Matrix Vector Research Articles

Monocular spatial geometrical measurement method based on local geometric elements associated with out-of-view datum

In the field of industrial inspection, visual non-contact measurement of the radial dimension of the extension end of the long pole structure is a difficult problem. Utilizing the principle of telecentric vision measurement, we propose a monocular spatial geometrical measurement method based on local geometric elements associated with out-of-view datum, focusing on key techniques such as visual calibration and global unification of separate dimensions. Firstly, the designed associated target is used to establish the conversion relationship between the measurement reference space and the camera FOV space. Singular Value Decomposition (SVD) is used to obtain the initial values R0 and T0 of the rotation matrix and translation vector during the three-dimensional coordinate system conversion. Then the initial values are linearized based on the Rodrigues iterative transformation to obtain the optimized R and T, thereby achieving the high-precision conversion of the coordinate system, realizing the global unification of the coordinates of the separated size elements. In order to verify the effectiveness of the method, an experimental measurement device was constructed. The experimental results show that the measurement uncertainty (95% confidence level) of the space radial dimension is ±10.37 µm, and the %R&R index is 12.91%. This method is suitable for applications such as rapid and precise measurement of narrow and long workpieces such as partial visible elements in vitro or cross-scale measurement.

Joint diagnosis of process mean vector and covariance matrix for multivariate statistical process control

The monitoring methodology in statistical process control is very useful and efficient to detect abnormal changes of a process, however diagnosis ability, accurate fault diagnosis of responsible components for the process change, is limited. Currently, most of work has focused on the diagnosis task of mean shifts. Nevertheless, the shifts of a process also likely occur in the variances/covariances. In this article, we develop a Bayesian procedure to simultaneously diagnose shifts in both mean vector and covariance matrix. Moreover, the proposed method can provide the directions of shifts and corresponding probability. These diagnostic information help decision makers to find quickly root causes of abnormal changes. Compared with existing methods, numerical simulations favor the proposed method. Finally, we use a real dataset from bolt production process to demonstrate the implementation of the proposed Bayesian method.

Enhanced transverse displacements analysis of transversely cracked beams with a linear variation of width due to axial tensile forces

Enhanced transverse displacements analysis of transversely cracked beams with a linear variation of width due to axial tensile forces

A Charge Domain SRAM Compute-in-Memory Macro With C-2C Ladder-Based 8-Bit MAC Unit in 22-nm FinFET Process for Edge Inference

Compute-in-memory (CiM) is one promising solution to address the memory bottleneck existing in traditional computing architectures. However, the tradeoff between energy efficiency and computing precision plagues most CiM implementations, and the low precision imposes a major limitation on CiM’s ability to support practical computational workloads. In this article, a static random access memory (SRAM)-based analog CiM macro is presented with the Intel 22FFL process. By introducing a 1-to-2 ratioed capacitor ladder (C-2C)-based charge domain computing scheme, the proposed CiM prototype chip demonstrates a maximum of 2k multiply-accumulate (MAC) operations in one clock cycle and achieves 32.2-TOPS/W peak power efficiency with 8-bit precision in both input activation and weight while ensuring accurate on-chip matrix–vector multiplications (MVMs) with a computation error less than 0.5%. A 4.0-TOPS/mm2 peak area efficiency is attained by adopting a local weight multiplexing scheme with a 9T SRAM cell, which improves the memory density and reduces the need to refresh the weight stored in the SRAM array. A variety of analog impairment factors, including parasitics, mismatch, and noise, were analyzed to guarantee a sufficiently high multibit linearity. The proposed passive analog computing mechanism ensures the computation accuracy over process–voltage–temperature (PVT), with the measured MVM error deviation of less than 1% over PVT variations.

RGB-D 카메라를 이용한 로봇 매니퓰레이터 기구학 캘리브레이션

This paper proposed the robot manipulator kinematic calibration method based on a distance error model using an easy-touse RGB-D(Depth) camera. The RGB-D camera attached to the robot end effector measures the checkerboard’s corner 3-D position in two different positions. The homogeneous transformation matrix having rotation matrix and translation vector between two different RGB-D camera positions is calculated from the acquired position data from the RGB-D camera. The distance error is measured by comparing the distance moved by the RGB-D camera from the derived homogeneous transformation matrix with the distance moved by the robot manipulator. Simulation and experiments have been conducted to verify the proposed robot manipulator kinematic calibration method with a 6-DOF robot manipulator.

