Matrix Vector Research Articles

An Integrated Kinematic Calibration and Dynamic Identification Method With Only Static Measurements for Serial Robot

In this article, we propose an integrated calibration and identification method that can identify kinematic and dynamic parameters at the same time. Only a series of static experiments are required in this method, which can significantly simplify the experimental operation and improve the accuracy of identification. A novel calibration model based on axis configuration space and adjoint error model considering joint compliance with only position measurements is developed and both joint compliance and joint zero-offset errors are included in the proposed model. Identifiability analysis shows which joint compliance can be identified and the relationships between the identifiability of joint compliance and the number of measurement points. A recursive algorithm considering physical consistency is newly derived to obtain the derivatives of estimated inertial matrix and gravity vector with respect to joint twists. In this way, the coupling between kinematic and dynamic model is solved and the optimal kinematic and dynamic parameters can be derived using gradient-based optimizer. Comparative study with experiments are reported to show the effectiveness of our algorithm.

Large Environment Indoor Localization Leveraging Semi-Tensor Product Compression Sensing

The sparsity of the localization problem makes the Compression Sensing (CS) theory suitable for indoor localization in Wireless Local Area Networks (WLAN). However, in practice, we find that the location errors and computing complexity increase significantly as the dimensionality of the sparse vector and measurement matrix are high in a large environment, so most CS-based localization techniques are accompanied by coarse localization and AP selection stages. Therefore, in this paper, we first deduced the relationship between the number of Access Points (APs) and the dimensionality of the sparse vector theoretically to give the guideline that the number of sub-databases and APs should be obtained. Then an Adaptive Intuitionistic Fuzzy C-ordered Mean (AIFCOM) clustering is designed for the data with outliers in the environment with multipath effects. Finally, in the fine localization stage, we propose a Semi-tensor Product Compression Sensing (STP-CS) model to construct the measurement matrix, compared with the traditional CS model, our model not only remains more number of APs, but also decreases the dimensionality of measurement matrix, which can reduce the storage space and improve localization accuracy simultaneously.

Chebyshev–Picard iteration methods for solving delay differential equations

In this paper, we propose an effective Chebyshev–Picard iteration (CPI) method for solving delay differential equations with a constant delay. This approach adopts the Chebyshev series to represent the solution and improves the accuracy of the solution by successive Picard iterations. The CPI method is implemented in a matrix–vector form efficiently without matrix inversion. We also present a multi-interval CPI method for solving long-term simulation problems. Further, the convergence of the CPI method is analyzed by evaluating the eigenvalues of the coefficient matrices of the iteration. Several numerical experiments including both the linear and nonlinear systems with delay effects are presented to demonstrate the high accuracy and efficiency of the CPI method by comparison with the classic methods.

Sonics: develop intuition on biomechanical systems through interactive error controlled simulations

We describe the SOniCS (SOFA + FEniCS) plugin to help develop an intuitive understanding of complex biomechanics systems. This new approach allows the user to experiment with model choices easily and quickly without requiring in-depth expertise. Constitutive models can be modified by one line of code only. This ease in building new models makes SOniCS ideal to develop surrogate, reduced order models and to train machine-learning algorithms for enabling real-time patient-specific simulations. SOniCS is thus not only a tool that facilitates the development of surgical training simulations but also, and perhaps more importantly, paves the way to increase the intuition of users or otherwise non-intuitive behaviors of (bio)mechanical systems. The plugin uses new developments of the FEniCSx project enabling automatic generation with FFCx of finite-element tensors, such as the local residual vector and Jacobian matrix. We verify our approach with numerical simulations, such as manufactured solutions, cantilever beams, and benchmarks provided by FEBio. We reach machine precision accuracy and demonstrate the use of the plugin for a real-time haptic simulation involving a surgical tool controlled by the user in contact with a hyperelastic liver. We include complete examples showing the use of our plugin for simulations involving Saint Venant–Kirchhoff, Neo-Hookean, Mooney–Rivlin, and Holzapfel Ogden anisotropic models as supplementary material.

