Coefficient Matrix Research Articles

МЕТОДИКА РАСЧЕТА КОМБИНИРОВАННОЙ КОНСТРУКЦИИ ПОКРЫТИЯ ШПРЕНГЕЛЬНОГО ТИПА

Hybrid building structures have advantages in terms of efficiency of using high-strength materials and reducing deformations under load. To expand the scope of their practical application, it is necessary to improve techniques for structural analysis and design methods. The object of the present research is a hybrid structure of the strutted-type. The top chord of the structure is formed by rectilinear beams arranged in radial direction and pivotally connected in the ridge joint. The bottom chord consists of high-strength cable elements and hinge struts. For the static analysis of the structure, its flat model is adopted. The static indeterminacy is solved by means of the method of redundant reactions. The applicability of the method is justified by restriction of structural deformations implied by the serviceability limit state. Analytical expressions are proposed to determine the forces and bending moments in the main structural elements. The resulting expressions are unified to perform the structural analysis under pre-stress and external loads by means of supplementary parameters introduced. An improved technique for finding the matrix of coefficients and the vector of free terms of the canonical system of the method of redundant reactions is proposed. The technique allows automating the calculation. A method for taking into account flexible cable elements is developed. The method includes step-by-step eliminating of compressed cables from the design scheme. The results of the work contribute to the development of hybrid strutted-type structures and can be used for developing optimal design solutions, as well as to identify patterns of stress-strain state of the hybrid structures by means of the numerical simulation.

Calibration Optimization of Kinematics and Dynamics for Delta Robot Driven by Integrated Joints in Machining Task

For the application of Delta robots with a 3-R(RPaR) configuration in machining tasks, this paper constructed a 54-parameter kinematic error model and a simplified dynamic model incorporating an integrated joint’s position error and friction, respectively. Utilizing Singular Value Decomposition (SVD) of the Linear Model Coefficient Matrix (LMCM) and the coefficient chart, a criterion for identifiability of error components is established. For good identification results, the optimal measurement surface with Fourier series form is obtained using a combination of the Hook–Jeeves Direct Search Algorithm (DSA) and Inner Point Method (IPM). The friction coefficients and other dynamic parameters are obtained through fitting the integrated joint torque-angle pairs measured along specific trajectories using nonlinear least squares regression. The validation of the calibration process is conducted through simulations and experiments. The calibration results provide a foundation for the precise control of integrated joints and the high-precision motion of robots.

Improved Model Predictive Control Path Tracking Approach Based on Online Updated Algorithm with Fuzzy Control and Variable Prediction Time Domain for Autonomous Vehicles

The design of trajectory tracking controllers for smart driving cars still faces problems, such as uncertain parameters and it being time-consuming. To improve the tracking performance of the trajectory tracking controller and reduce the computation of the controller, this paper proposes an improved model predictive control (MPC) method based on fuzzy control and an online update algorithm. First, a vehicle dynamics model is constructed and a feedforward MPC controller is designed; second, a real-time updating method of the time domain parameters is proposed to replace the previous method of empirically selecting the time domain parameters; lastly, a fuzzy controller is proposed for the real-time adjustment of the weight coefficient matrix of the model predictive controller according to the lateral and heading errors of the vehicle, and a state matrix-based cosine similarity updating mechanism is developed for determining the updating nodes of the state matrix to reduce the controller computation caused by the continuous updating of the state matrix when the longitudinal vehicle speed changes. Finally, the controller is compared with the traditional model prediction controller through the co-simulation of CARSIM and MATLAB/Simulink, and the results show that the controller has great improvement in terms of tracking accuracy and controller computational load.

Quaternion Differential Matrix Equations with Singular Coefficient Matrices

Quaternion Differential Matrix Equations with Singular Coefficient Matrices

Non-negative consistency affinity graph learning for unsupervised feature selection and clustering

Feature selection plays a crucial role in data mining and pattern recognition tasks. This paper proposes an efficient method for robust unsupervised feature selection, called joint local preserving and low-rank representation with nonnegative and symmetric constraint (JLPLRNS). This approach utilizes an indicator matrix instead of the row sparsity of the projection matrix to directly select some significant features from the original data and adaptively preserves the local geometric structure of original data into the low-dimensional embedded feature subspace via learned indicator matrix. By simultaneously imposing nonnegative symmetric and low-rank constraints on the representation coefficient matrix, it cannot only make this matrix discriminative, sparse and weight consistency for each pair of data, but also uncover the global structure of original data. These effectively will improve clustering performance. An algorithm based on the augmented Lagrange multiplier method with an alternating direction strategy is designed to resolve this model. Experimental results on various real datasets show that the proposed method can effectively identify some important features in data and outperforms many state-of-the-art unsupervised feature selection methods in terms of clustering performance.

