Reduction In Computation Time Research Articles

High-Performance Krawtchouk Polynomials of High Order Based on Multithreading

Orthogonal polynomials and their moments serve as pivotal elements across various fields. Discrete Krawtchouk polynomials (DKraPs) are considered a versatile family of orthogonal polynomials and are widely used in different fields such as probability theory, signal processing, digital communications, and image processing. Various recurrence algorithms have been proposed so far to address the challenge of numerical instability for large values of orders and signal sizes. The computation of DKraP coefficients was typically computed using sequential algorithms, which are computationally extensive for large order values and polynomial sizes. To this end, this paper introduces a computationally efficient solution that utilizes the parallel processing capabilities of modern central processing units (CPUs), namely the availability of multiple cores and multithreading. The proposed multi-threaded implementations for computing DKraP coefficients divide the computations into multiple independent tasks, which are executed concurrently by different threads distributed among the independent cores. This multi-threaded approach has been evaluated across a range of DKraP sizes and various values of polynomial parameters. The results show that the proposed method achieves a significant reduction in computation time. In addition, the proposed method has the added benefit of applying to larger polynomial sizes and a wider range of Krawtchouk polynomial parameters. Furthermore, an accurate and appropriate selection scheme of the recurrence algorithm is introduced. The proposed approach introduced in this paper makes the DKraP coefficient computation an attractive solution for a variety of applications.

3D analytical magnetic model calculation for Halbach PM induction heater planar topology

In this work, a 3D analytical magnetic model based on hybridation of the sub-domain’s method and the image’s theory to compute magnetic field and translational motion eddy current in the conducting plate of the Halbach permanent magnet induction heater planar topology is developed. The main objective is to remedy the problem of the transverse edge effect, and hence improving the efficiency of analytical model and the accuracy of results. The developed model also allows fast and precise simulations of 3D magnetic phenomena, and presents an important reduction in computation time compared to 3D finite element simulations.

AN EFFICIENT ITERATIVE METHOD TO SIMULATE THE VARYING STATIC RECEPTANCE OF A THIN-WALLED WORKPIECE

This paper introduces an accelerated iterative Conjugate Gradient method (CG-method) for simulating the varying static receptance of a thin-walled workpiece. The proposed approach enhances computational efficiency by computing an optimal initial displacement guess for a given cutter location. This guess is based on the previously calculated displacement vector from the preceding cutter location, serving as the start iteration vector for the CG-method. The validation of efficiency gains through this method is demonstrated by a significant reduction in computation time for a numerical example. Moreover, to ensure the accuracy of the accelerated iterative CG-method, comparisons are made with the Cholesky method. The results confirm the precision of the proposed approach.

A simplified GNSS/LEO joint orbit determination method

Joint orbit determination (JOD) of Global Navigation Satellite Systems (GNSS) satellites and low Earth orbit (LEO) satellites has been substantiated as an efficacious approach to compensate for the ground station geometry. In the traditional JOD, the precise orbit determination (POD) of LEO satellite is mainly processed by the reduced-dynamic approach, however, this approach involves complex calculations and the credibility of the determined positions diminishes when LEO satellites undergo orbital maneuvers. Therefore, a simplified JOD method is designed that employs kinematic approach to determine the LEO satellites orbit. To verify the effectiveness of the proposed method, the orbit of GPS satellites and LEO satellites are jointly estimated utilizing the regional and global networks. 8 LEO satellites, including GRACE-C/D, SWARM-A/B/C, SENTINEL-3A/B, and JASON-3, are chosen for JOD. The comparative analysis between the proposed method and traditional method are achieved in terms of GPS orbit accuracy, LEO orbit accuracy, computation time and the JOD performance during LEO maneuvers. Under regional station scenario, the GPS orbit accuracy determined using the proposed method and the traditional method is 3.64 cm and 2.52 cm, respectively. In the case of global station scenario, the accuracies are 1.71 cm and 1.64 cm. Additionally, the traditional method yields superior enhancement and higher accuracy of the LEO orbits. However, it exhibits a noticeable increase in computation time compared to the proposed method and the performance of JOD declines significantly when LEO satellites undergo orbital maneuvers. Alternatively, although the accuracy of the LEO orbits using the proposed method is comparatively lower, it offers a substantial reduction in the overall network computation time compared to traditional method. Moreover, the proposed method based on LEO kinematic precise orbit determination (KPOD) is nearly unaffected by orbital maneuvers of LEO satellites, presenting unique advantages in practical data processing.

