature (CRTF) and a fine registration algorithm based on Multi-level outlier elimination and Iterative Closest Point (MoeICP) for the reflector-based LiDAR positioning. The proposed coarse-to-fine positioning algorithm CRTF-MoeICP addresses the issue of reflector-based LiDAR positioning failure arising from the improper selection of the initial transformation matrix and outlier interference in indoor structured industrial environments. The experiment results show that the CRTF-MoeICP algorithm can ensure the stable registration of the LiDAR point cloud and the reflector map by completely removing all outliers, greatly improving the indoor positioning stability of LiDAR sensors. Besides, the proposed algorithm can be realized by LiDARs with different performance, and improve the static positioning repeatability to ±3 mm. The high precision and stable positioning results improve the motion accuracy, ensuring that the Automatic Guided Vehicle (AGV) can accurately and stably complete the handling task.

Complex system fault diagnosis based on interpretive structural model

To realize the fault diagnosis of complex systems, a fault diagnosis method for complex systems based on the explanatory structural model is proposed. According to the fault mechanism analysis, the fault association matrix of system elements is established. The explanatory structural model is applied to transform the fault association relationship of complex systems into an intuitive hierarchical structural model through matrix transformation, so as to realize the structuring and hierarchical propagation of system faults. The PageRank algorithm is introduced to evaluate the influence and impact of system element faults. According to the influence and impact of the same-layer components and the fault transmission logic, the main cause of system fault transmission is clarified, which provides a basis for fault diagnosis. Finally, a specific application is carried out with a certain device as an example to verify the effectiveness of the method.

Atomic force microscopy wide-field scanning imaging using homography matrix optimization

During the offline combination of multiple atomic force microscopy (AFM) images, changes in probe displacement can be affected by dynamic noise, leading to dislocation and tearing in the stitching. To overcome this, we designed a homography matrix optimization method to describe the relative positional relationship between images by constructing the original image matrix and applying singular value decomposition to denoise the homography matrix. Additionally, we implemented a scale-invariant feature transform (SIFT) to extract feature points. To verify the effectiveness of this method, the SIFT + RANSAC (R), SIFT + affine transformation (AT), and oriented FAST and rotated BRIEF (ORB) algorithms were compared with the proposed algorithm. The experimental results demonstrate that the proposed method precisely computes the transformation matrix, thereby guaranteeing the geometric consistency of mosaic imaging. The proposed method preserves the intricate details of the original image and enhances the stitching quality of wide-field images.

GNSS-assisted optimal alignment method for low-cost SINS motion of vehicle

Abstract To improve the alignment accuracy and environmental applicability of the micro-electromechanical system (MEMS)-based strapdown inertial navigation system (SINS), this study proposes a global navigation satellite system (GNSS)-assisted multi-vector determination of the attitude optimal indirect coarse alignment. Using the inertial information output from the inertial measurement unit and the velocity information from the GNSS, a simplified velocity observation vector is constructed and the velocity lever arm stemming from the mounting position inconsistencies of the GNSS and SINS is fed back into the velocity of the carrier system. When constructing the observation vectors, the integration interval is shortened by reconstructing the two-vector integration formula for reducing the cumulative error of the inertial device. The attitude matrix problem is defined as the Wahba problem, which is solved using the singular value decomposition method. Based on the relationship between gyro zero bias and misalignment angle, the corresponding state and measurement equations are designed. Furthermore, owing to the measurement noise uncertainty, the adaptive traceless Kalman filtering algorithm is introduced to realize the effective adaptation processing of the measurement noise. More accurate attitude matrix estimates are obtained by continuously correcting the carrier system transformation matrix. The running car experiment results show that the proposed method exhibits higher alignment accuracy and environmental applicability than the current MEMS strapdown inertial navigation coarse alignment method and the traditional optimization-based alignment method.

Industrial robot calibration optimization method based on R-optimal criterion and improved IOOPS algorithm

Abstract In this paper, a novel kinematic parameter calibration method based on the R-optimal criterion and the improved iterative one-by-one pose search (IOOPS) algorithm is proposed to improve the end-effector positioning accuracy of industrial robots. First, a novel industrial robot error calibration model based on the product of exponential model and generalized error model is established, and the ideal pose transformation matrix from the robot base coordinate system to the laser tracker measurement coordinate system is obtained using the least-squares method, thereby obtaining the initial parameter vector of the robot calibration system. Second, various joint angle values at different positions within the robot’s workspace and the corresponding end-effector coordinate data, namely calibration sampling point data, are collected. Subsequently, the improved IOOPS algorithm combined with the observability index O R proposed by the R-optimal criterion is used to select the optimized calibration sampling points. Finally, the optimized sampling point data are combined with the Levenberg–Marquardt algorithm to optimize the parameters and obtain the optimal kinematic parameters. The experimental results show that the average end-effector error of the robot decreases from 0.5822 to 0.2492 mm after calibration using this method, demonstrating the effectiveness of the optimized sampling points in the calibration process achieved through the improved algorithm and the new observability index.

