Efficient Computational Algorithm Research Articles

Vectfem: a generalized MATLAB-based vectorized algorithm for the computation of global matrix/force for finite elements of any type and approximation order in linear elasticity

In this paper, we introduce a new vectorized MATLAB-based algorithm for efficient serial computation of global matrix/force arising from finite element method (FEM) for meshes of any type and approximation order in linear elasticity. Because for-loops in MATLAB are very slow, we propose a modified process that takes advantage of vectorization and sparse assembly to achieve good performance while using the same memory as the standard algorithm. For this purpose, by using good programming practices, the implementation of this scheme is succinctly described and can be integrated into any MATLAB package dealing with FEM. Specifically, attention is paid to the calculation of the triplet (row index, column index, matrix components) as well as the assembly of the global stiffness matrix, mass matrix and force vector. Additionally, an extension of the proposed approach for Mindlin plate theory and functionally graded materials is outlined. Finally, the accuracy of this strategy is verified on selected numerical tests after comparing the obtained results with those of ABAQUS. In terms of performance, the study conducted on a set of meshes considering the standard algorithm and two other well-known MATLAB vectorized algorithms revealed that: (i) for a 2D beam problem meshed with P1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$P_{1}$$\\end{document}-triangle elements, a speedup of about 8 and 15 is achieved with sparse and fsparse, respectively. (ii) for a 3D plate problem meshed with P1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$P_{1}$$\\end{document}-tetrahedral elements, a speedup of about 4 and 8 is achieved with sparse and fsparse, respectively. When compared to ABAQUS performance, the proposed scheme results in a computational time that is about five times smaller.

An Improved Porosity Calculation Algorithm for Particle Flow Code

The widely used discrete-element particle flow software PFC’s (PFC 7.0 and previous versions) algorithm for calculating porosity is not sufficiently accurate. Because of this, when the particles are densely packed, the solution to the equation produces an algorithm exception for odd calculations of porosity, which results in the inability to calculate the results. This paper, based on a Darcy seepage model of fluid flow through a granular bed, analyzed the shortcomings of the two porosity calculation methods of PFC and the function analysis method. Combining this analysis with the theory of computer graphics, a new and efficient porosity calculation algorithm was proposed. The result showed that the new proposed porosity calculation algorithm calculated a more accurate and reasonable porosity field and made the iterative solution of the CFD equation more stable. This method makes porosity-related models of PFC more accurate. The algorithm can be not only used to calculate porosity, but also applied to other fields.

An Improved Porosity Calculation Algorithm for Particle Flow Code

The widely used discrete-element particle flow software PFC’s (PFC 7.0 and previous versions) algorithm for calculating porosity is not sufficiently accurate. Because of this, when the particles are densely packed, the solution to the equation produces an algorithm exception for odd calculations of porosity, which results in the inability to calculate the results. This paper, based on a Darcy seepage model of fluid flow through a granular bed, analyzed the shortcomings of the two porosity calculation methods of PFC and the function analysis method. Combining this analysis with the theory of computer graphics, a new and efficient porosity calculation algorithm was proposed. The result showed that the new proposed porosity calculation algorithm calculated a more accurate and reasonable porosity field and made the iterative solution of the CFD equation more stable. This method makes porosity-related models of PFC more accurate. The algorithm can be not only used to calculate porosity, but also applied to other fields.

Iterative flexibility compensation based high precision trajectory tracking for industrial manipulators

High precision industrial manipulators are widely demanded in precision machining and advanced manufacturing. To realize high precision trajectory tracking in task space, feedback plus model based feedforward control strategies are widely used in modern industrial manipulators. Furthermore, the accuracy of feedforward model determines the accuracy of trajectory tacking to a great extent, especially for elastic manipulators. In traditional feedforward controllers, the flexibilities out of the rotational plane are often neglected and thus the end-effector tracking performance can be degraded a lot. Therefore, an iterative flexibility compensation based feedforward controller is proposed to improve the end-effector trajectory tracking accuracy of industrial manipulators in this paper. First, the flexible deformations in all directions are described accurately by using the extended flexible joint model (EFJM) for industrial manipulators. Second, a feedforward controller is designed by using the dynamic inversion of EFJM. In the feedforward controller, an iterative flexibility compensation scheme is designed to transform the reference Cartesian trajectory into joint space and thus the limitation of the nonminimum phase characteristics of EFJM can be avoided. Moreover, the flexible deformations are predicted and compensated based on EFJM. After that, the feedforward torque is derived in joint space by using the efficient feedforward torque computation algorithm for EFJM. Simulation and experimental results demonstrate the effectiveness of the proposed method.