Extended finite element method with cell-based smoothing for modeling frictional contact crack-induced acoustic nonlinearity involving distorted mesh

This study proposes a 2D cell-based smoothed extended finite element method (CS-XFEM) for accurate and efficient simulation of nonlinear ultrasonic wave propagation in solid structures, specifically addressing the effects of frictional contact in cracks. Traditional mesh discretization methods for cracks often suffer from mesh distortion and computational instability owing to their high aspect ratios. To overcome this, CS-XFEM integrates a cell-based smoothing technique into XFEM to model the frictional contact of a crack. A comprehensive numerical example demonstrates the advantages of CS-XFEM. The results show that CS-XFEM exhibits a higher convergence rate and enables a larger critical time increment than XFEM. Specifically, the critical time increment of CS-XFEM was found to be twice that of XFEM, leading to a 50% reduction in the total computational time. These findings confirm that CS-XFEM is an efficient, accurate, and robust numerical method for studying the acoustic nonlinearity induced by crack-induced frictional contact.

Sample-Adaptive Classification Inference Network

Existing pre-trained models have yielded promising results in terms of computational time reduction. However, these models only focus on pruning simple sentences or less salient words, while neglecting the treatment of relatively complex sentences. It is frequently these sentences that cause the loss of model accuracy. This shows that the adaptation of the existing models is one-sided. To address this issue, in this paper, we propose a sample-adaptive training and inference model. Specifically, complex samples are extracted from the training datasets and a dedicated data augmentation module is trained to extract global and local semantic information of complex samples. During inference, simple samples can exit the model via the Sample Adaptive Exit Mechanism, Normal samples pass through the whole backbone model before inference, while complex samples are processed by the Characteristic Enhancement Module after passing through the backbone model. In this way, all samples are processed adaptively. Our extensive experiments on classification tasks datasets in the field of Natural Language Processing demonstrate that our method enhances model accuracy and reduces model inference time for multiple datasets. Moreover, our method is transferable and can be applied to multiple pre-trained models.

Efficient matrix profile computation with Euclidean distance using Eigen transformation: Performance evaluation based on beat-to-beat interval (BBI) data.

The matrix profile serves as a fundamental tool to provide insights into similar patterns within time series. Existing matrix profile algorithms have been primarily developed for the normalized Euclidean distance, which may not be a proper distance measure in many settings. The methodology work of this paper was motivated by statistical analysis of beat-to-beat interval (BBI) data collected from smartwatches to monitor e-cigarette users' heart rate change patterns for which the original Euclidean distance ( -norm) would be a more suitable choice. Yet, incorporating the Euclidean distance into existing matrix profile algorithms turned out to be computationally challenging, especially when the time series is long with extended query sequences. We propose a novel methodology to efficiently compute matrix profile for long time series data based on the Euclidean distance. This methodology involves four key steps including (1) projection of the time series onto eigenspace; (2) enhancing singular value decomposition (SVD) computation; (3) early abandon strategy; and (4) determining lower bounds based on the first left singular vector. Simulation studies based on BBI data from the motivating example have demonstrated remarkable reductions in computational time, ranging from one-fourth to one-twentieth of the time required by the conventional method. Unlike the conventional method of which the performance deteriorates sharply as the time series length or the query sequence length increases, the proposed method consistently performs well across a wide range of the time series length or the query sequence length.

Efficient Parallel FDTD Method Based on Non-Uniform Conformal Mesh

The finite-difference time-domain (FDTD) method is a versatile electromagnetic simulation technique, widely used for solving various broadband problems. However, when dealing with complex structures and large dimensions, especially when applying perfectly matched layer (PML) absorbing boundaries, tremendous computational burdens will occur. To reduce the computational time and memory, this paper presents a Message Passing Interface (MPI) parallel scheme based on non-uniform conformal FDTD, which is suitable for convolutional perfectly matched layer (CPML) absorbing boundaries, and adopts a domain decomposition approach, dividing the entire computational domain into several subdomains. More importantly, only one magnetic field exchange is required during the iterations, and the electric field update is divided into internal and external parts, facilitating the synchronous communication of magnetic fields between adjacent subdomains and internal electric field updates. Finally, unmanned helicopters, helical antennas, 100-period folded waveguides, and 16 × 16 phased array antennas are designed to verify the accuracy and efficiency of the algorithm. Moreover, we conducted parallel tests on a supercomputing platform, showing its satisfactory reduction in computational time and excellent parallel efficiency.