Other fundamental systems of solutions of the differential equation (D 2 – 2αD + α 2 + β 2) n y = 0, β ≠ 0

Abstract This paper generalizes the results of the first part of the paper [Fecenko, J.—Diekema, E.: On the linear (in)dependence of sequences of derivatives of the functions xn sin x and xn cos x, http://arxiv.org/abs/2305.11184]. The main goal is to prove that the sequence of functions f(x), Df(x), …, D 2n–1 f(x), where f(x) is x n−1e αx sin βx or x n−1 e αx cos βx for β ≠ 0, forms a fundamental system of solutions of the differential equation (D 2 – 2αD + α 2 + β 2) n y = 0. Or more generally, that the sequence of functions Dkf(x), D k+1 f(x), …, D 2n+k–1 f(x), k ∈ ℕ also forms a fundamental system of solutions of the aforementioned differential equation. The problem is solved using a suitable transformation of the Wronskian matrix, by solving a nonlinear differential equation and then calculating the determinant of the modified Wronskian matrix by applying Laplace’s generalized expansion.

Quasi-Diabatization Based on Minimizing Derivative Couplings in a Limited Configuration Space: Elimination of Boundary Condition Dependence.

Due to the cuspidal ridges of adiabatic potential energy surfaces (PESs) and singularities of nonadiabatic couplings (NACs), obtaining an analytical expression for the adiabatic Hamiltonian is difficult. Thereby, nonadiabatic dynamics simulations are often carried out on-the-fly, which is time-consuming. This motivates us to construct quasi-diabatic representations, which have smooth PESs and diabatic couplings. In this study, we propose a new quasi-diabatization method based on minimizing derivative couplings (MDC) in a limited configuration space. The boundary conditions are first considered and finally released to obtain the adiabatic-to-diabatic rotation angles and transformation matrices. As demonstrated in representative one- and two-dimensional models and the widely studied linear H3 molecule, MDC performs significantly better than the direct integration quasi-diabatization approach. In particular, accurate diabatic potential energy matrices have been successfully obtained even when the NACs of all configurations in the considered space are nonnegligible.

A precise registration method for large-scale urban point clouds based on phased and spatial geometric features

Abstract The dense high-rise buildings and multipath effects in urban areas significantly reduce the positioning signal accuracy of laser scanning systems, leading to layering and offset issues in the collected point cloud data on the same road. In order to acquire comprehensive and consistent three-dimensional information on the objects, thereby providing field inspection data for large-scale road traffic network scenarios, in this paper, an improved point cloud registration method is proposed to divide the registration process into two stages: elevation registration and plane registration. Elevation registration takes the ground point cloud as the registration primitive, reduces the number of point clouds through curvature down-sampling, and constrains the feature point sequence with a fixed range to provide a good initial pose for fine registration. The plane registration first inherits the elevation registration parameters, combining the dynamic distance parameters of spherical region step based on the median, using robust multi-scale loss functions to address residual points, effective adjacent point pairs are selected to obtain the spatial transformation matrix, and realizes accurate registration. Experimental results with multiple sets of urban point cloud data show that the root mean square error of point cloud registration can be controlled within 0.06 m, achieving a relatively superior registration accuracy, it can provide detailed prior data for measurement information analysis.

Information fusion in order-2 fuzzy environments: A matrix transformation perspective

Order-2 information granules, as a representation of multi-layer structured information, have recently rekindled discussions. It is usually generated by abstracting order-1 information granules. When the dependence relationship and corresponding membership function of the order-1 information granules (reference information granules) are known, Pedrycz et al. used a method based on gradient optimization to complete the aggregation of the order-2 information granules. In this paper, we discuss a more specific scenario: not only the dependencies between reference information granules are captured, but also the order-1 information granules can be expressed as specific fuzzy information distributions. For this, we propose a fusion scheme of order-2 fuzzy sets based on matrix transformation called CQRP. To our knowledge, it is the first method that completely integrates the structural information of the order-2 environment into the fusion of order-2 fuzzy sets. In the process, we also creatively proposed the attraction and exclusion of structural information, deepening the understanding of structural information. Through sufficient comparison and analysis, we prove that it makes fuller use of information in the order-2 environment and is more reasonable and effective in tasks such as classification and identification.

Research on the stiffness characteristics and contact status of matched angular contact ball bearings considering the effect of varying spatial position of rolling ball

In engineering practice, bearings used as support components are usually installed in pairs in various rotating machines. The mechanical and contact characteristics of bearings play a crucial role in determining the operational accuracy, safety performance and stability of equipment. Numerous studies focused on single bearings have been reported form diffident aspects for enhancing service performance. However, the literature reports on the matched bearings are scarce due to the mutual coupling of rolling elements and the extremely complex stress conditions. Especially the stiffness fluctuation and internal contact status affected by the ball position are difficult to be observed and tested experimentally because of the complex and compact structure, which significantly impacts the safe and reliable operation of rotating machines. To overcome the above shortcomings, this paper investigates the effect of ball position on the stiffness characteristics and contact status of matched angular contact ball bearings based on the coordinate matrix transformation approach and Jones’ statics model. Then, the stiffness results of published literature are used as a benchmark to validate the accuracy of solution method of this paper. Finally, 7206B bearings with different installing forms are used as a numerical example to reveal the effect of ball position on the stiffness characteristics and contact status of matched angular contact ball bearings under different working conditions. The study provides a scientific guidance to investigate the mechanical characteristics and contact mechanism of multi-bearing system.

