Sparse and low-rank methods in structural system identification and monitoring

The acquisition of channel state information (CSI) is essential in millimeter wave (mmWave) multiple-input multiple-output (MIMO) systems. The mmWave channel exhibits sparse scattering characteristics and a meaningful low-rank structure, which can be simultaneously employed to reduce the complexity of channel estimation. Most existing works recover the low-rank structure of channels using nuclear norm theory. However, solving the nuclear norm-based convex problem often leads to a suboptimal solution of the rank minimization problem, thus degrading the accuracy of channel estimation. Previous contributions recover the channel using over-complete dictionary with the assumption that the mmWave channel can be sparsely represented under some dictionary. While over-complete dictionary may increase the computational complexity. To address these problems, we propose a channel estimation framework based on non-convex low-rank approximation and dictionary learning by exploring the joint low-rank and sparse representations of wireless channels. We surrogate the widely used nuclear norm theory with non-convex low-rank approximation method and design a dictionary learning algorithm based on channel feature classification employing deep neural network (DNN). Our simulation results reveal the proposed scheme outperform the conventional dictionary learning algorithm, Bayesian framework algorithm, and compressed sensing-based algorithms.

Network-oriented research has been increasingly popular in many scientific areas. In neuroscience research, imaging-based network connectivity measures have become the key for understanding brain organizations, potentially serving as individual neural fingerprints. There are major challenges in analyzing connectivity matrices, including the high dimensionality of brain networks, unknown latent sources underlying the observed connectivity, and the large number of brain connections leading to spurious findings. In this paper we propose a novel blind source separation method with low-rank structure and uniform sparsity (LOCUS) as a fully data-driven decomposition method for network measures. Compared with the existing method that vectorizes connectivity matrices ignoring brain network topology, LOCUS achieves more efficient and accurate source separation for connectivity matrices using low-rank structure. We propose a novel angle-based uniform sparsity regularization that demonstrates better performance than the existing sparsity controls for low-rank tensor methods. We propose a highly efficient iterative node-rotation algorithm that exploits the block multiconvexity of the objective function to solve the nonconvex optimization problem for learning LOCUS. We illustrate the advantage of LOCUS through extensive simulation studies. Application of LOCUS to Philadelphia Neurodevelopmental Cohort neuroimaging study reveals biologically insightful connectivity traits which are not found using the existing method.

Summary Identifiability of parameters in structural system identification (SSI) is of primary importance in any SSI method. It depends on the number and the location of the measurements, which is linked with sensor configuration. In this paper, under the framework of SSI by observability method (OM), the number of necessary measurements to identify all parameters of structural system was clarified first. Then, an example was solved step by step to show the lacking constraints among unknowns in SSI by OM. In a frame example, it was found that no measurement set having as many measurements as the number of unknowns was able to identify all parameters. To further understand this phenomenon, the observability of a simply supported beam was analyzed in an exhaustive way using 252 possible measurement sets. Three quarters of these sets were not able to identify all the parameters. In order to solve this issue, for the very first time, SSI by constrained observability method (COM), which appends the nonlinear constraints to SSI by OM, was proposed. With SSI by COM applied, the observability of the structural parameters with respect to the 252 sets was greatly improved. Finally, the efficacy of SSI by COM was verified by a 13-story frame building.

Part-based visual tracking is advantageous due to its robustness against partial occlusion. However, how to effectively exploit the confidence scores of individual parts to construct a robust tracker is still a challenging problem. In this paper, we address this problem by simultaneously matching parts in each of multiple frames, which is realized by a locality-constrained low-rank sparse learning method that establishes multi-frame part correspondences through optimization of partial permutation matrices. The proposed part matching tracker (PMT) has a number of attractive properties. (1) It exploits the spatial-temporal locality-constrained property for robust part matching. (2) It matches local parts from multiple frames jointly by considering their low-rank and sparse structure information, which can effectively handle part appearance variations due to occlusion or noise. (3) The proposed PMT model has the inbuilt mechanism of leveraging multi-mode target templates, so that the dilemma of template updating when encountering occlusion in tracking can be better handled. This contrasts with existing methods that only do part matching between a pair of frames. We evaluate PMT and compare with 10 popular state-of-the-art methods on challenging benchmarks. Experimental results show that PMT consistently outperform these existing trackers.

