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Computation, Volume 12, Issue 8 (August 2024) – 13 articles

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28 pages, 3882 KiB  
Article
Short-Term Wind Speed Prediction via Sample Entropy: A Hybridisation Approach against Gradient Disappearance and Explosion
by Khathutshelo Steven Sivhugwana and Edmore Ranganai
Computation 2024, 12(8), 163; https://doi.org/10.3390/computation12080163 - 12 Aug 2024
Viewed by 225
Abstract
High-variant wind speeds cause aberrations in wind power systems and compromise the effective operation of wind farms. A single model cannot capture the inherent wind speed randomness and complexity. In the proposed hybrid strategy, wavelet transform (WT) is used for data decomposition, sample [...] Read more.
High-variant wind speeds cause aberrations in wind power systems and compromise the effective operation of wind farms. A single model cannot capture the inherent wind speed randomness and complexity. In the proposed hybrid strategy, wavelet transform (WT) is used for data decomposition, sample entropy (SampEn) for subseries complexity evaluation, neural network autoregression (NNAR) for deterministic subseries prediction, long short-term memory network (LSTM) for complex subseries prediction, and gradient boosting machine (GBM) for prediction reconciliation. The proposed WT-NNAR-LSTM-GBM approach predicts minutely averaged wind speed data collected at Southern African Universities Radiometric Network (SAURAN) stations: Council for Scientific and Industrial Research (CSIR), Richtersveld (RVD), Venda, and the Namibian University of Science and Technology (NUST). For comparison purposes, in WT-NNAR-LSTM-GBM, LSTM and NNAR are respectively replaced with a k-nearest neighbour (KNN) to form the corresponding hybrids: WT-NNAR-KNN-GBM and WT-KNN-LSTM-GBM. We assessed WT-NNAR-LSTM-GBM’s efficacy against NNAR, LSTM, WT-NNAR-KNN-GBM, and WT-KNN-LSTM-GBM as well as the naïve model. The comparative study found that the WT-NNAR-LSTM-GBM model was the most accurate, sharpest, and robust based on mean absolute error, median absolute deviation, and residual analysis. The study results suggest using short-term forecasts to optimise wind power production, enhance grid operations in real-time, and open the door to further algorithmic enhancements. Full article
(This article belongs to the Special Issue Signal Processing and Machine Learning in Data Science)
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Figure 1

Figure 1
<p>The time series and Q-Q plots of minutely averaged wind speed data for the CSIR (<b>a</b>), NUST (<b>b</b>), RVD (<b>c</b>), and Venda (<b>d</b>) stations. Blue lines represent QQ lines, while grey boxes indicate interquartile ranges.</p>
Full article ">Figure 1 Cont.
<p>The time series and Q-Q plots of minutely averaged wind speed data for the CSIR (<b>a</b>), NUST (<b>b</b>), RVD (<b>c</b>), and Venda (<b>d</b>) stations. Blue lines represent QQ lines, while grey boxes indicate interquartile ranges.</p>
Full article ">Figure 2
<p>Level three MODWT results for minutely averaged wind speed data for CSIR (<b>top left panel</b>), NUST (<b>top right panel</b>), Venda (<b>bottom left panel</b>) and RVD (<b>bottom right panel</b>). D1–D3 denote the detailed coefficients at different decomposition levels and A3 denotes the approximate signal of <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>Y</mi> </mrow> <mrow> <mi>t</mi> </mrow> </msub> </mrow> </semantics></math>.</p>
Full article ">Figure 3
<p>A typical NNAR (<span class="html-italic">p, k</span>) architecture consists of an input layer, a hidden layer, and an output layer [<a href="#B33-computation-12-00163" class="html-bibr">33</a>]. The values <math display="inline"><semantics> <mrow> <msub> <mrow> <mo>{</mo> <mi>y</mi> </mrow> <mrow> <mi>t</mi> <mo>−</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mrow> <mi>y</mi> </mrow> <mrow> <mi>t</mi> <mo>−</mo> <mn>2</mn> </mrow> </msub> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>,</mo> <msub> <mrow> <mi>y</mi> </mrow> <mrow> <mi>t</mi> <mo>−</mo> <mi>s</mi> </mrow> </msub> <mo>,</mo> <msub> <mrow> <mi>y</mi> </mrow> <mrow> <mi>t</mi> <mo>−</mo> <mn>2</mn> <mi mathvariant="normal">s</mi> </mrow> </msub> <mo>,</mo> <msub> <mrow> <mi>y</mi> </mrow> <mrow> <mi>t</mi> <mo>−</mo> <mi>p</mi> </mrow> </msub> <mo>}</mo> </mrow> </semantics></math> represent the lagged inputs of order <math display="inline"><semantics> <mrow> <mi>p</mi> </mrow> </semantics></math> with <math display="inline"><semantics> <mrow> <mi>s</mi> </mrow> </semantics></math> being the seasonality multiple. Number of neurons in the hidden layer are denoted by <math display="inline"><semantics> <mrow> <mi>k</mi> </mrow> </semantics></math> and the resultant output at time <math display="inline"><semantics> <mrow> <mi>t</mi> </mrow> </semantics></math> is given by <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>y</mi> </mrow> <mrow> <mi>t</mi> </mrow> </msub> </mrow> </semantics></math>.</p>
Full article ">Figure 4
<p>Schematic representation of an LSTM cell.</p>
Full article ">Figure 5
<p>Proposed WT-NNAR-LSTM-GBM model.</p>
Full article ">Figure 6
<p>Model comparisons using performance metrics for CSIR (<b>top left panel</b>), NUST (<b>top right panel</b>), RVD (<b>bottom left panel</b>), and Venda (<b>bottom right panel</b>).</p>
Full article ">Figure 7
<p>Comparison of 288 min predictions and actual wind speed data for CSIR (<b>Top panel</b>), NUST (<b>Second top panel</b>), RVD (<b>Second bottom panel</b>) and Venda (<b>Bottom panel</b>).</p>
Full article ">Figure 8
<p>Distributions of the residuals for CSIR (<b>top left panel</b>), NUST (<b>top right panel</b>), RVD (<b>bottom left panel</b>), and Venda (<b>bottom right panel</b>).</p>
Full article ">
13 pages, 2938 KiB  
Article
Numerical Method for Predicting Transient Aerodynamic Heating in Hemispherical Domes
by Arif Cem Gözükara and Uygar Ateş Ceylan
Computation 2024, 12(8), 162; https://doi.org/10.3390/computation12080162 - 12 Aug 2024
Viewed by 177
Abstract
In this research, a streamlined numerical approach designed for the quick estimation of temperature profiles across the finite thickness of a hemispherical dome subjected to aerodynamic heating is introduced. Hemispherical domes, with their advantageous aerodynamic, structural, and optical properties, are frequently utilized in [...] Read more.
In this research, a streamlined numerical approach designed for the quick estimation of temperature profiles across the finite thickness of a hemispherical dome subjected to aerodynamic heating is introduced. Hemispherical domes, with their advantageous aerodynamic, structural, and optical properties, are frequently utilized in the front sections of objects traveling at supersonic velocities, including missiles or vehicles. The proposed method relies on one-dimensional analyses of fluid dynamics and flow characteristics to approximate the local heat flux across the exterior surface of the dome. By calculating these local heat flux values, it is also possible to predict the temperature variations within the thickness of the dome by employing the finite difference technique, to solve the heat conduction equation in spherical coordinates. This process is iterated over successive time intervals, to simulate the entire flight duration. Unlike traditional Computational Fluid Dynamics (CFD) simulations, the proposed strategy offers the benefits of significantly lower computational time and resource demands. The primary objective of this work is to provide an efficient numerical tool for evaluating aerodynamic heating impact and temperature gradients on hemispherical domes under specific conditions. The effectiveness of the proposed method will be validated by comparing the temperature profiles derived for a standard flight scenario against those obtained from 2-D axisymmetric transient CFD simulations performed using ANSYS-Fluent 2022 R2. Full article
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Figure 1

Figure 1
<p>The Mach number (<b>a</b>) and altitude (<b>b</b>) profiles that summarize the flight scenario.</p>
Full article ">Figure 2
<p>The diagram shows the step-by-step process, starting with the initial conditions and freestream calculations, followed by the local flow and heat flux computations. It includes the solution of the heat conduction equation and the iterative updates for each time step, ending with the output generation. The iterations cease upon reaching the total flight time (<math display="inline"><semantics> <msub> <mi>t</mi> <mrow> <mi>t</mi> <mi>o</mi> <mi>t</mi> <mi>a</mi> <mi>l</mi> </mrow> </msub> </semantics></math>).</p>
Full article ">Figure 3
<p>3D representation of the hemispherical dome (<b>left</b>); 2D representation of the domain of interest (<b>right</b>).</p>
Full article ">Figure 4
<p>The visualization of the nodes used in finite-difference solution. The configuration of the points at the (<b>a</b>) symmetry axis boundary, (<b>b</b>) shoulder boundary.</p>
Full article ">Figure 5
<p>The computational domain and hemisphere-cylinder model used for CFD simulations.</p>
Full article ">Figure 6
<p>The mesh used for the CFD analysis.</p>
Full article ">Figure 7
<p>Time history of the maximum outer surface and recovery temperature during flight.</p>
Full article ">Figure 8
<p>Inner and outer temperature distributions for (<b>a</b>) 5 (<b>b</b>) 10 (<b>c</b>) 15 (<b>d</b>) 20 s of flight.</p>
Full article ">
18 pages, 3476 KiB  
Article
Exploring New Traveling Wave Solutions to the Nonlinear Integro-Partial Differential Equations with Stability and Modulation Instability in Industrial Engineering
by J. R. M. Borhan, I. Abouelfarag, K. El-Rashidy, M. Mamun Miah, M. Ashik Iqbal and Mohammad Kanan
Computation 2024, 12(8), 161; https://doi.org/10.3390/computation12080161 - 9 Aug 2024
Viewed by 319
Abstract
In this research article, we demonstrate the generalized expansion method to investigate nonlinear integro-partial differential equations via an efficient mathematical method for generating abundant exact solutions for two types of applicable nonlinear models. Moreover, stability analysis and modulation instability are also studied for [...] Read more.
