Fast Approximate Method Research Articles

A Novel Multi-Sensor Nonlinear Tightly-Coupled Framework for Composite Robot Localization and Mapping.

Composite robots often encounter difficulties due to changes in illumination, external disturbances, reflective surface effects, and cumulative errors. These challenges significantly hinder their capabilities in environmental perception and the accuracy and reliability of pose estimation. We propose a nonlinear optimization approach to overcome these issues to develop an integrated localization and navigation framework, IIVL-LM (IMU, Infrared, Vision, and LiDAR Fusion for Localization and Mapping). This framework achieves tightly coupled integration at the data level using inputs from an IMU (Inertial Measurement Unit), an infrared camera, an RGB (Red, Green and Blue) camera, and LiDAR. We propose a real-time luminance calculation model and verify its conversion accuracy. Additionally, we designed a fast approximation method for the nonlinear weighted fusion of features from infrared and RGB frames based on luminance values. Finally, we optimize the VIO (Visual-Inertial Odometry) module in the R3LIVE++ (Robust, Real-time, Radiance Reconstruction with LiDAR-Inertial-Visual state Estimation) framework based on the infrared camera's capability to acquire depth information. In a controlled study, using a simulated indoor rescue scenario dataset, the IIVL-LM system demonstrated significant performance enhancements in challenging luminance conditions, particularly in low-light environments. Specifically, the average RMSE ATE (Root Mean Square Error of absolute trajectory Error) improved by 23% to 39%, with reductions from 0.006 to 0.013. At the same time, we conducted comparative experiments using the publicly available TUM-VI (Technical University of Munich Visual-Inertial Dataset) without the infrared image input. It was found that no leading results were achieved, which verifies the importance of infrared image fusion. By maintaining the active engagement of at least three sensors at all times, the IIVL-LM system significantly boosts its robustness in both unknown and expansive environments while ensuring high precision. This enhancement is particularly critical for applications in complex environments, such as indoor rescue operations.

Geotechnical engineering surveys and soil testing in the construction of buildings and structures

The article suggests a way to increase the efficiency of geotechnical engineering surveys through the rational use of fast approximate methods of soil testing (“express methods”). Such tests are recommended to be carried out in large volume and considered as a means of assessing the geotechnical structure of the site as a whole. In this paper, these issues are considered by the example of determining the bearing capacity of piles according to static sounding data and static tests of full-scale piles. A mathematical model for assessing the information content of the test complex based on the concepts of information theory is proposed. Calculations based on this model show that the informativeness of a large number of approximate tests may (due to the heterogeneity of the soil) exceed the informativeness of a small number of accurate tests.

Multi exposure fusion for high dynamic range imaging via multi-channel gradient tensor

Multi-exposure fusion (MEF) is an effective technique for directly fusing a sequence of low dynamic range (LDR) images from a high dynamic range (HDR) natural scene. The goal is to generate an information enriched LDR image. Despite its effectiveness, current MEF methods often encounter issues such as detail loss and color degradation. Additionally, existing algorithms often struggle to balance image quality and computation time, particularly for large-sized images. This paper introduces an innovative MEF algorithm that address these challenges, offering improved performance and computational time across all image sizes. The algorithm employs a multi-channel gradient tensor on RGB images to effectively capture the contrast information among the three channels. This mechanism allows an edge-preserving image filter to maintain edges while smoothing weight maps. To enhance computational efficiency, the algorithm uses a fast approximation method suitable for large sized images. Our comprehensive experimental results demonstrate that the proposed method outperforms existing MEF techniques both quantitatively and qualitatively. Furthermore, our method reduces computational time by approximately 30% compared to the most recent state-of-the-art techniques.

A rapid phylogeny-based method for accurate community profiling of large-scale metabarcoding datasets.

