Distribution Of Sampling Points Research Articles

A dierential quadrature procedure for free vibration of rectangular plates involving free corners

The Di erential Quadrature Method (DQM) is one of the most powerful approximation methods for analyzing the free vibration of rectangular plates. It is easy to use and straightforward to implement. However, in spite of its many advantages, the conventional DQM has some limitations in determining the natural frequencies of rectangular plates involving free corners. This is because it is very dicult to implement the free corner boundary condition in conventional DQM. As a result, the method may exhibit some convergence problems and this may lead to erroneous and oscillatory results for natural frequencies of rectangular plates involving free corners. To overcome this diculty, this paper presents a simple DQM formulation in which all the natural boundary conditions, including the free corner boundary condition, are implemented in an easy manner. Its accuracy and eciency are demonstrated through the vibration analysis of rectangular plates with di erent combinations of free edges and free corners. Numerical results prove that the proposed method can produce much better accuracy than the conventional DQM while exhibiting a monotonic convergence behavior with respect to the number of sampling points. Furthermore, unlike the conventional DQM, solutions of the proposed method are not very sensitive to the sampling point distribution.

Optimization of Sample Points for Monitoring Arable Land Quality by Simulated Annealing while Considering Spatial Variations

With China’s rapid economic development, the reduction in arable land has emerged as one of the most prominent problems in the nation. The long-term dynamic monitoring of arable land quality is important for protecting arable land resources. An efficient practice is to select optimal sample points while obtaining accurate predictions. To this end, the selection of effective points from a dense set of soil sample points is an urgent problem. In this study, data were collected from Donghai County, Jiangsu Province, China. The number and layout of soil sample points are optimized by considering the spatial variations in soil properties and by using an improved simulated annealing (SA) algorithm. The conclusions are as follows: (1) Optimization results in the retention of more sample points in the moderate- and high-variation partitions of the study area; (2) The number of optimal sample points obtained with the improved SA algorithm is markedly reduced, while the accuracy of the predicted soil properties is improved by approximately 5% compared with the raw data; (3) With regard to the monitoring of arable land quality, a dense distribution of sample points is needed to monitor the granularity.

Modification of the Audze–Eglājs criterion to achieve a uniform distribution of sampling points

The Audze–Eglājs (AE) criterion was developed to achieve a uniform distribution of experimental points in a hypercube. However, the paper shows that the AE criterion provides strongly nonuniform designs due to the effect of the boundaries of the hypercube. We propose a simple remedy that lies in the assumption of periodic boundary conditions. The biased behavior of the original AE criterion and excellent performance of the modified criterion are demonstrated using simple numerical examples focused on (i) the uniformity of sampling density over the design space and, (ii) statistical sampling efficiency measured through the ability to correctly estimate the statistical parameters of functions of random variables. An engineering example of reliability calculation is presented, too.

HASEonGPU—An adaptive, load-balanced MPI/GPU-code for calculating the amplified spontaneous emission in high power laser media