In this research article, we demonstrate the generalized expansion method to investigate nonlinear integro-partial differential equations via an efficient mathematical method for generating abundant exact solutions for two types of applicable nonlinear models. Moreover, stability analysis and modulation instability are also studied for two types of nonlinear models in this present investigation. These analyses have several applications including analyzing control systems, engineering, biomedical engineering, neural networks, optical fiber communications, signal processing, nonlinear imaging techniques, oceanography, and astrophysical phenomena. To study nonlinear PDEs analytically, exact traveling wave solutions are in high demand. In this paper, the (1 + 1)-dimensional integro-differential Ito equation (IDIE), relevant in various branches of physics, statistical mechanics, condensed matter physics, quantum field theory, the dynamics of complex systems, etc., and also the (2 + 1)-dimensional integro-differential Sawda–Kotera equation (IDSKE), providing insights into the several physical fields, especially quantum gravity field theory, conformal field theory, neural networks, signal processing, control systems, etc., are investigated to obtain a variety of wave solutions in modern physics by using the mentioned method. Since abundant exact wave solutions give us vast information about the physical phenomena of the mentioned models, our analysis aims to determine various types of traveling wave solutions via a different integrable ordinary differential equation. Furthermore, the characteristics of the obtained new exact solutions have been illustrated by some figures. The method used here is candid, convenient, proficient, and overwhelming compared to other existing computational techniques in solving other current world physical problems. This article provides an exemplary practice of finding new types of analytical equations. Full article
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Figure 1

Figure 1
<p>Soliton for the solution <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>v</mi> </mrow> <mrow> <msub> <mrow> <mn>1</mn> </mrow> <mrow> <mn>1</mn> </mrow> </msub> </mrow> </msub> </mrow> </semantics></math> presented in (<b>a</b>) 3D structure, (<b>b</b>) showing the contour shape, and (<b>c</b>) displaying the 2D figure.</p>
Full article ">Figure 2
<p>Soliton for the solution <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>v</mi> </mrow> <mrow> <msub> <mrow> <mn>2</mn> </mrow> <mrow> <mn>2</mn> </mrow> </msub> </mrow> </msub> </mrow> </semantics></math> exhibited in (<b>a</b>) 3D structure, (<b>b</b>) showing the contour shape, and (<b>c</b>) displaying the 2D figure.</p>
Full article ">Figure 3
<p>Soliton for the solution <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>v</mi> </mrow> <mrow> <msub> <mrow> <mn>3</mn> </mrow> <mrow> <mn>7</mn> </mrow> </msub> </mrow> </msub> </mrow> </semantics></math> represented in (<b>a</b>) 3D structure, (<b>b</b>) depicting the contour shape, and (<b>c</b>) revealing the 2D figure.</p>
Full article ">Figure 4
<p>Soliton for the solution <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>c</mi> </mrow> <mrow> <msub> <mrow> <mn>1</mn> </mrow> <mrow> <mn>1</mn> </mrow> </msub> </mrow> </msub> </mrow> </semantics></math> shown in (<b>a</b>) 3D structure, (<b>b</b>) organized into the contour shape, and (<b>c</b>) exposing the 2D figure.</p>
Full article ">Figure 5
<p>Soliton for the solution <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>c</mi> </mrow> <mrow> <msub> <mrow> <mn>3</mn> </mrow> <mrow> <mn>2</mn> </mrow> </msub> </mrow> </msub> </mrow> </semantics></math> offered in (<b>a</b>) 3D structure, (<b>b</b>) delivering the contour shape, and (<b>c</b>) showing the 2D figure.</p>
Full article ">
20 pages, 4861 KiB  
Article
Evaluation of the Dynamics of Psychological Panic Factor, Glucose Risk and Estrogen Effects on Breast Cancer Model
by Zahraa Aamer, Shireen Jawad, Belal Batiha, Ali Hasan Ali, Firas Ghanim and Alina Alb Lupaş
Computation 2024, 12(8), 160; https://doi.org/10.3390/computation12080160 - 8 Aug 2024
Viewed by 334
Abstract
Contracting cancer typically induces a state of terror among the individuals who are affected. Exploring how glucose excess, estrogen excess, and anxiety work together to affect the speed at which breast cancer cells multiply and the immune system’s response model is necessary to [...] Read more.
Contracting cancer typically induces a state of terror among the individuals who are affected. Exploring how glucose excess, estrogen excess, and anxiety work together to affect the speed at which breast cancer cells multiply and the immune system’s response model is necessary to conceive of ways to stop the spread of cancer. This paper proposes a mathematical model to investigate the impact of psychological panic, glucose excess, and estrogen excess on the interaction of cancer and immunity. The proposed model is precisely described. The focus of the model’s dynamic analysis is to identify the potential equilibrium locations. According to the analysis, it is possible to establish four equilibrium positions. The stability analysis reveals that all equilibrium points consistently exhibit stability under the defined conditions. The transcritical bifurcation occurs when the glucose excess is taken as a bifurcation point. Numerical simulations are employed to validate the theoretical study, which shows that psychological panic, glucose excess, and estrogen excess could be significant contributors to the spread of tumors and weakness of immune function. Full article
(This article belongs to the Special Issue 10th Anniversary of Computation—Computational Biology)
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Figure 1

Figure 1
<p>Schematic sketch of the PPIGCNE model.</p>
Full article ">Figure 2
<p>The solution of the PPIGCNE system with the data is given in <a href="#computation-12-00160-t001" class="html-table">Table 1</a>. The initial conditions of immune cells, breast cancer cells, normal cells, and estrogen level are <math display="inline"><semantics> <mrow> <mi>I</mi> <mfenced separators="|"> <mrow> <mn>0</mn> </mrow> </mfenced> <mo>=</mo> <mn>0.25</mn> <mo>,</mo> <mo> </mo> <mn>0.75</mn> <mo>,</mo> <mo> </mo> <mn>1.3</mn> <mo>,</mo> <mo> </mo> <mn>2.7</mn> <mo> </mo> <mo>(</mo> <mi mathvariant="normal">c</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">l</mi> <mi mathvariant="normal">l</mi> <mi mathvariant="normal">s</mi> <mo>/</mo> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">g</mi> <mo>)</mo> <mo>,</mo> <mo> </mo> <mi>C</mi> <mfenced separators="|"> <mrow> <mn>0</mn> </mrow> </mfenced> <mo>=</mo> <mn>0.8</mn> <mo>,</mo> <mo> </mo> <mn>1.4</mn> <mo>,</mo> <mo> </mo> <mn>1.6</mn> <mo>,</mo> <mo> </mo> <mn>2.4</mn> <mo> </mo> <mo>(</mo> <mi mathvariant="normal">c</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">l</mi> <mi mathvariant="normal">l</mi> <mi mathvariant="normal">s</mi> <mo>/</mo> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">g</mi> <mo>)</mo> <mo>,</mo> <mo> </mo> <mi>N</mi> <mfenced separators="|"> <mrow> <mn>0</mn> </mrow> </mfenced> <mo>=</mo> <mn>0.94</mn> <mo>,</mo> <mo> </mo> <mn>0.84</mn> <mo> </mo> <mo>(</mo> <mi mathvariant="normal">c</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">l</mi> <mi mathvariant="normal">l</mi> <mi mathvariant="normal">s</mi> <mo>/</mo> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">g</mi> <mo>)</mo> <mo>,</mo> <mo> </mo> <mn>0.74</mn> <mo>,</mo> <mo> </mo> <mn>1.4</mn> <mo>,</mo> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>E</mi> <mfenced separators="|"> <mrow> <mn>0</mn> </mrow> </mfenced> <mo>=</mo> <mn>0.5</mn> <mo>,</mo> <mo> </mo> <mn>1</mn> <mo>,</mo> <mo> </mo> <mn>1.5</mn> <mo>,</mo> <mo> </mo> <mn>2</mn> </mrow> </semantics></math> ng/mL.</p>
Full article ">Figure 3