Anchor Fault Identification Method for High-Voltage DC Submarine Cable Based on VMD-Volterra-SVM

This article introduces a new method for identifying anchor damage faults in fiber composite submarine cables. The method combines the Volterra model of Variation Mode Decomposition (VMD) with singular value entropy to improve the accuracy of fault identification. First, the submarine cable vibration signal is decomposed into various Intrinsic Mode Functions (IMFs) using VMD. Then, a Volterra adaptive prediction model is established by reconstructing the phase space of each IMF, and the model parameters are used to form an initial feature vector matrix. Next, the feature vector matrix is subjected to singular value decomposition to extract the singular value entropy that reflects the fault characteristics of the submarine cable. Finally, singular value entropy is used as a feature value to input into the Support Vector Machine (SVM) for classification. Compared with Empirical Mode Decomposition (EMD) and Ensemble Empirical Mode Decomposition (EEMD), the proposed method achieves a higher fault identification accuracy and effectively identifies anchor damage faults in submarine cables. The results of this study demonstrate the feasibility and practicality of the proposed method.

Design of Computer-Aided Assessment and Recognition Platform for College Students' Innovative Training Plan with Data Matrix Mining

In this paper, an improved association rule algorithm based on vector product is used. This algorithm only needs to scan the transaction database once and does not generate a large number of frequent item candidate sets. The algorithm first maps the set of data transactions into a matrix of vectors, each column vector representing an attribute. Matrix factorization algorithms usually decompose the original data matrix into two or more low-dimensional matrices. This paper analyzes the common problems existing in society, colleges, and families in labor education, and innovatively proposes a four-dimensional comprehensive evaluation index system for labor education in colleges and universities, including “subject-dominated colleges—family education support—social environment support—college students’ individual characteristics”.

The secure judgment of graphic similarity against malicious adversaries and its applications

With the advent of the era of big data, privacy computing analyzes and calculates data on the premise of protecting data privacy, to achieve data ‘available and invisible’. As an important branch of secure multi-party computation, the geometric problem can solve practical problems in the military, national defense, finance, life, and other fields, and has important research significance. In this paper, we study the similarity problem of geometric graphics. First, this paper proposes the adjacency matrix vector coding method of isomorphic graphics, and use the Paillier variant encryption cryptography to solve the problem of isomorphic graphics confidentiality under the semi-honest model. Using cryptography tools such as elliptic curve cryptosystem, zero-knowledge proof, and cut-choose method, this paper designs a graphic similarity security decision protocol that can resist malicious adversary attacks. The analysis shows that the protocol has high computational efficiency and has wide application value in terrain matching, mechanical parts, biomolecules, face recognition, and other fields.

Vector-deductive Memory-based Transactions for Fault-as-address Simulation

The main idea is to create logic-free vector computing, using only read-write transactions on address memory. The strategic goal is to create a deterministic vector-quantum computing using photons for read-write transactions on stable subatomic memory elements. The main task is to implement new vector computing models and methods based on primitive read-write transactions in vector flexible interpretive fault modeling and simulation technology, where data is used as addresses for processing the data itself. The essence of vector computing is read-write transactions on vector data structures in address memory. Vector computing is a computational process based on elementary read-write transactions over cells of binary vectors that are stored in address memory and form a functionality where the input data to be processed is the addresses of these cells. The advantages of a vector universal model for a compact description of ordered processes, phenomena, functions, and structures are defined for the purpose of their parallel analysis. Analytical expressions of logic, which require algorithmically complex calculators, are replaced by output state vectors of elements and digital circuits, focused on the parallelism of register logical procedures on regular data structures. A vector-deductive method for formula synthesis for propagating input lists (data) of faults is proposed, which has a quadratic computational complexity of register operations. A new matrix of deductive vectors has been synthesized, which is characterized by the following properties: compactness, parallel data processing based on a single read-write transaction in memory, elimination of traditional logic from fault simulation procedures, full automation of its synthesis process, and focus on technological solving all problems of technical diagnosis. In the work, the transition to vector logic in the organization of computing and the elimination of traditional logic presented in the form of tables and analytical expressions were carried out. The use of read-write transactions on memory in the absence of a command system focuses the new vector-logic computing towards deterministic quantum architectures based on stable subatomic memory particles.

