Symmetric quadratic tetration interpolation using forward and backward operation combination

The existed interpolation method, based on the second-order tetration polynomial, has the asymmetric property. The interpolation results, for each considering region, give individual characteristics. Although the interpolation performance has been better than the conventional methods, the symmetric property for signal interpolation is also necessary. In this paper, we propose the symmetric interpolation formulas derived from the second-order tetration polynomial. The combination of the forward and backward operations was employed to construct two types of the symmetric interpolation. Several resolutions of the fundamental signals were used to evaluate the signal reconstruction performance. The results show that the proposed interpolations can be used to reconstruct the fundamental signal and its peak signal to noise ratio (PSNR) is superior to the conventional interpolation methods, except the cubic spline interpolation for the sine wave signal. However, the visual results show that it has a small difference. Moreover, our proposed interpolations converge to the steady-state faster than the cubic spline interpolation. In addition, the option number increasing will reinforce their sensitivity.

Spatio-Temporal Modeling of Ozone Distribution in Tehran, Iran Based on Neural Network and Geographical Information System

Background: Air pollution is one of the most important causes of respiratory diseases that people face in big cities today. Suspended particulates, carbon monoxide, sulfur dioxide, ozone, and nitrogen dioxide are the five major pollutants of air that pose many problems to human health. We aimed to provide an approach for modeling and analyzing the spatiotemporal model of ozone distribution based on Geographical Information System (GIS). Methods: In the first step, by considering the accuracy of different interpolation methods, the Inverse distance weighted (IDW) method was selected as the best interpolation method for mapping the concentration of ozone in Tehran, Iran. In the next step, according to the daily data of Ozone pollutants, the daily, monthly, and annual mean concentrations maps were prepared for the years 2015, 2016, and 2017. Results: Spatial and temporal analysis of the distribution of ozone pollutants in Tehran was performed. The highest concentrations of O3 are found in the southwest and parts of the central part of the city. Finally, a neural network was developed to predict the amount of ozone pollutants according to meteorological parameters. Conclusion: The results show that meteorological parameters such as temperature, velocity and direction of the wind, and precipitation are influential on O3 concentration.

Fast Barycentric-Based Evaluation Over Spectral/hp Elements

As the use of spectral/hp element methods, and high-order finite element methods in general, continues to spread, community efforts to create efficient, optimized algorithms associated with fundamental high-order operations have grown. Core tasks such as solution expansion evaluation at quadrature points, stiffness and mass matrix generation, and matrix assembly have received tremendous attention. With the expansion of the types of problems to which high-order methods are applied, and correspondingly the growth in types of numerical tasks accomplished through high-order methods, the number and types of these core operations broaden. This work focuses on solution expansion evaluation at arbitrary points within an element. This operation is core to many postprocessing applications such as evaluation of streamlines and pathlines, as well as to field projection techniques such as mortaring. We expand barycentric interpolation techniques developed on an interval to 2D (triangles and quadrilaterals) and 3D (tetrahedra, prisms, pyramids, and hexahedra) spectral/hp element methods. We provide efficient algorithms for their implementations, and demonstrate their effectiveness using the spectral/hp element library Nektar++ by running a series of baseline evaluations against the ‘standard’ Lagrangian method, where an interpolation matrix is generated and matrix-multiplication applied to evaluate a point at a given location. We present results from a rigorous series of benchmarking tests for a variety of element shapes, polynomial orders and dimensions. We show that when the point of interest is to be repeatedly evaluated, the barycentric method performs at worst $$50\%$$ 50 % slower, when compared to a cached matrix evaluation. However, when the point of interest changes repeatedly so that the interpolation matrix must be regenerated in the ‘standard’ approach, the barycentric method yields far greater performance, with a minimum speedup factor of $$7\times $$ 7 × . Furthermore, when derivatives of the solution evaluation are also required, the barycentric method in general slightly outperforms the cached interpolation matrix method across all elements and orders, with an up to $$30\%$$ 30 % speedup. Finally we investigate a real-world example of scalar transport using a non-conformal discontinuous Galerkin simulation, in which we observe around $$6\times $$ 6 × speedup in computational time for the barycentric method compared to the matrix-based approach. We also explore the complexity of both interpolation methods and show that the barycentric interpolation method requires $${\mathcal {O}}(k)$$ O ( k ) storage compared to a best case space complexity of $${\mathcal {O}}(k^2)$$ O ( k 2 ) for the Lagrangian interpolation matrix method.