Environmental DNA (eDNA) is becoming an increasingly important tool in diverse scientific fields from ecological biomonitoring to wastewater surveillance of viruses. The fundamental challenge in eDNA analyses has been the bioinformatical assignment of reads to taxonomic groups. It has long been known that full probabilistic methods for phylogenetic assignment are preferable, but unfortunately, such methods are computationally intensive and are typically inapplicable to modern next-generation sequencing data. We present a fast approximate likelihood method for phylogenetic assignment of DNA sequences. Applying the new method to several mock communities and simulated datasets, we show that it identifies more reads at both high and low taxonomic levels more accurately than other leading methods. The advantage of the method is particularly apparent in the presence of polymorphisms and/or sequencing errors and when the true species is not represented in the reference database.

Anchor-based fast spectral ensemble clustering

Ensemble clustering can obtain better and more robust results by fusing multiple base clusterings, which has received extensive attention. Although many representative algorithms have emerged in recent years, this field still has two tricky problems. First, spectral clustering can identify clusters of arbitrary shapes, but the high time and space complexity limit its application in generating base clusterings. Most existing algorithms utilize k-means to generate base clusterings, and the clustering effect on nonlinearly separable datasets needs further improvement. Second, ensemble clustering algorithms should generate multiple base clusterings. Even if low-complexity algorithms are applied, the running time is also long, which seriously affects the application of ensemble clustering algorithms on large-scale datasets. To tackle these problems, we propose a fast K-nearest neighbors approximation method, construct an anchor graph to approximate the similarity matrix, and use singular value decomposition (SVD) instead of eigenvalue decomposition (EVD) to reduce the time and space complexity of conventional spectral clustering. At the same time, we obtain multiple base clusterings by running spectral embedding once. Finally, we convert these base clusterings into a bipartite graph and use transfer cut to get the final clustering results. The proposed algorithms significantly reduce the running time of ensemble clustering. Experimental results on large-scale datasets fully prove the efficiency and superiority of our proposed algorithm.

Fast approximation of fiber reinforced injection molding processes using eikonal equations and machine learning

Injection molding is a popular production process for short fiber reinforced components. The mechanical properties of such components depend on process-induced fiber orientations which are commonly predicted via numerical simulations. However, high computational costs prevent process simulations from being used in iterative procedures, such as topology optimization or finding optimal injection locations. We propose a fast approximation method that extracts nodal features and train a regression model to predict fill states, cooling times, volumetric shrinkage, and fiber orientations. The features are determined by solving eikonal equations with a fast iterative method and computing spatial moments to characterize node-adjacent material distributions. Subsequently, we use these features to train feed forward neural networks and gradient boosted regression trees with simulation data of a large dataset of geometries. This approach is significantly faster than conventional methods, providing 20x speed-up for single simulations and more than 200x speed-up in gate location optimization. It generalizes to arbitrary geometries and injection locations.

The resonance frequency method for fast approximation of the bandwidth of resistive-capacitive high voltage dividers

The resonance frequency method for fast approximation of the bandwidth of resistive-capacitive high voltage dividers

A fast approach for predicting stress intensity factors in tortuous cracks under mixed-mode loading

Realistic crack morphologies are generally sinuous rather than straight, which brings a great challenge to capture accurately the stress intensity factors at the crack tip. In this paper, a fast approximation method for predicting stress intensity factors in tortuous cracks under mixed-mode loading is proposed in terms of geometry simplification and semi-theoretical calculation. First, the finite element results show that the main and branch two-segment crack geometry approximation possesses a good capability of predicting the stress intensity factors of tortuous cracks under mixed-mode loading, whereas the simplification strategy of one straight crack cannot characterize the crack tip field of sinuous cracks. Then, an efficient semi-theoretical estimation approach is proposed to obtain the stress intensity factors of the branch crack from those of the main crack, which is validated to further reduce the computational time, resulting in a two-step accelerated operation. Moreover, the effect of main crack offset is also discussed and some recommendations are given to ensure accurate predictions within an acceptable margin of error for microstructural design or other application purposes.

