Usage of composite kernel in the SPH method for simulating the movement of granular materials

В работе для моделирования движения сыпучей среды используется метод сглаженных частиц. Для аппроксимации искомых функций предложено новое составное ядро малой связности. Основой для разработки ядра послужило требование к условию о сохранении плотности единичной SPH-частицы. Выполнение данного условия позволяет правильно моделировать поле плотности на границах расчетной области, а также в случаях структурных изменений каркаса гранулированных частиц сыпучей среды. Из анализа решения задачи гидростатики методом SPH получена оценка значения масштаба сглаживающей длины ядра для двумерного случая. Выполнен расчет процесса обрушения гранулированного “столба” и проведено сравнение полученных численных результатов моделирования с экспериментальными данными. The purpose of the study is to improve the practice of the SPH methodology which is applied for modelling of movement in the various media. The basis of the SPH-approximation of the function fields is formed by the forms of the smoothing kernel and its derivatives. Popular forms of smoothing kernels are characterized by the presence of significant fatal approximation errors when modelling granular media. Methodology. The state of granular medium is described by the classical motion and mass conservation equations. Each granule of the medium corresponds to a separate SPH particle. To approximate the density and pressure fields in the SPH particle, a new combination of the smoothing core and its first derivative forms is proposed. Results. The proposed new composite core fulfills the conditions of mass conservation and density recovery in the particle during SPH modeling. It is shown that the new composite core is characterized by a minimum error of pressure gradient approximation - about 2%. A new estimate for the velocity of propagation of an elastic wave in a medium, sufficient to obtain a correct numerical solution, is proposed. A comparative analysis of the obtained solutions with experimental data is made. Findings. The proposed composite shape of the smoothing kernel allows correct simulation of the motion of a granular medium by the SPH method. Its compactness (unit smoothing radius and unit smoothing length) makes it possible to correctly reconstruct the density field at the boundaries of the computational domain and in cases of structural changes in the framework of the granular medium. The numerical solution of the problem of the collapse of a column of granules obtained using the proposed composite core shows good agreement with experimental data.

Multiscale Weighted Adjacent Superpixel-Based Composite Kernel for Hyperspectral Image Classification

This paper presents a composite kernel method (MWASCK) based on multiscale weighted adjacent superpixels (ASs) to classify hyperspectral image (HSI). The MWASCK adequately exploits spatial-spectral features of weighted adjacent superpixels to guarantee that more accurate spectral features can be extracted. Firstly, we use a superpixel segmentation algorithm to divide HSI into multiple superpixels. Secondly, the similarities between each target superpixel and its ASs are calculated to construct the spatial features. Finally, a weighted AS-based composite kernel (WASCK) method for HSI classification is proposed. In order to avoid seeking for the optimal superpixel scale and fuse the multiscale spatial features, the MWASCK method uses multiscale weighted superpixel neighbor information. Experiments from two real HSIs indicate that superior performance of the WASCK and MWASCK methods compared with some popular classification methods.

PolSAR Image Classification Using a Superpixel-Based Composite Kernel and Elastic Net

The presence of speckles and the absence of discriminative features make it difficult for the pixel-level polarimetric synthetic aperture radar (PolSAR) image classification to achieve more accurate and coherent interpretation results, especially in the case of limited available training samples. To this end, this paper presents a composite kernel-based elastic net classifier (CK-ENC) for better PolSAR image classification. First, based on superpixel segmentation of different scales, three types of features are extracted to consider more discriminative information, thereby effectively suppressing the interference of speckles and achieving better target contour preservation. Then, a composite kernel (CK) is constructed to map these features and effectively implement feature fusion under the kernel framework. The CK exploits the correlation and diversity between different features to improve the representation and discrimination capabilities of features. Finally, an ENC integrated with CK (CK-ENC) is proposed to achieve better PolSAR image classification performance with limited training samples. Experimental results on airborne and spaceborne PolSAR datasets demonstrate that the proposed CK-ENC can achieve better visual coherence and yield higher classification accuracies than other state-of-art methods, especially in the case of limited training samples.

Dependent-Gaussian-Process-Based Learning of Joint Torques Using Wearable Smart Shoes for Exoskeleton

Estimating the joint torques of lower limbs in human gait is a highly challenging task and of great significance in developing high-level controllers for lower-limb exoskeletons. This paper presents a dependent Gaussian process (DGP)-based learning algorithm for joint-torque estimations with measurements from wearable smart shoes. The DGP was established to perform data fusion, and serves as the mathematical foundation to explore the correlations between joint kinematics and joint torques that are embedded deeply in the data. As joint kinematics are used in the training phase rather than the prediction process, the DGP model can realize accurate predictions in outdoor activities by using only the smart shoe, which is low-cost, nonintrusive for human gait, and comfortable to wearers. The design methodology of dynamic specific kernel functions is presented in accordance to prior knowledge of the measured signals. The designed composite kernel functions can be used to model multiple features at different scales, and cope with the temporal evolution of human gait. The statistical nature of the proposed DGP model and the composite kernel functions offer superior flexibility for time-varying gait-pattern learning, and enable accurate joint-torque estimations. Experiments were conducted with five subjects, whose results showed that it is possible to estimate joint torques under different trained and untrained speed levels. Comparisons were made between the proposed DGP and Gaussian process (GP) models. Obvious improvements were achieved when all DGP r2 values were higher than those of GP.