Small Number Of Sampling Points Research Articles

Real-time non-line-of-sight computational imaging using spectrum filtering and motion compensation.

Non-line-of-sight (NLOS) imaging aims at recovering the shape and albedo of hidden objects. Despite recent advances, real-time video of complex and dynamic scenes remains a major challenge owing to the weak signal of multiply scattered light. Here we propose and demonstrate a framework of spectrum filtering and motion compensation to realize high-quality NLOS video for room-sized scenes. Spectrum filtering leverages a wave-based model for denoising and deblurring in the frequency domain, enabling computational image reconstruction with a small number of sampling points. Motion compensation tailored with an interleaved scanning scheme can compute high-resolution live video during the acquisition of low-quality image sequences. Together, we demonstrate live NLOS videos at 4 fps for a variety of dynamic real-life scenes. The results mark a substantial stride toward real-time, large-scale and low-power NLOS imaging and sensing applications.

Construction of Prediction Models of Mass Ablation Rate for Silicone Rubber-Based Flexible Ablative Composites Based on a Small Dataset

The prediction of the ablation rate of silicone rubber-based composites is of great significance to accelerate the development of flexible thermal protection materials. Herein, a method which combines uniform design experimentation, active learning, and virtual sample generation was proposed to establish a prediction model of the mass ablation rate based on a small dataset. Briefly, a small number of sample points were collected using uniform design experimentation, which were marked to construct the initial dataset and primitive model. Then, data points were acquired from the sample pool and iterated using various integrated algorithms through active learning to update the above dataset and model. Finally, a large number of virtual samples were generated based on the optimal model, and a further optimized prediction model was achieved. The results showed that after introducing 300 virtual samples, the average percentage error of the gradient boosting decision tree (GBDT) prediction model on the test set decreased to 3.1%, which demonstrates the effectiveness of the proposed method in building prediction models based on a small dataset.

Fourier-Based Function Generation of Four-Bar Linkages With an Improved Sampling Points Adjustment and Sylvester's Dialytic Elimination Method

Abstract Four-bar linkages are critical fundamental elements of many mechanical systems, and their design synthesis is often mathematically complicated with iterative numerical solutions. Analytical methods based on Fourier coefficients can circumvent these difficulties but have difficulties with sampling points adjustment and solutions of the design equations in previous studies. In this paper, an improved Fourier-based analytical synthesis method is presented, which transforms the function generation synthesis of planar four-bar linkages into a problem of solving design equations. Calculation of the Fourier coefficients is discussed, including the discretization of the prescribed function and an improved sampling points adjustment method. It is shown that the Fourier coefficients can be computed efficiently and accurately by discretizing the prescribed function with a small number of sampling points. The proposed sampling adjustment method overcomes the difficulty of easily resulting in non-Grashof solutions by considering the complete period of the prescribed function. An improved Sylvester's dialytic elimination method is presented to solve design equations. The method reduces the computation time and avoids cumbersome procedures without generating additional invalid solutions. Several examples are presented to demonstrate the advantages of the proposed synthesis method, which is easy-understanding and efficient, and yields more accurate solutions than available synthesis methods.

An adaptive multi-output Gaussian process surrogate model for large-scale parameter estimation problems

PurposeParameter estimation in complex engineering structures typically necessitates repeated calculations using simulation models, leading to significant computational costs. This paper aims to introduce an adaptive multi-output Gaussian process (MOGP) surrogate model for parameter estimation in time-consuming models.Design/methodology/approachThe MOGP surrogate model is established to replace the computationally expensive finite element method (FEM) analysis during the estimation process. We propose a novel adaptive sampling method for MOGP inspired by the traditional expected improvement (EI) method, aiming to reduce the number of required sample points for building the surrogate model. Two mathematical examples and an application in the back analysis of a concrete arch dam are tested to demonstrate the effectiveness of the proposed method.FindingsThe numerical results show that the proposed method requires a relatively small number of sample points to achieve accurate estimates. The proposed adaptive sampling method combined with the MOGP surrogate model shows an obvious advantage in parameter estimation problems involving expensive-to-evaluate models, particularly those with high-dimensional output.Originality/valueA novel adaptive sampling method for establishing the MOGP surrogate model is proposed to accelerate the procedure of solving large-scale parameter estimation problems. This modified adaptive sampling method, based on the traditional EI method, is better suited for multi-output problems, making it highly valuable for numerous practical engineering applications.