<p>The solution of the PPIGCNE system with various values of psychological scare rate <math display="inline"><semantics> <mrow> <mi>p</mi> </mrow> </semantics></math> and the initial conditions of immune cells, breast cancer cells, normal cells, and estrogen level are <math display="inline"><semantics> <mrow> <mi>I</mi> <mfenced separators="|"> <mrow> <mn>0</mn> </mrow> </mfenced> <mo>=</mo> <mn>0.25</mn> <mo> </mo> <mo>(</mo> <mi mathvariant="normal">c</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">l</mi> <mi mathvariant="normal">l</mi> <mi mathvariant="normal">s</mi> <mo>/</mo> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">g</mi> <mo>)</mo> <mo>,</mo> <mo> </mo> <mi>C</mi> <mfenced separators="|"> <mrow> <mn>0</mn> </mrow> </mfenced> <mo>=</mo> <mn>0.3</mn> <mo> </mo> <mo>(</mo> <mi mathvariant="normal">c</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">l</mi> <mi mathvariant="normal">l</mi> <mi mathvariant="normal">s</mi> <mo>/</mo> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">g</mi> <mo>)</mo> <mo>,</mo> <mo> </mo> <mi>N</mi> <mfenced separators="|"> <mrow> <mn>0</mn> </mrow> </mfenced> <mo>=</mo> <mn>0.3</mn> <mo> </mo> <mo>(</mo> <mi mathvariant="normal">c</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">l</mi> <mi mathvariant="normal">l</mi> <mi mathvariant="normal">s</mi> <mo>/</mo> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">g</mi> <mo>)</mo> <mo>,</mo> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>E</mi> <mfenced separators="|"> <mrow> <mn>0</mn> </mrow> </mfenced> <mo>=</mo> <mn>0.12</mn> </mrow> </semantics></math> ng/mL.</p>
Full article ">Figure 4
<p>The dynamics of immune and cancer cells with various values of <math display="inline"><semantics> <mrow> <mi>p</mi> </mrow> </semantics></math> and the initial conditions of immune cells, breast cancer cells, normal cells, and estrogen level are <math display="inline"><semantics> <mrow> <mi>I</mi> <mfenced separators="|"> <mrow> <mn>0</mn> </mrow> </mfenced> <mo>=</mo> <mn>1.6</mn> <mo> </mo> <mo>(</mo> <mi mathvariant="normal">c</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">l</mi> <mi mathvariant="normal">l</mi> <mi mathvariant="normal">s</mi> <mo>/</mo> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">g</mi> <mo>)</mo> <mo>,</mo> <mo> </mo> <mi>C</mi> <mfenced separators="|"> <mrow> <mn>0</mn> </mrow> </mfenced> <mo>=</mo> <mn>1.4</mn> <mo> </mo> <mo>(</mo> <mi mathvariant="normal">c</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">l</mi> <mi mathvariant="normal">l</mi> <mi mathvariant="normal">s</mi> <mo>/</mo> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">g</mi> <mo>)</mo> <mo>,</mo> <mo> </mo> <mi>N</mi> <mfenced separators="|"> <mrow> <mn>0</mn> </mrow> </mfenced> <mo>=</mo> <mn>0.8</mn> <mo> </mo> <mo>(</mo> <mi mathvariant="normal">c</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">l</mi> <mi mathvariant="normal">l</mi> <mi mathvariant="normal">s</mi> <mo>/</mo> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">g</mi> <mo>)</mo> <mo>,</mo> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>E</mi> <mfenced separators="|"> <mrow> <mn>0</mn> </mrow> </mfenced> <mo>=</mo> <mn>0.8</mn> <mo> </mo> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">g</mi> <mo>/</mo> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">L</mi> </mrow> </semantics></math>. <math display="inline"><semantics> <mrow> <mfenced separators="|"> <mrow> <mi>*</mi> </mrow> </mfenced> </mrow> </semantics></math> represents the final state of the solution and the number in the bracket denotes the equilibrium point with different values of <math display="inline"><semantics> <mrow> <mi>p</mi> </mrow> </semantics></math>.</p>
Full article ">Figure 5
<p>The solution of the PPIGCNE system in the absence of tumor cells with various values of <math display="inline"><semantics> <mrow> <mi>g</mi> </mrow> </semantics></math> and the initial conditions of immune cells, breast cancer cells, normal cells, and estrogen level are <math display="inline"><semantics> <mrow> <mi>I</mi> <mfenced separators="|"> <mrow> <mn>0</mn> </mrow> </mfenced> <mo>=</mo> <mn>0.25</mn> <mo> </mo> <mo>(</mo> <mi mathvariant="normal">c</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">l</mi> <mi mathvariant="normal">l</mi> <mi mathvariant="normal">s</mi> <mo>/</mo> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">g</mi> <mo>)</mo> <mo>,</mo> <mo> </mo> <mi>N</mi> <mfenced separators="|"> <mrow> <mn>0</mn> </mrow> </mfenced> <mo>=</mo> <mn>0.3</mn> <mo> </mo> <mo>(</mo> <mi mathvariant="normal">c</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">l</mi> <mi mathvariant="normal">l</mi> <mi mathvariant="normal">s</mi> <mo>/</mo> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">g</mi> <mo>)</mo> <mo>,</mo> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>E</mi> <mfenced separators="|"> <mrow> <mn>0</mn> </mrow> </mfenced> <mo>=</mo> <mn>0.12</mn> <mo> </mo> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">g</mi> <mo>/</mo> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">L</mi> </mrow> </semantics></math>.</p>
Full article ">Figure 6
<p>The solution of the PPIGCNE system with various values of <math display="inline"><semantics> <mrow> <mi>g</mi> </mrow> </semantics></math> and the initial conditions of immune cells, breast cancer cells, normal cells, and estrogen level are <math display="inline"><semantics> <mrow> <mi>I</mi> <mfenced separators="|"> <mrow> <mn>0</mn> </mrow> </mfenced> <mo>=</mo> <mn>0.25</mn> <mo> </mo> <mo>(</mo> <mi mathvariant="normal">c</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">l</mi> <mi mathvariant="normal">l</mi> <mi mathvariant="normal">s</mi> <mo>/</mo> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">g</mi> <mo>)</mo> <mo>,</mo> <mo> </mo> <mi>C</mi> <mfenced separators="|"> <mrow> <mn>0</mn> </mrow> </mfenced> <mo>=</mo> <mn>0.3</mn> <mo> </mo> <mo>(</mo> <mi mathvariant="normal">c</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">l</mi> <mi mathvariant="normal">l</mi> <mi mathvariant="normal">s</mi> <mo>/</mo> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">g</mi> <mo>)</mo> <mo>,</mo> <mo> </mo> <mi>N</mi> <mfenced separators="|"> <mrow> <mn>0</mn> </mrow> </mfenced> <mo>=</mo> <mn>0.3</mn> <mo> </mo> <mo>(</mo> <mi mathvariant="normal">c</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">l</mi> <mi mathvariant="normal">l</mi> <mi mathvariant="normal">s</mi> <mo>/</mo> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">g</mi> <mo>)</mo> <mo>,</mo> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>E</mi> <mfenced separators="|"> <mrow> <mn>0</mn> </mrow> </mfenced> <mo>=</mo> <mn>0.12</mn> <mo> </mo> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">g</mi> <mo>/</mo> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">L</mi> </mrow> </semantics></math>.</p>
Full article ">Figure 7
<p>The performance of the PPIGCNE system with various values of <math display="inline"><semantics> <mrow> <mi>g</mi> </mrow> </semantics></math> (<b>a</b>) The dynamics of immune and normal cells in the absence of tumor cells with various values of <math display="inline"><semantics> <mrow> <mi>g</mi> </mrow> </semantics></math> and the initial conditions are <math display="inline"><semantics> <mrow> <mi>I</mi> <mfenced separators="|"> <mrow> <mn>0</mn> </mrow> </mfenced> <mo>=</mo> <mn>1.6</mn> <mo> </mo> <mo>(</mo> <mi mathvariant="normal">c</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">l</mi> <mi mathvariant="normal">l</mi> <mi mathvariant="normal">s</mi> <mo>/</mo> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">g</mi> <mo>)</mo> <mo>,</mo> <mo> </mo> <mi>C</mi> <mfenced separators="|"> <mrow> <mn>0</mn> </mrow> </mfenced> <mo>=</mo> <mn>1.4</mn> <mo> </mo> <mo>(</mo> <mi mathvariant="normal">c</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">l</mi> <mi mathvariant="normal">l</mi> <mi mathvariant="normal">s</mi> <mo>/</mo> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">g</mi> <mo>)</mo> <mo>,</mo> <mo> </mo> <mi>N</mi> <mfenced separators="|"> <mrow> <mn>0</mn> </mrow> </mfenced> <mo>=</mo> <mn>1.5</mn> <mo> </mo> <mo>(</mo> <mi mathvariant="normal">c</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">l</mi> <mi mathvariant="normal">l</mi> <mi mathvariant="normal">s</mi> <mo>/</mo> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">g</mi> <mo>)</mo> <mo>,</mo> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>E</mi> <mfenced separators="|"> <mrow> <mn>0</mn> </mrow> </mfenced> <mo>=</mo> <mn>0.8</mn> </mrow> </semantics></math> ng/mL. (<b>b</b>) The dynamics of immune and cancer cells with various values