Diagonal Structure Research Articles

A two‐stage parallel method on GPU based on hybrid‐compression‐format for diagonal matrix

AbstractSpMV (Sparse matrix‐vector multiplication) is an important computing core in traditional high‐performance computing and also one of the emerging data‐intensive applications. For diagonal sparse matrices, it is frequently necessary to fill in a large number of zeros to maintain the diagonal structure as for using DIA (Diagonal) storage format. The fact that filling with zeros may consume additional computing and memory resources, will certainly lead to degradation of the parallel computing performance of SpMV, further causing computing and storage redundancy. To solve the deficiencies of the DIA format, a Two‐stage parallel SpMV method is presented in this paper, which can reasonably distribute the data of diagonal matrix and irregular matrix to different CUDA kernels. As different corresponding compression methods are particularly designed for different matrix forms, a partition‐based hybrid format of DIA and CSR (HPDC) is therefore adopted in the two‐stage method to ensure load balancing among computing resources and continuity of data access on the diagonal. Simultaneously, a standard deviation among blocks is used as a criterion to obtain the optimal number of blocks and distribution of data. The experimental data were implemented in the Florida data set. Compared to DIA, cuSPARSE‐CSR, HDC, and BRCSD, the execution time of the Two‐stage method is shortened by 4, 3.4, 1.9, and 1.15, respectively.

Experimental investigation of mechanical stiffness in lattice structures fabricated with PLA using fused deposition modelling

The objective of the paper is to design and characterise with polylactic acid (PLA) material three cellular structures in the form of lattices which are diagonal-octet-centred shapes for two sizes 6x6x6 and 12x12x12 with a compression test to examine their stiffness using FDM technology compared to polyjet technology.The study used two analytical approaches to investigate lattice structures: experimental analysis and theoretical analysis. Experimental methods such as compression tests were conducted to determine the characteristics of lattice structures. In addition, theoretical analysis was conducted using Hook's law and Ashby's Gibson model to predict appropriate behaviour. The combination of experimental and theoretical methods provided a comprehensive understanding of lattice structures and their properties.The experimental study examined the impact of the shape and size of a lattice structure on the stiffness and lightness of objects 3D printed with FDM technology by PLA material. The research revealed that the 6x6x6 diagonal lattice structure size provided a good balance between stiffness and lightness. While the 6x6x6 byte structure was even lighter, with a mass ratio of 2.09 compared to the diagonal structure, it was less rigid, with a ratio of 0.43, making the diagonal structure more suitable for certain applications. The study highlights the importance of considering both the shape and size of the lattice structure when designing 3D-printed objects with specific mechanical properties; the chosen structure could be a good choice for applications where stiffness and lightness are important.The limitations of the research lie in its limited scope, focusing primarily on the effect of shape (octet-diagonal centred) and unit cell size on Young's modulus of PLA material. Other aspects of 3D printing, such as material selection and thermal properties, were not considered. Furthermore, the results obtained are specific to the printing parameters and experimental conditions chosen, which limits their generalizability to other 3D printing configurations or methods. However, these results have important implications for optimising the PLA printing process. They enable the identification of optimal parameters, such as unit cell shape and size, to produce stiffer, higher-quality structures. In addition, the research is helping to improve the mechanical properties of 3D-printed lattice parts, paving the way for more efficient manufacturing methods and stronger components.Our analysis can be used as a decision aid for the design of FDM lattice parts. Indeed, we can choose the diagonal structure of 6x6x6, which would provide favourable stiffness for functional parts.The paper explores the compression test of lattice structures using FDM technology, which presents a new direction for additive manufacturing. The study takes an experimental approach to evaluate the reliability of various additive manufacturing technologies for creating lattice structures. The study results provide insight into the most reliable technology for producing lattice structures.