Wave propagation in a non-local magneto-thermoelastic medium permeated by heat source

In this paper, we consider the new concept of non-local heat conduction equation to generalized magneto-thermoelastic problem of two dimensional isotropic and homogeneous half-space in presence of heat-flux at the boundary surface. By using the harmonic plane waves, the governing equations are transformed to the vector matrix differential equation which is then solved by eigenvalue method. The analytical closed form solutions for displacement component, temperature distribution and stress components have been made and comparisons are also illustrated graphically with the theory of non-local dual-phase-lag (NLDPL) and non-local Lord-Shulman (NLLS) theory for different values of physical parameters. The significant effects of non-local variables as well as phase lagging parameters on displacements, temperature distribution and stress components are studied by means of graphically and concluding remarks are drawn.

Monte Carlo Methods for Estimating the Diagonal of a Real Symmetric Matrix

For real symmetric matrices that are accessible only through matrix vector products, we present Monte Carlo estimators for computing the diagonal elements. Our probabilistic bounds for normwise absolute and relative errors apply to Monte Carlo estimators based on random Rademacher, sparse Rademacher, and normalized and unnormalized Gaussian vectors and to vectors with bounded fourth moments. The novel use of matrix concentration inequalities in our proofs represents a systematic model for future analyses. Our bounds mostly do not depend explicitly on the matrix dimension, target different error measures than existing work, and imply that the accuracy of the estimators increases with the diagonal dominance of the matrix. Applications to derivative-based global sensitivity metrics and node centrality measures in network science corroborate this, as do numerical experiments on synthetic test matrices. We recommend against the use in practice of sparse Rademacher vectors, which are the basis for many randomized sketching and sampling algorithms, because they tend to deliver barely a digit of accuracy even under large sampling amounts.

A two-stage RNN-based deep reinforcement learning approach for solving the parallel machine scheduling problem with due dates and family setups

As an essential scheduling problem with several practical applications, the parallel machine scheduling problem (PMSP) with family setups constraints is difficult to solve and proven to be NP-hard. To this end, we present a deep reinforcement learning (DRL) approach to solve a PMSP considering family setups, aiming at minimizing the total tardiness. The PMSP is first modeled as a Markov decision process, where we design a novel variable-length representation of states and actions, so that the DRL agent can calculate a comprehensive priority for each job at each decision time point and then select the next job directly according to these priorities. Meanwhile, the variable-length state matrix and action vector enable the trained agent to solve instances of any scales. To handle the variable-length sequence and simultaneously ensure the calculated priority is a global priority among all jobs, we employ a recurrent neural network, particular gated recurrent unit, to approximate the policy of the agent. The agent is trained based on Proximal Policy Optimization algorithm. Moreover, we develop a two-stage training strategy to enhance the training efficiency. In the numerical experiments, we first train the agent on a given instance and then employ it to solve instances with much larger scales. The experimental results demonstrate the strong generalization capability of the trained agent and the comparison with three dispatching rules and two metaheuristics further validates the superiority of this agent.

Improved sparse low-rank model via periodic overlapping group shrinkage and truncated nuclear norm for rolling bearing fault diagnosis

The early faults of rolling bearings are the common causes of rotating machinery failures. Rolling bearings with local faults usually generate periodic shocks during operation, but the pulse information is easily masked by a large number of random shocks and noise. To effectively diagnose the early fault information of rolling bearings, a dual-dimensional sparse low-rank (DDSLR) model is proposed in this paper, which can simultaneously extract the sparsity within and across groups and periodic self-similarity of fault signal. In the DDSLR model, a newly developed dimension transformation operator is used to transform the fault signal between one-dimensional vector and low-rank matrix, and the periodic overlapping group shrinkage and truncated nuclear norm are used to improve the traditional sparse low-rank model. In addition, the setting rules of periodic prior and parameters in the DDSLR model are discussed, so that the DDSLR model has certain adaptive ability. Finally, the DDSLR model is proved to be a multi-convex optimization problem, and its solution algorithm is derived by using soft threshold operator and majorization-minimization algorithm under the framework of block coordinate descent method. The results of simulation analysis and experiments show that the proposed DDSLR model has higher fault signal estimation accuracy and better fault feature extraction performance than some classical sparse noise reduction models.