At the core of any inference procedure, deep neural networks are dot product operations, which are the component that requires the highest computational resources. For instance, deep neural networks, such as VGG-16, require up to 15-G operations in order to perform the dot products present in a single forward pass, which results in significant energy consumption and thus limits their use in resource-limited environments, e.g., on embedded devices or smartphones. One common approach to reduce the complexity of the inference is to prune and quantize the weight matrices of the neural network. Usually, this results in matrices whose entropy values are low, as measured relative to the empirical probability mass distribution of its elements. In order to efficiently exploit such matrices, one usually relies on, inter alia, sparse matrix representations. However, most of these common matrix storage formats make strong statistical assumptions about the distribution of the elements; therefore, cannot efficiently represent the entire set of matrices that exhibit low-entropy statistics (thus, the entire set of compressed neural network weight matrices). In this paper, we address this issue and present new efficient representations for matrices with low-entropy statistics. Alike sparse matrix data structures, these formats exploit the statistical properties of the data in order to reduce the size and execution complexity. Moreover, we show that the proposed data structures can not only be regarded as a generalization of sparse formats but are also more energy and time efficient under practically relevant assumptions. Finally, we test the storage requirements and execution performance of the proposed formats on compressed neural networks and compare them to dense and sparse representations. We experimentally show that we are able to attain up to ×42 compression ratios, ×5 speed ups, and ×90 energy savings when we lossless convert the state-of-the-art networks, such as AlexNet, VGG-16, ResNet152, and DenseNet, into the new data structures and benchmark their respective dot product.

<div class="htmlview paragraph">Structural system identification was applied to small sample problems and to large automotive structures. The technique combines mass and stiffness matrices from a finite element model with experimental mode shapes and natural frequencies to produce improved mass and stiffness matrices. In numerical experiments on small problems the procedure enabled us to identify regions of original finite element models where changes of model parameters were required to bring finite element predictions into better agreement with exact results. Also, node point displacements were calculated for small structures subjected to time-dependent sinusoidal loads, and it was found that predictions of displacements from “improved” models were more accurate than original finite element model predictions when forcing frequencies were within the range of experimental frequencies used with structural system identification calculations. When applied to two large automotive structures. regions within the finite element models identified as candidates for parameter changes to, in one case, bring about a shift in predicted frequencies, and, in the other case, improve correlation with test results, were found to be consistent with our engineering judgement.</div>

Hyperspectral images (HSIs) have a wealth of applications in many areas, due to their fine spectral discrimination ability. However, in the practical imaging process, HSIs are often degraded by a mixture of various types of noise, for example, Gaussian noise, impulse noise, dead pixels, dead lines, and stripe noise. Low-rank matrix decomposition theory has been widely used in HSI denoising, and has achieved competitive results by modeling the impulse noise, dead pixels, dead lines, and stripe noise as sparse components. However, the existing low-rank-based methods for HSI denoising cannot completely remove stripe noise when the stripe noise is no longer sparse. In this article, we extend the HSI observation model and propose a double low-rank (DLR) matrix decomposition method for HSI denoising and destriping. By simultaneously exploring the low-rank characteristic of the lexicographically ordered noise-free HSI and the low-rank structure of the stripe noise on each band of the HSI, the two low-rank constraints are formulated into one unified framework, to achieve separation of the noise-free HSI, stripe noise, and other mixed noise. The proposed DLR model is then solved by the augmented Lagrange multiplier (ALM) algorithm efficiently. Both simulation and real HSI data experiments were carried out to verify the superiority of the proposed DLR method.

When discrete response models arc estimated with multilevel, or clustered, data, there is much interest in the distribution of the residuals. With logistic regression it is usually assumed that these residuals are binomially distributed. A common real world situation is where the multilevel data structure is sparse, with relatively few individual cases per cluster. The impact of sparsity on estimates of binomial variation is explored using simulation techniques. This exploration demonstrates that sparsity leads to extra‐binomial variation. The results are discussed in relation to recent data on eyewitness line‐ups, an example with a sparse data structure.

This paper describes a numerical algorithm to determine the response of the structure due to a known force. The inverse dynamics problem in structural dynamics is to estimate the unknown forcing function using dynamic response. Theory of plates is employed to solve inverse problems in elasticity with specific applications to position and force sensing. In this paper, the contact force during the transverse impact of a plate is given and the response is solved. A Kalman filter technique was used to numerically estimate an applied force on the plate with the numerical response by an inverse method. In order to examine the accuracy of the proposed method, the plate is subjected to four type forces, which are triangular, sinusoidal, rectangular and random force. The estimated results have a good agreement with the exact values in all cases tested. Copyright © 2001 John Wiley & Sons, Ltd.