Conditional score approaches to errors-in-variables competing risks data in discrete time.

Analysis of competing risks data has been an important topic in survival analysis due to the need to account for the dependence among the competing events. Also, event times are often recorded on discrete time scales, rendering the models tailored for discrete-time nature useful in the practice of survival analysis. In this work, we focus on regression analysis with discrete-time competing risks data, and consider the errors-in-variables issue where the covariates are prone to measurement errors. Viewing the true covariate value as a parameter, we develop the conditional score methods for various discrete-time competing risks models, including the cause-specific and subdistribution hazards models that have been popular in competing risks data analysis. The proposed estimators can be implemented by efficient computation algorithms, and the associated large sample theories can be simply obtained. Simulation results show satisfactory finite sample performances, and the application with the competing risks data from the scleroderma lung study reveals the utility of the proposed methods.

A novel Bayesian computational approach for bridge-randomized quantile regression in high dimensional models

A bridge-randomized penalization that employs a prior for the shrinkage parameter, as opposed to the conventional bridge penalization with a fixed penalty, often delivers more superior performance compared to many other traditional shrinkage methods. In this paper, we develop an efficient Bayesian computational algorithm via the two-block Markov Chain Monte Carlo method for the bridge-randomized penalization in quantile regression to perform inference in the high-dimensional ‘large-p’ and ‘large-p-small-n’ settings. To construct a fully Bayesian formulation, we utilize the asymmetric Laplace distribution as an auxiliary error distribution and the generalized Gaussian distribution prior for the regression coefficients. Simulation studies encompassing a wide range of scenarios indicate that the proposed method performs at least as well as, and often better than, other existing procedures in terms of both parameter estimation and variable selection. Finally, a real-data application is provided for illustrative purposes.

Online Self-Calibration of Cable-Driven Parallel Robots Using Covariance-Based Data Quality Assessment Metrics

Abstract This paper presents an algorithm to perform self-calibration of cable-driven parallel robots (CDPRs), where the CDPR's end-effector pose is estimated in conjunction with the calibration of biases in the CDPR's measurements. Two new metrics, known as the position dilution of precision (PDOP) and orientation dilution of precision (ODOP) are introduced as a means to quantify the quality of data collected with regards to self-calibration. These metrics are based on a covariance matrix that is computed online as part of the proposed self-calibration algorithm, which results in the PDOP and ODOP directly corresponding to the standard deviation of the position and orientation errors, respectively. These metrics are used to intuitively select which data points contribute to improved calibration, resulting in a computationally-efficient algorithm requiring few data points to maintain accurate calibration. Additionally, the PDOP and ODOP provide a means to assess when sufficient calibration data has been collected. Numerical results involving an inverse kinematic simulation with rigid cables and a dynamic simulation with flexible cables indicate that the proposed algorithm is capable of performing self-calibration in a computationally-efficient manner. Moreover, the simulation results indicate that the proposed PDOP and ODOP metrics result in smaller position and orientation errors when used to prune the data set compared to the observability indices found in the literature. Accuracy of the proposed algorithm is also confirmed through experiments when compared to ground-truth pose data.

Discrete Morse Sandwich: Fast Computation of Persistence Diagrams for Scalar Data - An Algorithm and A Benchmark.

This paper introduces an efficient algorithm for persistence diagram computation, given an input piecewise linear scalar field f defined on a d-dimensional simplicial complex K, with d ≤ 3. Our work revisits the seminal algorithm "PairSimplices" [31], [103] with discrete Morse theory (DMT) [34], [80], which greatly reduces the number of input simplices to consider. Further, we also extend to DMT and accelerate the stratification strategy described in "PairSimplices" [31], [103] for the fast computation of the 0th and (d-1)th diagrams, noted D0(f) and Dd-1(f). Minima-saddle persistence pairs ( D0(f)) and saddle-maximum persistence pairs ( Dd-1(f)) are efficiently computed by processing , with a Union-Find , the unstable sets of 1-saddles and the stable sets of (d-1)-saddles. We provide a detailed description of the (optional) handling of the boundary component of K when processing (d-1)-saddles. This fast pre-computation for the dimensions 0 and (d-1) enables an aggressive specialization of [4] to the 3D case, which results in a drastic reduction of the number of input simplices for the computation of D1(f), the intermediate layer of the sandwich. Finally, we document several performance improvements via shared-memory parallelism. We provide an open-source implementation of our algorithm for reproducibility purposes. We also contribute a reproducible benchmark package, which exploits three-dimensional data from a public repository and compares our algorithm to a variety of publicly available implementations. Extensive experiments indicate that our algorithm improves by two orders of magnitude the time performance of the seminal "PairSimplices" algorithm it extends. Moreover, it also improves memory footprint and time performance over a selection of 14 competing approaches, with a substantial gain over the fastest available approaches, while producing a strictly identical output. We illustrate the utility of our contributions with an application to the fast and robust extraction of persistent 1-dimensional generators on surfaces, volume data and high-dimensional point clouds.

