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Computation
Volume 10
Issue 12
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Computation, Volume 10, Issue 12 (December 2022) – 22 articles

Cover Story (view full-size image): Construction of renewable energy power stations and offshore platforms greatly increases the demand for heavy-duty multitasking turning machines. Evaluations of the structure behaviors are very important at the design phase to ensure the machine tool meets the desired requirements. This study aimed to realize how the turning machine will behave when it carries a larger and long workpiece. The design issue was focused on analyzing structure rigidity against the bending deformation of a workpiece and vibration response characteristics during low-speed cutting via the finite element approach. We believe the results with the technologies involved in this study can help the machine designer to effectively evaluate the characteristics of the machine before prototyping. View this paper
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16 pages, 5907 KiB  
Article
Study of the Sloshing Dynamics in Partially Filled Rectangular Tanks with Submerged Baffles Using VOF and LES Turbulence Methods for Different Impact Angles
by Xavier Vallés Rebollo, Ehsan Sadeghi, Ibuki Kusano and Andrés-Amador García-Granada
Computation 2022, 10(12), 225; https://doi.org/10.3390/computation10120225 - 19 Dec 2022
Cited by 4 | Viewed by 2910
Abstract
This research studies how the angle and dimensions of a single baffle affect the dynamics of a fluid in a closed rectangular tank under an accelerated harmonic vibration in resonance. A half-filled non-deformable rectangular tank with a single centered submerged baffle has been [...] Read more.
This research studies how the angle and dimensions of a single baffle affect the dynamics of a fluid in a closed rectangular tank under an accelerated harmonic vibration in resonance. A half-filled non-deformable rectangular tank with a single centered submerged baffle has been simulated using ANSYS® FLUENT. The study aims to characterize the effect of changing the baffle’s angle; hence, 10 simulations have been performed: without a baffle, 90°, 30°, 60°, 120° and 150°, either maintaining the baffle’s length or the projected height constant. The computational fluid dynamics (CFD) method using volume of fluid (VOF) and large eddy simulation (LES) are used to predict the movement of the fluid in two dimensions, which have been benchmarked against experimental data with excellent agreement. The motion is sinusoidal in the +X direction, with a frequency of oscillation equal to its first vibration mode. The parameters studied have been the free surface elevation, values at three different points and maximum; the center of gravity’s position, velocity, and acceleration; and the forces against the tank’s walls. It has been found that the 90° angle has the most significant damping effect, stabilizing the free-surface elevation, reducing the center of gravity dispersion, and leveling the impacting forces. Smaller angles also tame the sloshing and stabilize it. Full article
(This article belongs to the Special Issue Application of Finite Element Methods)
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Figure 1

Figure 1
<p>Tank schematic for (<b>a</b>) <span class="html-italic">h</span> = 150 mm, <span class="html-italic">L</span> = 500 mm and (<b>b</b>) baffle configuration for fixed <span class="html-italic">H<sub>b</sub></span> = 75 mm and (<b>c</b>) for fixed <span class="html-italic">L<sub>b</sub></span> = 75 mms.</p> Full article ">Figure 2
<p>Free surface elevation along the tank length at <span class="html-italic">t</span> = 3.55 s (3 periods <span class="html-italic">T</span>). The dotted line represents the initial free surface elevation.</p> Full article ">Figure 3
<p>Comparison of the time series of the free surface elevation <span class="html-italic">h</span> at probe 1, probe 2, and probe 3, respectively.</p> Full article ">Figure 4
<p>Free surface elevation at WG1. The solid line represents the simulations where <span class="html-italic">H<sub>b</sub></span> = 75 mm, the dotted line where <span class="html-italic">L<sub>b</sub></span> = 75 mm.</p> Full article ">Figure 5
<p>Free surface elevation at WG3. The solid line represents the simulations where <span class="html-italic">H<sub>b</sub></span> = 75 mm, the dotted line where <span class="html-italic">L<sub>b</sub></span> = 75 mm.</p> Full article ">Figure 6
<p>Maximum free surface elevation through time, that is, the height of the wave through the simulation time.</p> Full article ">Figure 7
<p>Energy dissipation rate.</p> Full article ">Figure 8
<p>X and Y scattered plot for each angle. Left column for fixed <span class="html-italic">H<sub>b</sub></span> = 75 mm (<b>a</b>) CG position, (<b>b</b>) velocity and (<b>c</b>) acceleration and right column for fixed <span class="html-italic">L<sub>b</sub></span> = 75 mm (<b>d</b>) CG position, (<b>e</b>) velocity and (<b>f</b>) acceleration.</p> Full article ">Figure 8 Cont.
<p>X and Y scattered plot for each angle. Left column for fixed <span class="html-italic">H<sub>b</sub></span> = 75 mm (<b>a</b>) CG position, (<b>b</b>) velocity and (<b>c</b>) acceleration and right column for fixed <span class="html-italic">L<sub>b</sub></span> = 75 mm (<b>d</b>) CG position, (<b>e</b>) velocity and (<b>f</b>) acceleration.</p> Full article ">Figure 9
<p>Kernel density distribution. Left column for fixed <span class="html-italic">H<sub>b</sub></span> = 75 mm (<b>a</b>) CG position, (<b>b</b>) velocity and (<b>c</b>) acceleration in X direction and right column for fixed <span class="html-italic">L<sub>b</sub></span> = 75 mm (<b>d</b>) CG position, (<b>e</b>) velocity and (<b>f</b>) acceleration in Y direction.</p> Full article ">Figure 9 Cont.
<p>Kernel density distribution. Left column for fixed <span class="html-italic">H<sub>b</sub></span> = 75 mm (<b>a</b>) CG position, (<b>b</b>) velocity and (<b>c</b>) acceleration in X direction and right column for fixed <span class="html-italic">L<sub>b</sub></span> = 75 mm (<b>d</b>) CG position, (<b>e</b>) velocity and (<b>f</b>) acceleration in Y direction.</p> Full article ">Figure 9 Cont.
<p>Kernel density distribution. Left column for fixed <span class="html-italic">H<sub>b</sub></span> = 75 mm (<b>a</b>) CG position, (<b>b</b>) velocity and (<b>c</b>) acceleration in X direction and right column for fixed <span class="html-italic">L<sub>b</sub></span> = 75 mm (<b>d</b>) CG position, (<b>e</b>) velocity and (<b>f</b>) acceleration in Y direction.</p> Full article ">Figure 10
<p>Forces for left column for fixed <span class="html-italic">H<sub>b</sub></span> = 75 mm for (<b>a</b>) left wall, (<b>b</b>) right wall and right column for fixed <span class="html-italic">L<sub>b</sub></span> = 75 mm for (<b>c</b>) left wall, (<b>d</b>) right wall.</p> Full article ">
16 pages, 5864 KiB  
Article
Statistical Theory of Optimal Stochastic Signals Processing in Multichannel Aerospace Imaging Radar Systems
by Valeriy Volosyuk and Semen Zhyla
Computation 2022, 10(12), 224; https://doi.org/10.3390/computation10120224 - 18 Dec 2022
Cited by 1 | Viewed by 1845
Abstract
The work is devoted to solving current scientific and applied problems of the development of radar imaging methods. These developments are based on statistical theory of optimal signal processing. These developments allow researchers to create coherent high-resolution information-enriched images as well as incoherent [...] Read more.
The work is devoted to solving current scientific and applied problems of the development of radar imaging methods. These developments are based on statistical theory of optimal signal processing. These developments allow researchers to create coherent high-resolution information-enriched images as well as incoherent images. These methods can be practically applied in multichannel aerospace radars through the proposed programs and algorithms. Firstly, the following models of stochastic signals at the output of multichannel registration regions of scattered electro-magnetic fields, internal noise, and observation equations are developed and their statistical characteristics investigated. For the considered models of observation equations, the likelihood functional is defined. This definition is an important stage in optimizing spatial and temporal signal processing. These signals are distorted by internal receiver noises in radar systems. Secondly, by synthesising and analysing methods of measuring a radar cross section, the problem of incoherent imaging by aerospace radars with planar antenna array is solved. Thirdly, the obtained optimal mathematical operations are physically interpreted. The proposed interpretation helps to implement a quasi-optimal algorithm of radar cross section estimation in aerospace radar systems. Finally, to verify the proposed theory, a semi-natural experiment of real radio holograms processing was performed. These radio holograms are digital recordings of spatial and temporal signals by an airborne synthetic aperture radar (SAR) system. The results of the semi-natural experiment are presented and analysed in the paper. All the calculations, developments and results in this paper can be applied to new developments in areas such as remote sensing or non-destructive testing. Full article
(This article belongs to the Special Issue Integrated Computer Technologies in Mechanical Engineering – Synergetic Engineering Ⅱ)
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Graphical abstract

Graphical abstract
Full article ">Figure 1
<p>Generalized geometry of surfaces and objects imaging in multichannel aerospace radars.</p> Full article ">Figure 2
<p>Geometry of surface sensing.</p> Full article ">Figure 3
<p>Radar data before processing (“raw” data)—the whole image.</p> Full article ">Figure 4
<p>Part of the digital radio hologram of the mirror point on the surface.</p> Full article ">Figure 5
<p>The radar image recovered by the proposed method.</p> Full article ">Figure 6
<p>The result of the radar imaging: (<b>a</b>,<b>c</b>)—parts of the image obtained by the classical method; (<b>b</b>,<b>d</b>)—more informative image obtained in accordance with the new method of signal processing.</p> Full article ">Figure 6 Cont.
<p>The result of the radar imaging: (<b>a</b>,<b>c</b>)—parts of the image obtained by the classical method; (<b>b</b>,<b>d</b>)—more informative image obtained in accordance with the new method of signal processing.</p> Full article ">
20 pages, 974 KiB  
Article
A Comparison between Task Distribution Strategies for Load Balancing Using a Multiagent System
by Dumitru-Daniel Vecliuc, Florin Leon and Doina Logofătu
Computation 2022, 10(12), 223; https://doi.org/10.3390/computation10120223 - 17 Dec 2022
Cited by 2 | Viewed by 1912
Abstract
This work presents a comparison between several task distribution methods for load balancing with the help of an original implementation of a solution based on a multi-agent system. Among the original contributions, one can mention the design and implementation of the agent-based solution [...] Read more.