of <math display="inline"><semantics> <mrow> <mi>g</mi> </mrow> </semantics></math> and the initial conditions are <math display="inline"><semantics> <mrow> <mi>I</mi> <mfenced separators="|"> <mrow> <mn>0</mn> </mrow> </mfenced> <mo>=</mo> <mn>1.6</mn> <mo> </mo> <mo>(</mo> <mi mathvariant="normal">c</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">l</mi> <mi mathvariant="normal">l</mi> <mi mathvariant="normal">s</mi> <mo>/</mo> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">g</mi> <mo>)</mo> <mo>,</mo> <mo> </mo> <mi>C</mi> <mfenced separators="|"> <mrow> <mn>0</mn> </mrow> </mfenced> <mo>=</mo> <mn>2.4</mn> <mo> </mo> <mo>(</mo> <mi mathvariant="normal">c</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">l</mi> <mi mathvariant="normal">l</mi> <mi mathvariant="normal">s</mi> <mo>/</mo> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">g</mi> <mo>)</mo> <mo>,</mo> <mo> </mo> <mi>N</mi> <mfenced separators="|"> <mrow> <mn>0</mn> </mrow> </mfenced> <mo>=</mo> <mn>1.5</mn> <mo> </mo> <mo>(</mo> <mi mathvariant="normal">c</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">l</mi> <mi mathvariant="normal">l</mi> <mi mathvariant="normal">s</mi> <mo>/</mo> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">g</mi> <mo>)</mo> <mo>,</mo> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>E</mi> <mfenced separators="|"> <mrow> <mn>0</mn> </mrow> </mfenced> <mo>=</mo> <mn>0.8</mn> </mrow> </semantics></math> ng/mL.</p>
Full article ">Figure 8
<p>The solution of the PPIGCNE system in the absence of tumor cells with various values of <math display="inline"><semantics> <mrow> <mi>s</mi> </mrow> </semantics></math> and the initial conditions of immune cells, breast cancer cells, normal cells, and estrogen level are <math display="inline"><semantics> <mrow> <mi>I</mi> <mfenced separators="|"> <mrow> <mn>0</mn> </mrow> </mfenced> <mo>=</mo> <mn>0.25</mn> <mo> </mo> <mo>(</mo> <mi mathvariant="normal">c</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">l</mi> <mi mathvariant="normal">l</mi> <mi mathvariant="normal">s</mi> <mo>/</mo> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">g</mi> <mo>)</mo> <mo>,</mo> <mo> </mo> <mi>N</mi> <mfenced separators="|"> <mrow> <mn>0</mn> </mrow> </mfenced> <mo>=</mo> <mn>0.3</mn> <mo> </mo> <mo>(</mo> <mi mathvariant="normal">c</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">l</mi> <mi mathvariant="normal">l</mi> <mi mathvariant="normal">s</mi> <mo>/</mo> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">g</mi> <mo>)</mo> <mo>,</mo> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>E</mi> <mfenced separators="|"> <mrow> <mn>0</mn> </mrow> </mfenced> <mo>=</mo> <mn>0.12</mn> </mrow> </semantics></math> ng/mL.</p>
Full article ">Figure 9
<p>The solution of the PPIGCNE system with various values of <math display="inline"><semantics> <mrow> <mi>s</mi> </mrow> </semantics></math> and the initial conditions of immune cells, breast cancer cells, normal cells, and estrogen level are <math display="inline"><semantics> <mrow> <mi>I</mi> <mfenced separators="|"> <mrow> <mn>0</mn> </mrow> </mfenced> <mo>=</mo> <mn>0.25</mn> <mo> </mo> <mo>(</mo> <mi mathvariant="normal">c</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">l</mi> <mi mathvariant="normal">l</mi> <mi mathvariant="normal">s</mi> <mo>/</mo> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">g</mi> <mo>)</mo> <mo>,</mo> <mo> </mo> <mi>C</mi> <mfenced separators="|"> <mrow> <mn>0</mn> </mrow> </mfenced> <mo>=</mo> <mn>0.3</mn> <mo> </mo> <mo>(</mo> <mi mathvariant="normal">c</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">l</mi> <mi mathvariant="normal">l</mi> <mi mathvariant="normal">s</mi> <mo>/</mo> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">g</mi> <mo>)</mo> <mo>,</mo> <mo> </mo> <mi>N</mi> <mfenced separators="|"> <mrow> <mn>0</mn> </mrow> </mfenced> <mo>=</mo> <mn>0.3</mn> <mo> </mo> <mo>(</mo> <mi mathvariant="normal">c</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">l</mi> <mi mathvariant="normal">l</mi> <mi mathvariant="normal">s</mi> <mo>/</mo> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">g</mi> <mo>)</mo> <mo>,</mo> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>E</mi> <mfenced separators="|"> <mrow> <mn>0</mn> </mrow> </mfenced> <mo>=</mo> <mn>0.12</mn> </mrow> </semantics></math> ng/mL.</p>
Full article ">Figure 10
<p>The performance of the PPIGCNE system with various values of <math display="inline"><semantics> <mrow> <mi>s</mi> <mo>.</mo> </mrow> </semantics></math> (<b>a</b>) The dynamics of immune and normal cells in the absence of tumor cells with various values of <math display="inline"><semantics> <mrow> <mi>s</mi> </mrow> </semantics></math> and the initial conditions are <math display="inline"><semantics> <mrow> <mi>I</mi> <mfenced separators="|"> <mrow> <mn>0</mn> </mrow> </mfenced> <mo>=</mo> <mn>0.5</mn> <mo> </mo> <mo>(</mo> <mi mathvariant="normal">c</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">l</mi> <mi mathvariant="normal">l</mi> <mi mathvariant="normal">s</mi> <mo>/</mo> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">g</mi> <mo>)</mo> <mo>,</mo> <mo> </mo> <mi>C</mi> <mfenced separators="|"> <mrow> <mn>0</mn> </mrow> </mfenced> <mo>=</mo> <mn>1.4</mn> <mo> </mo> <mo>(</mo> <mi mathvariant="normal">c</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">l</mi> <mi mathvariant="normal">l</mi> <mi mathvariant="normal">s</mi> <mo>/</mo> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">g</mi> <mo>)</mo> <mo>,</mo> <mo> </mo> <mi>N</mi> <mfenced separators="|"> <mrow> <mn>0</mn> </mrow> </mfenced> <mo>=</mo> <mn>1.4</mn> <mo> </mo> <mo>(</mo> <mi mathvariant="normal">c</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">l</mi> <mi mathvariant="normal">l</mi> <mi mathvariant="normal">s</mi> <mo>/</mo> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">g</mi> <mo>)</mo> <mo>,</mo> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>E</mi> <mfenced separators="|"> <mrow> <mn>0</mn> </mrow> </mfenced> <mo>=</mo> <mn>0.8</mn> </mrow> </semantics></math> ng/mL. (<b>b</b>) The dynamics of immune and cancer cells with various values of <math display="inline"><semantics> <mrow> <mi>s</mi> </mrow> </semantics></math> and the initial conditions are <math display="inline"><semantics> <mrow> <mi>I</mi> <mfenced separators="|"> <mrow> <mn>0</mn> </mrow> </mfenced> <mo>=</mo> <mn>0.6</mn> <mo> </mo> <mo>(</mo> <mi mathvariant="normal">c</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">l</mi> <mi mathvariant="normal">l</mi> <mi mathvariant="normal">s</mi> <mo>/</mo> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">g</mi> <mo>)</mo> <mo>,</mo> <mo> </mo> <mi>C</mi> <mfenced separators="|"> <mrow> <mn>0</mn> </mrow> </mfenced> <mo>=</mo> <mn>1.3</mn> <mo> </mo> <mo>(</mo> <mi mathvariant="normal">c</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">l</mi> <mi mathvariant="normal">l</mi> <mi mathvariant="normal">s</mi> <mo>/</mo> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">g</mi> <mo>)</mo> <mo>,</mo> <mo> </mo> <mi>N</mi> <mfenced separators="|"> <mrow> <mn>0</mn> </mrow> </mfenced> <mo>=</mo> <mn>1.4</mn> <mo> </mo> <mo>(</mo> <mi mathvariant="normal">c</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">l</mi> <mi mathvariant="normal">l</mi> <mi mathvariant="normal">s</mi> <mo>/</mo> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">g</mi> <mo>)</mo> <mo>,</mo> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>E</mi> <mfenced separators="|"> <mrow> <mn>0</mn> </mrow> </mfenced> <mo>=</mo> <mn>0.8</mn> </mrow> </semantics></math> ng/mL.</p>
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15 pages, 3805 KiB  
Review
Systematic Review of Forecasting Models Using Evolving Fuzzy Systems
by Sebastian-Camilo Vanegas-Ayala, Julio Barón-Velandia and Efren Romero-Riaño
Computation 2024, 12(8), 159; https://doi.org/10.3390/computation12080159 - 8 Aug 2024
Viewed by 366
Abstract
Currently, the increase in devices capable of continuously collecting data on non-stationary and dynamic variables affects predictive models, particularly if they are not equipped with algorithms capable of adapting their parameters and structure, causing them to be unable to perceive certain time-varying properties [...] Read more.