WS-SSD: Achieving faster 3D object detection for autonomous driving via weighted point cloud sampling

Due to the limited computational resources of the onboard computing devices of autonomous vehicles, the development of lightweight 3D object detectors is essential. Point-based detectors that progressively sample raw point clouds reduce numerous redundant computations and facilitate the implementation of high-speed 3D object detectors. The farthest point sampling based on Euclidean distance (D-FPS) is frequently utilized in point-based 3D detectors for point cloud sampling to reduce computation overhead. D-FPS can ensure uniform point sampling, covering the entire point cloud space as much as possible. The ratio of foreground and background points does not change significantly in the sampling results; hence, foreground objects do not receive sufficient attention. In addition, the number of road reflection points is large, and these points are close to foreground objects, reducing the sampling accuracy for faint objects. We propose weighted farthest point sampling based on Euclidean distance (W-DFPS), which selectively discards some road reflection points in the point sampling process, thus increasing the weight of foreground points in sampling results. It reduces the likelihood of faint objects being lost in the sampling results, such that a small number of sampling points can also cover most foreground objects. W-DFPS replaces D-FPS in the single-stage detector based on instance-aware (IA-SSD), and the network structure is slightly modified, namely the single-stage detector based on weighted sampling (WS-SSD). We evaluate WS-SSD in the KITTI dataset with a single A100 GPU. When the number of sampling points for the first module of WS-SSD is consistent with IA-SSD, the pedestrian detection accuracy is improved by an average of 4.06 compared to IA-SSD. Although the number of sampling points for the first module of WS-SSD is reduced to 25% of IA-SSD, the object detection accuracy remains competitive; it also achieves a state-of-the-art inference speed of 150.76 frames per second (FPS), which is a 46% improvement over IA-SSD.

A fast computational method for internal temperature field in Oil-Immersed power transformers

In order to improve the computational efficiency of the steady-state temperature rise of oil-immersed power transformer windings, this paper proposes a temperature field reduced order model(ROM) based on proper orthogonal decomposition (POD) and response surface method(RSM). The method takes the operating conditions of the transformer as input and uses the POD method as a carrier, and establishes a fast calculation model of the steady-state temperature field through RSM, thus achieving fast calculation from transformer operating data to the entire temperature field. The paper first analyzes the reduction characteristics of the POD method, and then introduces the RSM to establish the correlation between the POD modal coefficients and the transformer conditions. Compared with traditional surrogate models, this method can obtain high-precision surrogate relationships with a small number of sample points, and the time cost of establishing is relatively low. The method aims to quickly obtain the POD modal coefficients through the winding conditions, thereby skipping the complex nonlinear calculation and efficiently reconstructing the winding temperature field with the reduced modal. The related examples show that the method has good computational accuracy and efficiency. In a 2D forced oil circulation cooling model, out of 100 test conditions, the error is not more than 2.0 K compared with the full-order calculation, and the total calculation time is only 3.13 s. Finally, based on a 35 kV natural oil circulation cooling transformer, a temperature rise test platform is constructed to verify the effectiveness of the method. The experimental results show that the calculated error of the ROM is not more than 5 K compared with the experimental results, and the single-step calculation time is only 0.73 s, which has greatly improved the computational efficiency compared with full-order calculation of the same scale. The proposed method in this study achieves a second-level calculation efficiency for the transformer winding temperature, providing a feasible solution for digital online monitoring of transformer temperatures.

Sensitivity-enhanced generalized polynomial chaos for efficient uncertainty quantification

We consider the Least Squares (LSQ) regression method for Uncertainty Quantification (UQ) using generalised polynomial chaos (gPC) and augment the linear system with the gradient of the Quantity of Interest (QoI) with respect to the stochastic variables. The gradient is computed very efficiently for all variables from the adjoint system of equations. To minimise the condition number of the augmented LSQ system, an effective sampling strategy of the stochastic space is required. We compare two strategies. In the first, we apply pivoted QR decomposition to the standard LSQ matrix and evaluate both the QoI and its gradient at the sample points identified. In the second strategy, we apply QR decomposition directly to the augmented matrix. We find that the first strategy is more efficient in terms of accuracy vs number of evaluations. We call the new approach sensitivity-enhanced generalised polynomial chaos, or se-gPC, and apply it to several test cases including an aerodynamic case with 40 stochastic parameters. The method can produce accurate estimations of the statistical moments using a small number of sampling points. The computational cost scales as ∼mp−1, instead of ∼mp of the standard LSQ formulation, where m is the number of stochastic variables and p the chaos order. The solution of the adjoint system of equations is implemented in many computational mechanics packages, thus the infrastructure exists for the application of the method to a wide variety of engineering problems.