This work presents a comparison between several task distribution methods for load balancing with the help of an original implementation of a solution based on a multi-agent system. Among the original contributions, one can mention the design and implementation of the agent-based solution and the proposal of various scenarios, strategies and metrics that are further analyzed in the experimental case studies. The best strategy depends on the context. When the objective is to use the processors at their highest processing potential, the agents preferences strategy produces the best usage of the processing resources with an aggregated load per turn for all PAs up to four times higher than the rest of the strategies. When one needs to have a balance between the loads of the processing elements, the maximum availability strategy is better than the rest of the examined strategies, producing the lowest imbalance rate between PAs out of all the strategies in most scenarios. The random distribution strategy produces the lowest average load especially for tasks with higher required processing time, and thus, it should generally be avoided. Full article
(This article belongs to the Special Issue Advanced Information, Computation, and Control Systems for Distributed Environments)
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Figure 1

Figure 1
<p>The main agents of the system.</p> Full article ">Figure 2
<p>The states of the dispatcher agent.</p> Full article ">Figure 3
<p>Communication diagram of dispatcher and processor agents.</p> Full article ">Figure 4
<p>Applied Round Robin example.</p> Full article ">Figure 4 Cont.
<p>Applied Round Robin example.</p> Full article ">Figure 5
<p>The first step of the agents preferences distribution strategy.</p> Full article ">Figure 6
<p>The second step of the agents preferences distribution strategy.</p> Full article ">Figure 7
<p>Average load per turn analysis based on average resources required, average task required processing time and distribution strategy.</p> Full article ">
14 pages, 3005 KiB  
Article
Principles of Building Digital Twins to Design Integrated Energy Systems
by Valery Stennikov, Evgeny Barakhtenko, Dmitry Sokolov and Gleb Mayorov
Computation 2022, 10(12), 222; https://doi.org/10.3390/computation10120222 - 16 Dec 2022
Cited by 8 | Viewed by 2396
Abstract
The design of integrated energy systems (IESs) is a challenging task by reason of the highly complex configurations of these systems, the wide range of equipment used, and a diverse set of mathematical models and dedicated software employed to model it. The use [...] Read more.
The design of integrated energy systems (IESs) is a challenging task by reason of the highly complex configurations of these systems, the wide range of equipment used, and a diverse set of mathematical models and dedicated software employed to model it. The use of digital twins allows modeling in virtual space for various IES configurations. As a result, an optimal option of IES is obtained, which is implemented in the construction or expansion of a real-world IES. The paper proposes the principles of building digital twins for solving the IES design problems. The paper presents a new methodological approach developed by the authors to design an IES with the help of its digital twin. This approach includes the following components: the architecture of the software platform to create digital twins, a set of technologies and tools to implement the platform, methods to automatically construct a digital twin based on the Model-Driven Engineering concept, an algorithm to design an IES based on its digital twin, and principles to organize a computational process using a multi-agent approach. The results of the computational experiment using the software implementation of the IES digital twin components are presented for a test energy supply scheme. Full article
(This article belongs to the Special Issue Advanced Information, Computation, and Control Systems for Distributed Environments)
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Figure 1
<p>Designing an integrated energy system based on its digital twin.</p> Full article ">Figure 2
<p>The architecture of the software platform for creating IES digital twins.</p> Full article ">Figure 3
<p>Diagram of the algorithm for solving the problem of IES design based on its digital twin.</p> Full article ">Figure 4
<p>The structure of a multi-agent system for solving the development problem.</p> Full article ">Figure 5
<p>The scheme of the modelled integrated energy system.</p> Full article ">Figure 6
<p>Results of the integrated energy system calculation.</p> Full article ">Figure 7
<p>The energy costs for prosumers.</p> Full article ">
13 pages, 8585 KiB  
Article
Development of Raspberry Pi 4 B and 3 B+ Micro-Kubernetes Cluster and IoT System for Mosquito Research Applications
by Zhihao Pan, Byul Hur, Kevin Myles and Zach Adelman
Computation 2022, 10(12), 221; https://doi.org/10.3390/computation10120221 - 16 Dec 2022
Cited by 2 | Viewed by 2830
Abstract
Detecting infected female mosquitoes can be vital when they transmit harmful diseases such as dengue, malaria, and others. Infected mosquitoes can lay hundreds of eggs in breeding locations, and newborns can transmit diseases to more victims. Hence, gathering and monitoring climate data and [...] Read more.
Detecting infected female mosquitoes can be vital when they transmit harmful diseases such as dengue, malaria, and others. Infected mosquitoes can lay hundreds of eggs in breeding locations, and newborns can transmit diseases to more victims. Hence, gathering and monitoring climate data and environmental conditions for mosquito research can be valuable in preventing mosquitoes from spreading diseases. To obtain microclimate data, users such as mosquito researchers may need weather stations in various locations and an inexpensive, effective IoT system for monitoring multiple specific locations. We can achieve this in each location by sending microclimate data from wireless sensor end-node devices to a nearby middle-node aggregator. Each location’s aggregator can send the data to a cluster, such as a customized Raspberry Pi-based cluster with Micro-Kubernetes as its distributed operating system. The applications, such as the database and web server, can be wrapped up by docker containers and deployed as containerized applications on the cluster. This cluster can store the data, available to be accessed via Android and web applications. The results of this work show that the measurement data of the specific locations are more accurate than those from nearby third-party weather stations. This proposed IoT cluster system in this paper can be used to provide accurate microclimate data for the selected locations. Full article
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Figure 1
<p>IoT system for mosquito research applications [<a href="#B14-computation-10-00221" class="html-bibr">14</a>,<a href="#B15-computation-10-00221" class="html-bibr">15</a>].</p> Full article ">Figure 2
<p>The MicroK8s architecture for the distributed system in this study [<a href="#B24-computation-10-00221" class="html-bibr">24</a>,<a href="#B25-computation-10-00221" class="html-bibr">25</a>].</p> Full article ">Figure 3
<p>The RPi MicroK8s cluster. (<b>a</b>) Front view of the cluster. (<b>b</b>) Top view of the cluster.</p> Full article ">Figure 4
<p>Remote data station, which is an aggregator between the cluster and the end-nodes.</p> Full article ">Figure 5
<p>Flowchart showing the sub-process of microclimate data transferring from a remote data station to the database.</p> Full article ">Figure 6
<p>Various data from the device ID 101 database.</p> Full article ">Figure 7
<p>Flowchart showing the data access via Android application and web browser using the Flask API.</p> Full article ">Figure 8
<p>Data access over the website.</p> Full article ">Figure 9
<p>Data access over the Android application.</p> Full article ">Figure 10
<p>Data measured on 28 August 2022 using remote data stations and the data from Weather Underground for comparison. Graphs (<b>a</b>–<b>c</b>) are the set for the test spot in College Station. And graphs (<b>d</b>–<b>f</b>) are the set for the test spot in Houston.</p> Full article ">
7 pages, 252 KiB  
Article
Characteristic Sequence of Strongly Minimal Directed Single Graphs of 1-Arity
by Abeer M. Albalahi
Computation 2022, 10(12), 220; https://doi.org/10.3390/computation10120220 - 15 Dec 2022
Viewed by 1300
Abstract
In this paper, we will classify the strongly minimal directed single graphs of 1-arity by axiomatizing the theory of characteristic sequence of such a graph. Then we will show this theory is complete by using Łos-Vaught test. Complete theory is important to capture [...] Read more.
In this paper, we will classify the strongly minimal directed single graphs of 1-arity by axiomatizing the theory of characteristic sequence of such a graph. Then we will show this theory is complete by using Łos-Vaught test. Complete theory is important to capture all the models of the theory and hence can be applied on mathematical structures which meet such a theory. The theory of algebraically closed fields with a given characteristic is complete. Thus, in this paper we will classify the strongly minimal directed single graphs of 1-arity with given characteristic sequence which can be applied on many mathematical structures not only algebraically closed fields. Full article
(This article belongs to the Special Issue Graph Theory and Its Applications in Computing)
12 pages, 756 KiB  
Article
Fundamental Results of Cyclic Codes over Octonion Integers and Their Decoding Algorithm
by Muhammad Sajjad, Tariq Shah, Robinson-Julian Serna, Zagalo Enrique Suárez Aguilar and Omaida Sepúlveda Delgado
Computation 2022, 10(12), 219; https://doi.org/10.3390/computation10120219 - 14 Dec 2022
Cited by 6 | Viewed by 1582
Abstract
Coding theory is the study of the properties of codes and their respective fitness for specific applications. Codes are used for data compression, cryptography, error detection, error correction, data transmission, and data storage. Codes are studied by various scientific disciplines, such as information [...] Read more.
Coding theory is the study of the properties of codes and their respective fitness for specific applications. Codes are used for data compression, cryptography, error detection, error correction, data transmission, and data storage. Codes are studied by various scientific disciplines, such as information theory, electrical engineering, mathematics, linguistics, and computer science, to design efficient and reliable data transmission methods. Many authors in the previous literature have discussed codes over finite fields, Gaussian integers, quaternion integers, etc. In this article, the author defines octonion integers, fundamental theorems related to octonion integers, encoding, and decoding of cyclic codes over the residue class of octonion integers with respect to the octonion Mannheim weight one. The comparison of primes, lengths, cardinality, dimension, and code rate with respect to Quaternion Integers and Octonion Integers will be discussed. Full article
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Figure 1

Figure 1
<p>Quaternion Primes vs. Octonion Primes.</p> Full article ">Figure 2
<p>Quaternion integers Code rate vs. Octonion integers Code rate.</p> Full article ">
15 pages, 6349 KiB  
Article
Functional Parametric Elasto-Dynamics for Efficient Multicomponent Design
by Jiajun Wu, Chady Ghnatios, Philippe Mordillat, Yves Tourbier and Francisco Chinesta
Computation 2022, 10(12), 218; https://doi.org/10.3390/computation10120218 - 13 Dec 2022
Cited by 2 | Viewed by 1371
Abstract
In industrial settings, engineering products are often divided into separate components for detailed conception. They often require iterative corrections between different designers/teams to optimize the final product with all components assembled into a system. This article proposes a surrogate modeling approach with functional [...] Read more.