Investigation of Viscoelastic Guided Wave Properties in Anisotropic Laminated Composites Using a Legendre Orthogonal Polynomials Expansion-Assisted Viscoelastodynamic Model.

This study investigates viscoelastic guided wave properties (e.g., complex-wavenumber-, phase-velocity-, and attenuation-frequency relations) for multiple modes, including different orders of antisymmetric, symmetric, and shear horizontal modes in viscoelastic anisotropic laminated composites. To obtain those frequency-dependent relations, a guided wave characteristic equation is formulated based on a Legendre orthogonal polynomials expansion (LOPE)-assisted viscoelastodynamic model, which fuses the hysteretic viscoelastic model-based wave dynamics and the LOPE-based mode shape approximation. Then, the complex-wavenumber-frequency solutions are obtained by solving the characteristic equation using an improved root-finding algorithm, which leverages coefficient matrix determinant ratios and our proposed local tracking windows. To trace the solutions on the dispersion curves of different wave modes and avoid curve-tracing misalignment in regions with phase-velocity curve crossing, we presented a curve-tracing strategy considering wave attenuation. With the LOPE-assisted viscoelastodynamic model, the effects of material viscosity and fiber orientation on different guided wave modes are investigated for unidirectional carbon-fiber-reinforced composites. The results show that the viscosity in the hysteresis model mainly affects the frequency-dependent attenuation of viscoelastic guided waves, while the fiber orientation influences both the phase-velocity and attenuation curves. We expect the theoretical work in this study to facilitate the development of guided wave-based techniques for the NDT and SHM of viscoelastic anisotropic laminated composites.

APPLICATION OF THE SINGULAR DECOMPOSITION OF THE MATRIX IN SOLVING INCORRECT GEODESIC PROBLEMS

The most reliable method for solving linear equations of the least squares principle, which can be used to solve incorrect geodetic problems, is based on matrix factorization, which is called a singular expansion. Some other methods require less machine time and memory. However, they are less effective in taking into account the errors of the source information, rounding errors, and linear dependence. The methodology of such research is that for any matrix A and any two orthogonal matrices U and V, there is a matrix , which is determined as T U AV  . The idea of a singular decomposition is that by choosing the right matrices U and V, you can convert most elements of the matrix  to zero and make it diagonal with non-negative elements. The novelty and relevance of scientific solutions lie in the feasibility of using a singular decomposition of the matrix to obtain linear equations of the least squares method, which can be used to solve incorrect geodetic problems. The purpose of scientific research is to obtain a stable solution of parametric equations of corrections to the results of mea- surements in incorrect geodetic problems. Based on the performed research on the application of the singular decomposition method for solving incorrect geodetic problems, we can summarize the following results. A singular expansion of a real matrix A is any factorization T A U W  of a matrix with orthogonal columns U, an orthogonal matrix W , and a diagonal matrix , the elements of which are called singular numbers of the matrix A, and the columns of matrices U and W — left and right singular vectors. If the matrix A has a full rank, then its solution will be unique and stable, which can be obtained by different methods. However, the method of singular decomposition, in contrast to other methods, makes it possible to solve problems with incomplete rank. Research shows that the method of solving normal equations by sequential exclusion of unknowns (Gaussian method), which is quite common in geod- esy, does not provide stable solutions for poorly conditioned or incorrect geodetic problems. Therefore, in the case of unstable systems of equations, it is proposed to use the method of singular matrix decomposition, which in computational mathematics is called SVD. The SVD singular decomposition method makes it possible to obtain stable solutions to both stable and by nature unstable problems. This possibility to solve incorrect geodetic problems is associated with the application of some limit , the choice of which can be made by the relative errors of the matrix of coefficients of parametric equations of corrections A and the vector of results of geodetic measurements L . Moreover, the solution of the system of normal equations obtained by the SVD method will have the shortest length. Thus, applying the apparatus of the singular decomposition of the matrix of coefficients of parametric equations of correc- tions to the results of geodetic measurements, we obtained new formulas for estimating the accuracy of the least squares method in solving incorrect geodetic problems. The derived formulas have a compact form and allow the easy calculation of elements  and XQ estimates of accuracy, almost ignoring the complex procedure of rotation of the matrix of coefficients of normal equations.