An Incremental Interpolation Scheme With Discrete Cosine Series Expansion for Multimaterial Topology Optimization

Abstract Topology optimization is a powerful tool for structural design, while its computational cost is quite high due to the large number of design variables, especially for multilateral systems. Herein, an incremental interpolation approach with discrete cosine series expansion (DCSE) is established for multilateral topology optimization. A step function with shape coefficients (i.e., ensuring that no extra variables are required as the number of materials increases) and the use of the DCSE together reduces the number of variables (e.g., from 8400 to 120 for the optimization of the clamped–clamped beam with four materials). Remarkably, the proposed approach can effectively bypass the checkerboard problem without using any filter. The enhanced computational efficiency (e.g., a ∼89.2% reduction in computation time from 439.1 s to 47.4 s) of the proposed approach is validated via both 2D and 3D numerical cases.

A computational efficient approach for distributionally robust unit commitment with enhanced disjointed layered ambiguity set

AbstractTo achieve the sustainable development of the society, renewable energy dominated power systems are gradually formed. However, the uncertainty of renewable power poses challenges for power system operations, such as balancing the load and generation in day‐ahead unit commitment problems. To address this issue, an enhanced disjointed layered ambiguity set is proposed in this paper to effectively capture the uncertainty of renewable generation forecast errors. On this basis, a two‐stage distributionally robust unit commitment optimization problem is formulated, which is computational challenge. To this end, a novel reformation approach and a worst‐case support set identification method are proposed to derive the optimal solution in a computationally efficient way. Simulation results demonstrate that the proposed ambiguity set brings lower operation costs of unit commitment while maintaining similar reliability compared to existing methods. In detail, the proposed ambiguity set achieves a reduction in operating costs of approximately 10.01%. The proposed novel reformation approach and solution method are also shown to have higher computation efficiency than the existing Benders decomposition method, resulting in a reduction in computation time to less than 3.78% of the original duration.

In Search of the Best Low-Cost Methods for Efficient Screening of Conformers.

Locating the lowest energy conformer is crucial for the accurate computation of equilibrium properties of molecular systems. This paper examines the performance of efficient low-cost methods in terms of the alignment and relative energies of their energy minima against the benchmark revDSD-PBEP86-D4/def2-TZVPP//MP2/cc-pVTZ potential energy surface. The low-cost methods considered include GFN-FF, GFN2-xTB, DFTB3, HF-3c, B97-3c, PBEh-3c, and r2SCAN-3c composite methods against a diverse test set of 20 compounds including alkanes, perfluoroalkyl molecules, peptides, open-shell radicals, and Zn(II) complexes of varying sizes. The "3c" composite methods are generally more accurate, but are at least 2-3 orders of magnitude more expensive than tight-binding methods which have energy minima that align well with the benchmark potential energy surface. The findings of this paper were further exploited to introduce a simple strategy involving Grimme's CENSO energy-sorting algorithm that resulted in up to an order of magnitude reduction in computational time for locating the lowest energy conformer on the revDSD-PBEP86-D4/def2-TZVPP//MP2/cc-pVTZ surface.

Continuous-time model identification of the subglottal system

Mathematical models that accurately simulate the physiological systems of the human body serve as cornerstone instruments for advancing medical science and facilitating innovative clinical interventions. One application is the modeling of the subglottal tract and neck skin properties for its use in the ambulatory assessment of vocal function, by enabling non-invasive monitoring of glottal airflow via a neck surface accelerometer. For the technique to be effective, the development of an accurate building block model for the subglottal tract is required. Such a model is expected to utilize glottal volume velocity as the input parameter and yield neck skin acceleration as the corresponding output. In contrast to preceding efforts that employed frequency-domain methods, the present paper leverages system identification techniques to derive a parsimonious continuous-time model of the subglottal tract using time-domain data samples. Additionally, an examination of the model order is conducted through the application of various information criteria. Once a low-order model is successfully fitted, an inverse filter based on a Kalman smoother is utilized for the estimation of glottal volume velocity and related aerodynamic metrics, thereby constituting the most efficient execution of these estimates thus far. Anticipated reductions in computational time and complexity due to the lower order of the subglottal model hold particular relevance for real-time monitoring. Simultaneously, the methodology proves efficient in generating a spectrum of aerodynamic features essential for ambulatory vocal function assessment.