Wideband beam domain sparse Bayesian learning passive focusing localisation algorithm

AbstractTo address the challenges of large‐aperture sonar systems passive localisation, this paper proposes the application of sparse Bayesian learning (SBL) for passive target localisation in the wideband beam domain. The proposed algorithm aims to overcome the issues of massive computational requirements for two‐dimensional SBL scanning and increased localisation errors due to interference energy leakage. The wideband beam domain SBL focusing localisation algorithm is developed by constructing an azimuth‐range two‐dimensional transformation matrix to preprocess array data, which effectively reduces the computational load of SBL processing while suppressing strong interference energy leakage in passive sonar operating environments, thus improving the range resolution and parameter estimation accuracy of focusing localisation. Simulation and sea trial data analyses demonstrate the feasibility of the proposed algorithm, with results indicating its superior performance compared to existing algorithms.

Analysis and Design of High Power Density Flyback Converter

ABSTRACTThis paper presents a flyback converter with high efficiency and high power density. An optimal design method for high power density planar transformers is presented. Applying the principle of flux cancellation, a matrix transformer that originally needed an independent magnetic core was integrated into a single magnetic core to reduce the volume of the core. This method effectively reduces the printed circuit board (PCB) layer number of the planar transformer and increases the possibility of the application of the planar transformer in the flyback converter. An optimized design method of the winding structure is given according to that model to further reduce the winding loss of the transformer. Meanwhile, the proposed structure is verified by finite element analysis software. Finally, a multi‐output flyback converter with a frequency of 100 kHz is designed to verify the practical performance of the proposed transformer.

Exploring the effects of finite size and indenter shape on the contact behavior of functionally graded thermoelectric materials

The performance enhancement of functionally graded thermoelectric (FGTE) devices is significantly influenced by contact studies of the FGTE materials. It is unclear how the finite thickness and the punch geometry influence the FGTE materials’ contact behaviors. This paper investigates the frictionless contact problem between three types of rigid punches (flat, triangular, and cylindrical) and the FGTE strip with finite thickness. The electric-thermo-elastic parameters of the FGTE strip vary in the thickness direction according to an exponential function. Based on the Fourier integral transform and the transformation matrix method, the problem is transformed into the numerical solution of three sets of singular integral equations. The presence of singular features on either side of the punch demands the adoption of specific collocation strategies. The distribution of the normal current density, the normal energy flux, and the normal contact stress is obtained by adjusting multiple electric-thermo-elastic parameters. The contact stresses in the case of punches with varying shapes can be effectively controlled by modulating the coefficient of thermal expansion and the strip thickness, whereas the effect of the electrical conductivity, the shear modulus, and the thermoelectric load on these stresses depends on whether they are increased or decreased.

Fault Isolation and Fault‐Tolerant Control Design for Non‐Gaussian Stochastic Distribution Control Systems With Multiple Sensor Faults

ABSTRACTA fault isolation, estimation and fault‐tolerant control algorithm is proposed for non‐Gaussian stochastic distribution control systems with disturbance and multiple sensor faults. Sensor faults are represented as actuator faults virtually, and an observer is devised to detect the sensor fault occurrence time. Then two subsystems are separated by the expanded system through introducing the coordinate transformation matrices. One subsystem contains only sensor faults and does not contain disturbance and the other contains sensor faults and disturbance, which provides convenience for fault isolation. The faults are estimated respectively by the multiple fault isolation observers with the same number of sensors. A fault‐tolerant control scheme is proposed after getting the fault information to compensated sensor faults and track the desired probability density function. Finally, a MATLAB simulation example is used to verify the feasibility of the algorithm.

Improvement of Planar Integrated Matrix Transformer for CM Noise Cancellation Applied to Full-Bridge LLC-DCX Converter

Improvement of Planar Integrated Matrix Transformer for CM Noise Cancellation Applied to Full-Bridge LLC-DCX Converter

Identification Source Term of the Distributed Order Time-Space Fractional Diffusion Equation

Abstract The inverse source problem for time-distributed order spatial fractional diffusion equations is examined in this study. The forward problem is solved by combining finite difference methods with matrix transformation techniques. The Tikhonov regularization approach is then applied to convert the inverse problem into a variational problem. The optimal perturbation approach is used to find the minimizer of the variational problem, leading to an approximation solution that depends solely on the time-dependent source term. The algorithm’s effectiveness and stability are demonstrated using numerical examples in one-dimensional domains.