Adaptive ensemble surrogate-based optimization and analysis of forklift pallet racks

As an important part of the lifting platform of pallet forklift trucks, how to reduce the deformation of the pallet rack under working conditions while reducing the mass to ensure the safety performance of forklift trucks is the most concerning issue in the design of forklift truck structure. The pallet rack structure is complex, and optimizing simulation using traditional high-precision simulation models takes much time and effort. Therefore, this paper takes the lifting platform of an unmanned AVG forklift truck as the research object and establishes a parametric model of the pallet rack using the 3D modelling software SolidWorks and the finite element analysis software ANSYS to carry out static analysis of it. Optimization design variables are selected, a single surrogate model and ensemble surrogate model are chosen for various surrogate model techniques, a small number of sample points are used to construct a low-precision model, and adaptive infilling technology is used to improve the model accuracy, and the structure is optimized, and the results show that, while the pallet rack structure meets the requirements of light weight and strength, the mass is reduced by 1.2%, and the morphology is reduced by 17.2%. Moreover, a global sensitivity analysis of each design parameter was carried out under the guidance of the surrogate model, highlighting the most influential design variable as the height of the channel steel and establishing the design variables that should be taken into account in the structural design. This paper compares the performance of the mainstream single-surrogate model and ensemble-surrogate model as well as the adaptive infilling strategy in engineering design and proves that the surrogate model optimization method has a certain guiding significance for the structural optimization design of pallet racking.

A Stochastic Switched Optimal Control Approach to Formation Mission Design for Commercial Aircraft

This article studies the formation mission design problem for commercial aircraft in the presence of uncertainties. Specifically, it considers uncertainties in the departure times of the aircraft and in the fuel burn savings for the trailing aircraft. Given several commercial flights, the problem consists in arranging them in formation or solo flights and finding the trajectories that minimize the expected value of the DOC of the flights. The formation mission design problem is formulated as an optimal control problem of a stochastic switched dynamical system and solved using nonintrusive gPC-based stochastic collocation. The stochastic collocation method converts the SSOCP into an augmented deterministic switched optimal control problem. With this approach, a small number of sample points of the random parameters are used to jointly solve particular instances of the switched optimal control problem. The obtained solutions are then expressed as orthogonal polynomial expansions in terms of the random parameters using these sample points. This technique allows statistical and global sensitivity analysis of the stochastic solutions to be conducted at a low computational cost. The aim of this article is to establish if, in the presence of uncertainties, a formation mission is beneficial with respect to solo flight in terms of the expected value of the direct operating costs. Several numerical experiments have been conducted in which uncertainties on the departure times and on the fuel saving during formation flight have been considered. The obtained results demonstrate that benefits can be achieved even in the presence of these uncertainties.

Polyharmonic splines for interpolation over sun path

The optimization of solar tower power plants and other concentrating solar power (CSP) systems requires a customized approach for interpolation over the annual sun path. A good interpolation should predict accurately the efficiency of the system for different positions of the sun by using a small number of sampling points. This is very important to reduce the amount of simulations (e.g. ray tracing, cone optics, etc.), which are necessary to evaluate the annual performance for different CSP system configurations. From a mathematical point of view, the interpolation over sun path is an example of bivariate interpolation over a domain of irregular shape, and many methods are available to address it. In this paper, the advantages of meshless methods are investigated. The obtained results show that polyharmonic splines provide a good fit for the optical efficiency of the heliostat field of a solar tower system. The interpolated optical efficiency simplifies the calculation of annual energy reflected from the heliostat field to the receiver, and the result has an absolute error of 0.1% for less than 30 sampling points.

Primena konačnih tačaka uzorkovanja u višekriterijumskoj optimizaciji zasnovanoj na verovatnoći pomoću uniformnog eksperimentalnog dizajna

Introduction/purpose: An approximation for assessing a definite integral is continuously an attractive topic owing to its practical needs in scientific and engineering areas. An efficient approach for preliminarily calculating a definite integral with a small number of sampling points was newly developed to get an approximate value for a numerical integral with a complicated integrand. In the present paper, an efficient approach with a small number of sampling points is combined to the novel probability-based multi-objective optimization (PMOO) by means of uniform experimental design so as to simplify the complicated definite integral in the PMOO preliminarily. Methods: The distribution of sampling points within its single peak domain is deterministic and uniform, which follows the rules of the uniform design method and good lattice points; the total preferable probability is the unique and deterministic index in the PMOO. Results: The applications of the efficient approach with finite sampling points in solving typical problems of PMOO indicate its rationality and convenience in the operation. Conclusion: The efficient approach with finite sampling points for assessing a definite integral is successfully combined with PMOO by means of the uniform design method and good lattice points.