An improved algorithm for Finite Particle Method considering Lagrange-type remainder

The Finite Particle Method (FPM) is a significant improvement to the traditional Smoothed Particle Hydrodynamics method (SPH), which can greatly improve the computational accuracy of the entire computational domain. However, unstable calculation results and long computational time are still major obstacles to the development of FPM. Based on matrix decomposition, the fundamental equations of the traditional Finite Particle Method are rewritten and a Generalized Finite Particle Method (GFPM) is derived by introducing Lagrange-type remainder. By deriving and rewriting the fundamental equations, the GFPM method can be theoretically proven to be always stable. Numerical examples show that the GFPM method can utilize a smaller computational scale to achieve the same computational accuracy as the FPM method, with a corresponding reduction in computational time. Finally, the GFPM method is applied to a one-dimensional stress wave propagation problem and a one-dimensional heat conduction problem, and the computational results are compared with those of the SPH method and the FPM method, which verify that the GFPM has higher computational accuracy and stability.

Differences in violin sounds caused by changes on arching profiles

An experimentally calibrated numerical model was employed to examine the vibroacoustic impact of the arching profile in a violin soundbox, a study unattainable through experimental means alone. The finite element method successfully modeled the soundbox using the material properties of an actual violin, albeit with a simplified representation of the coupling with the air in the cavity and the forces from the strings. Achieving agreement with the real counterpart necessitated careful adjustment of the modal damping in the simulation. Damped models of violins are infrequently encountered. The impulse response of the soundbox model was obtained through the calculation of thousands of substeps induced by forced vibration. To streamline the time-domain analysis, the superimposed method was implemented instead of the more commonly used full option, resulting in a significant reduction in computational time. Additionally, synthetic musical notes, accounting for how the force of the strings is transmitted through the bridge, were employed as input to the soundbox model. Subsequently, the impulse responses were convolved with the synthetic notes to generate sounds. Through these procedures, the violin’s performance was assessed as the height of the arching profile of the plates was adjusted. The results demonstrated that higher arching profiles led to a general increase in the resonant frequencies of the violin, perceptible in the sound generated by the model.

Comparing regularized Kelvinlet functions and the finite element method for registration of medical images to sparse organ data

Image-guided surgery collocates patient-specific data with the physical environment to facilitate surgical decision making. Unfortunately, these guidance systems commonly become compromised by intraoperative soft-tissue deformations. Nonrigid image-to-physical registration methods have been proposed to compensate for deformations, but clinical utility requires compatibility of these techniques with data sparsity and temporal constraints in the operating room. While finite element models can be effective in sparse data scenarios, computation time remains a limitation to widespread deployment. This paper proposes a registration algorithm that uses regularized Kelvinlets, which are analytical solutions to linear elasticity in an infinite domain, to overcome these barriers. This algorithm is demonstrated and compared to finite element-based registration on two datasets: a phantom liver deformation dataset and an in vivo breast deformation dataset. The regularized Kelvinlets algorithm resulted in a significant reduction in computation time compared to the finite element method. Accuracy as evaluated by target registration error was comparable between methods. Average target registration errors were 4.6 ± 1.0 and 3.2 ± 0.8 mm on the liver dataset and 5.4 ± 1.4 and 6.4 ± 1.5 mm on the breast dataset for the regularized Kelvinlets and finite element method, respectively. Limitations of regularized Kelvinlets include the lack of organ-specific geometry and the assumptions of linear elasticity and infinitesimal strain. Despite limitations, this work demonstrates the generalizability of regularized Kelvinlets registration on two soft-tissue elastic organs. This method may improve and accelerate registration for image-guided surgery, and it shows the potential of using regularized Kelvinlets on medical imaging data.

Real-time improvement method of turbo-shaft engine component-level model based on dimensional reduction of residual iterative equation

This paper explores a method to improve the real-time computation performance of turbo-shaft engine component-level model by reducing the dimensionality of residual equations set. For turbo-shaft engine, nozzle typically operates in a subcritical working state, assuming that the gas total temperature and pressure parameters of power turbine inlet are the same, and by assuming the gas flow balance between gas generator outlet and nozzle inlet, the iterative solution of the pressure drop of nozzle can be obtained. Then the pressure ratio of power turbine is naturally obtained, thereby achieving the objective of dimensionality reduction of the residual equations set. The component-level model’s steady-state and transient performance were simulated on a desktop computer with a clock frequency of 2.6 GHz. Simulation results show that, with a 2% margin of error, the steady state computation time for the component-level model was reduced by 54.8%, while the transient performance computation time was reduced by 18.6%. This represents a noticeable improvement in real-time performance. Simulation results on the P2020 embedded processor platform with an 800MHz clock frequency indicate a 22.3% reduction in single-step maximum transient performance computation time of the reduced dimensional model, compared to the original model. This demonstrates the effectiveness of dimensionality reduction of the residual equations set in enhancing the model real-time computation performance.