Transform-Based Feature Map Compression Method for Video Coding for Machines (VCM)

The burgeoning field of machine vision has led to the development by the Moving Picture Experts Group (MPEG) of a new type of compression technology called video coding for machines (VCM), to enhance machine recognition through video information compression. This research proposes a principal component analysis (PCA)-based compression methodology for multi-level feature maps extracted from the feature pyramid network (FPN) structure. Unlike current PCA-based studies that independently carry out PCA for each feature map, our approach employs a generalized basis matrix and mean vector derived from channel correlations by a generalized PCA process to eliminate the need for a PCA process. Further compression is achieved by amalgamating high-dimensional feature maps, capitalizing on the spatial redundancy within these multi-level feature maps. As a result, the proposed VCM encoder forgoes the PCA process, and the generalized data do not incur any compression loss. It only requires compressing the coefficients for each feature map using versatile video coding (VVC). Experimental results demonstrate superior performance by our method over all feature anchors for each machine vision task, as specified by the MPEG-VCM common test conditions, outperforming previous PCA-based feature map compression methods. Notably, it achieved an 89.3% BD-rate reduction for instance segmentation tasks.

Determination of influence lines for structural responses with uncertainties in properties of the structure

Classical ways of determination of influence lines for structural responses are often inefficient due to high computational cost, especially if properties of the structure are uncertain. The combination of Muller-Breslau principle and the finite element analysis can resolve this problem. In this study, formulations for new finite elements tailored for use in determination of influence lines for structural responses are proposed. They are then used in the problem of uncertainty propagation to obtain uncertain ordinates of the influence lines. The expressions for the element stiffness matrix and equivalent nodal load vector are derived consistently from the proposed displacement field of the element. The proposed finite elements can be adapted directly in existing finite element packages since they do not need remeshing. Studied examples show the correctness and the efficiency of the proposed method. From the results of uncertainty propagation problem, large uncertainties in the ordinates of influence lines for structural responses due to small uncertainties in structural properties should be aware of.

An efficient framework for matrix-free SpMV computation on GPU for elastoplastic problems

High computational cost in elastoplastic analysis is often handled by the use of high performance parallel computers. However, the presence of both elastic and plastic states leads to the branching issue, which prevents the realization of true parallel performance. The computational efficiency of an elastoplastic analysis using finite element method is largely determined by the performance of repeated solution of linearized system of equations. In this paper, we propose GPU-based matrix-free strategies to compute sparse matrix–vector multiplication (SpMV) in Conjugate Gradient (CG) iterative solver for the acceleration of solution of linear system of equations. Matrix-free solvers never assemble large sparse global tangent matrix and perform the computation directly with small dense elemental matrices, reducing the storage requirement and preventing the use of problematic sparse storage formats. A uniform treatment of elements in elastic and plastic regions is achieved by the proposed single kernel strategy, which prevents branching, avoids redundant computation and provides efficient memory access. In addition, we propose node-based and degrees-of-freedom (DOF)-based parallel strategies for effective implementation of matrix-free SpMV on a GPU. The proposed strategies use single elemental tangent matrix for all elements in elastic region and individual tangent matrices in plastic region. The computational experiments over three large-scale benchmark examples of elastoplasticity reveal that the performance of the node-based and DOF-based parallelization strategies depends on the amount of plasticity in the body. At low plasticity levels, node-based strategy performs best, achieving 3.2× speedup over an existing GPU-based matrix-free SpMV strategy in the literature. For moderate to high amount of plasticity, the DOF-based strategy outperforms every other strategy and obtains speedups of up to 3.5× over the existing SpMV strategy.

Electro-erosion fault identification of motor bearing based on ASMOTE-CFR

In view of the problem that the electro-erosion fault signal is rare and weak during motor operation, and the database is seriously imbalanced, this paper proposes an ASMOTE-CFR training model based on adaptive minority oversampling technology. Four bearing vibration acceleration signals in different states were collected through experiments, and each signal obtained 32 sets of energy features using wavelet packet decomposition. Then ASMOTE technology is used to balance the energy features of electro-erosion fault signal. And construct a vector matrix combined by energy features and bearing fault state features. Finally, the collaborative filter model of matrix decomposition is used to train and identify. The results show that the recognition rate of the ASMOTE-CFR model proposed in this paper is 98.46 %, which improves by 7 % compared with the traditional CFR, which verifies the effectiveness of this method.