Fast approximation methods for credit portfolio risk calculations

Credit risk is one of the main risks financial institutions are exposed to. Within the last two decades, simulation-based credit portfolio models became extremely popular and replaced closed-form analytical ones as computers became more powerful. However, especially for non-homogenous and non-granular portfolios, a full simulation of a credit portfolio model is still time consuming, which can be disadvantageous within some use cases like credit pricing or within stress testing situations where results must be available very quickly. For this purpose, we investigate if methods based on artificial intelligence (AI) can be helpful to approximate a credit portfolio model. We compare the performance of AI-based methods within three different use cases with suitable non AI-based regression methods. As a result, we see that AI-based methods can generally capture portfolio characteristics and speed-up calculations but - depending on the specific use case and the availability of training data - they are not necessarily always the best choice. Particularly, considering the time and costs for collecting data and training of the complex algorithms, non-AI-based methods can be as good as or even better than AI-based ones, while requiring less computational effort.

Reparameterization of B-spline surface and its application in ship hull modeling

NURBS are widely used in the design of free curves and surfaces and have been the industrial standard for product design in CAD/CAM. Ship hull surfaces are complex doubly-curved surfaces and usually decomposed into patches based on feature curves. Due to the topologically rectangular limitations of tensor-product NURBS surfaces and the inevitable problem of surface merging caused by decomposition, the reconstruction of ship hull still remains a complicated problem. The theoretical research of merging NURBS surfaces is relatively comprehensive, but the difficulty lies in how to merge surfaces defined in different knot vectors at the common boundary curve since control meshes form T-junctions. This paper proposes a methodology of reparameterizing B-spline surfaces, using a fast progressive-iterative approximation (FPIA) method to refit section curves or isoparametric curves with constraints, thus making the topological structure of control meshes regular, uniform and orthogonal. Subsequently, a KCS container ship with bulbous bow and stern is utilized as an illustration for reconstructing with B-splines. The lighting effects and lines plan derived from the hull surface demonstrate that this approach can achieve fair, smooth and watertight surfaces. The approach exhibits strong robustness, versatility and generalization ability, and provides theoretical innovation and practical design methods for representing and reconstructing complex ship hull.

Time of flight fast approximation method for ultrasound sub-surface imaging

Time-Of-Flight (TOF) computations are needed in all ultrasound imaging methods. In Non Destructive Testing (NDT), where ultrasound inspections are frequently done using a coupling medium between the transducer and the test piece, wave refraction complicates TOF computations and iterative methods are needed, which hinders frame rate. For fast imaging simple approximation methods are needed. In this work we propose a TOF fast approximation method for the particular case of sub-surface imaging.

Approximation of Uncoupled Quasi-Static Thermoelasticity Solutions Based on Gaussians

A fast approximation method to three dimensional equations in quasi-static uncoupled thermoelasticity is proposed. We approximate the density via Gaussian approximating functions introduced in the method approximate approximations. In this way the action of the integral operators on such functions is presented in a simple analytical form. If the density has separated representation, the problem is reduced to the computation of one-dimensional integrals which admit efficient cubature procedures. The comparison of the numerical and exact solution shows that these formulas are accurate and provide the predicted approximation rate 2,4,6 and 8.

A Circular Total Focusing Method with Eccentricity Correction and Intensity Compensation for Endoscopic Ultrasound Imaging of Dual-layered Media.

Present endoscopic ultrasound (EUS) imaging methods for circular array suffer from the non-uniform spatial resolution in the imaging of a dual-layered media, such as the tubes' immersion EUS inspection. The problem is mainly attributed to the restricted focus and beam de-focusing at the interface. In this paper, a circular total focusing method (CTFM) is proposed, which leverages the concept of the conventional total focusing method and makes three vital improvements to overcome the challenges. First, to obtain the accurate time-of-flight (TOF) in the dual-layered media, a fourth-order equation of Snell's law is built and solved in polar coordinate system. Second, a fast geometric approximation method is derived to correct the TOF distortion caused by the transducer's eccentricity. Third, the intensity compensation is applied to flatten the imaging intensity at different positions by considering the directivity of element, transmission at interface, and divergence in media. The CTFM is validated on a tube's immersion EUS using a 10 MHz circular array with 128 elements. Experiment results demonstrate that the proposed CTFM outperforms existing imaging methods. The lateral and axial resolution are 0.71 mm and 0.30 mm, which are 27.5% and 33.3% higher than those of the classic delay-and-sum method. The CTFM image shows high and uniform SNR which is 33.6% higher than that of delay-and-sum images. The CTFM provides a novel EUS imaging modality which can be applied in both medical and non-destructive testing domains.