Ultrasonic phased array imaging of multi-layered structures using full-matrix migration and normalized cross-correlation matching technique

Multi-layered structures play a critical role in aerospace, automotive and electrical industries, so the non-destructive evaluation and maintenance of such structures must be accurate and rapid. The application of conventional ultrasonic phased array imaging methods is limited due to computational complexity, image quality and image size. In this paper, we proposed a cost-effective, high-quality imaging method that uses full-matrix migration total focus method (FM-TFM) and produces large-area scanned image with the aid of normalized cross-correlation (NCC) template matching technique. The FM-TFM method eliminated the need for iterative refraction point calculations by using full matrix migration extrapolation, and the optimization of NCC was also investigated in the study. The verification was divided into two parts, fixed transducer experiment and manual scanned experiment, to demonstrate the advantages of FM-TFM with improved SNR (22 % or greater) and one order of magnitude reduction in computational time when compared to ray tracing total focus method (RT-TFM) and NCC matching accuracy of multilayer specimen, respectively. The proposed method can help eliminate the need for costly scanning equipment and shows great potential for extension to other TFM-based approaches.

Electrification-driven circular economy with machine learning-based multi-scale and cross-scale modelling approach

Community energy systems, integrating electricity storage, smart transportation, and flexible energy interactions can mitigate renewable energy intermittency and uncertainty, and stabilize local grids. The battery circular economy, involving cascade use, reuse and recycling, aims to reduce energy storage costs and associated carbon emissions. However, developing multi-scale and cross-scale models based on physical mechanisms faces challenges due to insufficient expertise and temporal discrepancies among subsystems. This study proposes a general machine learning approach for a source-grid-demand-storage community with a battery circular economy, streamlining data preparation, model training, validation, and testing. Machine learning models replace traditional physical models for energy consumption, renewable energy supply, and battery cycling ageing, improving computational efficiency. Furthermore, a battery circular economy principle is proposed, which suggests reusing 80 % capacity retired electric vehicle batteries in buildings and recycling at 60 % capacity. The study validates machine learning-based surrogate models against traditional physical models. Results show an 82.5 % reduction in computational time, from 40 to 7 min without significant deviation in techno-economic-environmental performance (relative difference ≤3 %). This study offers a framework for machine learning in the 'source-grid-demand-storage' system within a battery circular economy, enhancing computation efficiency and accuracy for low-carbon transitions and informing multi-scale, cross-scale model advancement.

Low fidelity data driven machine learning based optimisation method for box-wing configuration

Wing design optimization traditionally involves computationally expensive high-fidelity simulations, limiting the exploration of design spaces. In this study, we propose a methodology that combines low-fidelity numerical models with machine learning algorithms to efficiently navigate the complex parameter space of box-wing configurations. Through the utilisation of a surrogate model trained on a limited dataset derived from low-fidelity simulations, our method strives to predict results within an acceptable range, significantly curtailing computational costs and time. The effectiveness of this methodology is demonstrated through a series of case studies, involving the Onera M6 and NASA CRM wing as test cases and Bionica box-wing optimization as an application case. The initial application of the proposed methodology to the box-wing case successfully achieved an almost 9.82 % increase in overall aerodynamic efficiency. Its competitive performance compared to conventional optimization methods, along with its substantial reduction in computational time and resource requirements, is evident. This efficient methodology holds promise for enhancing the design optimization process for aviation start-ups by efficiently exploring complex design spaces with reduced computational burden.

Fully coupled nonlinear thermomechanical modeling of composites using mean-field Mori–Tanaka scheme combined with TFA theory

This article aims at proposing a new mean-field homogenization framework for the study of composites undergoing fully coupled thermomechanical processes. Strongly dissipative phenomena during high or moderate cyclic loading conditions in a structural component made of a composite material cause significant interplay between mechanical and thermal fields. The proposed framework attempts to address such effect by combining the Mori–Tanaka scheme and the Transformation Field Analysis (TFA) theory and by developing a multiscale framework capable of taking into account thermomechanically coupled processes. The numerical simulations performed in the examples section and validations with computations using periodic homogenization and full-structure analysis demonstrate the proposed strategy’s accuracy and robustness. The numerical simulation of a tube shows the model’s ability to simulate cyclic loading conditions with significantly less computational cost than the alternative FE2 computation strategies. This drastic computational time reduction is due to the semi-analytical formalism of the micromechanics methodology.