In industrial settings, engineering products are often divided into separate components for detailed conception. They often require iterative corrections between different designers/teams to optimize the final product with all components assembled into a system. This article proposes a surrogate modeling approach with functional descriptions of parts in the model and aims to accelerate the design and optimization phase in real projects. The approach is applied to a vibration problem of a two-component plate structure, where the model estimates the dynamic behavior of the assembled system when only the properties of each individual part are available. A database is built using high-fidelity numerical simulations, and neural-network-based regressions provide reliable predictions on unseen data. Full article
(This article belongs to the Section Computational Engineering)
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Figure 1
<p>Sketch of the two-component plate model. Red cross indicates the output node location.</p> Full article ">Figure 2
<p>Eigenfrequencies of individual parts of configuration <math display="inline"><semantics> <mrow> <msup> <mi>μ</mi> <msub> <mi>P</mi> <mn>1</mn> </msub> </msup> <mo>=</mo> <msup> <mi>μ</mi> <msub> <mi>P</mi> <mn>2</mn> </msub> </msup> <mo>=</mo> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>3</mn> </mrow> </msup> </mrow> </semantics></math> in DOE, with demonstration of mode shapes. (<b>Left</b>): first 8 modes for part <math display="inline"><semantics> <msub> <mi>P</mi> <mn>1</mn> </msub> </semantics></math>. (<b>Right</b>): first 9 modes for part <math display="inline"><semantics> <msub> <mi>P</mi> <mn>2</mn> </msub> </semantics></math>. The amplitude of mode shapes are normalized independently for each mode to the range of [−1, 1].</p> Full article ">Figure 3
<p>Histogram depicting the distribution of the first 11 eigenfrequencies of the system. For all 100 configurations, the first eigenfrequency <math display="inline"><semantics> <msubsup> <mi>ω</mi> <mn>1</mn> <mrow> <msub> <mi>P</mi> <mn>1</mn> </msub> <mo>+</mo> <msub> <mi>P</mi> <mn>2</mn> </msub> </mrow> </msubsup> </semantics></math> presents a narrow distribution between 5 and 8 Hz. For modes of higher order, curves cover a wider range, meaning that variations between configurations are huge.</p> Full article ">Figure 4
<p>Overview of <span class="html-italic">z</span>-component displacement amplitude profiles, with visible variations among all 100 configurations in database. Each curve here represents for one configuration.</p> Full article ">Figure 5
<p>Distribution in parametric space of training and testing sets for model <math display="inline"><semantics> <msub> <mi mathvariant="script">H</mi> <mn>1</mn> </msub> </semantics></math>.</p> Full article ">Figure 6
<p>Graphical diagram of neural network structure for model <math display="inline"><semantics> <msub> <mi mathvariant="script">H</mi> <mn>1</mn> </msub> </semantics></math>.</p> Full article ">Figure 7
<p>Convergence curve of network training.</p> Full article ">Figure 8
<p>Comparison of predicted and original values of system eigenfrequencies for the training set.</p> Full article ">Figure 9
<p>Results of surrogate model <math display="inline"><semantics> <msub> <mi mathvariant="script">H</mi> <mn>1</mn> </msub> </semantics></math> for testing set. (<b>a</b>) Comparison of predicted and original values of system eigenfrequencies. (<b>b</b>) Comparison for sample <math display="inline"><semantics> <mrow> <msup> <mi>μ</mi> <msub> <mi>P</mi> <mn>1</mn> </msub> </msup> <mo>=</mo> <mn>2.4</mn> </mrow> </semantics></math> mm, <math display="inline"><semantics> <mrow> <msup> <mi>μ</mi> <msub> <mi>P</mi> <mn>2</mn> </msub> </msup> <mo>=</mo> <mn>2.5</mn> </mrow> </semantics></math> mm in DOE with minimum MAPE <math display="inline"><semantics> <mrow> <mo>=</mo> <mn>0.347</mn> <mo>%</mo> </mrow> </semantics></math>. (<b>c</b>) Comparison for sample <math display="inline"><semantics> <mrow> <msup> <mi>μ</mi> <msub> <mi>P</mi> <mn>1</mn> </msub> </msup> <mo>=</mo> <mn>2.4</mn> </mrow> </semantics></math> mm, <math display="inline"><semantics> <mrow> <msup> <mi>μ</mi> <msub> <mi>P</mi> <mn>2</mn> </msub> </msup> <mo>=</mo> <mn>1.2</mn> </mrow> </semantics></math> mm in DOE with maximum MAPE <math display="inline"><semantics> <mrow> <mo>=</mo> <mn>2.378</mn> <mo>%</mo> </mrow> </semantics></math>.</p> Full article ">Figure 10
<p>Sample distribution in parametric space of training and testing sets for model <math display="inline"><semantics> <msub> <mi mathvariant="script">H</mi> <mn>2</mn> </msub> </semantics></math>.</p> Full article ">Figure 11
<p>Results of surrogate model <math display="inline"><semantics> <msub> <mi mathvariant="script">H</mi> <mn>2</mn> </msub> </semantics></math>. (<b>a</b>) Comparison of predicted and original values for training set. (<b>b</b>) Comparison of predicted and original values for testing set. (<b>c</b>) Comparison for sample <math display="inline"><semantics> <mrow> <msup> <mi>μ</mi> <msub> <mi>P</mi> <mn>1</mn> </msub> </msup> <mo>=</mo> <msup> <mi>μ</mi> <msub> <mi>P</mi> <mn>2</mn> </msub> </msup> <mo>=</mo> <mn>2.2</mn> </mrow> </semantics></math> mm in DOE with minimum <math display="inline"><semantics> <mrow> <mi>ϵ</mi> <mo>=</mo> <mn>0.031</mn> <mo>%</mo> </mrow> </semantics></math>. (<b>d</b>) Comparison for sample <math display="inline"><semantics> <mrow> <msup> <mi>μ</mi> <msub> <mi>P</mi> <mn>1</mn> </msub> </msup> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math> mm, <math display="inline"><semantics> <mrow> <msup> <mi>μ</mi> <msub> <mi>P</mi> <mn>2</mn> </msub> </msup> <mo>=</mo> <mn>1.6</mn> </mrow> </semantics></math> mm in DOE with maximum <math display="inline"><semantics> <mrow> <mi>ϵ</mi> <mo>=</mo> <mn>1.333</mn> <mo>%</mo> </mrow> </semantics></math>.</p> Full article ">Figure 12
<p>Sample distribution in parametric space of training and testing sets for model <math display="inline"><semantics> <msub> <mi mathvariant="script">H</mi> <mn>3</mn> </msub> </semantics></math>.</p> Full article ">Figure 13
<p>Results of surrogate model <math display="inline"><semantics> <msub> <mi mathvariant="script">H</mi> <mn>3</mn> </msub> </semantics></math> for 20 samples in the testing set. Thickness values in subfigure titles are expressed in mm.</p> Full article ">Figure 14
<p>Graphical diagram of connected neural network structure for model <math display="inline"><semantics> <msubsup> <mi mathvariant="script">H</mi> <mn>3</mn> <mi>I</mi> </msubsup> </semantics></math>.</p> Full article ">Figure 15
<p>Comparison of prediction accuracy between models <math display="inline"><semantics> <msub> <mi mathvariant="script">H</mi> <mn>3</mn> </msub> </semantics></math> and <math display="inline"><semantics> <msubsup> <mi mathvariant="script">H</mi> <mn>3</mn> <mi>I</mi> </msubsup> </semantics></math> on the testing set.</p> Full article ">Figure 16
<p>Results of surrogate model <math display="inline"><semantics> <msubsup> <mi mathvariant="script">H</mi> <mn>3</mn> <mi>I</mi> </msubsup> </semantics></math> for 20 samples in the testing set. Thickness values in subfigure titles are expressed in mm.</p> Full article ">
10 pages, 241 KiB  
Article
Online Bottleneck Matching Problem with Two Heterogeneous Sensors in a Metric Space
by Man Xiao, Yaru Yang and Weidong Li
Computation 2022, 10(12), 217; https://doi.org/10.3390/computation10120217 - 9 Dec 2022
Cited by 2 | Viewed by 1412
Abstract
In this paper, we consider the online matching problem with two heterogeneous sensors s1 and s2 in a metric space (X,d). If a request r is assigned to sensor s1, the service cost of [...] Read more.
In this paper, we consider the online matching problem with two heterogeneous sensors s1 and s2 in a metric space (X,d). If a request r is assigned to sensor s1, the service cost of r is the distance d(r,s1). Otherwise, r is assigned to sensor s2, and the service cost of r is d(r,s2)w, where w≥1 is the weight of sensor s2. The goal is to minimize the maximum matching cost, we design an optimal online algorithm with a competitive ratio of 1+w+1w for 1≤w≤1.839, and an optimal online algorithm with a competitive ratio of w+1+w2+6w+12 for w>1.839. Full article
(This article belongs to the Special Issue Graph Theory and Its Applications in Computing)
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<p>Two competitive ratios in this paper.</p> Full article ">Figure 2
<p>The locations of sensors and requests.</p> Full article ">Figure 3
<p>The locations of sensors and requests.</p> Full article ">
14 pages, 306 KiB  
Article
Applications of Double ARA Integral Transform
by Rania Saadeh
Computation 2022, 10(12), 216; https://doi.org/10.3390/computation10120216 - 8 Dec 2022
Cited by 17 | Viewed by 1981
Abstract
This paper describes our construction of a new double transform, which we call the double ARA transform (DARAT). Our novel double-integral transform can be used to solve partial differential equations and other problems. We discuss some fundamental characteristics of our approach, including existence, [...] Read more.