We present an adaptive Monte Carlo algorithm for computing the amplified spontaneous emission (ASE) flux in laser gain media pumped by pulsed lasers. With the design of high power lasers in mind, which require large size gain media, we have developed the open source code HASEonGPU that is capable of utilizing multiple graphic processing units (GPUs). With HASEonGPU, time to solution is reduced to minutes on a medium size GPU cluster of 64 NVIDIA Tesla K20m GPUs and excellent speedup is achieved when scaling to multiple GPUs. Comparison of simulation results to measurements of ASE in Y b3+:Y AG ceramics show perfect agreement. Program summaryProgram title: HASEonGPUCatalogue identifier: AFAM_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AFAM_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: GNU General Public License, version 3No. of lines in distributed program, including test data, etc.: 84610No. of bytes in distributed program, including test data, etc.: 3791861Distribution format: tar.gzProgramming language: C++, Matlab.Computer: GPU cluster or workstation with CUDA-capable GPUs (compute capability ≥2.0).Operating system: Linux.Has the code been vectorized or parallelized?: Yes, can utilize 1 CPU core per compatible GPU.RAM: Several Gb, depending on input size and number of GPUs. 4000000000 bytes (4 GB) per GPU is recommended.Classification: 4.13, 6.5, 15.External routines: CUDA, Boost Program Options, OpenMPINature of problem:The algorithm described by D. Albach in [1, 2] uses ray-tracing techniques and Monte Carlo integration to calculate Amplified Spontaneous Emission (ASE) with high precision. It requires a high number of sampling points as well as a high number of rays to reach the desired results. Additionally, reflections on the upper and lower surfaces of the medium increase the workload by an order of magnitude. On traditional CPU-based systems the computation is time-consuming, which limits the number of simulations that can be performed.Solution method:HASEonGPU uses a non-uniform distribution of sampling points within the gain medium to focus computation on areas of interest. This is further improved by combining the Monte Carlo integration with importance sampling [3]. To improve execution time further, the algorithm is highly parallelized to run on a GPU and supports adaptive sampling resolutions and random restarts. It can also be executed in a GPU cluster, where linear scaling is achieved by a coarse-granular load balancing that distributes the workload among all GPUs in a master–worker-scheme over MPI.Restrictions:Presently, the number of rays used for the Monte Carlo integration of a single sampling point within the gain medium is limited by the available memory on the GPU (about 108 rays per GB of GPU memory). Furthermore, when using MPI as a workload distribution mechanism, one of the MPI processes will act as a scheduling master and its GPU cannot participate in the computation.Unusual features:The software can run on a workstation (threaded) as well as on a large-scale GPU cluster (MPI) that provides the required GPU hardware. The simulation parameters include polychromatic laser pulses as well as surface coatings, cladding, and refractive indices of the gain medium. This also allows the simulation of reflections on the upper and lower surfaces of the medium. If a desired mean square error metric is not met with a set number of rays, the algorithm can automatically increase the number of rays to improve the results.Additional comments:The source code also includes a MATLAB script that can be used to call HASEonGPU directly from MATLAB code to integrate it into existing simulation setups. There are also examples included on how to execute HASEonGPU from the command line as well as an example experiment that uses MATLAB and the provided script. More detailed information can be found in the README file.Running time:Depending on the number of sampling points, desired sampling resolution for each point, and number of GPUs, the execution time can vary strongly. A typical cylindrical gain medium of 6 cm diameter simulated with 4210 non-uniformly distributed sampling points can be simulated with a sufficient precision in 1 min on a single NVIDIA Tesla K20m GPU. Running time as well as precision can be further optimized through various parameters.

Optimal design of additional sampling pattern for drinking-water quality control

A crucial step in complementary studies of the water quality determination is to design the additional sampling pattern or, in other words, to determine the number and location of the additional samples. Since location and number of samples highly affect decisions’ uncertainties, and because sampling process is quite costly and time-consuming, optimization of the sampling pattern will enhance the efficiency and productivity. Solution of such an optimization problem requires defining an objective function and constraints. There exist many previous studies regarding locating additional samples in other environmental problems wherein the objective function is defined as the minimization of the kriging variance (based on the problem nature), but the point is that kriging variance is not sensitive to local variability. Since manner and extent of small-scale variations are both important and necessary in water quality studies, it is required to resolve this shortcoming of the traditional objective function. Solution is to make use of the combined variance consisting of kriging and local variances. In this study, the applicability and efficiency of the minimization of combined variance as the objective function of the additional sampling was adopted and proved for a salt marsh (east of Iran) on the basis of a simulated annealing-based algorithm. It was shown, practically, that the locational distribution of additional sampling points is quite logical and more compatible with experts’ proposed methods using this objective function (compared to the traditional one).

Design space exploration using Self-Organizing Map based adaptive sampling

In engineering design, a set of potentially competitive designs is conceived in the early part of the design process. The purpose of this research is to help such a process by investigating algorithm that enables approximate identification of a set of inputs of real variables that return desired responses from a function or a computer simulation. We explore sequential or adaptive sampling methods based on Self-Organizing Maps (SOM). The proposed method does not rely on parameterized distributions, and can sample from multi-modal and non-convex distributions. Furthermore, the proposed merit function provides infill characteristics by favoring sampling points that lay farther from existing points.The results indicate that multiple feasible solutions can be efficiently obtained by the new adaptive sampling algorithm. The iterative use of the SOM in density learning to identify feasible or good designs is our new contribution and it shows a very rapid increase in number of feasible solutions to total number of function evaluation ratio. Application examples to planing hull designs (such as in powerboats and seaplanes) indicate the merits of the feasible region approach to observe trends and design rules. Additionally, the well distributed sampling points of the proposed method played favorable effect in improving the prediction performance of a classification problem learned by Support Vector Machine.