A Bayesian quantile joint modeling of multivariate longitudinal and time-to-event data.

Linear mixed models are traditionally used for jointly modeling (multivariate) longitudinal outcomes and event-time(s). However, when the outcomes are non-Gaussian a quantile regression model is more appropriate. In addition, in the presence of some time-varying covariates, it might be of interest to see how the effects of different covariates vary from one quantile level (of outcomes) to the other, and consequently how the event-time changes across different quantiles. For such analyses linear quantile mixed models can be used, and an efficient computational algorithm can be developed. We analyze a dataset from the Acute Lymphocytic Leukemia (ALL) maintenance study conducted by Tata Medical Center, Kolkata. In this study, the patients suffering from ALL were treated with two standard drugs (6MP and MTx) for the first two years, and three biomarkers (e.g. lymphocyte count, neutrophil count and platelet count) were longitudinally measured. After treatment the patients were followed nearly for the next three years, and the relapse-time (if any) for each patient was recorded. For this dataset we develop a Bayesian quantile joint model for the three longitudinal biomarkers and time-to-relapse. We consider an Asymmetric Laplace Distribution (ALD) for each outcome, and exploit the mixture representation of the ALD for developing a Gibbs sampler algorithm to estimate the regression coefficients. Our proposed model allows different quantile levels for different biomarkers, but still simultaneously estimates the regression coefficients corresponding to a particular quantile combination. We infer that a higher lymphocyte count accelerates the chance of a relapse while a higher neutrophil count and a higher platelet count (jointly) reduce it. Also, we infer that across (almost) all quantiles 6MP reduces the lymphocyte count, while MTx increases the neutrophil count. Simulation studies are performed to assess the effectiveness of the proposed approach.

Automatic computation of bending sequences for double-head wire bending machines

ABSTRACT Determining a feasible bending sequence for a double-head bending machine is a challenging and time-consuming task, even for an expert operator. An automatic bending sequence computation algorithm for a single-head bending machine was proposed in a previous work, exploiting A ⋆ graph search algorithm and the representation of the workpiece as an equivalent manipulator. This paper extends that approach to the case of a double-head bending machine, whose complexity, in terms of number of possible solutions to the problem of computing the feasible bending sequences, and of determination of the better sequences, that should exploit parallelism thanks to the execution of simultaneous bends on the two heads, is definitely higher. In this case, the wire has been modelled using two serial-link manipulators with a common base, and the A ⋆ cost function has been modified to promote simultaneous bends. An axes reachability-based path generator and the possibility of partial sequence search have been incorporated as well, to manage the run-time challenges due to an increased number of bends. In this way, an efficient bending sequence computation algorithm for a double-head wire bending machine has been devised, whose performance has been assessed on two industrial test cases, demonstrating its effectiveness and usefulness.

Bayesian Semiparametric Longitudinal Inverse-Probit Mixed Models for Category Learning.

Understanding how the adult human brain learns novel categories is an important problem in neuroscience. Drift-diffusion models are popular in such contexts for their ability to mimic the underlying neural mechanisms. One such model for gradual longitudinal learning was recently developed in Paulon et al. (J Am Stat Assoc 116:1114-1127, 2021). In practice, category response accuracies are often the only reliable measure recorded by behavioral scientists to describe human learning. Category response accuracies are, however, often the only reliable measure recorded by behavioral scientists to describe human learning. To our knowledge, however, drift-diffusion models for such scenarios have never been considered in the literature before. To address this gap, in this article, we build carefully on Paulon et al. (J Am Stat Assoc 116:1114-1127, 2021), but now with latent response times integrated out, to derive a novel biologically interpretable class of 'inverse-probit' categorical probability models for observed categories alone. However, this new marginal model presents significant identifiability and inferential challenges not encountered originally for the joint model in Paulon et al. (J Am Stat Assoc 116:1114-1127, 2021). We address these new challenges using a novel projection-based approach with a symmetry-preserving identifiability constraint that allows us to work with conjugate priors in an unconstrained space. We adapt the model for group and individual-level inference in longitudinal settings. Building again on the model's latent variable representation, we design an efficient Markov chain Monte Carlo algorithm for posterior computation. We evaluate the empirical performance of the method through simulation experiments. The practical efficacy of the method is illustrated in applications to longitudinal tone learning studies.