This paper describes our construction of a new double transform, which we call the double ARA transform (DARAT). Our novel double-integral transform can be used to solve partial differential equations and other problems. We discuss some fundamental characteristics of our approach, including existence, linearity, and several findings relating to partial derivatives and the double convolution theorem. DARAT can be used to precisely solve a variety of partial differential equations, including the heat equation, wave equation, telegraph equation, Klein–Gordon equation, and others, all of which are crucial for physical applications. Herein, we use DARAT to solve model integral equations to obtain exact solutions. We conclude that our novel method is easier to use than comparable transforms. Full article
(This article belongs to the Topic Mathematical Modeling)
15 pages, 4444 KiB  
Article
Parallelization of Runge–Kutta Methods for Hardware Implementation
by Petr Fedoseev, Konstantin Zhukov, Dmitry Kaplun, Nikita Vybornov and Valery Andreev
Computation 2022, 10(12), 215; https://doi.org/10.3390/computation10120215 - 7 Dec 2022
Viewed by 2365
Abstract
Parallel numerical integration is a valuable tool used in many applications requiring high-performance numerical solvers, which is of great interest nowadays due to the increasing difficulty and complexity in differential problems. One of the possible approaches to increase the efficiency of ODE solvers [...] Read more.
Parallel numerical integration is a valuable tool used in many applications requiring high-performance numerical solvers, which is of great interest nowadays due to the increasing difficulty and complexity in differential problems. One of the possible approaches to increase the efficiency of ODE solvers is to parallelize recurrent numerical methods, making them more suitable for execution in hardware with natural parallelism, e.g., field-programmable gate arrays (FPGAs) or graphical processing units (GPUs). Some of the simplest and most popular ODE solvers are explicit Runge–Kutta methods. Despite the high implementability and overall simplicity of the Runge–Kutta schemes, recurrent algorithms remain weakly suitable for execution in parallel computers. In this paper, we propose an approach for parallelizing classical explicit Runge–Kutta methods to construct efficient ODE solvers with pipeline architecture. A novel technique to obtain parallel finite-difference models based on Runge–Kutta integration is described. Three test initial value problems are considered to evaluate the properties of the obtained solvers. It is shown that the truncation error of the parallelized Runge–Kutta method does not significantly change after its known recurrent version. A possible speed up in calculations is estimated using Amdahl’s law and is approximately 2.5–3-times. Block diagrams of fixed-point parallel ODE solvers suitable for hardware implementation on FPGA are given. Full article
(This article belongs to the Special Issue Mathematical Modeling and Study of Nonlinear Dynamic Processes)
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<p>Streaming algorithm graph.</p> Full article ">Figure 2
<p>Operations in typical computer with von Neumann architecture.</p> Full article ">Figure 3
<p>Scheme representing a parallel computing process.</p> Full article ">Figure 4
<p>The use of parallel processors in relation to pipeline strategy.</p> Full article ">Figure 5
<p>The proposed multi-pipeline computational structure.</p> Full article ">Figure 6
<p>Absolute truncation error plots given relatively to the analytical solution for classical serial Runge–Kutta method and proposed parallel scheme (<b>a</b>). Difference between the truncation errors of parallel and serial solvers (<b>b</b>). Simulation time 5 s, step value 0.001 s.</p> Full article ">Figure 7
<p>Absolute truncation error plots given relatively to the analytical solution for recurrent Runge–Kutta method and proposed parallel scheme (<b>a</b>). Difference between the truncation errors for parallel and serial solvers (<b>b</b>). Simulation time 100 s, step size value 0.001 s.</p> Full article ">Figure 8
<p>Absolute truncation error plots given relatively to the analytical solution for the recurrent Runge–Kutta method and proposed parallel scheme (<b>a</b>). Difference between the truncation errors for parallel and serial solvers (<b>b</b>). Simulation time 5 s, step size value 0.001 s.</p> Full article ">Figure A1
<p>Graphical code for software ODE solver with parallel 5-processor computational structure for test problem (13). Double-precision floating point data type used.</p> Full article ">Figure A2
<p>Graphical code of hardware FPGA ODE solver with multi-pipeline parallel computational structure for test problem (13). Fixed-Point data type with scaling.</p> Full article ">Figure A3
<p>Graphical code for software ODE solver with parallel 2-processor computational structure for test problem (17). Floating point data type used.</p> Full article ">Figure A4
<p>Graphical code for software ODE solver with multi-pipeline parallel 3-processor computational structure for test problem (19). Floating-point data type used.</p> Full article ">
19 pages, 3385 KiB  
Article
Forecasting the Cumulative COVID-19 Cases in Indonesia Using Flower Pollination Algorithm
by Afiahayati, Yap Bee Wah, Sri Hartati, Yunita Sari, I Nyoman Prayana Trisna, Diyah Utami Kusumaning Putri, Aina Musdholifah and Retantyo Wardoyo
Computation 2022, 10(12), 214; https://doi.org/10.3390/computation10120214 - 7 Dec 2022
Cited by 1 | Viewed by 1931
Abstract
Coronavirus disease 2019 (COVID-19) was declared as a global pandemic by the World Health Organization (WHO) on 12 March 2020. Indonesia is reported to have the highest number of cases in Southeast Asia. Accurate prediction of the number of COVID-19 cases in the [...] Read more.
Coronavirus disease 2019 (COVID-19) was declared as a global pandemic by the World Health Organization (WHO) on 12 March 2020. Indonesia is reported to have the highest number of cases in Southeast Asia. Accurate prediction of the number of COVID-19 cases in the upcoming few days is required as one of the considerations in making decisions to provide appropriate recommendations in the process of mitigating global pandemic infectious diseases. In this research, a metaheuristics optimization algorithm, the flower pollination algorithm, is used to forecast the cumulative confirmed COVID-19 cases in Indonesia. The flower pollination algorithm is a robust and adaptive method to perform optimization for curve fitting of COVID-19 cases. The performance of the flower pollination algorithm was evaluated and compared with a machine learning method which is popular for forecasting, the recurrent neural network. A comprehensive experiment was carried out to determine the optimal hyperparameters for the flower pollination algorithm and recurrent neural network. There were 24 and 72 combinations of hyperparameters for the flower pollination algorithm and recurrent neural network, respectively. The best hyperparameters were used to develop the COVID-19 forecasting model. Experimental results showed that the flower pollination algorithm performed better than the recurrent neural network in long-term (two weeks) and short-term (one week) forecasting of COVID-19 cases. The mean absolute percentage error (MAPE) for the flower pollination algorithm model (0.38%) was much lower than that of the recurrent neural network model (5.31%) in the last iteration for long-term forecasting. Meanwhile, the MAPE for the flower pollination algorithm model (0.74%) is also lower than the recurrent neural network model (4.8%) in the last iteration for short-term forecasting of the cumulative COVID-19 cases in Indonesia. This research provides state-of-the-art results to help the process of mitigating the global pandemic of COVID-19 in Indonesia. Full article
(This article belongs to the Special Issue Computation to Fight SARS-CoV-2 (CoVid-19))
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<p>Cumulative confirmed cases of COVID-19 in Indonesia.</p> Full article ">Figure 2
<p>Unfolded recurrent neural network.</p> Full article ">Figure 3
<p>Bar chart of RMSE for long-term forecasting in testing data.</p> Full article ">Figure 4
<p>Bar chart of MAPE for long-term forecasting in testing data.</p> Full article ">Figure 5
<p>Actual and long-term forecasting for cumulative COVID-19 cases using the FPA model.</p> Full article ">Figure 6
<p>Actual and long-term forecasting for cumulative COVID-19 case using the RNN model.</p> Full article ">Figure 7
<p>Bar chart of RMSE for short-term forecasting in testing data.</p> Full article ">Figure 8
<p>Bar chart of MAPE for short-term forecasting in testing data.</p> Full article ">Figure 9
<p>Actual and short-term forecasting for cumulative COVID-19 cases using the FPA model.</p> Full article ">Figure 10
<p>Actual and short-term forecasting for cumulative COVID-19 cases using the RNN model.</p> Full article ">
20 pages, 2783 KiB  
Article
Statistical Theory of Optimal Functionally Deterministic Signals Processing in Multichannel Aerospace Imaging Radar Systems
by Valeriy Volosyuk and Semen Zhyla
Computation 2022, 10(12), 213; https://doi.org/10.3390/computation10120213 - 3 Dec 2022
Cited by 1 | Viewed by 2016
Abstract
The theory of the optimal formation of coherent and incoherent images is developed using the foundations of the statistical theory of optimization of radio engineering information-measuring systems. The main operations necessary for synthesizing optimal methods of spatio-temporal processing of functionally deterministic signals in [...] Read more.
The theory of the optimal formation of coherent and incoherent images is developed using the foundations of the statistical theory of optimization of radio engineering information-measuring systems. The main operations necessary for synthesizing optimal methods of spatio-temporal processing of functionally deterministic signals in on-board radio imaging radars with antenna arrays are shown. Models of radio engineering signals and noise have been developed. The statistical and correlation characteristics of spatio-temporal signals and noises in the area of their observation by antenna systems have been investigated. The technique for estimating the limiting errors of the measured characteristics of the studying media is presented. Using the developed theory, a new method for high-resolution radar imaging of the surface from a wide swath was obtained. This method has a new optimal observation mode combining the advantages of several terrain observation modes and fully complies with modern trends in the creation of cognitive radars with the possibility of restructuring the antenna pattern in space and adaptive receiving of reflected signals. The principles of construction and algorithmic support of high-precision airborne radars with an extended observation area are formulated. The effectiveness of the obtained results is investigated by simulation, taking into account the phenomenological approach to the description of electromagnetic fields and coherent images. Full article
(This article belongs to the Special Issue Integrated Computer Technologies in Mechanical Engineering – Synergetic Engineering Ⅱ)
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Graphical abstract

Graphical abstract
Full article ">Figure 1
<p>Geometry of surface sensing.</p> Full article ">Figure 2
<p>New mode of high resolution and wide-swath surface sensing.</p> Full article ">Figure 3
<p>Altitude profile of the simulation model: (<b>a</b>) the model of the entire observation area, (<b>b</b>) the top projection, (<b>c</b>) the model of the building, (<b>d</b>) the model of the tractor with trailer, (<b>e</b>) the model of tanks, (<b>f</b>) the model of the forest, (<b>g</b>) the model of anti-aircraft missile system, (<b>h</b>) the model aircraft.</p> Full article ">Figure 3 Cont.