Efikasan pristup izračunavanju određenog integrala sa oko desetak tačaka uzorkovanja

Introduction/purpose: An approximate approach to definite integral calculation has been an attractive problem continuously since the creation of integration due to practical needs in scientific and engineering areas. In most practical cases, the integrand is complex, which leads to a difficulty of obtaining an exact value of integration, so an approximate value of the definite integral with certain accuracy is satisfactory for practical applications. In this paper, an efficient approach for calculating a definite integral with a small number of sampling points is proposed based on the uniform design method from the viewpoint of practical application. Methods: The distribution of sampling points in its single peak domain is deterministic and uniform, which follows the rule of the uniform design method and good lattice points. Results: The efficient evaluation of a definite integral for a periodical function in its single peak domain can be obtained by using 11 sampling points in one dimension, 17 sampling points in two dimensions, and 19 sampling points in three dimensions. Conclusion: The efficient approach for a definite integral developed here on the basis of the uniform test design method is promised from the viewpoint of practical application; the sampling points are deterministically and uniformly distributed according to the rule of the uniform design method and "good lattice points". The efficient approach developed in this article will be beneficial to relevant research and application.

Fourier Ring Correlation and Anisotropic Kernel Density Estimation Improve Deep Learning Based SMLM Reconstruction of Microtubules.

Single-molecule super-resolution microscopy (SMLM) techniques like dSTORM can reveal biological structures down to the nanometer scale. The achievable resolution is not only defined by the localization precision of individual fluorescent molecules, but also by their density, which becomes a limiting factor e.g., in expansion microscopy. Artificial deep neural networks can learn to reconstruct dense super-resolved structures such as microtubules from a sparse, noisy set of data points. This approach requires a robust method to assess the quality of a predicted density image and to quantitatively compare it to a ground truth image. Such a quality measure needs to be differentiable to be applied as loss function in deep learning. We developed a new trainable quality measure based on Fourier Ring Correlation (FRC) and used it to train deep neural networks to map a small number of sampling points to an underlying density. Smooth ground truth images of microtubules were generated from localization coordinates using an anisotropic Gaussian kernel density estimator. We show that the FRC criterion ideally complements the existing state-of-the-art multiscale structural similarity index, since both are interpretable and there is no trade-off between them during optimization. The TensorFlow implementation of our FRC metric can easily be integrated into existing deep learning workflows.

Research on Three-Dimensional Interpolation Modeling Method of Micro - and Nanometer Controllable Surface

The fundamental cause of friction and wear is the effect of force, resulting in material heating, deformation, fatigue, adhesion and furrow effect, which is closely related to the micro-topography of the contact surface of friction pair. How to establish the real three-dimensional (3D) rough surface, using inter-polation surface reconstruction based on real data, especially in the three dimensional precision measurement data processing, etc, also the lack of research and practice, so in this paper, fractal interpolation and spline interpolation, Fourier interpolation surface modeling interpolation algorithm of three methods for modeling, a detailed analysis and expounds the advantages and disadvantages of the three ways of modeling with surface, and finally to the surface of the atomic force microscope to measure the actual extraction of a small number of sampling points are simulated.

Locally adaptive thresholding centroid localization in confocal microscopy

We introduce an iteration-free approach, based on a centroid algorithm with a locally adaptive threshold, for nanometer-level peak position localization of the axial response signal in confocal microscopy. This approach has localization accuracies that are near theoretical limits, especially when there is a small number of sampling points within the discrete signal. The algorithm is also orders of magnitude faster compared to fitting schemes based on maximum likelihood estimation. Simulations and experiments demonstrate the localization performance of the approach.

Active Sampling Based Polynomial-Chaos–Kriging Model for Orbital Uncertainty Propagation

Propagating uncertainties usually requires repeated evaluation of the subject model for a large number of different input parameters. Surrogate models have been widely used to avoid this computationally intensive uncertainty propagation by replacing the original model by an easy-to-evaluate function model. In this Paper, the polynomial chaos based Kriging is used as such a surrogate model for orbital uncertainty propagation. The polynomial chaos represents the global trend of the uncertainty distribution, while the Kriging describes the local variations. Such a combination can provide a more precise surrogate model than individual polynomial chaos or ordinary Kriging representation. To further enhance the accuracy, a new active sampling strategy is proposed to incrementally build and improve the polynomial chaos based Kriging model. This new modeling scheme only requires a small number of sampling points while achieving close performance to the Monte Carlo based propagation. It is also more accurate than the random sampling based Kriging model. Three orbital uncertainty propagation examples are used to demonstrate the effectiveness of the proposed surrogate model.