Motion capture method for college basketball training based on AR/VR technology

Abstract To improve the effectiveness of basketball running training, this paper proposes an AR/VR technology-based motion capture method for college basketball sports training. This paper first describes the method steps of virtual reality motion capture technology, data fusion and skeletal data normalization of skeletal data, and calibration to obtain the rotation matrix and displacement vector of each Kinect sensor to integrate the skeleton data. Then the data features are extracted, 3D joint position, joint velocity, joint angle and angular velocity are extracted from the fused skeleton information of each frame, and then the LSTM algorithm is used to obtain the timing information in the action sequence and to classify the action for recognition. Finally, the method’s performance is evaluated in terms of accuracy, recall, and response time. Regarding accuracy, the recognition rates of “shooting” and “defense” were around 85%, while the recognition rates of other actions were 93% and above. In terms of recognition time, the recognition time of common equipment is about 350ms, while the recognition time of virtual reality equipment is about 210ms, which is 100ms less than that of traditional equipment, demonstrating the effectiveness and feasibility of this method.

Dynamical Optimal Values of Parameters in the SSOR, AOR, and SAOR Testing Using Poisson Linear Equations

This paper proposes a dynamical approach to determine the optimal values of the parameters used in each iteration of the symmetric successive over-relaxation (SSOR), accelerated over-relaxation (AOR), and symmetric accelerated over-relaxation (SAOR) methods for solving linear equation systems. When the optimal values of the parameters in the SSOR, AOR, and SAOR are hard to determine as some fixed values, they are obtained by minimizing the merit functions, which are based on the maximal projection technique between the left- and right-hand-side vectors, which involves the input vector, the previous step values of the variables, and the parameters. The novelty is a new concept of the dynamical optimal values of the parameters, instead of the fixed values and the maximal projection technique. In a preferred range, the optimal values of the parameters can be quickly determined by using the golden section search algorithm with a loose convergence criterion. Without knowing and having the theoretical optimal values in general, the new methods might provide an alternative and proper choice of the values of the parameters for accelerating the convergence speed. Numerical testings of the linear Poisson equation discretized to a matrix–vector form and a Lyapunov equation form were used to assess the performance of the DOSSOR, DOAOR, and DOSAOR dynamical optimal methods.

MPS-VQE: A variational quantum computational chemistry simulator with matrix product states

Quantum computing is attracting more and more attention in material and biological science. In the noisy intermediate-scale quantum (NISQ) computing era, the variational quantum eigensolver (VQE) is expected as an effective method to solve quantum chemistry problems which has potential quantum advantage. Classically simulating quantum algorithms plays a critical role in algorithmic development and the validation of noisy quantum devices before large-scale, fully fault-tolerant quantum computers are developed. However, most existing simulators are based on the state vector or density matrix representation of the quantum state which is faced with the memory bottleneck due to the exponential growth of memory requirement as the number of qubits increases. In this work, we present a VQE simulator based on the matrix product states (MPS) method from quantum many-body physics, and a detailed study of our MPS-VQE simulator in quantum chemistry applications. The memory requirement of MPS-VQE grows only polynomially and we demonstrate that accurate results can be obtained despite the truncation of the smallest singular values during the algorithm. A distributed parallelization scheme is also presented for massively parallel computer systems, and different implementations of the parallelization scheme based on the Julia language are benchmarked which demonstrate the efficiency and scalability of our method. Our method could open a new avenue towards large-scale classical simulation of quantum computational chemistry.

Enhanced DOA Estimation With Co-Prime Array in the Scenario of Impulsive Noise: A Pseudo Snapshot Augmentation Perspective

Co-prime array configuration is popular in the recent development of array signal processing by exploiting the sparse arrangement of arrays and the co-prime feature of the number of subarray elements. However, the assumption of Gaussian noise in most co-prime array processing research might lead to model mismatch in practical scenarios of impulsive noise, and therefore have an adverse impact on the estimation of direction of arrival (DOA). Moreover, co-prime array builds an enlarged virtual array by vectorizing the covariance matrix of the received signals, where the equivalent received signals of the virtual array have only a single snapshot. In this paper, we propose an enhanced fractional low-order method (EFLOM) for co-prime array configuration in scenarios of impulsive noise, from the perspective of pseudo snapshot increment. Since impulsive noise does not have finite second-order statistics or high-order cumulant, we construct a series of equivalent covariance matrices by using phased fractional low-order moments with different orders of the received signals. Then, the vectorization of multiple equivalent covariance matrices can be formed as the equivalent received signals of the virtual array with multiple snapshots. Since the reformed observations of the equivalent received signals are from the same sources, additional spatial smoothing preprocessing operations are still needed for decorrelation. While in this paper, we propose an improved spatial smoothing (ISS) technique by applying the information of both autocorrelation and cross subarray correlation of the covariance matrix. Afterwards, the classical multiple signal classification (MUSIC) is applied for the estimation of DOAs. The performance of the proposed method is theoretically verified and simulations are also provided to show its effectiveness in terms of the generalized signal to noise ratio (GSNR), parameter of impulsive noise, and angle separation.