<p>Altitude profile of the simulation model: (<b>a</b>) the model of the entire observation area, (<b>b</b>) the top projection, (<b>c</b>) the model of the building, (<b>d</b>) the model of the tractor with trailer, (<b>e</b>) the model of tanks, (<b>f</b>) the model of the forest, (<b>g</b>) the model of anti-aircraft missile system, (<b>h</b>) the model aircraft.</p> Full article ">Figure 4
<p>Characteristics of the test surface: (<b>a</b>) the radar cross section, (<b>b</b>) the real part of the complex scattering coefficient, (<b>c</b>) the top projection of <math display="inline"><semantics> <mrow> <mi mathvariant="normal">Re</mi> <mo>{</mo> <mover accent="true"> <mi mathvariant="normal">F</mi> <mo>˙</mo> </mover> <mo stretchy="false">(</mo> <mi mathvariant="normal">x</mi> <mo>,</mo> <mi mathvariant="normal">y</mi> <mo stretchy="false">)</mo> <mo>}</mo> </mrow> </semantics></math>.</p> Full article ">Figure 5
<p>The optimal output effect of the radar system <math display="inline"><semantics> <mrow> <mo>|</mo> <mover accent="true"> <mi mathvariant="normal">Y</mi> <mo>˙</mo> </mover> <mo stretchy="false">(</mo> <mover accent="true"> <mi mathvariant="normal">r</mi> <mo stretchy="false">→</mo> </mover> <mo stretchy="false">)</mo> <mo>|</mo> </mrow> </semantics></math>: (<b>a</b>) for the uncertainty function with dimensions <math display="inline"><semantics> <mrow> <mn>3</mn> <mo> </mo> <mi mathvariant="normal">m</mi> <mo>×</mo> <mn>3</mn> <mo> </mo> <mi mathvariant="normal">m</mi> </mrow> </semantics></math>, (<b>b</b>) projection of the radar image, when the uncertainty function has dimensions <math display="inline"><semantics> <mrow> <mn>3</mn> <mo> </mo> <mi mathvariant="normal">m</mi> <mo>×</mo> <mn>3</mn> <mo> </mo> <mi mathvariant="normal">m</mi> </mrow> </semantics></math>, (<b>c</b>) for the uncertainty function with dimensions <math display="inline"><semantics> <mrow> <mn>1</mn> <mo> </mo> <mi mathvariant="normal">m</mi> <mo>×</mo> <mn>1</mn> <mo> </mo> <mi mathvariant="normal">m</mi> </mrow> </semantics></math>, (<b>d</b>) projection of the radar image, when the uncertainty function has dimensions <math display="inline"><semantics> <mrow> <mn>1</mn> <mo> </mo> <mi mathvariant="normal">m</mi> <mo>×</mo> <mn>1</mn> <mo> </mo> <mi mathvariant="normal">m</mi> </mrow> </semantics></math>.</p> Full article ">Figure 6
<p>Optimal output effects of the radar system <math display="inline"><semantics> <mrow> <mo>|</mo> <mover accent="true"> <mi mathvariant="normal">Y</mi> <mo>˙</mo> </mover> <mo stretchy="false">(</mo> <mover accent="true"> <mi mathvariant="normal">r</mi> <mo stretchy="false">→</mo> </mover> <mo stretchy="false">)</mo> <mo>|</mo> </mrow> </semantics></math>: (<b>a</b>) true coherent image, (<b>b</b>) radar system with one beam, (<b>c</b>) incoherent addition of processing results from two beams, (<b>d</b>) incoherent addition of processing results from three beams, (<b>d</b>) optimal method of processing received space–time signals.</p> Full article ">
13 pages, 3376 KiB  
Article
Analysis of Methane–Air Mixture Dynamics in a Dead-End Drift Ventilated Using an Exhaust System
by Mikhail Semin and Aleksey Isaevich
Computation 2022, 10(12), 212; https://doi.org/10.3390/computation10120212 - 2 Dec 2022
Cited by 2 | Viewed by 1834
Abstract
The dynamics of methane–air mixtures in a dead-end drift of a potash mine are investigated in this study. Methane release is associated with the destruction of potash ore during mining operations. The studied dead-end drift is ventilated using an exhaust ventilation system in [...] Read more.
The dynamics of methane–air mixtures in a dead-end drift of a potash mine are investigated in this study. Methane release is associated with the destruction of potash ore during mining operations. The studied dead-end drift is ventilated using an exhaust ventilation system in which fresh air is supplied through the drift, and polluted air is removed through a ventilation duct equipped with a fan. The regularities of the stationary distribution of methane in the drift are described using a 3D multiparametric numerical simulation. The size and shape of the methane cloud at the roof of the dead-end drift were analyzed depending on the ratio of the main mass transfer mechanisms in the system: forced convection due to the action of the fan, free convection due to the differing densities of the methane–air mixture, and turbulent diffusion. A criterion linking the Reynolds number, the gas Grashof number, and the length of the accumulated methane cloud is determined. Overall, the results of this study have important implications for developing new effective auxiliary mine ventilation systems that can improve the safety of mining operations. Full article
(This article belongs to the Section Computational Engineering)
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<p>The geometric model.</p> Full article ">Figure 2
<p>Dependence of the maximum concentration on the domain symmetry surface on the number of cells.</p> Full article ">Figure 3
<p>Part of the domain with the computational mesh.</p> Full article ">Figure 4
<p>Distributions of methane concentration in a drift at different rates of methane emission; the red line marks the right boundary of the methane cloud flowing against the main airflow.</p> Full article ">Figure 5
<p>Volume distribution of methane concentrations in a dead-end drift at different methane emission rates.</p> Full article ">Figure 6
<p>Methane concentration profiles along the line <span class="html-italic">Y</span> = 3.95 m for two different methane emission rates: 0.003 m<sup>3</sup>/s (orange curve, <span class="html-italic">E</span><sub>1</sub>) and 0.012 m<sup>3</sup>/s (blue curve, <span class="html-italic">E</span><sub>2</sub>).</p> Full article ">Figure 7
<p>Methane cloud length <span class="html-italic">E</span> as a function of air velocity for four different methane emission intensities; the dots show the numerical solution, the solid lines show the approximating function (20).</p> Full article ">Figure 8
<p>Isolines of the dimensional length <span class="html-italic">E</span> of the methane cloud in the phase plane of dimensionless parameters <span class="html-italic">Re-Gr</span>.</p> Full article ">Figure 9
<p>Dependence of (<b>a</b>) the length <span class="html-italic">E</span> and (<b>b</b>) the maximum methane concentration on the angle of inclination (<span class="html-italic">α</span>) of a dead-end drift.</p> Full article ">
2 pages, 162 KiB  
Correction
Correction: Oluwagbemi et al. Bioinformatics, Computational Informatics, and Modeling Approaches to the Design of mRNA COVID-19 Vaccine Candidates. Computation 2022, 10, 117
by Olugbenga Oluseun Oluwagbemi, Elijah K. Oladipo, Olatunji M. Kolawole, Julius K. Oloke, Temitope I. Adelusi, Boluwatife A. Irewolede, Emmanuel O. Dairo, Ayodele E. Ayeni, Kehinde T. Kolapo, Olawumi E. Akindiya, Jerry A. Oluwasegun, Bamigboye F. Oluwadara and Segun Fatumo
Computation 2022, 10(12), 211; https://doi.org/10.3390/computation10120211 - 2 Dec 2022
Cited by 1 | Viewed by 1304
Abstract
The following information was missing in the original manuscript [...] Full article
16 pages, 1068 KiB  
Article
On Alternative Algorithms for Computing Dynamic Mode Decomposition
by Gyurhan Nedzhibov
Computation 2022, 10(12), 210; https://doi.org/10.3390/computation10120210 - 1 Dec 2022
Cited by 2 | Viewed by 2801
Abstract
Dynamic mode decomposition (DMD) is a data-driven, modal decomposition technique that describes spatiotemporal features of high-dimensional dynamic data. The method is equation-free in the sense that it does not require knowledge of the underlying governing equations. The main purpose of this article is [...] Read more.