Currently, the increase in devices capable of continuously collecting data on non-stationary and dynamic variables affects predictive models, particularly if they are not equipped with algorithms capable of adapting their parameters and structure, causing them to be unable to perceive certain time-varying properties or the presence of missing data in data streams. A constantly developing solution to such problems is evolving fuzzy inference systems. The aim of this work was to systematically review forecasting models implemented through evolving fuzzy inference systems, identifying the most common structures, implementation outcomes, and predicted variables to establish an overview of the current state of this technique and its possible applications in other unexplored fields. This research followed the PRISMA methodology of systematic reviews, including scientific articles and patents from three academic databases, one of which offers free access. This was achieved through an identification, selection, and inclusion workflow, obtaining 323 records on which analyses were carried out based on the proposed review questions. In total, 62 investigations were identified, proposing 115 different system structures, mainly focused on increasing precision, in addition to addressing eight main fields of application and some optimization techniques. It was observed that these systems have been successfully implemented in forecasting variables with dynamic behavior and handling missing values, continuous data flows, and non-stationary characteristics. Thus, their use can be extended to phenomena with these properties. Full article
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Figure 1
<p>Description of the methodology following the systematic review flow chart according to PRISMA [<a href="#B20-computation-12-00159" class="html-bibr">20</a>,<a href="#B21-computation-12-00159" class="html-bibr">21</a>].</p>
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<p>Co-authorship network by number of documents on EFSs.</p>
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<p>Keyword co-occurrence map of each document on EFSs.</p>
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<p>Keyword co-occurrence map of each document on EFSs over time.</p>
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<p>Histogram of the distribution of the amount of research on EFSs over time.</p>
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<p>Pie chart of the distribution of EFS types applied to prediction problems.</p>
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<p>Pie chart of the distribution of the variable types in research that applies EFSs.</p>
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18 pages, 549 KiB  
Article
EOFA: An Extended Version of the Optimal Foraging Algorithm for Global Optimization Problems
by Glykeria Kyrou, Vasileios Charilogis and Ioannis G. Tsoulos
Computation 2024, 12(8), 158; https://doi.org/10.3390/computation12080158 - 5 Aug 2024
Viewed by 374
Abstract
The problem of finding the global minimum of a function is applicable to a multitude of real-world problems and, hence, a variety of computational techniques have been developed to efficiently locate it. Among these techniques, evolutionary techniques, which seek, through the imitation of [...] Read more.
The problem of finding the global minimum of a function is applicable to a multitude of real-world problems and, hence, a variety of computational techniques have been developed to efficiently locate it. Among these techniques, evolutionary techniques, which seek, through the imitation of natural processes, to efficiently obtain the global minimum of multidimensional functions, play a central role. An evolutionary technique that has recently been introduced is the Optimal Foraging Algorithm, which is a swarm-based algorithm, and it is notable for its reliability in locating the global minimum. In this work, a series of modifications are proposed that aim to improve the reliability and speed of the above technique, such as a termination technique based on stochastic observations, an innovative sampling method and a technique to improve the generation of offspring. The new method was tested on a series of problems from the relevant literature and a comparative study was conducted against other global optimization techniques with promising results. Full article
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<p>The steps of the proposed method.</p>
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<p>Statistical representation of the function calls for different optimization methods.</p>
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<p>Scatter plot representation of optimization methods with Kruskal–Wallis Ranking.</p>
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<p>Statistical representation for different sampling methods.</p>
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<p>Scatter plot representation of the used distributions with Kruskal–Wallis Ranking.</p>
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<p>Different variations of the ELP problem.</p>
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22 pages, 4764 KiB  
Article
The Effect of Proportional, Proportional-Integral, and Proportional-Integral-Derivative Controllers on Improving the Performance of Torsional Vibrations on a Dynamical System
by Khalid Alluhydan, Ashraf Taha EL-Sayed and Fatma Taha El-Bahrawy
Computation 2024, 12(8), 157; https://doi.org/10.3390/computation12080157 - 3 Aug 2024
Viewed by 281
Abstract
The primary goal of this research is to lessen the high vibration that the model causes by using an appropriate vibration control. Thus, we begin by implementing various controller types to investigate their impact on the system’s reaction and evaluate each control’s outcomes. [...] Read more.
The primary goal of this research is to lessen the high vibration that the model causes by using an appropriate vibration control. Thus, we begin by implementing various controller types to investigate their impact on the system’s reaction and evaluate each control’s outcomes. The controller types are presented as proportional (P), proportional-integral (PI), and proportional-integral-derivative (PID) controllers. We employed PID control to regulate the torsional vibration behavior on a dynamical system. The PID controller aims to increase system stability after seeing the impact of P and PI control. This kind of control ensures that there are no unstable components in the system. By using the multiple time scale perturbation (MTSP) technique, a first-order approximate solution has been obtained. Using the frequency response function approach, the stability and steady-state response of the system at the primary resonance scenario (Ω1ω1,Ω2ω2) are considered as the worst resonance and addressed. Additionally examined are the nonlinear dynamical system’s chaotic response and the numerical solution for various parameter values. The MATLAB programs are utilized to attain simulation outcomes. Full article
(This article belongs to the Special Issue Nonlinear System Modelling and Control)
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Figure 1
<p>Model of schematic diagram of main system.</p>
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<p>Model of schematic diagram of main system with PID controllers.</p>
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<p><b>The</b> time diagram without any controller (<b>a</b>) the first part of the system, <math display="inline"><semantics> <mrow> <msub> <mi>φ</mi> <mn>1</mn> </msub> </mrow> </semantics></math> (<b>b</b>) the response of its velocity, <math display="inline"><semantics> <mrow> <msub> <mover accent="true"> <mi>φ</mi> <mo>˙</mo> </mover> <mn>1</mn> </msub> </mrow> </semantics></math>.</p>
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<p>The time diagram without any controller (<b>a</b>) the second part of the system, <math display="inline"><semantics> <mrow> <msub> <mi>φ</mi> <mn>2</mn> </msub> </mrow> </semantics></math> (<b>b</b>) response of its velocity, <math display="inline"><semantics> <mrow> <msub> <mover accent="true"> <mi>φ</mi> <mo>˙</mo> </mover> <mn>2</mn> </msub> </mrow> </semantics></math>.</p>
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<p>Responses in closed loop using P, PI, and PID controller. (<b>a</b>) the first part of the system <math display="inline"><semantics> <mrow> <msub> <mi>φ</mi> <mn>1</mn> </msub> </mrow> </semantics></math> (<b>b</b>) the response of its velocity <math display="inline"><semantics> <mrow> <msub> <mover accent="true"> <mi>φ</mi> <mo>˙</mo> </mover> <mn>1</mn> </msub> </mrow> </semantics></math> (<b>c</b>) the second part of the system <math display="inline"><semantics> <mrow> <msub> <mi>φ</mi> <mn>2</mn> </msub> </mrow> </semantics></math> (<b>d</b>) the response of its velocity<math display="inline"><semantics> <mrow> <msub> <mover accent="true"> <mi>φ</mi> <mo>˙</mo> </mover> <mn>2</mn> </msub> </mrow> </semantics></math>.</p>
Full article ">Figure 6
<p>The time diagram in the primary resonance situation with the PID controller (<b>a</b>) the first part of the system <math display="inline"><semantics> <mrow> <msub> <mi>φ</mi> <mn>1</mn> </msub> </mrow> </semantics></math> (<b>b</b>) the response of its velocity <math display="inline"><semantics> <mrow> <msub> <mover accent="true"> <mi>φ</mi> <mo>˙</mo> </mover> <mn>1</mn> </msub> </mrow> </semantics></math>.</p>
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<p>The time diagram in the primary resonance situation with the PID controller (<b>a</b>) the second part of the system <math display="inline"><semantics> <mrow> <msub> <mi>φ</mi> <mn>2</mn> </msub> </mrow> </semantics></math> (<b>b</b>) the response of its velocity<math display="inline"><semantics> <mrow> <msub> <mover accent="true"> <mi>φ</mi> <mo>˙</mo> </mover> <mn>2</mn> </msub> </mrow> </semantics></math>.</p>
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<p>The phase plane of the system’s (<b>a</b>) <math display="inline"><semantics> <mrow> <msub> <mi>φ</mi> <mn>1</mn> </msub> </mrow> </semantics></math> with angular velocities <math display="inline"><semantics> <mrow> <msub> <mover accent="true"> <mi>φ</mi> <mo>˙</mo> </mover> <mn>1</mn> </msub> </mrow> </semantics></math> in the primary resonance situation without control (<b>b</b>) <math display="inline"><semantics> <mrow> <msub> <mi>φ</mi> <mn>1</mn> </msub> </mrow> </semantics></math> with angular velocities <math display="inline"><semantics> <mrow> <msub> <mover accent="true"> <mi>φ</mi> <mo>˙</mo> </mover> <mn>1</mn> </msub> </mrow> </semantics></math> in the primary resonance situation with the PID controller (<b>c</b>) <math display="inline"><semantics> <mrow> <msub> <mi>φ</mi> <mn>2</mn> </msub> </mrow> </semantics></math> with angular velocities <math display="inline"><semantics> <mrow> <msub> <mover accent="true"> <mi>φ</mi> <mo>˙</mo> </mover> <mn>2</mn> </msub> </mrow> </semantics></math> in the primary resonance situation without control (<b>d</b>) <math display="inline"><semantics> <mrow> <msub> <mi>φ</mi> <mn>2</mn> </msub> </mrow> </semantics></math> with angular velocities <math display="inline"><semantics> <mrow> <msub> <mover accent="true"> <mi>φ</mi> <mo>˙</mo> </mover> <mn>2</mn> </msub> </mrow> </semantics></math> in the primary resonance situation with the PID controller.</p>
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<p>The frequency response curves on the plane <math display="inline"><semantics> <mrow> <msub> <mi>σ</mi> <mn>1</mn> </msub> </mrow> </semantics></math> and the first part of the system (<math display="inline"><semantics> <mrow> <msub> <mi>a</mi> <mn>1</mn> </msub> </mrow> </semantics></math>) (<b>a</b>) without a controller, (<b>b</b>) with a P controller, (<b>c</b>) with a PI controller, and (<b>d</b>) with a PID controller. (<b>red color</b>) unstable region (<b>black color</b>) stable region</p>
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<p>The frequency response curves on plane <math display="inline"><semantics> <mrow> <msub> <mi>σ</mi> <mn>2</mn> </msub> </mrow> </semantics></math> and the first part of the system (<math display="inline"><semantics> <mrow> <msub> <mi>a</mi> <mn>2</mn> </msub> </mrow> </semantics></math>) (<b>a</b>) without a controller, (<b>b</b>) with a P controller, (<b>c</b>) with a PI controller, and (<b>d</b>) with PID controller. (<b>red color</b>) unstable region (<b>black color</b>) stable region.</p>
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<p>Frequency response before and after PID: (<b>a</b>) first main system <math display="inline"><semantics> <mrow> <msub> <mi>a</mi> <mn>1</mn> </msub> </mrow> </semantics></math> and (<b>b</b>) first main system <math display="inline"><semantics> <mrow> <msub> <mi>a</mi> <mn>2</mn> </msub> </mrow> </semantics></math>.</p>