Effect of inlet and outlet positions on heat dissipation performance of lithium-ion battery cold plates: An analysis based on topology optimization

This study applied topology optimization methods to design a cold plate with topology channels for a square battery. With maximum heat transfer as the optimization objectives of the cold plate channel, and the performance of the cold plate at different inlet and outlet positions was systematically analyzed, effectively harnessing the potential of topology optimization. Based on the results of the topology analysis, a simplified three-dimensional cooling model was established and numerically investigated. The optimized design was explored considering different inlet and outlet arrangements, channel depths, and mass flow rates. The results demonstrated that a channel depth of 4 mm, an inlet temperature of 25 °C, and a mass flow rate of 12 g·s−1 was the ideal choice for a 1 C discharge cooling system. The different inlet and outlet positions had a greater impact on the performance of the cold plate at this time. The parallel diagonal structure (Case A-6) could lower the pressure drop by a maximum of 16.41% and improve the heat transfer efficiency by 6.10%, and the pumping power was only 0.003 W, which could obtain high heat transfer efficiency with low pump consumption; The straight-in and straight-out structure (Case B-6) was the most superior in maximum temperature and temperature deviation, with a maximum temperature of only 33.11 °C and a temperature deviation of 1.28 °C, which could decrease by 1.25 and 0.35 °C respectively compared with other structures, improving the upper limit of working temperature and the uniformity of temperature distribution. Finally, the optimized cold plates were experimentally validated. The experimental error was within 4%, proving the simulation analysis's accuracy.

Experimental study on seismic performance of super high-rise building with topology optimized diagonal mega frame

Diagrid system has received increasing attention by designers and researchers of high-rise building. In this paper, an innovative super high-rise diagonal mega frame-core tube structure adopting topology optimization for two-dimensional diagrid mesh and shape optimization for three-dimensional outline was introduced. Different from traditional diagrid structures, eight corner columns and a number of corner beams were used in the external diagrid frame, leading to unique spatial working capacity. In order to assess and study the seismic performance of this innovative structure, a series of shaking table tests on a 1/35 scaled model were conducted. Three earthquake waves and three seismic intensity levels were considered during the tests and the external diagrid frame tube showed strong lateral stiffness while severe tensile damage occurred at the bottom of corner columns under maximum considered earthquakes. Then repair work of the test model was initiated and second part of shake table test was conducted which covered the same loading steps of the first part test and more loading steps of two higher seismic levels. Based on a large amount of test data recorded, the acceleration response, displacement response, strain response, seismic fragility and hysteretic energy dissipation of this structure were analyzed. This structure performed satisfactory seismic performance and collapse resistance capacity without obvious whiplash effect and weak story. Corner columns became the key components due to their tremendous axial forces and welding connections of corner columns became the comparatively weak parts in this system, which need be carefully concerned in practical project.

Adaptive multi-granularity sparse subspace clustering

Sparse subspace clustering (SSC) focuses on revealing data distribution from algebraic perspectives and has been widely applied to high-dimensional data. The key to SSC is to learn the sparsest representation and derive an adjacency graph. Theoretically, the adjacency matrix with proper block diagonal structure leads to a desired clustering result. Various generalizations have been made through imposing Laplacian regularization or locally linear embedding to describe the manifold structure based on the nearest neighborhoods of samples. However, a single set of nearest neighborhoods cannot effectively characterize local information. From the perspective of granular computing, the notion of scored nearest neighborhoods is introduced to develop multi-granularity neighborhoods of samples. The multi-granularity representation of samples is integrated with SSC to collaboratively learn the sparse representation, and an adaptive multi-granularity sparse subspace clustering model (AMGSSC) is proposed. The learned adjacency matrix has a consistent block diagonal structure at all granularity levels. Furthermore, the locally linear relationship between samples is embedded in AMGSSC, and an enhanced AMGLSSC is developed to eliminate the over-sparsity of the learned adjacency graph. Experimental results show the superior performance of both models on several clustering criteria compared with state-of-the-art subspace clustering methods.