Correlation and K-means clustering based small current ground fault line selection algorithm

The existing small current grounding line selecting technique has consequences by transition resistance, fault closure angles, and the fault location, and there is a problem of low selection accuracy, which is addressed by proposing a line-choosing algorithm that employs a combination of transient zero-sequential current (TZSC) waveform correlation and K-means clustering. First, to obtain the correlation coefficient matrix, the correlation analysis is performed for each line of the zero-sequence currents transient measurement values; second, to address the issue of the difficulties in manually setting the threshold, we apply the K-mean cluster analysis algorithm to group the row vectors of the correlation coefficients matrices; and finally, we output the label of the cluster to realize the fault line selection. Simulation and real-world fault data validate the method, showing that it is independent of transition resistance, fault closure angles, and fault location. It can achieve precise and dependable line selectivity.

Numerical approach to solve imprecisely defined systems using Inner Outer Direct Search optimization technique

In this paper, the Inner–Outer Direct Search (IODS) optimization technique is extended in the fuzzy environment to solve a fuzzy system of nonlinear equations. The proposed approach of fuzzy IODS converts the fuzzy system of nonlinear equations to an unconstrained fuzzy optimization problem. Then, the unconstrained fuzzy optimization problem is studied through the IODS technique. To validate the proposed algorithm, convergence analysis is performed. Further, three different fuzzy system of nonlinear equations are considered to demonstrate the algorithm. The fuzzy system of nonlinear equations is divided into various cases viz. fully fuzzy (when both the coefficient matrix and right-side vector are fuzzy) and only fuzzy (when either of the coefficient matrix or the right-side vector is fuzzy). For each individual case the numerical and graphical convergence of the obtained solutions were established. One electrical circuit problem is investigated to obtain the current in fuzzy environment and the same is compared with an existing method. It is observed that the closed form of the fuzzy solution contains the solution of the corresponding crisp system as well as the compared method. Finally, it can be noted that the proposed IODS approach can be applied to find the united fuzzy solutions for various science and engineering problems with easy implementation.

SAMBA: Sparsity Aware In-Memory Computing Based Machine Learning Accelerator

Machine Learning (ML) inference is typically dominated by highly data-intensive Matrix Vector Multiplication (MVM) computations that may be constrained by the memory bottleneck due to massive data movement between processor and memory units. Although analog in-memory computing (IMC) ML accelerators have been proposed to execute MVM with high efficiency, the latency and energy of such analog computing systems can be dominated by the large latency and energy costs from analog-to-digital converters (ADC). Leveraging sparsity in ML workloads, reconfigurable ADCs can improve the MVM energy and latency by reducing the required ADC bit precision. However, such improvement in latency can be hindered by non-uniform sparsity of the weight matrices mapped into hardware. Moreover, data movement between MVM processing cores may become another factor that delays the overall system-level performance. To address these issues, we propose SAMBA, Sparsity Aware IMC Based Machine Learning Accelerator. First, we propose load balancing at the mapping of weight matrices into physical crossbars. The goal of load balancing is to accommodate reconfigurable ADCs and address the possible delay of MVM processing caused by non-uniform sparsity in the weight matrices. Second, we propose optimizations in arranging and scheduling the tiled MVM hardware to minimize the overhead of data movement across multiple processing cores. Our evaluations show that the proposed load balancing technique can achieve performance improvement by eliminating the non-uniformity in the sparsity of mapped matrices. Moreover, we demonstrate that data movement optimizations can further improve both performance and energy efficiency regardless of sparsity condition. With the combination of load balancing and data movement optimization in conjunction with reconfigurable ADCs, our proposed approach provides up to 2.38x speed-up and 1.54x energy efficiency over state-of-art analog IMC based ML accelerators for ImageNet datasets on Resnet-50 architecture.