Digital mapping of soil organic and inorganic carbon status in India

Reliable mapping of soil organic carbon (SOC) and Soil Inorganic Carbon (SIC) densities and estimates of their pool size are important from global warming perspective to understand the sequestration potential and losses. In this study, first spatially explicit mapping of SOC and SIC at 250m resolution and an estimate of their pool size in India was undertaken using a large number of remote sensing derived data layers and data mining approach. The SOC and SIC densities up to 100cm depth or paralithic contact (whichever is shallower) were estimated for 1198 soil samples located across India using a stratified random sampling that integrated land use, soil, topography and agro-ecological regions.Using Random forests (RF) based spatial prediction procedure with climatic, land cover, rock type, soil type, multi-year NDVI, irrigation status as independent input variables, models for predicting carbon density at 250m spatial resolution were developed. For modelling with RF algorithm, about 898 soil profile observations (75% observations) were used, while the rest of 300 (25% of total observations) were used for validation. It was observed that the data distribution of sample points don't have significant influence on RF model predictions. The relationship between observed and predicted values was characterized by Mean Squared Deviation (MSD) and Root Mean Squared Error (RMSE) parameters. The SOC, SIC and total soil carbon pool size of India has been estimated at 22.72±0.93 Pg,12.83±1.35 Pg and 35.55±1.87 Pg, respectively, which are comparable to previous studies while providing first spatially explicit 250m map of their distribution. The spatial distribution indicates that majority of the carbon stock resides in the northern part of India. The soil carbon stock of eastern India has contribution from organic carbon, while the western portion has contribution mainly from inorganic carbon.

Sampling design schemes for distributed parameter estimation networks

This paper proposes two sampling schemes for distributed parameter estimation networks. The estimation network comprises a number of remotely located sensors which process the observed signal locally and then convey the processed data to a data fusion centre to make the final estimate of the parameter of interest. In the first sampling scheme, all sensors utilise same number of sampling points, and the distribution of sampling points at each sensor is determined to maximise the estimation accuracy. By contrast, in the second one, the sensors are assigned a different number of sampling points, and the objective is to determine the sampling point assignment which maximises the overall estimation performance given a constraint on the total number of sampling points available. The two sampling design problems are solved by minimising the Fisher information loss. The validity of the proposed sampling design schemes is demonstrated by means of two numerical examples.

采样点分布对基于面形斜率径向基模型的自由曲面拟合精度的影响

采样点分布对基于面形斜率径向基模型的自由曲面拟合精度的影响

Comparison of sampling schemes for the spatial prediction of soil organic matter in a typical black soil region in China

Data on the spatial distribution of soil organic matter (SOM) are important for the spatio-temporal modeling of soil organic carbon dynamics and soil carbon sequestration potential estimates. A total of 175 topsoil samples (0–20 cm) were collected from a typical black soil area in central Hailun County in northeastern China. Seven sampling design schemes, ordinary kriging (OK), and regression kriging (RK) were applied to the re-sampled SOM data for predicting the spatial distribution of SOM. The results showed that single sampling designs, such as simple random, stratified random (STR), and conditional Latin hypercube (CLH), produced poor estimates of SOM, while hybrid sampling designs, such as uniform distribution of point pairs for variogram estimation combined with spatial coverage, STR combined with spatial coverage (STRC), and CLH combined with spatial coverage (CLHC), had a higher predicting accuracy when the sample size was relatively small (≤262). For square grid sampling, a higher predicting accuracy could be achieved only when the sample size was sufficiently large (i.e., ≥402). The inclusion of prior knowledge or SOM-related secondary data in the sampling design and the trade-off between the even and uneven distribution of sampling points are especially important for designing a small-size sampling scheme. Moreover, although the SOM-predicting accuracy of RK was not as good as OK in this study, increasing the sample size may improve the predicting accuracy of SOM. Therefore, the optimal sampling design and spatial predicting method are both important for the predictive mapping of SOM spatial distribution in this area.