WaterKit: Thermodynamic Profiling of Protein Hydration Sites.

Water desolvation is one of the key components of the free energy of binding of small molecules to their receptors. Thus, understanding the energetic balance of solvation and desolvation resulting from individual water molecules can be crucial when estimating ligand binding, especially when evaluating different molecules and poses as done in High-Throughput Virtual Screening (HTVS). Over the most recent decades, several methods were developed to tackle this problem, ranging from fast approximate methods (usually empirical functions using either discrete atom-atom pairwise interactions or continuum solvent models) to more computationally expensive and accurate ones, mostly based on Molecular Dynamics (MD) simulations, such as Grid Inhomogeneous Solvation Theory (GIST) or Double Decoupling. On one hand, MD-based methods are prohibitive to use in HTVS to estimate the role of waters on the fly for each ligand. On the other hand, fast and approximate methods show an unsatisfactory level of accuracy, with low agreement with results obtained with the more expensive methods. Here we introduce WaterKit, a new grid-based sampling method with explicit water molecules to calculate thermodynamic properties using the GIST method. Our results show that the discrete placement of water molecules is successful in reproducing the position of crystallographic waters with very high accuracy, as well as providing thermodynamic estimates with accuracy comparable to more expensive MD simulations. Unlike these methods, WaterKit can be used to analyze specific regions on the protein surface, (such as the binding site of a receptor), without having to hydrate and simulate the whole receptor structure. The results show the feasibility of a general and fast method to compute thermodynamic properties of water molecules, making it well-suited to be integrated in high-throughput pipelines such as molecular docking.

A fast approximate method for k-edge connected component detection in graphs with high accuracy

Finding k-edge connected components (k-ECCs) is widely used to investigate the major cohesive structures within a graph. Traditional methods utilizing global minimum cut to split the graph iteratively are too slow to deal with graphs of a large size. Recently, approximate algorithms based on a decomposition framework have been proposed to speed up the process. However, these algorithms produce low-quality results in graphs containing vertex pairs that are k-connected but do not belong to a k-ECC. In this paper, we propose a decomposition framework that utilizes a local edge connectivity check method to obtain high-quality results in a shorter period. The proposed method utilizes an improved maximum flow algorithm to detect k-ECCs from local k-cores by merging more vertices in each iteration than existing methods. Moreover, a pruning strategy is applied in the decomposition framework to reduce unnecessary branches in the decomposition tree. Our experimental results on both synthetic and real graphs show that our proposed algorithm is faster than the state-of-the-art algorithms in most datasets and achieves effective results among the approximate algorithms with a 96% accuracy on our experimental datasets.

High-Resolution Hemodynamic Analysis of a Wearable Oxygenator Using High-Performance Computing

In this paper, we study the hydrodynamics of a wearable oxygenator using computational fluid dynamics on a supercomputer. In this computation, the fiber bundle of the oxygenator is modeled by a porous medium model, and the incompressible Navier-Stokes equations with a K-ε turbulence model are used to model the flow in the channels. The blood flow velocity, pressure, and shear stress are carefully studied and the hemolysis index of the oxygenator NIH is calculated by using the fast three-dimensional numerical hemolysis approximation method, which is in the range 0.006 ~ 0.094 g/100L. The results show that the pressure loss of the wearable oxygenator mainly occurs in the fiber bundle area. The inlet, outlet, and channels have relatively high shear stress, which may damage the red blood cells. When the flow rate ranges from 2.0 L/min to 5.0 L/min, the estimated hemolysis meets the applicable range allowed by human physiology. In addition, the parallel performance is studied on a supercomputer, which shows that, for the simulation with over 9 million mesh cells, it scales up to 720 processors and the parallel efficiency is over 60%.