Optimal Operation of a Microgrid with Hydrogen Storage Based on Deep Reinforcement Learning

Microgrid with hydrogen storage is an effective way to integrate renewable energy and reduce carbon emissions. This paper proposes an optimal operation method for a microgrid with hydrogen storage. The electrolyzer efficiency characteristic model is established based on the linear interpolation method. The optimal operation model of microgrid is incorporated with the electrolyzer efficiency characteristic model. The sequential decision-making problem of the optimal operation of microgrid is solved by a deep deterministic policy gradient algorithm. Simulation results show that the proposed method can reduce about 5% of the operation cost of the microgrid compared with traditional algorithms and has a certain generalization capability.

Generalized Empirical Interpolation Method With H1 Regularization: Application to Nuclear Reactor Physics

The generalized empirical interpolation method (GEIM) can be used to estimate the physical field by combining observation data acquired from the physical system itself and a reduced model of the underlying physical system. In presence of observation noise, the estimation error of the GEIM is blurred even diverged. We propose to address this issue by imposing a smooth constraint, namely, to constrain the H1 semi-norm of the reconstructed field of the reduced model. The efficiency of the approach, which we will call the H1 regularization GEIM (R-GEIM), is illustrated by numerical experiments of a typical IAEA benchmark problem in nuclear reactor physics. A theoretical analysis of the proposed R-GEIM will be presented in future works.

Air Quality Measurement Using an IoT Network: a Case Study

Context: The evaluation of air quality in Colombia is localized; it does not go beyond determining whether the level of the polluting gas at a specific point of the monitoring network has exceeded a threshold, according to a norm or standard, in order to trigger an alarm. It is not committed to objectives as important as the real-time identification of the dispersion dynamics of polluting gases in an area, or the prediction of the newly affected population. From this perspective, the presence of polluting gases was evaluated on the university campus of Escuela Colombiana de Ingeniería Julio Garavito, located north of the city of Bogotá, and the affected population was estimated for the month of October, 2019, using the Kriging geostatistical technique. Method: This study is part of the design and construction of an auxiliary mobile station that monitors and reports complementary information (CO and SO2 gases) to that provided by the Guaymaral meteorological station, located in the north of Bogotá. This information is transmitted through an IoT network to a server, where a database is created which stores the information on polluting gases reported by the 14 stations of the Bogotá air quality monitoring network, the information sent by the auxiliary station, and the statistical information of the population present on the university campus. Pollutant gas data and population information recorded from October 1st to 31st, 2019, are the input for data analysis using the Kriging interpolation method and predicting the affected population on said campus. Results: There is a particulate matter concentration of 29 µg/m3 of PM10 in the coliseum and 12,6 µg/m3 of PM2,5 in building G, in addition to 9,8 ppb of O3 in building I, 14,9 ppb of NO2 in that same building, 0,79 ppb of CO in building C, and 0,65 ppb of SO2 also in building C, thus allowing to infer, according to the Bogotá air quality index, a favorable air quality for a population of 2.131 people who visited the campus university during the aforementioned period. Conclusions: The correct integration of the data in the web server and their analysis, carried out in the R language, allowed determining the approximate indicators of the polluting factors around Escuela Colombiana de Ingeniería Julio Garavito. Additionally, to determine the affected population, these indicators were correlated with the information on the registered population that entered the campus during the period under study. Based on the results obtained, it was concluded that the air quality on the campus of Escuela Colombiana de Ingeniería Julio Garavito is favorable, and that 2.131 people benefited daily from these conditions.