New fast Walsh–Hadamard–Hartley transform algorithm

<span lang="EN-US">This paper presents an efficient fast Walsh–Hadamard–Hartley transform (FWHT) algorithm that incorporates the computation of the Walsh-Hadamard transform (WHT) with the discrete Hartley transform (DHT) into an orthogonal, unitary single fast transform possesses the block diagonal structure. The proposed algorithm is implemented in an integrated butterfly structure utilizing the sparse matrices factorization approach and the Kronecker (tensor) product technique, which proved a valuable and fast tool for developing and analyzing the proposed algorithm. The proposed approach was distinguished by ease of implementation and reduced computational complexity compared to previous algorithms, which were based on the concatenation of WHT and FHT by saving up to 3N-4 of real multiplication and 7.5N-10 of real addition.</span>

On the numerical properties of high‐order spectral (Euler‐Bernoulli) beam elements

AbstractIn this paper, the numerical properties of a recently developed high‐order Spectral Euler‐Bernoulli Beam Element (SBE) featuring a C1‐continuous approximation of the displacement field are assessed. The C1‐continuous shape functions are based on two main ingredients, which are an Hermitian interpolation scheme and the use of Gauß‐Lobatto‐Legendre (GLL) points. Employing GLL‐points does not only avoid Runge oscillations, but also yields a diagonal mass matrix when exploiting the nodal quadrature technique as a mass lumping scheme. Especially in high‐frequency transient analyses, where often explicit time integration schemes are utilized, having a diagonal mass matrix is an attractive property of the proposed element formulation. This is, however, achieved at the cost of an under‐integration of the mass matrix. Therefore, a special focus of this paper is placed on the evaluation of the numerical properties, such as the conditioning of the element matrices and the attainable rates of convergence (ROCs). To this end, the numerical behavior of the SBEs is comprehensively analyzed by means of selected benchmark examples. In a nutshell, the obtained results demonstrate that the element yields good accuracy in combination with an increased efficiency for structural dynamics exploiting the diagonal structure of the mass matrix.

Modeling covariance structures for genetic and non‐genetic effects in cowpea multi‐environment trials

AbstractIn cowpea breeding, multi‐environment trials are conducted to select lines with high yield. The occurrence of genetic and/or statistical imbalance is common in these experiments, in addition to the possibility of (co)variance between genetic and non‐genetic effects. We explore the restricted maximum likelihood/best linear unbiased prediction features to select the model with the most appropriated covariance structure and compare the results with the traditional model (homogenous variances and no covariances). Then, 17 inbred lines and three cultivars were evaluated in six experiments during two crop years in the semiarid zone of Northeast Brazil. The trait evaluated was the 100‐grain weight. We selected the best model considering the Akaike Information Criterion. The model with diagonal structure for the residual effects and heterogeneous compound symmetry for the genetic effects had the best fit. The predicted genetic gain of lines selected in this model was 1.18% higher compared to the traditional model. Modeling different (co)variance structures for genetic and non‐genetic effects is an efficient approach in selecting superior genotypes in multi‐environment trials in cowpea breeding.

Robust Subspace Clustering with Block Diagonal Representation for Noisy Image Datasets

As a relatively advanced method, the subspace clustering algorithm by block diagonal representation (BDR) will be competent in performing subspace clustering on a dataset if the dataset is assumed to be noise-free and drawn from the union of independent linear subspaces. Unfortunately, this assumption is far from reality, since the real data are usually corrupted by various noises and the subspaces of data overlap with each other, the performance of linear subspace clustering algorithms, including BDR, degrades on the real complex data. To solve this problem, we design a new objective function based on BDR, in which l2,1 norm of the reconstruction error is introduced to model the noises and improve the robustness of the algorithm. After optimizing the objective function, we present the corresponding subspace clustering algorithm to pursue a self-expressive coefficient matrix with a block diagonal structure for a noisy dataset. An affinity matrix is constructed based on the coefficient matrix, and then fed to the spectral clustering algorithm to obtain the final clustering results. Experiments on several artificial noisy image datasets show that the proposed algorithm has robustness and better clustering performance than the compared algorithms.