Fast Magnetic Field Approximation Method for Simulation of Coaxial Magnetic Gears Using AI

Artificial intelligence and deep learning have been widely used in recent years to explore the possibility of accelerating computation. However, it has very few applications in magnetic field calculation. This article employs a conditional generative adversarial network (cGAN) to approximate the magnetic field of a coaxial magnetic gear and calculate the magnetic torque through postprocessing. The working principle of magnetic field approximation using cGAN and the training process is introduced in this study. We adopted conditional image-to-image translation technology in cGAN and compared different loss functions and residual structures combinations. Then, we found the best combination, which can accelerate convergence, reduce errors, and improve the generator's performance. Numerical experiments have verified the effectiveness of the proposed cGAN, and the average numerical error can be as small as 1%. At the same time, its speedup ratio is as high as 200 compared to the finite element method.

An approach for obtaining estimation of stability of large communication network taking into account its dependent paths

The physical data layer transmits bits over physical communication channels, such as coaxial cable or twisted pair. That is, it is this level that directly transmits data. At this level, the characteristics of electrical signals that transmit discrete information are determined. After that it is necessary to consider the control of the communication network, its various algorithms. When designing a communication network, a prerequisite is to calculate its stability, and in the case of large scale communication networks, this is a big problem. The most common deterministic, as well as fairly fast approximate method, which is often implemented at the present time, is the method by which the stability of the communication direction which is estimated by analyzing independent paths only. The main disadvantage of this method is obtaining an understated estimate of stability due to unaccountable dependent routes of communication directions. And this leads to inefficient use of resources. Our proposed methodology allows to take into not only independent paths, but also dependent ones, which is the basis for obtaining a significantly more correct estimate. It is based on an algorithm for checking the presence of a certain path and, based on it, an algorithm for obtaining an exact assessment of stability. The paper also provides analytical and statistical analysis of the considered algorithms. In particular, a special parameter was introduced that characterizes the probability of a failure event of communication lines, in which the number of failed communication lines lies in a certain specified range; after which a study of the function describing this parameter was carried out.

Fast and Accurate Approximation Methods for Trigonometric and Arctangent Calculations for Low-Performance Computers

In modern computers, complicated signal processing is highly optimized with the use of compilers and high-speed processing using floating-point units (FPUs); therefore, programmers have little opportunity to care about each process. However, a highly accurate approximation can be processed in a small number of computation cycles, which may be useful when embedded in a field-programmable gate array (FPGA) or micro controller unit (MCU), or when performing many large-scale operations on a graphics processing unit (GPU). It is necessary to devise algorithms to obtain the desired calculated values without an accelerator or compiler assistance. The residual correction method (RCM) developed here can produce simple and accurate approximations of certain nonlinear functions with minimal multiply–add operations. In this study, we designed an algorithm for the approximate computation of trigonometric and inverse trigonometric functions, which are nonlinear elementary functions, to achieve their fast and accurate computation. A fast first approximation and a more accurate second approximation of each function were created using RCM with a less than 0.001 error using multiply–add operations only. This achievement is particularly useful for MCUs, which have a low power consumption but limited computational power, and the proposed approximations are candidate algorithms that can be used to stabilize the attitude control of robots and drones, which require real-time processing.

A fast approximate method for simulating thermal pile heat exchangers

Ground source heat pump systems, operating in conjunction with vertical ground heat exchangers, will play a key role in decarbonising heating and cooling of buildings. Design of traditional borehole heat exchangers relies on tools which implement routine analytical relationships between heat transferred and the temperature change in the ground and circulating thermal fluid. However, for novel piled foundations used as ground heat exchangers, there are few such analytical solutions available that are practical for routine implementation. This paper examines the use of a radial approximation to simulate the dynamic thermal behaviour of pile heat-exchangers. Originally developed for small diameter and high aspect ratio borehole heat exchangers, the approach is more challenging for piles since unsteady heat transfer within the pile material is more significant over typical timescales. Nonetheless, we demonstrate that for pile diameters between 300 mm and 1200 mm, generally the error is <1 °C with centrally placed heat transfer pipes or four or more pipes placed near the edge with circumferential spacing less than 550 mm. The radial model is therefore practical for most pile configurations. The strong performance of the model is demonstrated for a year of hypothetical heating and cooling cycles, and also against a field-scale thermal response test.