Dynamic mode decomposition (DMD) is a data-driven, modal decomposition technique that describes spatiotemporal features of high-dimensional dynamic data. The method is equation-free in the sense that it does not require knowledge of the underlying governing equations. The main purpose of this article is to introduce new alternatives to the currently accepted algorithm for calculating the dynamic mode decomposition. We present two new algorithms which are more economical from a computational point of view, which is an advantage when working with large data. With a few illustrative examples, we demonstrate the applicability of the introduced algorithms. Full article
(This article belongs to the Special Issue Mathematical Modeling and Study of Nonlinear Dynamic Processes)
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<p>Spatiotemporal dynamics of two signals (<b>a</b>) <math display="inline"><semantics> <mrow> <msub> <mi>f</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>, (<b>b</b>) <math display="inline"><semantics> <mrow> <msub> <mi>f</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>, and mixed signal in (<b>c</b>) <math display="inline"><semantics> <mrow> <mi>x</mi> <mo>=</mo> <msub> <mi>f</mi> <mn>1</mn> </msub> <mo>+</mo> <msub> <mi>f</mi> <mn>2</mn> </msub> </mrow> </semantics></math>. Singular values of <span class="html-italic">X</span> are shown in (<b>d</b>).</p> Full article ">Figure 2
<p>Rank−2 reconstructions of the signal <span class="html-italic">X</span> by: standard DMD (<b>a</b>) and Alternative DMD (<b>b</b>).</p> Full article ">Figure 3
<p>Firts two DMD modes: true modes, modes extracted by standard DMD and modes extracted by Alternative DMD.</p> Full article ">Figure 4
<p>Some vorticity field snapshots for the wake behind a cylinder at <math display="inline"><semantics> <mrow> <mi>R</mi> <mi>e</mi> <mo>=</mo> <mn>100</mn> </mrow> </semantics></math> are shown in (<b>a</b>–<b>c</b>).</p> Full article ">Figure 5
<p>Singular values of <span class="html-italic">X</span> (<b>a</b>) and DMD eigenvalues computed by Algorithms 1 and 2 (<b>b</b>).</p> Full article ">Figure 6
<p>The first six DMD modes computed by Algorithm 1 are shown in (<b>a</b>–<b>f</b>). Corresponding DMD modes computed by Algorithm 2 are in (<b>g</b>–<b>l</b>).</p> Full article ">Figure 7
<p>The full simulation of the NLS Equation (<a href="#FD7-computation-10-00210" class="html-disp-formula">7</a>) in (<b>a</b>) and DMD reconstruction (<b>b</b>) by standard DMD algorithm, where the observable is given by <math display="inline"><semantics> <mrow> <msub> <mi>g</mi> <mrow> <mi>D</mi> <mi>M</mi> <mi>D</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">x</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi mathvariant="bold">x</mi> </mrow> </semantics></math>, where <math display="inline"><semantics> <mrow> <mi mathvariant="bold">x</mi> <mo>=</mo> <mi>q</mi> <mo>(</mo> <mi>ξ</mi> <mo>,</mo> <mi>t</mi> <mo>)</mo> </mrow> </semantics></math>, in panel (<b>b</b>).</p> Full article ">Figure 8
<p>DMD reconstructions, based on new observable <math display="inline"><semantics> <msub> <mi>g</mi> <mn>1</mn> </msub> </semantics></math> defined by (<a href="#FD31-computation-10-00210" class="html-disp-formula">31</a>). Reconstruction by Algorithm 1 in (<b>a</b>) and by Algorithm 2 in (<b>b</b>).</p> Full article ">Figure 9
<p>Relative errors (<b>a</b>) and DMD eigenvalues (<b>b</b>).</p> Full article ">Figure 10
<p>Two approximations of Brent Crude Oil price for the period 1 February 2022–28 February 2022 by Standard DMD and Alternative DMD approaches.</p> Full article ">
16 pages, 4833 KiB  
Article
Precision Calibration of Omnidirectional Camera Using a Statistical Approach
by Vasilii P. Lazarenko, Valery V. Korotaev, Sergey N. Yaryshev, Marin B. Marinov and Todor S. Djamiykov
Computation 2022, 10(12), 209; https://doi.org/10.3390/computation10120209 - 30 Nov 2022
Viewed by 2390
Abstract
Omnidirectional optoelectronic systems (OOES) find applications in many areas where a wide viewing angle is crucial. The disadvantage of these systems is the large distortion of the images, which makes it difficult to make wide use of them. The purpose of this study [...] Read more.
Omnidirectional optoelectronic systems (OOES) find applications in many areas where a wide viewing angle is crucial. The disadvantage of these systems is the large distortion of the images, which makes it difficult to make wide use of them. The purpose of this study is the development an algorithm for the precision calibration of an omnidirectional camera using a statistical approach. The calibration approach comprises three basic stages. The first stage is the formation of a cloud of points characterizing the view field of the virtual perspective camera. In the second stage, a calibration procedure that provides the projection function for the camera calibration is performed. The projection functions of traditional perspective lenses and omnidirectional wide-angle fisheye lenses with a viewing angle of no less than 180° are compared. The construction of the corrected image is performed in the third stage. The developed algorithm makes it possible to obtain an image for part of the field of view of an OOES by correcting the distortion from the original omnidirectional image.Using the developed algorithm, a non-mechanical pivoting camera based on an omnidirectional camera is implemented. The achieved mean squared error of the reproducing points from the original omnidirectional image onto the image with corrected distortion is less than the size of a very few pixels. Full article
(This article belongs to the Section Computational Engineering)
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<p>Perspective geometric models: (<b>a</b>) of the lens and (<b>b</b>) of an extra wide-angle fisheye lens.</p> Full article ">Figure 2
<p>Geyer and Daniilidis Unified Imaging Model (adapted from [<a href="#B7-computation-10-00209" class="html-bibr">7</a>], p. 344).</p> Full article ">Figure 3
<p>Geometric projection models: (<b>a</b>) catadioptric omnidirectional camera, (<b>b</b>) camera with a fisheye lens, and (<b>c</b>) coordinates on the plane of the camera receiver.</p> Full article ">Figure 4
<p>Distortions caused by the discretization process (using rectangular pixels) and the displacement of the camera and mirror (lens) axes.</p> Full article ">Figure 5
<p>The three main steps of the algorithm.</p> Full article ">Figure 6
<p>Virtual camera field of view with <math display="inline"><semantics> <mrow> <mi>φ</mi> <mo>=</mo> <mn>0</mn> <mo>,</mo> <mi>θ</mi> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>.</p> Full article ">Figure 7
<p>Field of view slope of the virtual camera at an angle <math display="inline"><semantics> <mi>θ</mi> </semantics></math>.</p> Full article ">Figure 8
<p>Field of view rotation of the virtual camera at an angle <math display="inline"><semantics> <mi>φ</mi> </semantics></math> relative to the <math display="inline"><semantics> <mi>Z</mi> </semantics></math> axis.</p> Full article ">Figure 9
<p>Calibration results using the OCamCalib toolkit. (<b>a</b>) An example of the wrong determination of the calibration parameters [<a href="#B32-computation-10-00209" class="html-bibr">32</a>]; (<b>b</b>) the result of the experimental calibration is the position where calibration points and re-projected points coincide, which confirms the correct determination of calibration parameters. Yellow crosses denote the determined calibration points of the test object, and red crosses—the result of projecting the calibration points with three-dimensional coordinates, calculated during the calibration process, back to the image. The size of each square of the test object is 20 mm estimated center coordinates of the circular image.</p> Full article ">Figure 10
<p>The implementation of the algorithm in the “Typhoon” system: (<b>a</b>) the original image; (<b>b</b>) virtual PTZ camera, guided by a motion detector.</p> Full article ">Figure 11
<p>Initial image with the test object for calibration.</p> Full article ">Figure 12
<p>Images obtained after applying the algorithm to a field of view of (<b>a</b>) 90 degrees and (<b>b</b>) 120 degrees.</p> Full article ">
11 pages, 335 KiB  
Article
Some Remarks on Malicious and Negligent Data Breach Distribution Estimates
by Maria Francesca Carfora and Albina Orlando
Computation 2022, 10(12), 208; https://doi.org/10.3390/computation10120208 - 30 Nov 2022
Cited by 2 | Viewed by 2161
Abstract
Digitization offers great opportunities as well as new challenges. Indeed, these opportunities entail increased cyber risks, both from deliberate cyberattacks and from incidents caused by inadvertent human error. Cyber risk must be mastered, and to this aim, its quantification is an urgent challenge. [...] Read more.
Digitization offers great opportunities as well as new challenges. Indeed, these opportunities entail increased cyber risks, both from deliberate cyberattacks and from incidents caused by inadvertent human error. Cyber risk must be mastered, and to this aim, its quantification is an urgent challenge. There is a lot of interest in this topic from the insurance community in order to price adequate coverage to their customers. A key first step is to investigate the frequency and severity of cyber incidents. On the grounds that data breaches seem to be the main cause of cyber incidents, the aim of this paper is to give further insights about the frequency and severity statistical distributions of malicious and negligent data breaches. For this purpose, we refer to a publicly available dataset: the Chronology of Data Breaches provided by the Privacy Rights Clearinghouse. Full article
(This article belongs to the Special Issue Computational Issues in Insurance and Finance)
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<p>Empirical distribution of the (logarithm of the) number of breached records, assumed to be a measure of the breach severity for (<b>a</b>) MED type organizations and (<b>b</b>) all but MED type organizations. Data reported in the PRC dataset in the time period 2010–2019.</p> Full article ">Figure 2
<p>Empirical (light gray) vs. estimated (dark gray) distributions of the daily frequency of breaches for (<b>a</b>) malicious and (<b>b</b>) negligent breach types, respectively. Data for all but MED type companies as reported in the PRC dataset in the time period 2010–2019.</p> Full article ">Figure 3
<p>Empirical (histograms) vs. estimated (red line) distributions of the severity of breaches, measured by the number of breached records for (<b>a</b>) malicious and (<b>b</b>) negligent breach types, respectively. Data for all but MED type companies as reported in the PRC dataset in the time period 2010–2019.</p> Full article ">Figure 4
<p>The empirical distribution function of the (logarithm of the) number of breached records (circles) compared to the estimated distribution function (black line) for (<b>a</b>) malicious and (<b>b</b>) negligent breach types, respectively. Data for all but MED type companies as reported in the PRC dataset in the time period 2010–2019.</p> Full article ">
18 pages, 7318 KiB  
Article
Modeling the Static and Dynamic Behaviors of a Large Heavy-Duty Lathe Machine under Rated Loads
by Chien-Yu Lin, Yuan-Ping Luh, Wei-Zhu Lin, Bo-Chen Lin and Jui-Pin Hung
Computation 2022, 10(12), 207; https://doi.org/10.3390/computation10120207 - 25 Nov 2022
Cited by 3 | Viewed by 5335
Abstract
The static and dynamic performances of a machine tool structure are considered to constitute the primary factors affecting the load-carrying capacity, geometric accuracy and surface precision of the workpiece. The machining performance of a large machine tool under stable conditions is effectively determined [...] Read more.