Aggregated type handling in CoDiPack

AbstractThe development of algorithmic differentiation (AD) tools focuses mostly on handling floating point types in the target language. Taping optimizations in these tools mostly focus on specific operations like matrix vector products. Aggregated types like std::complex are usually handled by specifying the AD type as a template argument. This approach provides exact results, but prevents the use of expression templates. If AD tools are extended and specialized such that aggregated types can be added to the expression framework, then this will result in reduced memory utilization and improve the timing for applications where aggregated types such as complex number or matrix vector operations are used. Such an integration requires a reformulation of the stored data per expression and a rework of the tape evaluation process. We will demonstrate the overheads on a synthetic benchmark and show the improvement when aggregated types are handled properly by the expression framework of the AD tool.

EANet: A Point Cloud Registration Network Based on EdgeConv with Dual Attention Mechanism

In machine vision, point cloud registration is one of the core elements, which has been applied to many fields such as robot localisation, medical image processing, and autonomous driving. The main problem solved by point cloud registration is to solve the rotation matrix and translation vectors from one point cloud to another. This paper proposes a point cloud registration network based on EdgeConv with spatial attention mechanism. EdgeConv can dynamically construct graph structure and build topological relationships within the point cloud, so that each point can obtain multi-level feature representation; the attention mechanism can capture contextual information and improve the accuracy of the registration. Experimental results show that EANet has higher registration accuracy, stronger generalisation ability and robustness compared to ICP, Go ICP, FGR, PCRNet and PointNetLK.

DEVELOPMENT OF ALGORITHMS AND SOFTWARE FOR MODELING CONTROLLED DYMAMIC SYSTEMS USING SYMBOLIC COMPUTATIONS AND STOCHASTIC METHODS

The development of software for synthesizing and analyzing models of controlled systems taking into account their deterministic and stochastic description is an important direction of research. Results of the development of software for modeling dynamic systems the behavior of which can be described by onestep processes are presented. Models of population dynamics are considered as an example. The software uses a deterministic description of the model at its input to obtain a corresponding stochastic model in symbolic form and also analyze the model in detail (calculate trajectories in the deterministic and stochastic cases, find control functions, and visualize the results). An important aspect of the development is the use of computer algebra for analyzing the model and synthesizing controls. Methods and algorithms based on deterministic and stochastic Runge–Kutta methods, stability and control theory, methods for designing self-consistent stochastic models, numerical optimization algorithms, and artificial intelligence are implemented. The software was developed using high-level programming languages Python and Julia. As the basic tools, high-performance libraries for vector–matrix computations, symbolic computation libraries, libraries for the numerical solution of ordinary differential equations, and libraries of global optimization algorithms are used.

Natural Frequency Perturbations Using a Scalar Expression with Reference Plots to Predict Associated Errors

PurposeEigenvalues are the natural frequencies of system squared. When designing a system it is important to know the natural frequencies, because if the system is forced near one of these natural frequencies the magnitude of vibration becomes very large. The eigenvalues are typically determined by solving an eigenvalue problem, which is an iterative produce that is expensive for larger systems. If multiple perturbations to the system are made or tested re-solving an eigenvalue problem every time becomes prohibitive. Perturbation methods exist to predict perturbed eigenvalues more quickly. However, these methods typically require matrix–vector products and do not quantify what is considered a small enough perturbation to use these methods.MethodsThis paper looks to address these issues using a scalar perturbed eigenvalue expression that avoids calculating matrix–vector products for every perturbation and developing reference plots that can be used to predict the associated error. The reference plots may be used to predict errors in the approximated natural frequencies from nominal modal parameters. The scalar perturbed eigenvalue expression and reference plots for errors were tested using numerical examples.ResultsIn every case tested the plots were able to accurately predict the expected errors, to be within a predicted range.ConclusionThe proposed method allows one to use the developed scalar expression to predict perturbed eigenvalues, and the developed reference plots may be used to predict the errors associated with using the proposed expression.

On eigenvalues of symmetric matrices with PSD principal submatrices

We investigate convexity properties of the set of eigenvalue tuples of n×n real symmetric matrices, all of whose k×k (where k≤n is fixed) minors are positive semidefinite. We prove that the set λ(Sn,k) of eigenvalue vectors of all such matrices is star-shaped with respect to the nonnegative orthant R≥0n and not convex already when (n,k)=(4,2). We also show that k is the smallest integer such that Sn,k is a linear projection of a set described by linear matrix inequalities of size k.