Fast and Accurate Transient Analysis of Large Grounding Systems in Multilayer Soil

One of the most accurate approaches to the lightning-related transient analysis of grounding systems in layered soil is based on the method of moments solution of the integral form of the Maxwell equations. The practical application of this rigorous model to large systems is hindered by a great amount of computer time required for the numerical integration of oscillatory and slowly convergent Sommerfeld integrals (SI). As a result, approximate methods that avoid the solution of SI, e.g., image theory-based methods, are often used for computation of the response of large grounding systems. In this article, we extend the application of the rigorous model for large grounding systems in multilayered soil by applying a procedure that minimizes the number of direct computations of the SI using interpolation over a grid of a small number of sample points. We implement a three-dimensional interpolation scheme that adapts to the problem to minimize the interpolation grid, maintaining the accuracy of the rigorous approach. The developed model is applied for the analysis of transient voltages that might couple to secondary cables and disrupt the operation of connected equipment in case of lightning. The analysis shows that there are cases when the image theory-based models might underestimate the possibly harmful transient voltages.

A surrogate-assisted particle swarm optimization using ensemble learning for expensive problems with small sample datasets

Solving the real-world optimization problems often needs a large number of expensive function evaluations (FEs) by using evolutionary algorithms (EAs). To alleviate this difficulty, surrogate-assisted EAs (SAEAs) have attracted more and more attention from academia and industry. However, the existing SAEAs need a large amount of sample points to construct surrogate model within the expected times of FEs, otherwise it cannot achieve satisfactory prediction accuracy. Few SAEAs can reduce the times of expensive FEs while a high-quality surrogate model is constructed using a small number of sample points. In this paper, a novel SAEAs inspired from ensemble learning is proposed. In the proposed algorithm, the small sample date set is divided into multiple subsets, and the surrogate model is trained on each subset. Two new model management strategies based on ensemble learning are applied to global search and local search respectively. Two search methods are cleverly combined to form a high precision surrogate ensemble. In order to verify the performance of the proposed method, we performed comprehensive tests on eight benchmark functions from 10 to 50 dimensions, and compared their result with the five state-of-the-art SAEAs. Experimental results demonstrate that the proposed method shows superior performance in a majority of benchmarks when only a limited computational budget is available. In addition, we apply the proposed algorithm to three real-time optimization problems. The results of each problem are compared with the solutions to verify the effectiveness of the algorithm in solving engineering application problems.

A comparative study of two interval-random models for hybrid uncertainty propagation analysis

Abstract A wide variety of uncertainty propagation methods have been developed to deal with the single uncertainty; however, different kinds of uncertainties may exist simultaneously in many engineering practices. By using random variables and interval variables to quantify the probabilistic and non-probabilistic uncertainties respectively, this paper proposes two different interval-random models and a universal numerical approach for hybrid uncertainty propagation analysis. In the first model, uncertain parameters are treated as either random variables or interval variables with deterministic distributions, which exist independently. In the second model, uncertain parameters are quantified as random interval variables, where the bounds of interval variables are expressed as random variables instead of deterministic values. In both models, the effect of input hybrid uncertainties on output response is interpreted by an interval number with random bounds. To predict the moments of random bounds of interval response, a double-loop numerical analysis framework is constructed, where the outer loop is executed to traverse the discrete points for random variables and the inner loop is implemented to capture the response extreme values for interval variables. To further solve the computationally expensive issue caused by the full-scale finite element simulations, a cross validation-based adaptive surrogate model is introduced as an approximation, which can achieve an acceptable accuracy through a small number of sample points. Finally, a transient heat conduction example demonstrates the feasibility of the proposed models and method.

Estimation of atmospheric light based on gaussian distribution

Existing defogging algorithms use a small number of sample points to estimate the atmospheric light, which leads to poor defogging effect. To solve this problem, a novel Gaussian distribution based algorithm for atmospheric light estimation is proposed. The algorithm has the following features: it uses a brightness threshold to select the candidate points to increase the number of initial samples; it uses clustering algorithms to merge the point clusters for increasing the samples included in the candidate point cluster; it uses a proportional threshold to filter out unreasonable point clusters; it regards each candidate point cluster as a single light source and calculates their influence on surrounding pixels with a Gaussian-distribution-based model; and it uses an atmospheric light map (instead of a constant value) to restore the image. The experimental results suggest that the defogging results produced by the proposed algorithm look more natural than the original algorithm under subjective vision and the objective image quality evaluation indicators are also excellent.