A study on partial pivot ACA boundary element method for elasticity problems

The boundary element method (BEM) employing the partial pivot adaptive cross approximation (PACA) algorithm has been observed to experience convergence failures and reduced solution accuracy when solving elasticity problems, especially at large scales. To address this issue, this paper proposes an improved algorithm for both 2D and 3D elasticity problems.Our investigations revealed that when the normal of an element is parallel to the coordinate axes and the element is in the same plane as the source point, zero entries with regular distributions will appear in the coefficient matrix. This results in the premature satisfaction of the convergence criterion of the PACA algorithm, leading to the omission of some rows and columns of the coefficient matrix. To address this issue, this paper proposes improvements to the PACA algorithm through the Coordinate Rotation Method (CRM) and the Component Traversal Method (CTM), and validates the effectiveness of these two improved methods.Furthermore, we investigate reasons behind the decrease in accuracy when employing the CTM to solve large-scale problems. We attribute this to the oscillatory nature of the estimated relative error and propose the modified PACA (M-PACA) algorithm. M-PACA not only maintains the advantages of the PACA algorithm in reducing storage space and accelerating coefficient matrix generation but also addresses its limitations, ensuring more accurate and reliable solutions for elasticity problems.

Comprehensive sensitivity analysis of repeated eigenvalues and eigenvectors for structures with viscoelastic elements

The paper discusses systems with viscoelastic elements that exhibit repeated eigenvalues in the eigenvalue problem. The mechanical behavior of viscoelastic elements can be described using classical rheological models as well as models that involve fractional derivatives. Formulas have been derived to calculate first- and second-order sensitivities of repeated eigenvalues and their corresponding eigenvectors. A specific case was also examined, where the first derivatives of eigenvalues are repeated. Calculating derivatives of eigenvectors associated with repeated eigenvalues is complex because they are not unique. To compute their derivatives, it is necessary to identify appropriate adjacent eigenvectors to ensure stable control of eigenvector changes. The derivatives of eigenvectors are obtained by dividing them into particular and homogeneous solutions. Additionally, in the paper, a special factor in the coefficient matrix has been introduced to reduce its condition number. The provided examples validate the correctness of the derived formulas and offer a more detailed analysis of structural behavior for structures with viscoelastic elements when altering a single design parameter or simultaneously changing multiple parameters.

Identification of dynamic coefficient matrix for drilling process simulations from measured tool geometry, axial force and torque

This paper aims to quantitatively analyze the relationship between forces acting on the tool tip and tool movement during drilling operations. The study encompasses axial and lateral vibrations superimposed on the nominal tool movement, arising from rigid body motion (rotational and axial velocities). Specifically, only forces attributed to the cutting process are considered, excluding considerations of indentation forces around the chisel edge. The research adopts a generalized approach, spanning from tool measurements to establishing the force model. The investigation involves measuring cutting forces and correlating them with the varying rake and inclination angles of the drill’s cutting edges. An analytical model is proposed to describe the distribution of all local force components along drill edges, considering the evolution of forces and geometry. The dynamic coefficient matrix is evaluated by using the identified cutting coefficient and tool geometry. Validation of the proposed methodology is demonstrated through drilling experiments on Ti6Al4V alloy, utilizing three solid carbide drills with distinct geometries. The proposed procedure allows complete identification of the dynamic characteristics from the measurements taken at the entrance stage of hole drilling operation. Moreover, the influence of tool geometry on cutting coefficients and dynamic coefficient matrices are discussed.

Imbalanced and missing multi-label data learning with global and local structure

Label missing and class imbalance problems are two hot research topics in machine learning, and they have been impeding the improvement of model performance, especially in the multi-label learning. Although some existing methods have proven to be effective, they are suitable for only one case. How to effectively address above two issues simultaneously is a challenging problem. In this paper, we propose a novel model named Imbalanced and Missing multi-Label data learning with Global and Local structure (IMLGL) to address the aforementioned challenge. There are following three advantages. At the empirical risk level, we introduce the label correlation matrix C into the loss function and devise a dynamic weighting method to address the aforementioned challenge. At the data level, we analyze the structural characteristics of the data, and introduce local low-rank and global high-rank term to enhance the generalization performance of the model. At the label level, a smoothing term is also introduced for learning the constraint classifier coefficient matrix W. Our method utilizes alternative optimization technique and alternating minimization method for solving. Extensive experiments on six datasets demonstrate the competitiveness of our approach.