Semi-supervised non-negative matrix tri-factorization with adaptive neighbors and block-diagonal learning

Graph-regularized non-negative matrix factorization (GNMF) is proved to be effective for the clustering of nonlinear separable data. Existing GNMF variants commonly improve model performance by adding different additional constraints or refining the model factorization form, which can lead to problems such as increased algorithm complexity or insufficient performance release. In this paper, we propose semi-supervised non-negative matrix tri-factorization with adaptive neighbors and block-diagonal (ABNMTF). Different from existing methods, in ABNMTF the similarity graph matrix is learned from the original data by adaptive neighbors k-nearest model, and a block diagonal matrix is constructed based on a few labeled data to update the similarity matrix. Our approach reconstructs the block diagonal structure into the adaptive similarity matrix, which enables simultaneous learning of the similarity matrix and label binding during factorization, engendering a distinguishable subspace representation matrix and therefore improving the clustering performance without significantly increasing the complexity of the algorithm. We also represent an optimization method to solve the ABNMTF and provide analyses of convergence and computational complexity. Extensive experiments on 8 real image datasets show that the proposed algorithm reports superior performance against several state-of-the-art approaches. Code has been made available at:https://github.com/LstinWh/ABNMTF.

A novel generating machining process for screw-rotors using an internal-cylindrical skiving cutter on a new CNC skiving machine

To reduce machining time and improve accuracy for producing screw rotors, this study proposes a generating machining process using an internal-cylindrical skiving cutter on a new CNC skiving machine. An internal-barrel rotor is first generated based on a conjugation relationship with a male/female rotor. Then, the cutting edges of the internal-cylindrical skiving cutter are defined by the intersection curves between the rake plane and the barrel rotor surface. A geometrical analysis of the clearance angle allows adjustment of the relative position between the cylindrical cutter and the skived rotor on the cutter's axis. Furthermore, a general model for the skiving process is presented. The result shows that the normal deviations on the skived screw rotors are very close to zero. In addition, a new CNC skiving machine is proposed to perform the cutting process when considering the influence of feed rate. Accordingly, the surface morphology of the skived screw rotor is in the form of micro-size waves arranged in a diagonal structure. Finally, the skived screws surface with a predefined grinding stock is achieved by modifying the cutter geometric.

Kinematic-chemical Analysis and Time Tagging for the Diagonal Ridge Structure of the Galactic Outer Disk with LAMOST Red-giant Branch Stars

We investigate the kinematic-chemical distribution of red-giant branch stars from the LAMOST survey crossed matched with Gaia DR2 proper motions, and present time tagging for the well-known ridge structures (diagonal distributions for V R in the R, V ϕ plane) in the range of Galactocentric distance R = 8 to 15 kpc. We detect six ridge structures, including five ridges apparent in the radial velocity distribution and three ridges apparent in the vertical velocity, the sensitive time of which to the perturbations are from young population (0–3 Gyr) to old population (9–14 Gyr). Based on an analysis of the evolution of angular momentum distribution, we find that four ridges are relatively stationary, while another is evolving with time, which is confirmed by the difference analysis at different populations and supporting that there might be two kinds of dynamical origins. Furthermore, ridge features are also vividly present in the chemical properties ([Fe/H], [α/Fe]). The comparison between the north and south hemispheres of the Galaxy does show some differences and the ridge features are asymmetrical. Moreover, we find that diagonal ridge structures may affect the shape of the rotation curve, which is manifested as fluctuations and undulations on top of a smooth profile. Finally we speculate that the bar dynamics should be not enough to explain all ridge properties including the break feature in the V Z –L Z plane.

Joint structured constraint discriminant analysis dictionary learning for pattern classification

Analysis dictionary learning (DL) has been successfully applied to the field of pattern classification. However, it is still a challenge to utilize the local structure information and the class information of samples to improve the discrimination capability of analysis dictionary. We proposed a joint structured constraint discriminant analysis DL (ADL) method (JSCDADL) to learn a structured discriminant analysis dictionary by combining the local structure information and the structured information of samples. Specifically, we first designed an adaptive local structure preserving term (ALSPT) to improve the discrimination capability of analysis dictionary. It adaptively transmits the local structure information of samples to analysis dictionary, which ensures that the same class of samples has similar sparse codes under the action of the analysis dictionary. Then, we designed a discriminative sparse coding error term that forces the coding coefficient matrix to have the desired block diagonal structure. To further enhance the discrimination capability of analysis dictionary, we designed an analysis dictionary combination term by constantly approximating the two analysis dictionaries learned to obtain an analysis dictionary with the local structure information and the structured information of samples. Moreover, we designed an effective iterative algorithm to solve the optimization problem of JSCDADL. Extensive experimental results on six datasets demonstrate that JSCDADL can achieve satisfactory classification performance compared with some state-of-the-art methods.