Measurements and computational analysis of the natural decay of Lu176

Background: Mainly because of its long half-life and despite its scientific relevance, spectroscopic measurements of $^{176}\mathrm{Lu}$ forbidden $\ensuremath{\beta}$ decays are very limited and lack formulation of shape factors. A direct precise measurement of its Q value is also presently unreported. In addition, the description of forbidden decays provides interesting challenges for nuclear theory. The comparison of precise experimental results with theoretical calculations for these decays can help to test underlying models and can aid the interpretation of data from other experiments.Purpose: Perform the first precision measurements of $^{176}\mathrm{Lu}\phantom{\rule{4pt}{0ex}}\ensuremath{\beta}$-decay spectra and attempt the observation of its electron capture decays, as well as perform the first precision direct measurement of the $^{176}\mathrm{Lu}\phantom{\rule{4pt}{0ex}}\ensuremath{\beta}$-decay Q value. Compare the shape of the precisely determined experimental $\ensuremath{\beta}$ spectra to theoretical calculations, and compare the end point energy to that obtained from an independent Q value measurement.Method: The $^{176}\mathrm{Lu}\phantom{\rule{4pt}{0ex}}\ensuremath{\beta}$-decay spectra measurements and the search for electron capture decays were performed with an experimental setup that employed lutetium-containing scintillator crystals and a NaI(Tl) spectrometer for coincidence counting. The $\ensuremath{\beta}$ decay Q value was determined via high-precision Penning trap mass spectrometry (PTMS) with the LEBIT facility at the National Superconducting Cyclotron Laboratory. The $\ensuremath{\beta}$-spectrum calculations were performed within the Fermi theory formalism with nuclear structure effects calculated using a shell model approach.Results: Both $\ensuremath{\beta}$ transitions of $^{176}\mathrm{Lu}$ were experimentally observed and corresponding shape factors formulated in their entire energy ranges. The search for electron capture decay branches led to an experimental upper limit of $6.3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$ relative to its $\ensuremath{\beta}$ decays. The $^{176}\mathrm{Lu}\phantom{\rule{4pt}{0ex}}\ensuremath{\beta}$-decay and electron capture Q values were measured using PTMS to be 1193.0(6) and 108.9(8) keV, respectively. This enabled precise $\ensuremath{\beta}$ end point energies of 596.2(6) and 195.3(6) keV to be determined for the primary and secondary $\ensuremath{\beta}$ decays, respectively. The conserved vector current hypothesis was applied to calculate the relativistic vector matrix elements. The $\ensuremath{\beta}$-spectrum shape was shown to significantly depend on the Coulomb displacement energy and on the value of the axial vector coupling constant ${g}_{A}$, which was extracted according to different assumptions.Conclusion: The implemented self-scintillation method has provided unmatched observations of $^{176}\mathrm{Lu}$, independently validated by the first direct measurements of its $\ensuremath{\beta}$-decay Q value by Penning trap mass spectrometry. Theoretical study of the main $\ensuremath{\beta}$ transition led to the extraction of very different effective ${g}_{A}$ and ${log}_{10}\phantom{\rule{0.16em}{0ex}}f$ values, showing that a high-precision description of this transition would require a realistic nuclear structure with nucleus deformation.

Dynamic Synthesis of Three−Point Circle Peripheral Docking Technology Pose

Research on space docking technology was first motivated by the application scenario of space station docking in the aviation field. Due to the maturity of this technology, its application field is expanding to other industries. To benefit the intelligent transportation field, this study uses space docking technology to realize combination and reconstruction between car bodies. Different spatial docking methods and structural characteristics are determined by different application scenarios. The docking of the space station is completed in the suspended state of the body in the outer space environment, which requires advanced technology, is high in hardware cost, and involves a small channel diameter. In this study, the docking of the reconstructed vehicle is completed on the ground; thus, it is low in hardware cost and involves a large channel diameter. Based on the above technical requirements, a three−point circular peripheral docking method is designed for the reconstructed vehicle. A visual positioning system is built, the mapping relationship between the camera coordinate system and the landmark coordinate system rotation matrix and translation vector is established, and the adaptive capture behavior is realized by path planning through the inverse pose solution model. Simulation experiments demonstrate that the active and passive vehicle bodies can achieve compliance capture with small collision force under the two conditions of forward collision and oblique collision, and the recovery coefficient after collision and docking is in the range of (0, 0.01). The acceleration decay process under two working conditions is measured in the crash test of a sample vehicle, which verifies the feasibility of the space reconstruction of the vehicle docking mechanism and the ability of this configuration to achieve tasks, providing a constructive idea for space docking technology with a large channel diameter.