Structural system identification is a critical task in resilience assessments, especially following a natural hazard. In this paper, we propose PIDynNet, a novel physicsinformed approach that produces an ordinary differential equation-constrained neural network model for structural system identification. PIDynNet improves the estimation of structural parameters of nonlinear structural systems by embedding an auxiliary physicsbased loss term into the overall loss function as well as a supervised data-driven loss term. The proposed framework has the generalization capability to predict nonlinear structural response given unseen ground excitations. Two nonlinear numerical experiments are conducted to demonstrate the advantage of PIDynNet over other identification methods in problems with or without latent variables.

<p> The structural response of any structure is traditionally predicted by simplistic physics-based models. In these models the mechanical and geometrical properties are assumed as known. Nevertheless, this is not the case in most actual structures where the values of the actual properties (such as axial or flexural stiffness) are unknown due to uncertainties in the materials, in the construction methods or in the stress state. In some cases, a calibration of the computer models is required to improve de accuracy of the predicted structural response. To carry out this task Structural System Identification (SSI) methods can be used.</p><p> In this paper, a new parametric method for SSI from static excitation response is proposed. This method is based on the observability of the structure, understanding as such the problem of identifying which is the subset of characteristics of the structure, such as Young’s modulus, area, inertia, and/or products of them (axial or flexural stiffnesses) that may be uniquely determined when a subset of deflections and forces at nodes is provided. This method has lead to the development of a powerful mathematical tool to deal efficiently with polynomial systems of equations with a number of applications in many fields of science and engineering.</p><p> To illustrate the applicability of the proposed method, the analysis of the SSI of two structures of growing complexity is presented.</p>

In this paper, we propose a sparse coding algorithm based on matrix rank minimization and k-means clustering and for recognition. We consider the problem of removing the noise in the training samples and generating more samples at the same time. To accomplish this, we extended the matrix rank minimization problem to cope with complex data. Samples from the same class are segmented into several groups by k-means clustering algorithm, and matrix rank minimization is applied on the clustered data to separate the noises and recover the low-rank structures in the grouped data. An over-complete dictionary is constructed by connecting the low-rank structures and the training samples together to keep the samples diversity. Sparse representation is operated based on this over-complete dictionary for recognition. Furthermore, a parameter is introduced to adjust the weighting of the coefficients that code the noises. We apply the proposed algorithm for character and face recognition. Experiments with improved performances validate the effectiveness of the proposed algorithm.

Low-rank matrix recovery algorithms aim to recover a corrupted low-rank matrix with sparse errors. However, corrupted errors may not be sparse in real-world problems and the relationship between ℓ1 regularizer on noise and robust M-estimators is still unknown. This paper proposes a general robust framework for low-rank matrix recovery via implicit regularizers of robust M-estimators, which are derived from convex conjugacy and can be used to model arbitrarily corrupted errors. Based on the additive form of half-quadratic optimization, proximity operators of implicit regularizers are developed such that both low-rank structure and corrupted errors can be alternately recovered. In particular, the dual relationship between the absolute function in ℓ1 regularizer and Huber M-estimator is studied, which establishes a connection between robust low-rank matrix recovery methods and M-estimators based robust principal component analysis methods. Extensive experiments on synthetic and real-world data sets corroborate our claims and verify the robustness of the proposed framework.

The concepts of sparse data structures and related algorithms for phase field simulations are discussed. Simulations of polycrystalline grain growth with a conventional phase field method and with sparse data structures are compared. It is shown that memory usage and simulation time scale with the number of nodes but are independent of the number of order parameters when a sparse data structure is used.

Graph neural networks (GNNs) have a powerful ability to capture long-range spatial correlations in hyperspectral images (HSIs). However, existing GNN-based HSI classification methods are vulnerable to hand-crafted graphs, as the manner in which these graphs are constructed are often inappropriate and are likely to violate intrinsic graph properties, such as sparsity and low-rank. More importantly, the goal of HSI classification is to categorize each individual pixel into a land-cover class, but existing methods usually overuse global dependencies and ignore the importance of individualized spectral characteristics. Therefore, this paper proposes a Global-to-Local decoupling Graph network (GoLoG) to conduct HSI classification in a global-to-local framework, which jointly optimizes the graph structure and network parameters guided by both intrinsic graph properties and classification loss. Specifically, a novel global-to-local network framework with successive global and local graph convolutional stages is constructed. By decoupling global and local stages, global contextual information can be exploited, and the individualized information of each hyperspectral pixel can be emphasized for HSI classification. Second, a sparse and low-rank graph structure learning model is proposed to refine and renovate the initial-construct graph. Finally, to unify graph structure learning and network training, a joint alternating update algorithm is introduced to jointly optimize the sparse and low-rank graph structure learning model and the global-to-local network framework. Extensive experiments demonstrate that the proposed GoLoG has obvious advantages compared with other state-of-the-art HSI classification methods.