The static and dynamic performances of a machine tool structure are considered to constitute the primary factors affecting the load-carrying capacity, geometric accuracy and surface precision of the workpiece. The machining performance of a large machine tool under stable conditions is effectively determined by its dynamic response to the cutting force at low-frequency excitation. This study, therefore, investigated the static and dynamic characteristics of a large heavy-duty lathe machine tool in which the headstock and tailstock comprised critical component modules supporting a large workpiece during low-speed machining. Using a finite element model, the influences of the structural modules on the static and dynamic characteristics of the lathe were analyzed, considering the effects of the workpiece load. The results indicated that the fundamental vibration modes of the lathe were primarily dominated by headstock, tailstock, and workpiece behaviors. The maximum compliances of the lathe under the rated load were found to occur at relatively low frequencies (22, 40.7, and 82.7 Hz) and increase with the reduction in workpiece weight. Notably, these modal frequencies were significantly higher than the maximum rotational speed of the spindle (450 rpm). In addition, the dynamic rigidity corresponding to the rated speed was higher than that induced at the natural frequency. These results indicate that the subject lathe possesses sufficient capacity to sustain the cutting load during stable turning machining. This study can, therefore, help designers improve the performance of machine tools for future fabrication. Full article
(This article belongs to the Special Issue Application of Finite Element Methods)
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<p>Solid model of the five-axis turning-milling lathe and its primary structure modules (headstock with spindle chuck, milling tool, tool carriage, and tailstock).</p> Full article ">Figure 1 Cont.
<p>Solid model of the five-axis turning-milling lathe and its primary structure modules (headstock with spindle chuck, milling tool, tool carriage, and tailstock).</p> Full article ">Figure 2
<p>Simplified model of the entire turning-milling lathe with workpiece in length of 11.866 m and diameter of 0.8 m.</p> Full article ">Figure 3
<p>Finite element model of lathe machine without (<b>top</b>) and with (<b>bottom</b>) a workpiece.</p> Full article ">Figure 4
<p>Modeling of the bearings in the spindle, (<b>a</b>) Schematic of angular contact bearing, (<b>b</b>) Modelling of the contact interface in bearing [<a href="#B25-computation-10-00207" class="html-bibr">25</a>].</p> Full article ">Figure 5
<p>Schematic of the harmonic force acting on the tailstock and the spindle chuck in the lateral and vertical directions.</p> Full article ">Figure 6
<p>Schematic of the cutting force acting on the workpiece, which was decomposed into components in the cutting direction (<span class="html-italic">F<sub>c</sub></span>), feeding direction (<span class="html-italic">F<sub>f</sub></span>) and radial direction (<span class="html-italic">F<sub>r</sub></span>).</p> Full article ">Figure 7
<p>Deformation of the machine structure under rated workpiece load of 60 tons.</p> Full article ">Figure 7 Cont.
<p>Deformation of the machine structure under rated workpiece load of 60 tons.</p> Full article ">Figure 8
<p>Fundamental vibration modes of the headstock with chuck, including the lower- and higher-frequency modes associated with the bending motion of spindle shaft with and without the chuck.</p> Full article ">Figure 9
<p>Fundamental vibration modes of the headstock with the chuck.</p> Full article ">Figure 10
<p>Fundamental vibration modes of the entire lathe machine with a workpiece.</p> Full article ">Figure 11
<p>Predicted FRFs for the spindle chuck.</p> Full article ">Figure 12
<p>Predicted FRFs for the tailstock.</p> Full article ">Figure 13
<p>Predicted FRFs of the workpiece in the three orthogonal directions under force excitation.</p> Full article ">Figure 13 Cont.
<p>Predicted FRFs of the workpiece in the three orthogonal directions under force excitation.</p> Full article ">Figure 14
<p>Predicted FRFs of headstock in the three orthogonal directions under force excitation.</p> Full article ">Figure 15
<p>Predicted FRFs of the tailstock in the three orthogonal directions under force excitation.</p> Full article ">
16 pages, 2123 KiB  
Article
Asymptotic Characteristics of the Non-Iterative Estimates of the Linear-by-Linear Association Parameter for Ordinal Log-Linear Models
by Sidra Zafar, Salman A. Cheema, Eric J. Beh and Irene L. Hudson
Computation 2022, 10(12), 206; https://doi.org/10.3390/computation10120206 - 24 Nov 2022
Viewed by 1361
Abstract
Over the past decade, a series of procedures has been introduced to estimate, using a non-iterative method, the linear-by-linear association parameter of an ordinal log-linear model. This paper will examine the two key non-iteratively determined estimates of the parameter for the analysis of [...] Read more.
Over the past decade, a series of procedures has been introduced to estimate, using a non-iterative method, the linear-by-linear association parameter of an ordinal log-linear model. This paper will examine the two key non-iteratively determined estimates of the parameter for the analysis of the association between the two categorical variables that form a contingency table; these are the log and the Beh-Davy non-iterative estimates, referred to simply as the LogNI and the BDNI estimates, respectively. Such an examination will focus on determining their asymptotic characteristics. To do so, a computational study was undertaken for tables of varying sizes to show that these two estimates are asymptotically unbiased. It is also shown that both estimates are asymptotically normally distributed. On the basis of the standard errors, their relative efficiency was established for the 13 commonly analysed contingency tables that appear throughout the literature. Full article
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<p>Sampling distribution of <math display="inline"><semantics> <mrow> <msub> <mrow> <mover> <mi mathvariant="sans-serif">φ</mi> <mo>^</mo> </mover> </mrow> <mrow> <mi>LogNI</mi> </mrow> </msub> </mrow> </semantics></math> for various λ and n.</p> Full article ">Figure 2
<p>Graphical display of asymptotic distribution of <math display="inline"><semantics> <mrow> <msub> <mrow> <mover> <mi mathvariant="sans-serif">φ</mi> <mo>^</mo> </mover> </mrow> <mrow> <mi>BDNI</mi> </mrow> </msub> <mo>.</mo> </mrow> </semantics></math>.</p> Full article ">
23 pages, 13628 KiB  
Article
Numerical Simulation of Phase Transitions in Porous Media with Three-Phase Flows Considering Steam Injection into the Oil Reservoir
by Sergey Bublik and Mikhail Semin
Computation 2022, 10(12), 205; https://doi.org/10.3390/computation10120205 - 24 Nov 2022
Cited by 3 | Viewed by 2175
Abstract
This study focuses on the analysis of an approach to the simulation of the phase transition in porous media when hot steam is injected into the oil reservoir. The reservoir is assumed to consist of a porous medium with homogeneous thermal properties. Its [...] Read more.
This study focuses on the analysis of an approach to the simulation of the phase transition in porous media when hot steam is injected into the oil reservoir. The reservoir is assumed to consist of a porous medium with homogeneous thermal properties. Its porous space is filled with a three-phase mixture of steam, water, and oil. The problem is considered in a non-stationary and non-isothermal formulation. Each phase is considered to be incompressible, with constant thermal properties, except for the dynamic viscosity of oil, which depends on the temperature. The 1D mathematical model of filtration, taking into account the phase transition, consists of continuity, Darcy, and energy equations. Steam injection and oil production in the model are conducted via vertical or horizontal wells. In the case of horizontal wells, the influence of gravity is also taken into account. The Lee model is used to simulate the phase transition between steam and water. The convective terms in the balance equations are calculated without accounting for artificial diffusion. Spatial discretization of the 1D domain is carried out using the finite volume method, and time discretization is implemented using the inverse (implicit) Euler scheme. The proposed model is analyzed in terms of the accuracy of the phase transition simulation for various sets of independent phases and combinations of continuity equations. In addition, we study the sensitivity of the model to the selected independent phases, to the time step and spatial mesh parameters, and to the intensity of the phase transition. The obtained results allow us to formulate recommendations for simulations of the phase transition using the Lee model. Full article
(This article belongs to the Section Computational Engineering)
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<p>Schematic representation of the approaches to steam injection into the reservoir: (<b>a</b>) injection and production by vertical wells; (<b>b</b>) injection and production by horizontal wells.</p> Full article ">Figure 2
<p>Geometry of the computational domain.</p> Full article ">Figure 3
<p>Scheme of computational mesh.</p> Full article ">Figure 4
<p>Dynamic viscosity of oil as a function of temperature (<b>a</b>), and phase transition temperature as a function of pressure (<b>b</b>).</p> Full article ">Figure 5
<p>Distributions of steam saturation (<b>a</b>), water saturation (<b>b</b>), and oil saturation (<b>c</b>) at a constant phase transition temperature of 100 °C, with intensities of condensation and vaporization equal to 1 day<sup>−1</sup>. Gravity is not taken into account; the purple vertical line is the position of the phase transition boundary, and the black horizontal dotted line is the initial oil saturation of the reservoir.</p> Full article ">Figure 6
<p>Distributions of steam saturation (<b>a</b>), water saturation (<b>b</b>), and oil saturation (<b>c</b>) at a constant phase transition temperature of 100 °C, with intensities of condensation and vaporization equal to 1 day<sup>−1</sup>. Gravity is taken into account; the purple vertical line is the position of the phase transition boundary, and the black horizontal dotted line is the initial oil saturation of the reservoir.</p> Full article ">Figure 7
<p>Distributions of steam saturation (<b>a</b>), water saturation (<b>b</b>), and oil saturation (<b>c</b>) for Combination No. 1 at a constant phase transition temperature of 100 °C, with the parameters of condensation and vaporization intensity equal to 1 day<sup>−1</sup>. Gravity is not taken into account. The purple vertical line is the position of the phase transition boundary, and the black horizontal dotted line is the initial oil saturation of the formation. The number of cells is 50.</p> Full article ">Figure 8
<p>Distributions of steam saturation (<b>a</b>), water saturation (<b>b</b>), and oil saturation (<b>c</b>) for Combination No. 2 at a constant phase transition temperature of 100 °C, with the parameters of condensation and vaporization intensity equal to 1 day<sup>−1</sup>. Gravity is not taken into account. The purple vertical line is the position of the phase transition boundary, and the black horizontal dotted line is the initial oil saturation of the formation. The number of cells is 50.</p> Full article ">Figure 9