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<p>(<b>a</b>) The FRC of the external force action <math display="inline"><semantics> <mrow> <msub> <mi>f</mi> <mn>1</mn> </msub> </mrow> </semantics></math>. (<b>b</b>) Natural frequency <math display="inline"><semantics> <mrow> <msub> <mi>ω</mi> <mn>1</mn> </msub> </mrow> </semantics></math>. (<b>c</b>) Damping coefficient <math display="inline"><semantics> <mi>ζ</mi> </semantics></math>. (<b>d</b>) Linear parameter <math display="inline"><semantics> <mi>β</mi> </semantics></math>. (<b>e</b>) Nonlinear parameter <math display="inline"><semantics> <mrow> <msub> <mi>α</mi> <mn>2</mn> </msub> </mrow> </semantics></math>. All of these regard the first part of the system <math display="inline"><semantics> <mrow> <msub> <mi>a</mi> <mn>1</mn> </msub> </mrow> </semantics></math>.</p>
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<p>(<b>a</b>) The FRC of the external force action <math display="inline"><semantics> <mrow> <msub> <mi>f</mi> <mn>1</mn> </msub> </mrow> </semantics></math>. (<b>b</b>) Natural frequency <math display="inline"><semantics> <mrow> <msub> <mi>ω</mi> <mn>1</mn> </msub> </mrow> </semantics></math>. (<b>c</b>) Damping coefficient <math display="inline"><semantics> <mi>ζ</mi> </semantics></math>. (<b>d</b>) Linear parameter <math display="inline"><semantics> <mi>β</mi> </semantics></math>. (<b>e</b>) Nonlinear parameter <math display="inline"><semantics> <mrow> <msub> <mi>α</mi> <mn>2</mn> </msub> </mrow> </semantics></math>. All of these regard the first part of the system <math display="inline"><semantics> <mrow> <msub> <mi>a</mi> <mn>1</mn> </msub> </mrow> </semantics></math>.</p>
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<p>(<b>a</b>) The FRC of the external force action <math display="inline"><semantics> <mrow> <msub> <mi>f</mi> <mn>2</mn> </msub> </mrow> </semantics></math>. (<b>b</b>) Natural frequency <math display="inline"><semantics> <mrow> <msub> <mi>ω</mi> <mn>2</mn> </msub> </mrow> </semantics></math>. (<b>c</b>) Nonlinear parameter <math display="inline"><semantics> <mrow> <msub> <mi>α</mi> <mn>4</mn> </msub> </mrow> </semantics></math>. All of these regard the second part of system <math display="inline"><semantics> <mrow> <msub> <mi>a</mi> <mn>2</mn> </msub> </mrow> </semantics></math>.</p>
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<p>Response curve for the system amplitudes with (<b>a</b>)<math display="inline"><semantics> <mrow> <msub> <mi>K</mi> <mi>p</mi> </msub> </mrow> </semantics></math> (<b>b</b>) <math display="inline"><semantics> <mrow> <msub> <mi>K</mi> <mi>i</mi> </msub> </mrow> </semantics></math> (<b>c</b>) <math display="inline"><semantics> <mrow> <msub> <mi>K</mi> <mi>d</mi> </msub> </mrow> </semantics></math>.</p>
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<p>Comparison of numerical simulation and perturbation analysis for both framework modes in PID controllers. (<b>a</b>) the first part of the system <math display="inline"><semantics> <mrow> <msub> <mi>φ</mi> <mn>1</mn> </msub> </mrow> </semantics></math> (<b>b</b>) the second part of the system <math display="inline"><semantics> <mrow> <msub> <mi>φ</mi> <mn>2</mn> </msub> </mrow> </semantics></math></p>
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<p>Contrast between the FRC solution and RK- 4 solution for both systems (<b>a</b>) the first part of the system <math display="inline"><semantics> <mrow> <msub> <mi>a</mi> <mn>1</mn> </msub> </mrow> </semantics></math> (<b>b</b>) the second part of the system <math display="inline"><semantics> <mrow> <msub> <mi>a</mi> <mn>2</mn> </msub> </mrow> </semantics></math>.</p>
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27 pages, 31485 KiB  
Article
A Dynamic Analysis of a Poly-Articulated Robot
by Sorin Dumitru, Cristian Copilusi, Nicolae Dumitru and Ionut Geonea
Computation 2024, 12(8), 156; https://doi.org/10.3390/computation12080156 - 2 Aug 2024
Viewed by 257
Abstract
This paper studies the kinematics and dynamics of a poly-articulated robot. The robot can be used in hardly accessible places and special environments. The poly-articulated robot includes two main parts: a flexible unit and an actuation unit. The flexible unit consists of three [...] Read more.
This paper studies the kinematics and dynamics of a poly-articulated robot. The robot can be used in hardly accessible places and special environments. The poly-articulated robot includes two main parts: a flexible unit and an actuation unit. The flexible unit consists of three modules specially designed for serving in a complex 3D workspace. Each module has flexible vertebrae and rigid disks. The poly-articulated robot simulation is achieved with the MSC Adams 2012 and ANSYS R14.5 software. Thus, we aim to determine whether the variation laws depend on the time of the kinematic parameters for each part in a specific motion, considering each part has to act as a rigid body or a deformable body. Using the finite element method, the stress and deformations for normal and critical positions are calculated for the poly-articulated robot. To validate the simulation models designed in this research, an experimental analysis of the proposed poly-articulated robot is developed. The command and control unit was equipped with motion sensors that allow to identify the position of each flexible unit module. Full article
(This article belongs to the Section Computational Engineering)
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<p>Flexible unit types proposed through this research: (<b>a</b>) flexible unit with a cylindrical architecture, and (<b>b</b>) flexible unit with a tronconic form.</p>
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<p>Virtual model of the poly-articulated robot in a parametrized form.</p>
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<p>A virtual model of the poly-articulated robot—expanded view.</p>
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<p>Poly-articulated cylindrical robot kinematic models using (<b>a</b>) MSC Adams and (<b>b</b>) ANSYS software.</p>
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<p>Poly-articulated tronconic robot kinematic models using (<b>a</b>) MSC Adams and (<b>b</b>) ANSYS software.</p>
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<p>Coordinate systems location on a flexible body for the Craig–Bampton method.</p>
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<p>Motor joint displacement setup on a 3-s time interval for both analyzed flexible units.</p>
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<p>Deformed shapes of the flexible unit for both analyzed forms processed under the MSC Adams environment.</p>
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<p>Translational deformation components for the distal module corresponding to the node from disk D11 vs. time.</p>
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<p>Translational deformation components for the distal module corresponding to the node from disk D7 vs. time.</p>
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<p>Contact definition between elastic vertebrae and flexible unit disks.</p>
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<p>Definition of the flexible unit motor elements in case of the cylindrical form.</p>
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<p>The displacement component variation on the X-axis for the final disk from the distal module in a local coordinate system vs. time.</p>
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<p>The displacement component variation on the Z-axis for the final disk from the distal module in a local coordinate system vs. time.</p>
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<p>The elastic displacement variation of the final disk marker from the proximal module vs. time.</p>
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<p>The variation of the deformed shape of the flexible unit across the Y-axis of the local coordinate system across time ((<b>a</b>)—isometric view; (<b>b</b>)—rotated view in the X–Y plane).</p>
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<p>The resulting displacement variation for vertebrae in a global coordinate system vs. time ((<b>a</b>)—motor vertebrae; (<b>b</b>)—driven vertebrae).</p>
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<p>The resulting displacement variation for the vertebrae of the median module in the global coordinate system vs. time ((<b>a</b>)—motor vertebrae; (<b>b</b>)—driven vertebrae).</p>
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<p>The resulting displacement variation for the vertebrae of the proximal module in the global coordinate system vs. time ((<b>a</b>)—motor vertebrae; (<b>b</b>)—driven vertebrae).</p>
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<p>Snapshots of the acquired distribution of elastic displacement for various temporal moments vs. time.</p>
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<p>Equivalent von Mises stress distribution vs. time.</p>
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<p>Actuation modes represented in steps vs. time for the whole flexible unit.</p>
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<p>The reaction force distribution for the motor vertebra of the distal module depends on the time interval of 2 s (1 to 3 s).</p>
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<p>The reaction force distribution for a driven vertebra of the distal module depends on the time interval of 1 s.</p>
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<p>The reaction force distribution for the motor vertebra of the median module depends on the time interval of 2 s.</p>
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<p>The reaction force distribution for a driven vertebra of the median module depends on the time interval of 1 s.</p>
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<p>The reaction force distribution for a driven vertebra of the proximal module depends on a time interval of 1 s.</p>
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<p>The frictional stress distribution depends on time.</p>
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<p>The penetration contact variation for the mechanical system contact definition vs. time.</p>
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<p>The poly-articulated robotic system prototype equipped with the two flexible unit forms: (<b>a</b>) cylindrical form and (<b>b</b>) tronconic form.</p>
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<p>The poly-articulated robotic actuation unit.</p>
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<p>Guiding systems for the nut–screw mechanical transmissions.</p>
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<p>CONTEMPLAS motion analysis workflow.</p>
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<p>Experimental analysis setup for the analyzed robotic system.</p>
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<p>Marker attachment on the poly-articulated robotic system.</p>
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<p>Some snapshots during the experimental tests for trajectory evaluation.</p>
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<p>Total displacement on the X-axis of the poly-articulated robotic system vs time: A—Experimental tronconic model; B—Adams virtual model with a cylindrical flexible unit; C—Adams virtual model with a tronconic form of the flexible unit.</p>
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<p>Total displacement on the Y-axis of the poly-articulated robotic system vs time: A—Experimental tronconic model; B—Adams virtual model with a cylindrical flexible unit; C—Adams virtual model with a tronconic form of the flexible unit.</p>
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<p>Total displacement on the Z-axis of the poly-articulated robotic system vs time: A—Experimental tronconic model; B—Adams virtual model with a cylindrical flexible unit; C—Adams virtual model with a tronconic form of the flexible unit.</p>
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22 pages, 954 KiB  
Article
A Novel Mixed Finite/Infinite Dimensional Port–Hamiltonian Model of a Mechanical Ventilator
by Milka C. I. Madahana, John E. D. Ekoru and Otis T. C. Nyandoro
Computation 2024, 12(8), 155; https://doi.org/10.3390/computation12080155 - 31 Jul 2024
Viewed by 355
Abstract
Mechanical ventilation is a life-saving treatment for critically ill patients who are struggling to breathe independently due to injury or disease. Globally, per year, there has always been a large number of individuals who have required mechanical ventilation. The COVID-19 pandemic brought to [...] Read more.