Nonconvex low-rank tensor approximation with graph and consistent regularizations for multi-view subspace learning

Multi-view clustering is widely used to improve clustering performance. Recently, the subspace clustering tensor learning method based on Markov chain is a crucial branch of multi-view clustering. Tensor learning is commonly used to apply tensor low-rank approximation to represent the relationships between data samples. However, most of the current tensor learning methods have the following shortcomings: the information of the local graph is not taken into account, the relationships between different views are not shown, and the existing tensor low-rank representation takes a biased tensor rank function for estimation. Therefore, a nonconvex low-rank tensor approximation with graph and consistent regularizations (NLRTGC) model is proposed for multi-view subspace learning. NLRTGC retains the local manifold information through graph regularization, and adopts a consistent regularization between multi-views to keep the diagonal block structure of representation matrices. Furthermore, a nonnegative nonconvex low-rank tensor kernel function is used to replace the existing classical tensor nuclear norm via tensor-singular value decomposition (t-SVD), so as to reduce the deviation from rank. Then, an alternating direction method of multipliers (ADMM) which makes the objective function monotonically non-increasing is proposed to solve NLRTGC. Finally, the effectiveness and superiority of the NLRTGC are shown through abundant comparative experiments with various state-of-the-art algorithms on noisy datasets and real world datasets.

Transmission-type coding metasurface with ultra-broadband polarization conversion

The advent of coding metasurfaces (MSs) has established a bond between electromagnetic scattering and digital control. Given that most of the current coding MSs are based on reflection-type, we investigate a novel transmission-type MS that can achieve ultra-wideband and efficient polarization conversion. A new double diagonal split ring resonator structure is designed to mainly constitute the unit. The 1-bit and 2-bit coding arrays are constructed using the proposed polarization rotation mechanism of the MS unit combined with the dimensional transformation to achieve beam focusing, beam deflection, and beam splitting. Finally, the broadband focusing characteristic of the coding MS is also demonstrated. Numerical simulation results demonstrate that the transmission coefficient of the proposed MS is above 90% in the frequency range of 0.4 to 2 THz, with a relative bandwidth of 133.3%. Asymmetric transmission phenomenon is observed in the range of 0.4 to 2 THz, with coefficients remaining above 80% in all ranges.The proposed coding MS can be used in terahertz polarization converters and unidirectional transmission devices due to its superior polarization conversion performance.

Balancing domain decomposition method for large-scale analysis of an assembly structure having millions of multipoint constraints

A method by which to incorporate multipoint constraints (MPCs) into the balancing domain decomposition (BDD) method proposed in a previous study (BDD-MPC method) is investigated, improved, and applied to realistic and complex problems. First, the effects of the penalty term to take into account the MPCs in the coarse-grid problem of the BDD method are investigated. Then, improved implementation techniques for the BDD-MPC method are proposed. The computation speed of the projection procedure in the conjugate projected gradient method is improved using the block diagonal structure of the constraint matrix. The parallel solution procedure for the coarse-grid problem considering the MPCs that are projected to the coarse space is also improved. The improved MPC-BDD method is implemented in ADVENTURE_Solid, which is a parallel finite element structural analysis code. The code is parallelized using an MPI-OpenMP hybrid parallel implementation framework. In the previous study, the BDD-MPC method was applied to only simple numerical examples. In the present study the performance of the improved method is demonstrated by solving super-high-rise building models having very complex geometry and several million MPCs.