Load Identification in Steel Structural Systems Using Machine Learning Elements: Uniform Length Loads and Point Forces

Actual load identification is a most important task solved in the course of (1) engineering inspections of steel structures, (2) the design of systems rising or restoring the bearing capacity of damaged structural frames, and (3) structural health monitoring. Actual load values are used to determine the stress–strain state (SSS) of a structure and accomplish various engineering objectives. Load identification can involve some uncertainty and require soft computing techniques. Towards this end, the article presents an integrated method combining basic provisions of structural mechanics, machine learning, and artificial neural networks. This method involves decomposing structures into primitives, using machine learning data to make projections, and assembling structures to make final projections for steel frame structures subjected to elastic strain. Final projections serve to identify parameters of point forces and loads distributed along the length of rods. The process of identification means checking the difference between (1) weight coefficient matrices applied to unit loads and (2) actual loads standardized using maximum load values. Cases of neural network training and parameters identification are provided for simple beams. The aim of this research is to enhance the reliability and durability of steel structures by predicting consequences of unfavorable load, including emergency impacts. The novelty of this study lies in the co-use of artificial intelligence elements and structural mechanics methods to predict load parameters using actual displacement curves of structures. This novel approach will enable engineering inspection teams to predict unfavorable load peaks, prevent emergency situations, and identify actual causes of emergencies triggered by excessive loading.

Sparse group principal component analysis using elastic-net regularisation and its application to virtual metrology in semiconductor manufacturing

Principal component analysis (PCA) is a widely used statistical technique for dimensionality reduction, extracting a low-dimensional subspace in which the variance is maximised (or the reconstruction error is minimised). To improve the interpretability of learned representations, several variants of PCA have recently been developed to estimate the principal components with a small number of input features (variable), such as sparse PCA and group sparse PCA. However, most existing methods suffer from either the requirement of measuring all the input variables or redundancy in the set of selected features. Another challenge for these methods is that they need to specify the sparsity level of the coefficient matrix in advance. To address the above issues, in this paper, we propose an elastic-net regularisation for sparse group PCA (ESGPCA), which incorporates sparsity constraints into the objective function to consider both within-group and between-group sparsities. Such a sparse learning approach allows us to automatically discover the sparse principal loading vectors without any prior assumption of the input features. We solve the non-smooth regularised problem using the alternating direction method of multipliers (ADMM), an efficient distributed optimisation technique. Empirical evaluations on both synthetic and real datasets demonstrate the effectiveness and promising performance of our sparse group PCA than other compared methods.

Customised product design optimisation considering module synergy effects and expert preferences

ABSTRACT Fierce marketing competition and varied customer requirements on products make a lot of companies transfer to the customisation strategy. However, customers may be overwhelmed by the vast assortment of products and options. This paper proposes a methodology aimed at optimising the range of customised product varieties considering synergy effects of modules and preferences of experts. The methodology outlines key steps required for a successful customised product configuration. Firstly, a questionnaire based on the Kano model is designed to identify customer preferences for product module customisation. The potential customers can be segmented based on the distance among their multidimensional preferences. Secondly, within each segmented market, the customer satisfaction function that considers module synergies is established using the quantified Kano model and coefficient matrix. Thirdly, the cost function that considers experts' preferences is established based on the prospect theory. Finally, a bi-objective optimisation model is formulated to maximise customer satisfaction and minimise cost under technical constraints. Pareto solutions are obtained by solving the model with the non-dominated sorting genetic algorithm II (NSGA-II). Modules and attributes available to customers can be determined by the solutions. An illustrative example of modular laptop computers confirms the methodology's effectiveness in optimising product configuration.

Chemical composition, source characteristics, and hygroscopic properties of organic-enriched aerosols in the high Arctic during summer

Arctic regions are extremely sensitive to global warming. Aerosols are one of the most important short-lived climate-forcing agents affecting the Arctic climate. The present study examines the summertime chemical characteristics and potential sources of various organic and inorganic aerosols at a Norwegian Arctic site, Ny-Ålesund (79°N). The results show that organic matter (OM) accounts for 60 % of the total PM10 mass, followed by sulfate (SO42−). Water-soluble organic carbon (WSOC) contributes 62 % of OC. Photochemical processes involving diverse anthropogenic and biogenic precursor compounds are identified as the major sources of WSOC, while water-insoluble organic carbon (WIOC) aerosols are predominantly linked to primary marine emissions. Despite being a remote pristine site, the aerosols show a sign of chemical aging, evidenced by a significant chloride depletion, which was about 82 % on average during the study period. Nitrogen-containing aerosols are likely stemming from migratory seabird colonies and local dust sources around the sampling site. While biogenic, crustal, and sea salt-derived SO42- account for 37%, 8%, and 5% respectively, the remaining 50% is attributed to anthropogenic SO42-. Through chemical tracers, Pearson correlation coefficient matrix, and Hierarchical Cluster Analysis (HCA), the present study identifies soil biota (terrestrial biogenic) and marine emissions, along with their photochemical oxidation processes, as potential sources of Arctic aerosols during summer, while biomass burning and combustion-related sources have a minor contribution. The chemical closure of hygroscopicity highlights that while organics predominantly control aerosol hygroscopicity in the Arctic summer, specific inorganic components like (NH4)2SO4 can significantly increase it on certain days, affecting aerosol-cloud interactions and climate processes over the Arctic during summer. The present study highlights the high abundance of organics and their vital role in the Arctic climate during summer when natural aerosols are conquered.

