Displacement Structure of Core-EP Inverses

In this paper,we study the displacement rank of the Core-EP inverse.Both Sylvester displacement and generalized displacement are discussed.We present upper bounds for the ranks of the displacements of the Core-EP inverse.Numerical experiments are presented to demonstrate the efficiency and accuracy.

Robust vision-based displacement measurement and acceleration estimation using RANSAC and Kalman filter

Computer vision(CV)-based techniques have been widely used in the field of structural health monitoring(SHM)owing to ease of installation and cost-effectiveness for displacement measurement.This paper introduces computer vision based method for robust displacement measurement under occlusion by incorporating random sample consensus(RANSAC).The proposed method uses the Kanade-Lucas-Tomasi(KLT)tracker to extract feature points for tracking,and these feature points are filtered through RANSAC to remove points that are noisy or occluded.With the filtered feature points,the proposed method incorporates Kalman filter to estimate acceleration from velocity and displacement extracted by the KLT.For validation,numerical simulation and experimental validation are conducted.In the simulation,performance of the proposed RANSAC filtering was validated to extract correct displacement out of group of displacements that includes dummy displacement with noise or bias.In the experiment,both RANSAC filtering and acceleration measurement were validated by partially occluding the target for tracking attached on the structure.The results demonstrated that the proposed method successfully measures displacement and estimates acceleration as compared to a reference displacement sensor and accelerometer,even under occluded conditions.

A fast algorithm for multivariate Hermite interpolation

Multivariate Hermite interpolation is widely applied in many fields, such as finite element construction, inverse engineering, CAD etc.. For arbitrarily given Hermite interpolation conditions, the typical method is to compute the vanishing ideal I （the set of polynomials satisfying all the homogeneous interpolation conditions are zero） and then use a complete residue system modulo I as the interpolation basis. Thus the interpolation problem can be converted into solving a linear equation system. A generic algorithm was presented in [18], which is a generalization of BM algorithm [22] and the complexity is O（τ^3） where r represents the number of the interpolation conditions. In this paper we derive a method to obtain the residue system directly from the relative position of the points and the corresponding derivative conditions （presented by lower sets） and then use fast GEPP to solve the linear system with O（（τ ＋ 3）τ^2） operations, where τ is the displacement-rank of the coefficient matrix. In the best case τ = 1 and in the worst case τ = [τ/n], where n is the number of variables.

Fast Cholesky Factorization Algorithm for s. p. d Block-Toeplitz Matrices

A fast Cholesky factorization algorithm based on the classical Schur algorithm for themp×mp symmetric positive definite (s. p. d) block-Toeplitz matrices is presented. The relation between the generator and the Schur complement of the matrices is explored. Besides, by applying the hyperbolic Householder transformations, we can reach an improved algorithm whose computational complexity is2p 2m3?4pm3+3/2m3+O(pm).

Fast Parallel QR Decomposition of Block-Toeplitz Matrices

A fast algorithm FBTQ is presented which computes the QR factorization a block-Toeplitz matrix A (A∈R) in O(mns3) multiplications. We prove that the QR decomposition of A and the inverse Cholesky decomposition can be computed in parallel using the sametransformation.We also prove that some kind of Toeplltz-block matrices can he transformed into the corresponding block-Toeplitz matrices.

Nodes2STRNet for structural dense displacement recognition by deformable mesh model and motion representation

Displacement is a critical indicator for mechanical systems and civil structures.Conventional vision-based displacement recognition methods mainly focus on the sparse identification of limited measurement points,and the motion representation of an entire structure is very challenging.This study proposes a novel Nodes2STRNet for structural dense displacement recognition using a handful of structural control nodes based on a deformable structural three-dimensional mesh model,which consists of control node estimation subnetwork(NodesEstimate)and pose parameter recognition subnetwork(Nodes2PoseNet).NodesEstimate calculates the dense optical flow field based on FlowNet 2.0 and generates structural control node coordinates.Nodes2PoseNet uses structural control node coordinates as input and regresses structural pose parameters by a multilayer perceptron.A self-supervised learning strategy is designed with a mean square error loss and L2 regularization to train Nodes2PoseNet.The effectiveness and accuracy of dense displacement recognition and robustness to light condition variations are validated by seismic shaking table tests of a four-story-building model.Comparative studies with image-segmentation-based Structure-PoseNet show that the proposed Nodes2STRNet can achieve higher accuracy and better robustness against light condition variations.In addition,NodesEstimate does not require retraining when faced with new scenarios,and Nodes2PoseNet has high self-supervised training efficiency with only a few control nodes instead of fully supervised pixel-level segmentation.