A fault diagnosis method based on hybrid sampling algorithm with energy entropy under unbalanced conditions

For the degraded performance of the fault diagnosis model caused by massive normal samples and scarce fault samples under unbalanced conditions, a new fault diagnosis method based on a hybrid sampling algorithm and energy entropy, namely HSEEFD is proposed in this paper. In the proposed method, Empirical Modal Decomposition is employed to decompose the vibration signals into Intrinsic Mode Functions (IMFs), and the energy entropy feature of each IMF component is extracted to construct a feature vector matrix. Then, a new hybrid sampling algorithm using Tomek’s Links algorithm, Euclidean distance, K-means algorithm, and synthetic minority over-sampling technique (SMOTE), namely TSHSA is designed to balance the extracted features. Tomek’s Links algorithm is used to identify and remove the confusable majority class samples at the boundary. Euclidean distance is applied to find the suspected noise points in minority class samples and remove them. The k-means algorithm is employed to cluster the minority class samples and SMOTE is used to deal with each cluster according to the density of the clusters to synthesize new features. Finally, the support vector machine is applied to classify faults and realize fault diagnosis. The experiment results on the actual imbalanced data show that the proposed HSEEFD method can effectively improve the accuracy (AUC) of the fault diagnosis under unbalanced conditions by increasing the AUC value by more than 2.1%, and the AUC and G-mean by more than 0.7%, 2.1%, respectively.

A norm stability condition of neutral-type Cohen-Grossberg neural networks with multiple time delays

By constructing an appropriate Lyapunov functional, this paper obtains a novel delay-independent stability criterion of neutral-type Cohen-Grossberg neural networks possessing multiple time delays. Although this type of system cannot be represented as vector–matrix form due to the presence of multiple delays, our stability conclusion is fully defined by the infinite norm of parametric matrices and the network parameters first time. Due to the feasibility and simplicity of method proposed, our stability conclusion reducing the computational complexity while also reducing the conservatism compared with several onetime literature. Two concrete neural network models are applied to confirm the effectiveness and superiority of our conclusion.

Equivalent estimation method (EEM) for quasi-distributed bridge-deflection measurement using only strain data

Deflection is a crucial parameter for bridge health monitoring procedures. In this paper, an equivalent estimation method (EEM) is proposed for quasi-distributed deflection estimation using onboard strain data. Leveraging the installation of the self-designed sensing bar on the bridge girder, an equivalent analysis model is established. An innovative inverse finite element method (iFEM) is employed to discretize the model and to establish a strain-deflection transformation matrix. Then, quasi-distributed bridge deflections are estimated by reconstructing the deformed shape of the equivalent analysis model. The present model is simple and independent of the typology of bridge structures, making the EEM sufficiently general to analyse complex bridges. The EEM framework is computationally fast, powerful, and robust for real-time applications since iFEM enables deformation predictions by simple matrix–vector multiplication without a priori loading and material information. Experimental validation cases have been performed, and they demonstrate the excellent quasi-distributed sensing capability of the EEM.

Unitarity of some barycentric rational approximants

Abstract The exponential function maps the imaginary axis to the unit circle and for many applications this unitarity property is also desirable from its approximations. We show that this property is conserved not only by the $(k,k)$-rational interpolant of the exponential on the imaginary axis, but also by $(k,k)$-rational barycentric approximants that minimize a linearized approximation error. These results are a consequence of certain properties of singular vectors of Loewner-type matrices associated to linearized approximation errors. Prominent representatives of this class are rational approximants computed by the adaptive Antoulas–Anderson (AAA) method and the AAA–Lawson method. Our results also lead to a modified procedure with improved numerical stability of the unitarity property and reduced computational cost.

A new method for single‐phase high resistance grounding fault protection in low resistance grounded distribution networks

AbstractThe neutral point of the distribution network is grounded with low resistance, which can quickly remove single‐phase grounding fault and effectively suppress overvoltage. However, the existing zero‐sequence overcurrent protection has a high setting value. In the case of large fault resistance and weak fault current, the existing protection methods may refuse to operate. Based on the waveform characteristics of the zero‐sequence current of each outgoing line in the distribution network, this article proposes a new method for single‐phase high resistance grounding fault protection in low resistance grounded distribution network, which combines cosine distance and improved K‐means algorithm. First, the cosine distance between zero‐sequence current of every two outgoing lines is obtained, and the cosine distance matrix used to describe the fault characteristics is constructed. Then the improved K‐means algorithm is used to cluster the row vectors of the cosine distance matrix to obtain the convergent cluster center and cluster label, so that the fault line can be determined. This protection method does not need to set the threshold value manually, and has strong ability to handle large fault resistance. It can effectively deal with noise interference and intermittent arc grounding fault, and still has good adaptability in scenarios such as change of fault initial phase angle, change of fault location, access of distributed generations and occurrence of two outgoing lines in phase to grounding fault. Finally, a model is built, and the effectiveness of the proposed method is proved by the simulation of grounding fault.