Computational approach to solving problems of spatial processing of point sets on two-dimensional regular grids

The paper presents an approach to solving problems of spatial processing on sets of points on a plane. The presented method consists in plotting regions of an arbitrary geometric shape near given points of the set on a regular grid and determining the intersection points of the regions using spatial hash tables to improve the efficiency of operations. The proposed approach is implemented in the form of software for determining the spatial relationships between points as a sequence of operations with discretized sets and allows visualization of research results. Figs.: 2. Refs.: 13. Keywords: spatial processing task; point set; plane; regular grid; spatial hash table.

Environmental Aspect of Population Organisation of Terrestrial Mollusk Brephulopsis cylindrica (Pulmonata, Buliminidae) in Space and Time at a Remediation Territory (Nikopol Manganese ore Basin)

Density variability of a population of the mollusk Brephulopsis cylindrica (Menke, 1828) was studied at a reclaimed site in the Nikopol manganese ore basin. This study was conducted on sod-lithogenic soil on grey-green clay. The samples were collected over 3 years, 3 times a year, on a regular grid. Lexis aggregation index (λ) and geostatistical tools were used to characterise spatial distribution of the mollusks. The correlation between the distribution of B. cylindrica and environmental factors was established using correlation analysis. Valid correlations were identified between distribution of the mollusk and variation of the fraction content in composition of structural aggregates of soil. Also, valid correlations were identified with plant species composition at the reclaimed site.

Quality of the Wind Wave Forecast in the Black Sea Including Storm Wave Analysis

This paper presents the results of wind wave forecasts for the Black Sea. Three different versions utilized were utilized: the WAVEWATCH III model with GFS 0.25 forcing on a regular grid, the WAVEWATCH III model with COSMO-RU07 forcing on a regular grid, and the SWAN model with COSMO-RU07 forcing on an unstructured grid. AltiKa satellite altimeter data were used to assess the quality of wind and wave forecasts for the period from 1 April to 31 December 2017. Wave height and wind speed forecast data were obtained with a lead time of up to 72 h. The presented models provide an adequate forecast in terms of modern wave modeling (a correlation coefficient of 0.8–0.9 and an RMSE of 0.25–0.3 m) when all statistics were analyzed. A clear improvement in the wave forecast quality with the high-resolution wind forecast COSMO-RU07 was not registered. The bias error did not exceed 0.5 m in an SWH range from 0 to 3 m. However, the bias sharply increased to −2 or −3 m for an SWH range of 3–4 m. Wave forecast quality assessments were conducted for several storm cases.

Trapezoid-grid finite difference frequency domain method for seismic wave simulation

The large computational cost and memory requirement for the finite difference frequency domain (FDFD) method limit its applications in seismic wave simulation, especially for large models. For conventional FDFD methods, the discretisation based on minimum model velocity leads to oversampling in high-velocity regions. To reduce the oversampling of the conventional FDFD method, we propose a trapezoid-grid FDFD scheme to improve the efficiency of wave modeling. To alleviate the difficulty of processing irregular grids, we transform trapezoid grids in the Cartesian coordinate system to square grids in the trapezoid coordinate system. The regular grid sizes in the trapezoid coordinate system correspond to physical grid sizes increasing with depth, which is consistent with the increasing trend of seismic velocity. We derive the trapezoid coordinate system Helmholtz equation and the corresponding absorbing boundary condition, then get the FDFD stencil by combining the central difference method and the average-derivative method (ADM). Dispersion analysis indicates that our method can satisfy the requirement of maximum phase velocity error less than $1\%$ with appropriate parameters. Numerical tests on the Marmousi model show that, compared with the regular-grid ADM 9-point FDFD scheme, our method can achieve about $80\%$ computation efficiency improvement and $80\%$ memory reduction for comparable accuracy.

Microlandform classification method for grid DEMs based on support vector machine

Microlandform classification of grid digital elevation models (DEMs) is the foundation of digital landform refinement applications. To solve the shortcomings of the traditional regular grid DEM microlandform classification method, including low automation and incomplete classification results, a support vector machine (SVM) classifier was designed for grid DEM microlandform classification, and an automatic grid-based DEM microlandform classification method based on the SVM method was created. The experiment applies the SVM-based grid DEM microlandform classification method to identify different hill positions, namely, the summit, shoulder, back-slope, foot-slope, toe-slope, and alluvium. The results show that this method is most efficient in identifying the toe-slope, with an accuracy rate of 99.60%, and least efficient in identifying the foot-slope, with an accuracy rate of 98.18%. The kappa coefficient and model evaluation index F1-score verify that the method and model are reliable when applied to grid DEM microlandform classification problems.

Formalization of task of movement in longitudinal-transverse plane of tele-controlled underwater vehicles

В статье рассматривается модель движения телеуправляемого необитаемого подводного аппарата в продольной и поперечной плоскостях. Движение телеуправляемого аппарата в маршевом режиме или режимах компенсации перемещений рабочих инструментов достигается комбинацией упоров движителей. Новизна полученных результатов состоит в получении наборов компенсирующих коэффициентов в трёхмерной задаче интерполяции на регулярной сетке. Решение задачи – это частное решение системы дифференциальных уравнений, описывающих динамику телеуправляемого необитаемого аппарата с учётом изменения угла атаки, скольжения и скоростного крена в условиях наиболее распространённого типа движения телеуправляемого необитаемого аппарата. Перекосы в системе управления движителями вызваны неточностями установки в плане прямоугольной платформы с уравновешивающими блоками плавучести движителей, погрешностями изготовления элементов движительно-рулевого комплекса. Динамика движения рассматривается как статистическая задача с усреднением и линеаризацией характеристик упоров движителей, размещённых в плане платформы нулевой плавучести в продольной плоскости. Компенсация перекосов упоров в движительно-рулевом комплексе достигается вычислением коэффициентов компенсации в системе управления по статистикам, полученным в испытательном бассейне методом наименьших квадратов. Скомпенсированная система управления соответствует линейной модели управления телеуправляемого необитаемого аппарата. The article illustrates model of motion of a tele-controlled uninhabited underwater vehicle in longitudinal and transverse planes is considered. Motion of ROV in marching mode or modes of compensation of movements of working tools is achieved by combination of thrusts of propellers. The novelty of the results obtained consists in obtaining sets of compensating coefficients in the three-dimensional interpolation problem on a regular grid. The solution of the problem is a partial solution of a system of differential equations describing the dynamics of a tele-controlled uninhabited apparatus, taking into account changes in the angle of attack, sliding and speed roll in the conditions of the most common type of movement of a tele-controlled uninhabited apparatus. Distortions in the propulsion control system are caused by inaccuracies in the installation in plan of a rectangular platform with balancing units of buoyancy of propulsors, errors in the manufacture of elements of the propulsion-steering system. Motion dynamics is considered as a statistical problem with averaging and linearization of the characteristics of the thrusters of the movers located in terms of the zero buoyancy platforms in the longitudinal plane. Compensation of thrust distortions in the propulsion-steering system is achieved by calculation of compensation coefficients in the control system according to statistics obtained in the test basin using the least squares method. The compensated control system corresponds to a linear control model of a tele-controlled uninhabited apparatus.

Inverses of Matérn Covariances on Grids

We conduct a study of the aliased spectral densities of Matérn covariance functions on a regular grid of points, providing clarity on the properties of a popular approximation based on stochastic partial differential equations. While others have shown that it can approximate the covariance function well, we find that it assigns too much power at high frequencies and does not provide increasingly accurate approximations to the inverse as the grid spacing goes to zero, except in the one-dimensional exponential covariance case.