A Unified Framework for Correlation Mining in Ultra-High Dimension

Many applications benefit from theory relevant to the identification of variables having large correlations or partial correlations in high dimension. Recently there has been progress in the ultra-high dimensional setting when the sample size <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula> is fixed and the dimension <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$p$ </tex-math></inline-formula> tends to infinity. Despite these advances, the correlation screening framework suffers from practical, methodological and theoretical deficiencies. For instance, previous correlation screening theory requires that the population covariance matrix be sparse and block diagonal. This block sparsity assumption is however restrictive in practical applications. As a second example, correlation and partial correlation screening requires the estimation of dependence measures, which can be computationally prohibitive. In this paper, we propose a unifying approach to correlation and partial correlation mining that is not restricted to block diagonal correlation structure, thus yielding a methodology that is suitable for modern applications. By making connections to random geometric graphs, the number of highly correlated or partial correlated variables are shown to have compound Poisson finite-sample characterizations, which hold for both the finite <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$p$ </tex-math></inline-formula> case and when <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$p$ </tex-math></inline-formula> tends to infinity. The unifying framework also demonstrates a duality between correlation and partial correlation screening with theoretical and practical consequences.

Block Diagonal Representation Learning for Hyperspectral Band Selection

Hyperspectral band selection is viewed as an effective dimension reduction method. Recently, researchers present graph-based clustering for hyperspectral image (HSI) processing. However, most of them conduct clustering on a fixed data matrix so that it is sensitive to the quality of initial matrix. Moreover, these algorithms apply spectral clustering to obtain the final clustering result in increasing the time consumption. Based on these facts, we propose a block diagonal representation learning algorithm (BDRLA) in this paper. BDRLA generates a high-quality similarity matrix by approximating the initial affinity matrix. Meanwhile, motivated to the spectral bands distance similarity matrix has a clear diagonal structure, a block diagonal similarity matrix with ordered partition points based upon the ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> -norm is constructed. By doing so, the obtained similarity matrix is directly applied to subsequent processing without extracting the clustering indicators. Additionally, in order to estimate the importance of bands, dictionary learning is adopted to select the representative band in each cluster. Extensive experiment results on three public datasets indicate that the bands selected by the proposed method achieve satisfactory performance.

Multi-order similarity learning for multi-view spectral clustering

This paper explores the problem of multi-view spectral clustering (MVSC) based on multi-order similarity learning. Unlike the existing methods that focus on direct similarity of pairwise data points without considering the hidden multi-order similarity among different data points, a novel multi-order similarity learning model for MVSC (MOSL) is proposed. Specifically, the first-order similarity (FOS) and second-order similarity (SOS) are learned to excavate the local structure relation and adjacent structure relation of pairwise data points. Afterwards, the third-order similarity (TOS) based on low-rank tensor is learned to excavate the view-specific information and consensus information from multiple views. Moreover, a trace constraint on each affinity graph from multiple views is learned to ensure the strict block diagonal structure of each affinity graph. Extensive experiments on six commonly benchmark datasets show that the proposed method outperforms state-of-the-art methods in most scenarios and is capable of revealing a reliable affinity graph structure concealed in different data points.

Mechanical Properties of LPBF-Built Titanium Lattice Structures—A Comparative Study of As-Built and Hot Isostatic Pressed Structures for Medical Implants

We compare different lattice structures with various elementary cell sizes built by laser powder bed fusion with and without hot isostatic pressing as post treatment. Cylindrical lattice structures are mechanically tested upon static and dynamic load in order to achieve high elasticity, high fracture strength and a high number of cycles to failure with respect to applications as medical implants. Evaluating the Young’s modulus, a high stiffness for the body diagonal structure and a low fracture stress for the G-structure are measured. Hot isostatic pressing results in a higher Young’s modulus and is ambiguous in terms of fractural stress. While samples without hot isostatic pressing reveal a shear fracture, the hot isostatic pressed samples have a high ductile area where the lattice layers are wrapped and pressed into the underlying layers without a fracture. Under dynamic load, the samples without hot isostatic pressing mostly are unable withstand 106 cycles at typical loads of the human body. Hot isostatic pressing has no significant influence on the strength at high loads and low cycle numbers, but at low loads all samples survived 106 cycles. As a consequence, dode-thick and rhombic dodecahedrons with 2 mm and 1.5 mm lattice size after hot isostatic pressing are recommended for medical implants because of the high elasticity, high fracture stress and high resistance against dynamic loads, which fulfill implant requirements.