<p>Distributions of steam saturation (<b>a</b>), water saturation (<b>b</b>), and oil saturation (<b>c</b>) for Combination No. 3 at a constant phase transition temperature of 100 °C, with the parameters of condensation and vaporization intensity equal to 1 day<sup>−1</sup>. Gravity is not taken into account. The purple vertical line is the position of the phase transition boundary, and the black horizontal dotted line is the initial oil saturation of the formation. The number of cells is 50.</p> Full article ">Figure 10
<p>The distributions of steam saturation (<b>a</b>), water saturation (<b>b</b>), and oil saturation (<b>c</b>) for Combination No. 1 at a constant phase transition temperature of 100 °C, with the parameters of condensation and vaporization intensity equal to 1 day<sup>−1</sup>. Gravity is taken into account. The purple vertical line is the position of the phase transition boundary, and the black horizontal dotted line is the initial oil saturation of the formation. The number of cells is 50.</p> Full article ">Figure 11
<p>The distributions of steam saturation (<b>a</b>), water saturation (<b>b</b>), and oil saturation (<b>c</b>) for Combination No. 2 at a constant phase transition temperature of 100 °C, with the parameters of condensation and vaporization intensity equal to 1 day<sup>−1</sup>. Gravity is taken into account. The purple vertical line is the position of the phase transition boundary, and the black horizontal dotted line is the initial oil saturation of the formation. The number of cells is 50.</p> Full article ">Figure 12
<p>The distributions of steam saturation (<b>a</b>), water saturation (<b>b</b>), and oil saturation (<b>c</b>) for Combination No. 3 at a constant phase transition temperature of 100 °C, with the parameters of condensation and vaporization intensity equal to 1 day<sup>−1</sup>. Gravity is taken into account. The purple vertical line is the position of the phase transition boundary, and the black horizontal dotted line is the initial oil saturation of the formation. The number of cells is 50.</p> Full article ">Figure 13
<p>The distributions of steam saturation (<b>a</b>), water saturation (<b>b</b>), and oil saturation (<b>c</b>) for Combination No. 1 at a constant phase transition temperature of 100 °C, with the parameters of condensation and vaporization intensity equal to 1 day<sup>−1</sup>. Gravity is not taken into account. The purple vertical line is the position of the phase transition boundary, and the black horizontal dotted line is the initial oil saturation of the formation. The time step is 0.005 days.</p> Full article ">Figure 14
<p>The distributions of steam saturation (<b>a</b>), water saturation (<b>b</b>), and oil saturation (<b>c</b>) for Combination No. 2 at a constant phase transition temperature of 100 °C, with the parameters of condensation and vaporization intensity equal to 1 day<sup>−1</sup>. Gravity is not taken into account. The purple vertical line is the position of the phase transition boundary, and the black horizontal dotted line is the initial oil saturation of the formation. The time step is 0.005 days.</p> Full article ">Figure 15
<p>The distributions of steam saturation (<b>a</b>), water saturation (<b>b</b>), and oil saturation (<b>c</b>) for Combination No. 3 at a constant phase transition temperature of 100 °C, with the parameters of condensation and vaporization intensity equal to 1 day<sup>−1</sup>. Gravity is not taken into account. The purple vertical line is the position of the phase transition boundary, and the black horizontal dotted line is the initial oil saturation of the formation. The time step is 0.005 days.</p> Full article ">Figure 16
<p>The distributions of steam saturation (<b>a</b>), water saturation (<b>b</b>), and oil saturation (<b>c</b>) for Combination No. 1 at a constant phase transition temperature of 100 °C, with the parameters of condensation and vaporization intensity equal to 1 day<sup>−1</sup>. Gravity is taken into account. The purple vertical line is the position of the phase transition boundary, and the black horizontal dotted line is the initial oil saturation of the formation. The time step is 0.005 days.</p> Full article ">Figure 17
<p>The distributions of steam saturation (<b>a</b>), water saturation (<b>b</b>), and oil saturation (<b>c</b>) for Combination No. 2 at a constant phase transition temperature of 100 °C, with the parameters of condensation and vaporization intensity equal to 1 day<sup>−1</sup>. Gravity is taken into account. The purple vertical line is the position of the phase transition boundary, and the black horizontal dotted line is the initial oil saturation of the formation. The time step is 0.005 days.</p> Full article ">Figure 18
<p>The distributions of steam saturation (<b>a</b>), water saturation (<b>b</b>), and oil saturation (<b>c</b>) for Combination No. 3 at a constant phase transition temperature of 100 °C, parameters of condensation and vaporization intensity equal to 1 day<sup>−1</sup>. Gravity is taken into account. The purple vertical line is the position of the phase transition boundary, and the black horizontal dotted line is the initial oil saturation of the formation. The time step is 0.005 days.</p> Full article ">Figure 19
<p>The distributions of steam saturation (<b>a</b>), water saturation (<b>b</b>), and oil saturation (<b>c</b>) for Combination No. 2 at a constant phase transition temperature of 100 °C, with the parameters of condensation and vaporization intensity equal to 1 day<sup>−1</sup>. Gravity is not taken into account. The purple vertical line is the position of the phase transition boundary, and the black horizontal dotted line is the initial oil saturation of the formation. The time step is 0.00125 days, and the number of computational cells is 200.</p> Full article ">Figure 20
<p>The distributions of steam saturation (<b>a</b>), water saturation (<b>b</b>), and oil saturation (<b>c</b>) for Combination No. 2 at a constant phase transition temperature of 100 °C, with the parameters of condensation and vaporization intensity equal to 1 day<sup>−1</sup>. Gravity is taken into account. The purple vertical line is the position of the phase transition boundary, and the black horizontal dotted line is the initial oil saturation of the formation. The time step is 0.00125 days, and the number of computational cells is 200.</p> Full article ">Figure 21
<p>Distributions of steam saturation (<b>a</b>), water saturation (<b>b</b>), and oil saturation (<b>c</b>) for Combination No. 1 at a constant phase transition temperature of 100 °C, with various parameters of condensation and vaporization intensity. Gravity is not taken into account. The purple vertical line is the position of the phase transition boundary, and the black horizontal dotted line is the initial oil saturation of the reservoir.</p> Full article ">Figure 22
<p>Distributions of steam saturation (<b>a</b>), water saturation (<b>b</b>), and oil saturation (<b>c</b>) for Combination No. 2 at a constant phase transition temperature of 100 °C, with various parameters of condensation and vaporization intensity. Gravity is not taken into account. The purple vertical line is the position of the phase transition boundary, and the black horizontal dotted line is the initial oil saturation of the reservoir.</p> Full article ">Figure 23
<p>Distributions of steam saturation (<b>a</b>), water saturation (<b>b</b>), and oil saturation (<b>c</b>) for Combination No. 3 at a constant phase transition temperature of 100 °C, with various parameters of condensation and vaporization intensity. Gravity is not taken into account. The purple vertical line is the position of the phase transition boundary, and the black horizontal dotted line is the initial oil saturation of the reservoir.</p> Full article ">Figure 24
<p>Comparison of distributions of pressure (<b>a</b>), temperature (<b>b</b>), mixture filtration velocity (<b>c</b>), steam saturation (<b>d</b>), water saturation (<b>e</b>), and oil saturation (<b>f</b>) for different combinations. The phase transition temperature is a function of pressure, and gravity is not considered. The black horizontal dotted line is the initial oil saturation of the reservoir.</p> Full article ">Figure 25
<p>Comparison of distributions of pressure (<b>a</b>), temperature (<b>b</b>), mixture filtration velocity (<b>c</b>), steam saturation (<b>d</b>), water saturation (<b>e</b>), and oil saturation (<b>f</b>) for different combinations. The phase transition temperature is a function of pressure, and gravity is considered. The black horizontal dotted line is the initial oil saturation of the reservoir.</p> Full article ">
19 pages, 4564 KiB  
Article
GSTARI-X-ARCH Model with Data Mining Approach for Forecasting Climate in West Java
by Putri Monika, Budi Nurani Ruchjana and Atje Setiawan Abdullah
Computation 2022, 10(12), 204; https://doi.org/10.3390/computation10120204 - 23 Nov 2022
Cited by 4 | Viewed by 1700
Abstract
The spatiotemporal model consists of stationary and non-stationary data, respectively known as the Generalized Space–Time Autoregressive (GSTAR) model and the Generalized Space–Time Autoregressive Integrated (GSTARI) model. The application of this model in forecasting climate with rainfall variables is also influenced by exogenous variables [...] Read more.
The spatiotemporal model consists of stationary and non-stationary data, respectively known as the Generalized Space–Time Autoregressive (GSTAR) model and the Generalized Space–Time Autoregressive Integrated (GSTARI) model. The application of this model in forecasting climate with rainfall variables is also influenced by exogenous variables such as humidity, and often the assumption of error is not constant. Therefore, this study aims to design a spatiotemporal model with the addition of exogenous variables and to overcome the non-constant error variance. The proposed model is named GSTARI-X-ARCH. The model is used to predict climate phenomena in West Java, obtained from National Aeronautics and Space Administration Prediction of Worldwide Energy Resources (NASA POWER) data. Climate data are big data, so we used knowledge discovery in databases (KDD) in this study. The pre-processing step is collecting and cleaning data. Then, the data mining process with the GSTARI-X-ARCH model follows the Box–Jenkins procedure: model identification, parameter estimation, and diagnostic checking. Finally, the post-processing step for visualization and interpretation of forecast results was conducted. This research is expected to contribute to developing the spatiotemporal model and forecast results as recommendations to the relevant agencies. Full article
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<p>GSTARI-X-ARCH model procedure.</p> Full article ">Figure 2
<p>KDD procedure in data mining.</p> Full article ">Figure 3
<p>Pre-processing step.</p> Full article ">Figure 4
<p>STACF (<b>a</b>) and STPACF (<b>b</b>) diagrams.</p> Full article ">Figure 5
<p>QQ Plot.</p> Full article ">Figure 6
<p>Actual and forecast plots of climate phenomena at 11 locations in West Java.</p> Full article ">Figure 7
<p>Rainfall forecast map in West Java for December 2020 (<b>a</b>), January 2021 (<b>b</b>), and February 2021 (<b>c</b>).</p> Full article ">
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