Optimal sampling points in reproducing kernel Hilbert spaces

The recent development of compressed sensing seeks to extract information from as few samples as possible. In such applications, since the number of samples is restricted, one should deploy the sampling points wisely. We are motivated to study the optimal distribution of finite sampling points in reproducing kernel Hilbert spaces, the natural background function spaces for sampling. Formulation under the framework of optimal reconstruction yields a minimization problem. In the discrete measure case, we estimate the distance between the optimal subspace resulting from a general Karhunen–Loève transform and the kernel space to obtain another algorithm that is computationally favorable. Numerical experiments are then presented to illustrate the effectiveness of the algorithms for the searching of optimal sampling points.

Detecting natural scenes text via auto image partition, two-stage grouping and two-layer classification

Text detection in natural scene images is important and challenging work for image analysis. In this paper, we present a robust system to detect natural scene text according to text region appearances. The framework includes three parts: auto image partition, two-stage grouping and two-layer classification. The first part partitions images into unconstrained sub-images through statistical distribution of sampling points. The designed two-stage grouping method performs grouping in each sub-image in first stage and connects different partitioned image regions in second stage to group connected components (CCs) to text regions. Then a two-layer classification mechanism is designed for classifying candidate text regions. The first layer is to compute the similarity score of region blocks and the second layer is a SVM classifier using HOG features. We add a normalization step to rectify perspective distortion before candidate text region classification which improves the accuracy and robustness of the final output result. The proposed system is evaluated on four types datasets including two ICDAR Robust Reading Competition datasets, a born-digital image dataset, a video image dataset and a perspective distortion image dataset. The experimental results demonstrate that our proposed framework outperforms state-of-the-art localization algorithms and is robust in dealing with multiple background outliers.

New adaptive sampling method in particle image velocimetry

This study proposes a new adaptive method to enable the number of interrogation windows and their positions in a particle image velocimetry (PIV) image interrogation algorithm to become self-adapted according to the seeding density. The proposed method can relax the constraint of uniform sampling rate and uniform window size commonly adopted in the traditional PIV algorithm. In addition, the positions of the sampling points are redistributed on the basis of the spring force generated by the sampling points. The advantages include control of the number of interrogation windows according to the local seeding density and smoother distribution of sampling points. The reliability of the adaptive sampling method is illustrated by processing synthetic and experimental images. The synthetic example attests to the advantages of the sampling method. Compared with that of the uniform interrogation technique in the experimental application, the spatial resolution is locally enhanced when using the proposed sampling method.

A new planning method for sample points of free-form curved surface

To acquire the precise appearance feature of free-form curved surface, an adaptive planning strategy for sample points of free-form curved surface, which combines the principle of circular interpolation and the self-organising characteristics of material centre theorem, is presented, and a solution algorithm suitable for surface digitising is proposed. The experimental results show that the adaptive planning algorithm for sample points of free-form curved surface is simple. It makes up the distribution defects of sample points based on circular interpolation, and avoids the enormous resource consumption in solving the complex non-linear equations. The sample points could distribute well according to the surface appearance characteristics, and the distribution of sample points under the required planning accuracy can be found via iteration.

Fault Diagnosis of Supervision and Homogenization Distance Based on Local Linear Embedding Algorithm

In view of the problems of uneven distribution of reality fault samples and dimension reduction effect of locally linear embedding (LLE) algorithm which is easily affected by neighboring points, an improved local linear embedding algorithm of homogenization distance (HLLE) is developed. The method makes the overall distribution of sample points tend to be homogenization and reduces the influence of neighboring points using homogenization distance instead of the traditional Euclidean distance. It is helpful to choose effective neighboring points to construct weight matrix for dimension reduction. Because the fault recognition performance improvement of HLLE is limited and unstable, the paper further proposes a new local linear embedding algorithm of supervision and homogenization distance (SHLLE) by adding the supervised learning mechanism. On the basis of homogenization distance, supervised learning increases the category information of sample points so that the same category of sample points will be gathered and the heterogeneous category of sample points will be scattered. It effectively improves the performance of fault diagnosis and maintains stability at the same time. A comparison of the methods mentioned above was made by simulation experiment with rotor system fault diagnosis, and the results show that SHLLE algorithm has superior fault recognition performance.