Cycle Bases of Graphs for the Analysis of Frames Structures Using Force Method

The formation of suitable cycle bases corresponding to sparse flexibility matrices for the force method of frame analysis has always been an interesting problem in structural mechanics. These cycle bases are needed for the formation of static bases for efficient force method of structural analysis. Similarly, such bases are required in the mesh analysis of other networks. This paper reviews methods for the cycle basis selection by utilizing different embeddings on higher dimensional topological spaces, and using the ideas and concept from this study, graph theory algorithms are developed for efficient computational algorithms for the formation of subminimal, and minimal cycle bases.

A Gibbs Posterior Framework for Fair Clustering.

The rise of machine learning-driven decision-making has sparked a growing emphasis on algorithmic fairness. Within the realm of clustering, the notion of balance is utilized as a criterion for attaining fairness, which characterizes a clustering mechanism as fair when the resulting clusters maintain a consistent proportion of observations representing individuals from distinct groups delineated by protected attributes. Building on this idea, the literature has rapidly incorporated a myriad of extensions, devising fair versions of the existing frequentist clustering algorithms, e.g., k-means, k-medioids, etc., that aim at minimizing specific loss functions. These approaches lack uncertainty quantification associated with the optimal clustering configuration and only provide clustering boundaries without quantifying the probabilities associated with each observation belonging to the different clusters. In this article, we intend to offer a novel probabilistic formulation of the fair clustering problem that facilitates valid uncertainty quantification even under mild model misspecifications, without incurring substantial computational overhead. Mixture model-based fair clustering frameworks facilitate automatic uncertainty quantification, but tend to showcase brittleness under model misspecification and involve significant computational challenges. To circumnavigate such issues, we propose a generalized Bayesian fair clustering framework that inherently enjoys decision-theoretic interpretation. Moreover, we devise efficient computational algorithms that crucially leverage techniques from the existing literature on optimal transport and clustering based on loss functions. The gain from the proposed technology is showcased via numerical experiments and real data examples.

Multidisciplinary high-throughput screening of metal–organic framework for ammonia-based green hydrogen production

This study presents a comprehensive, multidisciplinary approach to high-throughput screening (HTS) of metal–organic frameworks (MOFs) for efficient ammonia-based green hydrogen production. Previous HTS methods, relying on molecular simulations, often estimate adsorption uptakes under constant conditions, leading to inadequate evaluation of MOFs for practical applications where competitive adsorption and varying operating conditions are critical. To address this limitation, we propose a multidisciplinary HTS method employing an efficient computational algorithm that minimizes the number of molecular simulations while generating isotherm models across a wide pressure range. Our algorithm strategically selects simulations for further analysis based on initial results. Using this innovative approach, we screened 12,020 MOFs. Furthermore, as the next step of the multidisciplinary approach, we performed pressure swing adsorption (PSA) process simulations to assess MOFs’ potential for purifying green hydrogen derived from decomposed ammonia, which can be produced by sustainable energy sources and transported intercontinentally. The top-performing MOFs were evaluated for stability based on literature data and MOFSimplify, a neural network model estimating thermal stability. By considering adsorption process operation and MOF stability, the proposed HTS methodology identified 10 high-performing materials, with RAVXIX ranking as the top adsorbent. This comprehensive evaluation advances the search for efficient MOFs in green hydrogen production, contributing to the development of a more sustainable hydrogen-based economy.

Blockchain-Empowered Edge Intelligence for TACS Obstacle Detection: System Design and Performance Optimization

With the significant advantages of system complexity and operating costs, Train Autonomous Circumambulate System (TACS) is gradually replacing the traditional Communication Based Train Control (CBTC) system as the next-generation train operation control system development direction. As train operation and control become more decentralized and autonomous, real-time and accurate obstacle detection, apart from route-level protection, is quite desirable in TACS. Most of the existing researches about obstacle detection focus on detection algorithm optimization based on the once-deployed lifelong use principle, while model re-optimization based on the actual operating environment under unexpected situations and model sharing among multi-users are largely ignored. In this paper, we design a novel obstacle detection system in TACS based on blockchain-empowered Edge Intelligence (EI). To make full use of the massive raw unannotated data collected online, we first propose an SSL-based TACS obstacle detection model. Considering the resource-hungry model training, we introduce EI into TACS and propose a MARL-based task offloading algorithm for secure and efficient computation offloading coordination. Furthermore, we propose a blockchain-based model sharing scheme to facilitate the multi-model parameter exchange and improve the obstacle detection accuracy. Extensive simulation results show that the designed obstacle detection system can effectively improve the TACS obstacle detection performance.