Mechanical ventilation is a life-saving treatment for critically ill patients who are struggling to breathe independently due to injury or disease. Globally, per year, there has always been a large number of individuals who have required mechanical ventilation. The COVID-19 pandemic brought to light the significance of mechanical ventilation, which played a significant role in sustaining COVID-19-infected critically ill patients who could not breathe on their own. The pandemic drew the attention of the world to the shortage of ventilators globally. Some of the challenges to providing an adequate number of ventilators include: increased demand for ventilators, supply chain disruptions, manufacturing constraints, distribution inequalities, financial constraints, maintenance and logistics difficulties, training and expertise shortages, and the lack of design and development of affordable mechanical ventilators that satisfy the stipulated requirements. This research work presents the formulation of a detailed Port–Hamiltonian model of a mechanical ventilator integrated with the human respiratory system. The interconnection and coupling conditions for the various subsystems within the mechanical ventilator and the coupling between the mechanical ventilator and the human respiratory system are also presented. Structure-preserving discretization is provided alongside numerical simulations and results. The obtained results are found to be comparable to results presented in the literature. Future work will include the design of suitable controllers for the system. Full article
(This article belongs to the Section Computational Engineering)
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<p>Energy storage, routing and dissipation.</p>
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<p>Schematic diagram of a mechanical ventilator.</p>
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<p>Diagram of a solenoid valve in (<b>i</b>) the open position, which allows fluid flow, and (<b>ii</b>) the closed position, which stops fluid flow.</p>
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<p>Solenoid coordinate system.</p>
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<p>Pipe segment coordinate system.</p>
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<p>Circuit diagram of an electric model of a lung of a fully sedated patient [<a href="#B26-computation-12-00155" class="html-bibr">26</a>].</p>
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<p>The graph associated with the circuit diagram given in <a href="#computation-12-00155-f006" class="html-fig">Figure 6</a>.</p>
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<p>Simplified graph of the mechanical ventilator given in <a href="#computation-12-00155-f002" class="html-fig">Figure 2</a> indicating the elements belonging to the patient, given by the arcs <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="script">A</mi> <msub> <mi>O</mi> <mn>21</mn> </msub> </msub> <mo>∈</mo> <msub> <mi mathvariant="script">A</mi> <mi>O</mi> </msub> </mrow> </semantics></math> and vertices <math display="inline"><semantics> <mrow> <mfenced separators="" open="{" close="}"> <msub> <mi mathvariant="script">V</mi> <msub> <mi>O</mi> <mn>1</mn> </msub> </msub> <mo>,</mo> <msub> <mi mathvariant="script">V</mi> <msub> <mi>O</mi> <mn>2</mn> </msub> </msub> </mfenced> <mo>∈</mo> <msub> <mi mathvariant="script">V</mi> <mi>O</mi> </msub> </mrow> </semantics></math>, as well as elements of the inspiratory and expiratory arcs and vertices, given by <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="script">V</mi> <mi>I</mi> </msub> <mo>,</mo> <msub> <mi mathvariant="script">V</mi> <mi>E</mi> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="script">A</mi> <mrow> <mi>I</mi> <mi>O</mi> </mrow> </msub> <mo>,</mo> <msub> <mi mathvariant="script">A</mi> <mrow> <mi>O</mi> <mi>E</mi> </mrow> </msub> </mrow> </semantics></math>, respectively.</p>
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<p>Detailed graph of the mechanical ventilator given in <a href="#computation-12-00155-f008" class="html-fig">Figure 8</a> indicating the patient vertex <math display="inline"><semantics> <msub> <mi mathvariant="script">V</mi> <mi>O</mi> </msub> </semantics></math> as well as the arcs and vertices along the inspiratory and expiratory paths.</p>
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<p>Staggered grid discretization of the one-dimensional Port–Hamiltonian pipe dynamic model.</p>
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<p>Graph of air pressure versus time.</p>
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<p>Graph of volume flow versus time.</p>
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16 pages, 2332 KiB  
Article
Bayesian Approach to Stochastic Estimation of Population Survival Curves in Chile Using ABC Techniques and Its Impact over Social Structures
by Rolando Rubilar-Torrealba, Karime Chahuán-Jiménez, Hanns de la Fuente-Mella and Claudio Elórtegui-Gómez
Computation 2024, 12(8), 154; https://doi.org/10.3390/computation12080154 - 29 Jul 2024
Viewed by 396
Abstract
In Chile and worldwide, life expectancy has consistently increased over the past six decades. Thus, the purpose of this study was to identify, measure, and estimate the population mortality ratios in Chile, mortality estimates are used to calculate life expectancy when constructing life [...] Read more.
In Chile and worldwide, life expectancy has consistently increased over the past six decades. Thus, the purpose of this study was to identify, measure, and estimate the population mortality ratios in Chile, mortality estimates are used to calculate life expectancy when constructing life tables. The Bayesian approach, specifically through Approximate Bayesian Computation (ABC) is employed to optimize parameter selection for these calculations. ABC corresponds to a class of computational methods rooted in Bayesian statistics that could be used to estimate the posterior distributions of the model parameters. For this research, ABC was applied to estimate the mortality ratios in Chile, using information available from 2004 to 2021. The results showed heterogeneity in the results when selecting the best model. Additionally, it was possible to generate projections for the next 10 years for the series analysed in the research. Finally, the main contribution of this research is that we measured and estimated the population mortality rates in Chile, defining the optimal selection of parameters, in order to contribute to creating a link between social and technical sciences for the advancement and implementation of current knowledge in the field of social structures. Full article
(This article belongs to the Special Issue Computational Social Science and Complex Systems—2nd Edition)
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<p>Evolution of life expectancy in Chile.</p>
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<p>Different survival curves with synthetic data.</p>
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<p>Summary of the methodology used in the research.</p>
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<p>Projection of the parameter <math display="inline"><semantics> <mover accent="true"> <mi>p</mi> <mo stretchy="false">^</mo> </mover> </semantics></math> for different ages and different sexes.</p>
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<p>Evolution of the projection for the expected value of population decay. The shift to the right implies improvements in the life expectancy of the population.</p>
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<p>Estimation of population projections until 2030. The dotted lines correspond to the mean value of the projections.</p>
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25 pages, 12360 KiB  
Article
Identification and Dynamics Understanding of Novel Inhibitors of Peptidase Domain of Collagenase G from Clostridium histolyticum
by Farah Anjum, Ali Hazazi, Fouzeyyah Ali Alsaeedi, Maha Bakhuraysah, Alaa Shafie, Norah Ali Alshehri, Nahed Hawsawi, Amal Adnan Ashour, Hamsa Jameel Banjer, Afaf Alharthi and Maryam Ishrat Niaz
Computation 2024, 12(8), 153; https://doi.org/10.3390/computation12080153 - 25 Jul 2024
Viewed by 440
Abstract
Clostridium histolyticum is a Gram-positive anaerobic bacterium belonging to the Clostridium genus. It produces collagenase, an enzyme involved in breaking down collagen which is a key component of connective tissues. However, antimicrobial resistance (AMR) poses a great challenge in combating infections caused by [...] Read more.