Estimation of Crosswind Disturbances for a Vehicle by LPV‐MHE and its Application to Disturbance Cancellation

Crosswinds and transverse slopes of the road surface affect the motion of a ground vehicle as disturbances. The objective of this paper is to develop a method for estimating crosswind disturbances and lateral force disturbances caused by transverse slopes of the road surface under the variation of the vehicle speed. Firstly, a dynamical model of a vehicle is described as a Linear Parameter‐Varying (LPV) system in which the value of the coefficient matrices vary with the vehicle velocity. Then, an algorithm to estimate the disturbance is derived based on Moving Horizon Estimation (MHE) and applied to the derived LPV system. Furthermore, a simple control law which counteracts the effects of the disturbances on the lateral velocity and the yaw rate in steady‐state based on the estimates of the disturbances is presented. The effectiveness of the proposed method is demonstrated by a numerical example. © 2024 The Author(s). IEEJ Transactions on Electrical and Electronic Engineering published by Institute of Electrical Engineers of Japan and Wiley Periodicals LLC.

Phase division and recognition of crystal HRTEM images based on machine learning and deep learning

The High Resolution Transmission Electron Microscope (HRTEM) images provide valuable insights into the atomic microstructure, dislocation patterns, defects, and phase characteristics of materials. However, the current analysis and research of HRTEM images of crystal materials heavily rely on manual expertise, which is labor-intensive and susceptible to subjective errors. This study proposes a combined machine learning and deep learning approach to automatically partition the same phase regions in crystal HRTEM images. The entire image is traversed by a sliding window to compute the amplitude spectrum of the Fast Fourier Transform (FFT) in each window. The generated data is transformed into a 4-dimensional (4D) format. Principal component analysis (PCA) on this 4D data estimates the number of feature regions. Non-negative matrix factorization (NMF) then decomposes the data into a coefficient matrix representing feature region distribution, and a feature matrix corresponding to the FFT magnitude spectra. Phase recognition based on deep learning enables identifying the phase of each feature region, thereby achieving automatic segmentation and recognition of phase regions in HRTEM images of crystals. Experiments on zirconium and oxide nanoparticle HRTEM images demonstrate the proposed method achieve the consistency of manual analysis. Code and supplementary material are available at https://github.com/rememberBr/HRTEM2.

A new family of robust quantile-regression-based mean estimators using Sarndal approach

In presence of extreme-values or outliers, the ratio-type mean estimators are prominently developed by using the robust coefficients of regression and covariance matrices. In this article, we consider quantile regression coefficients while estimating the finite population mean. Incorporating Sarndal concept, we offer quantile-regression-based mean estimators under a simple random sample design. We calculate the mean squared error (MSE) for the suggested estimators and discover that they perform better than the existing estimators. Moreover, numerical representations and a simulation study support our discoveries in theory.

Adaptive denoising for pipe leak vibroacoustic in multiple conditions using correlation coefficient matrix and multi-objective optimization

To achieve adaptive denoising of pipe leak vibroacoustic under low signal to noise ratio (SNR), a novel method based on correlation coefficient matrix was proposed for selecting the effective mode components obtained using variational mode decomposition (VMD). For the leak signals detected under different conditions, new indicators were designed to evaluate the denoising performance without using the prior knowledge of pure signals, and they were introduced as the objective function of multi-objective grey wolf optimizer (MOGWO). Subsequently, the best mode number K and penalty factor η of VMD were determined according to Pareto front, thus achieving adaptive denoising under multi-condition. To verify the proposed method, an experimental rig was built to simulate gas pipe leaks under multiple conditions with a SNR range from – 8 dB to 4 dB. The results showed that the proposed VMD-based denoising method achieved using the improved MOGWO can effectively suppress noise.

AN ALGEBRAIC SOLUTION OF DUAL FUZZY COMPLEX LINEAR SYSTEMS

The main aims of this research is to solve the dual fuzzy complex linear system AX +C =BX +D, where A,B are crisp coefficient matrices and C ,D are fuzzy number matrices. The research findings indicate that the system of two fuzzy complex linear equations can be solved under the conditional that (A-B)^(-1) and (|B|-|A|)^(-1) exists.