Improved Algorithm for Efficient Computation of Slepian Functions Over Arbitrary Regions on the Sphere

Improved Algorithm for Efficient Computation of Slepian Functions Over Arbitrary Regions on the Sphere

Пространственная фильтрационная модель гидратосодержащих сред с неклассическим законом движения

The work provides a description of the spatial filtration problem in a three-phase hydrate equilibrium zone. A mathematical model is presented for studying two-dimensional fluid flows taking into account the solid hydrate phase and the irregular structure of formations. A non-classical form of the motion law is used, applicable at low permeability and low pressure drops. Efficient computational algorithms based on the support operator method are proposed that make it possible to separate the hyperbolic and dissipative subsystems of the problem. The algorithms are implemented on meshes of irregular structure to model the two-dimensional multiphase processes of gas hydrate dissociation. Testing is carried out on model piezoconductive processes with saturation transfer, where it is shown that depression processes are less expressed when using a nonlinear law of motion.

Mortar Method for 2D Elastic Bounded Contact Problems

Abstract This paper presents a contribution to the field of numerical solutions for contact problems, which pose significant challenges in engineering and simulations. Specifically, we address the intricate task of connecting bodies that have been discretized using non-conforming and non-overlapping meshes. Our primary focus lies in investigating the efficacy of the mortar method with a segment-to-segment approach. In this context, we provide a concise overview of the underlying theoretical framework and present our implementation in the MATLAB programming environment. To ascertain the reliability and accuracy of our proposed methodology, we conduct a rigorous validation study by comparing the outcomes obtained from our implementation with those derived from the widely adopted commercial software, ANSYS. To enable a comprehensive evaluation, we select specific benchmark problems that involve the interaction of two elastic bodies. Through a meticulous analysis and comparison of results, we demonstrate the effectiveness and robustness of our approach. The findings of this study contribute substantively to the advancement of numerical techniques for solving contact problems. The validated methodology not only establishes a solid foundation for future research endeavors but also offers a reliable framework for conducting simulations in this domain. Furthermore, the insights gained from this study can potentially facilitate the development of more efficient and accurate computational algorithms for addressing contact problems encountered in various engineering applications.

Simulation of a clear sky satellite image in water vapor and infrared satellite M.S.G channel’s

Radiative transfer models are an important tool for the scientific community. Such models simulate the radiative transfer processes of the atmosphere at a given wavelength or spectral region for a given set of surface and atmospheric conditions. It is used to simulate the radiances and brightness temperatures of various satellite sensors. RTTOV stands for ‘Radiative Transfer for TIROS Operational Vertical Sounder’ and refers to the computational efficient algorithms that have been developed by Eumetsat within the framework of SAF to meet the requirements of the operational data assimilation system. The aim of our work is to allow a simulation of infrared image of MSG2 satellite, by the RTTOV model, starting from the temperature and humidity profiles resulting from a weather forecasting model. The results are satisfactory, the evaluation have shown that the RTTOV model is effective enough for water vapor channels, while it appears less effective for the rest of the channels.

Bayesian nonparametric method for genetic dissection of brain activation region.

Biological evidence indicewates that the brain atrophy can be involved at the onset of neuropathological pathways of Alzheimer's disease. However, there is lack of formal statistical methods to perform genetic dissection of brain activation phenotypes such as shape and intensity. To this end, we propose a Bayesian hierarchical model which consists of two levels of hierarchy. At level 1, we develop a Bayesian nonparametric level set (BNLS) model for studying the brain activation region shape. At level 2, we construct a regression model to select genetic variants that are strongly associated with the brain activation intensity, where a spike-and-slab prior and a Gaussian prior are chosen for feature selection. We develop efficient posterior computation algorithms based on the Markov chain Monte Carlo (MCMC) method. We demonstrate the advantages of the proposed method via extensive simulation studies and analyses of imaging genetics data in the Alzheimer's disease neuroimaging initiative (ADNI) study.