Application of Response Surface Model on Aerodynamic Characteristic of Airfoil

To reduce the computational resources, experimental design and response surface method (RSM) were employed to investigate the aerodynamic drag coefficient (CD) and lift coefficient (CL) of airfoils by using CFD methods. The selection of sample points, development and validation of response surface model and the effects of different sample points on approximation model were discussed. The results indicates that the number and distribution of sample points have a significant impact on model accuracy and optimize results. Also this method can greatly reduce calculation amount.

A self-adaptive sampling digital image correlation algorithm for accurate displacement measurement

Digital image correlation (DIC) is nowadays widely applied to many engineering areas as an effective optical displacement measurement technique. To minimize the potential effect of spatial sampling locations on full-field displacement measurement, this paper develops a self-adaptive sampling DIC algorithm for accurate and reliable displacement computation over entire specimen surfaces. Depending on local deformation states, the algorithm can automatically optimize spatial distribution of sampling points over specimen surfaces in a self-adaptive manner in combination with the well-developed DIC algorithm with Gaussian windows. Both a series of well-designed computer-simulated speckle images and actual cell-substrate deformation ones are employed to verify the feasibility and effectiveness of the proposed algorithm, which demonstrates that the set of self-adaptive sampling algorithm is capable of recovering more accurate and precise full-field displacements compared to the conventional DIC algorithm with equidistant sampling.

On the selection of sampling points for myocardial T1 mapping.

To provide a method for the optimal selection of sampling points for myocardial T1 mapping, and to evaluate how this selection affects the precision. The Cramér-Rao lower bound on the variance of the unbiased estimator was derived for the sampling of the longitudinal magnetization curve, as a function of T1 , signal-to-noise ratio, and noise mean. The bound was then minimized numerically over a search space of possible sampling points to find the optimal selection of sampling points. Numerical simulations were carried out for a saturation recovery-based T1 mapping sequence, comparing the proposed point selection method to a uniform distribution of sampling points along the recovery curve for various T1 ranges of interest, as well as number of sampling points. Phantom imaging was performed to replicate the scenarios in numerical simulations. In vivo imaging for myocardial T1 mapping was also performed in healthy subjects. Numerical simulations show that the precision can be improved by 13-25% by selecting the sampling points according to the target T1 values of interest. Results of the phantom imaging were not significantly different than the theoretical predictions for different sampling strategies, signal-to-noise ratio and number of sampling points. In vivo imaging showed precision can be improved in myocardial T1 mapping using the proposed point selection method as predicted by theory. The framework presented can be used to select the sampling points to improve the precision without penalties on accuracy or scan time.

Multi-resolution imaging with an optimized number and distribution of sampling points.

We propose an approach of interest in Imaging and Synthetic Aperture Radar (SAR) tomography, for the optimal determination of the scanning region dimension, of the number of sampling points therein, and their spatial distribution, in the case of single frequency monostatic multi-view and multi-static single-view target reflectivity reconstruction. The method recasts the reconstruction of the target reflectivity from the field data collected on the scanning region in terms of a finite dimensional algebraic linear inverse problem. The dimension of the scanning region, the number and the positions of the sampling points are optimally determined by optimizing the singular value behavior of the matrix defining the linear operator. Single resolution, multi-resolution and dynamic multi-resolution can be afforded by the method, allowing a flexibility not available in previous approaches. The performance has been evaluated via a numerical and experimental analysis.

Post-Processing of Phased-Array Ultrasonic Inspection Data with Parallel Computing for Nondestructive Evaluation

Phased-array ultrasonic nondestructive evaluation is an effective tool of safety assurance for key structural components. The paper presents a general post-processing methodology for phased-array ultrasonic inspection data. The methodology is developed to integrate three components: mapping of sampling points to structure model, re-sampling from non-uniformly distributed sampling points in phased-array to a uniform volume, and data fusion strategies for multiple channels. An adaptive method called spatially adaptive Gaussian splatting is proposed for data re-sampling and fusion considering the reconstruction resolution and local characteristics of ultrasonic sound paths. This adaptivity provides a viable approach to minimize the effects of under-sampling, over-sampling, and holes which are introduced by the non-uniformly distributed sampling points. The processing of large scale data through segmentation and parallelization techniques is discussed in detail. The effectiveness and performance of the proposed methodology are investigated using actual phased-array ultrasonic testing data.