Clostridium histolyticum is a Gram-positive anaerobic bacterium belonging to the Clostridium genus. It produces collagenase, an enzyme involved in breaking down collagen which is a key component of connective tissues. However, antimicrobial resistance (AMR) poses a great challenge in combating infections caused by this bacteria. The lengthy nature of traditional drug development techniques has resulted in a shift to computer-aided drug design and other modern drug discovery approaches. The above method offers a cost-effective means for gathering comprehensive information about how ligands interact with their target proteins. The objective of this study is to create novel, explicit drugs that specifically inhibit the C. histolyticum collagenase enzyme. Through structure-based virtual screening, a library containing 1830 compounds was screened to identify potential drug candidates against collagenase enzymes. Following that, molecular dynamic (MD) simulation was performed in an aqueous solution to evaluate the behavior of protein and ligand in a dynamic environment while density functional theory (DFT) analysis was executed to predict the molecular properties and structure of lead compounds, and the WaterSwap technique was utilized to obtain insights into the drug–protein interaction with water molecules. Furthermore, principal component analysis (PCA) was performed to reveal conformational changes, salt bridges to express electrostatic interaction and protein stability, and absorption, distribution, metabolism, excretion, and toxicity (ADMET) to assess the pharmacokinetics profile of top compounds and control molecules. Three potent drug candidates were identified MSID000001, MSID000002, MSID000003, and the control with a binding score of −10.7 kcal/mol, −9.8 kcal/mol, −9.5 kcal/mol, and −8 kcal/mol, respectively. Furthermore, Molecular Mechanics Poisson–Boltzmann Surface Area (MMPBSA) analysis of the simulation trajectories revealed energy scores of −79.54 kcal/mol, −73.99 kcal/mol, −62.26 kcal/mol, and −70.66 kcal/mol, correspondingly. The pharmacokinetics properties exhibited were under the acceptable range. The compounds hold the potential to be novel drugs; therefore, further investigation needs to be conducted to find out their anti-collagenase action against C. histolyticum infections and antibiotic resistance. Full article
(This article belongs to the Special Issue 10th Anniversary of Computation—Computational Biology)
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<p>The integrated computational workflow begins with (i) structure retrieval and preparation followed by (ii) compound preparation and (iii) molecular docking. Next, DFT analysis to estimate electronic properties and structure (iv), ADMET to assess pharmacokinetics profile (v), and MD simulation, (vi) PCA analysis as well as (vii) secondary structure analysis, (viii) hydrogen bond analysis. (ix) Salt bridges, (x) MMPBSA, (xi) Entropy energy calculation, and finally (xii) water swap energy estimation.</p>
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<p>Highlights the labeled active site residues GLU498, TRP539, HIS523, TYR607, GLU555, and TYR599 in the three-dimensional (3D) structure of the collagenase enzyme.</p>
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<p>The three-dimensional (3D) docking interaction and binding poses of target enzyme with ligands as MSID000001 (<b>A</b>), MSID000002 (<b>B</b>), MSID000003 (<b>C</b>), and Control (<b>D</b>).</p>
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<p>The two-dimensional (2D) interaction between the target enzyme collagenase and ligands MSID000001 (<b>A</b>), MSID000002 (<b>B</b>), MSID000003 (<b>C</b>), and Control (<b>D</b>).</p>
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<p>Optimized structures of the studied compounds at the B3LYP/6–311+G(d, p) level of DFT analysis in the gas phase.</p>
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<p>The contour plots of HOMOs and LUMOs of studied compounds.</p>
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<p>Molecular Electrostatic Potential (MEP) maps for the studied compounds.</p>
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<p>The MSID000001, MSID000002, and MSID000003 complexes and control molecule flexibility, compactness, and stability through (<b>A</b>) RMSD, (<b>B</b>) RMSF, (<b>C</b>) RoG, and (<b>D</b>) β-factors.</p>
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<p>Insights into the top three complexes and control with target enzyme collagenase.</p>
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<p>The principal component analysis of MSID000001 (<b>A</b>), MSID000002 (<b>B</b>), MSID000003 (<b>C</b>) and Control (<b>D</b>), respectively.</p>
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<p>Predicted WaterSwap binding energy for MSID000001, MSID000002, and MSID000003, and Control.</p>
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9 pages, 5096 KiB  
Article
Ultrashort Echo Time and Fast Field Echo Imaging for Spine Bone Imaging with Application in Spondylolysis Evaluation
by Diana Vucevic, Vadim Malis, Yuichi Yamashita, Anya Mesa, Tomosuke Yamaguchi, Suraj Achar, Mitsue Miyazaki and Won C. Bae
Computation 2024, 12(8), 152; https://doi.org/10.3390/computation12080152 - 24 Jul 2024
Viewed by 460
Abstract
Isthmic spondylolysis is characterized by a stress injury to the pars interarticularis bones of the lumbar spines and is often missed by conventional magnetic resonance imaging (MRI), necessitating a computed tomography (CT) for accurate diagnosis. We compare MRI techniques suitable for producing CT-like [...] Read more.
Isthmic spondylolysis is characterized by a stress injury to the pars interarticularis bones of the lumbar spines and is often missed by conventional magnetic resonance imaging (MRI), necessitating a computed tomography (CT) for accurate diagnosis. We compare MRI techniques suitable for producing CT-like images. Lumbar spines of asymptomatic and low back pain (LBP) subjects were imaged at 3-Tesla with multi-echo ultrashort echo time (UTE) and field echo (FE) sequences followed by simple post-processing of averaging and inverting to depict spinal bones with a CT-like appearance. The contrast-to-noise ratio (CNR) for bone was determined to compare UTE vs. FE and single-echo vs. multi-echo data. Visually, both sequences depicted cortical bone with good contrast; UTE-processed sequences provided a flatter contrast for soft tissues that made them easy to distinguish from bone, while FE-processed images had better resolution and bone–muscle contrast, which are important for fracture detection. Additionally, multi-echo images provided significantly (p = 0.03) greater CNR compared with single-echo images. Using these techniques, progressive spondylolysis was detected in an LBP subject. This study demonstrates the feasibility of using spine bone MRI to yield CT-like contrast. Through the employment of multi-echo UTE and FE sequences combined with simple processing, we observe sufficient enhancements in image quality and contrast to detect pars fractures. Full article
(This article belongs to the Special Issue Computational Medical Image Analysis—2nd Edition)
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<p>Raw MRI images of a lumbar spine acquired by (<b>A</b>) T2-weighted fat-suppressed fast spin echo (FSE T2 FS), (<b>B</b>,<b>C</b>) 3D ultrashort echo time (UTE) at varying echo times (TEs), and (<b>D</b>,<b>E</b>) 3D field echo (FE) at varying TEs.</p>
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<p>Processed images to create CT-like contrast from (<b>A</b>) the UTE 1<sup>st</sup>-echo image, (<b>B</b>) UTE multi-echo images, (<b>C</b>) the FE 1<sup>st</sup>-echo image, and (<b>D</b>) FE multi-echo images. Differences between sequences (UTE vs. FE) and improvements in contrast and image quality from multi-echo processing are apparent.</p>
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<p>Regions of interest (blue-enclosed areas), including bone of the pars interarticularis, paraspinal muscles, and air, which were analyzed to determine the SNR and CNR.</p>
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<p>Detection of a moderately sized pars defect (arrows) in an adolescent athlete with persistent low back pain using FSE T2 FS (<b>A</b>), UTE multi-echo processing (<b>B</b>), and FE multi-echo processing (<b>C</b>). The processed images may enable an easier and more confident diagnosis of isthmic spondylolysis.</p>
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29 pages, 11922 KiB  
Article
Using Machine Learning Algorithms to Develop a Predictive Model for Computing the Maximum Deflection of Horizontally Curved Steel I-Beams
by Elvis Ababu, George Markou and Sarah Skorpen
Computation 2024, 12(8), 151; https://doi.org/10.3390/computation12080151 - 24 Jul 2024
Viewed by 370
Abstract
Horizontally curved steel I-beams exhibit a complicated mechanical response as they experience a combination of bending, shear, and torsion, which varies based on the geometry of the beam at hand. The behaviour of these beams is therefore quite difficult to predict, as they [...] Read more.
Horizontally curved steel I-beams exhibit a complicated mechanical response as they experience a combination of bending, shear, and torsion, which varies based on the geometry of the beam at hand. The behaviour of these beams is therefore quite difficult to predict, as they can fail due to either flexure, shear, torsion, lateral torsional buckling, or a combination of these types of failure. This therefore necessitates the usage of complicated nonlinear analyses in order to accurately model their behaviour. Currently, little guidance is provided by international design standards in consideration of the serviceability limit states of horizontally curved steel I-beams. In this research, an experimentally validated dataset was created and was used to train numerous machine learning (ML) algorithms for predicting the midspan deflection at failure as well as the failure load of numerous horizontally curved steel I-beams. According to the experimental and numerical investigation, the deep artificial neural network model was found to be the most accurate when used to predict the validation dataset, where a mean absolute error of 6.4 mm (16.20%) was observed. This accuracy far surpassed that of Castigliano’s second theorem, where the mean absolute error was found to be equal to 49.84 mm (126%). The deep artificial neural network was also capable of estimating the failure load with a mean absolute error of 30.43 kN (22.42%). This predictive model, which is the first of its kind in the international literature, can be used by professional engineers for the design of curved steel I-beams since it is currently the most accurate model ever developed. Full article
(This article belongs to the Special Issue Computational Methods in Structural Engineering)
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<p>Additional rolls to prevent web buckling on an I-section [<a href="#B4-computation-12-00151" class="html-bibr">4</a>].</p>
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<p>Variation of deflection coefficients with span angle for curved beams loaded with a concentrated load [<a href="#B8-computation-12-00151" class="html-bibr">8</a>].</p>
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<p>Basic schematic of the curved beam experimental setup (all dimensions are in millimetres).</p>
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<p>Schematic of the experiment with fixed support (all dimensions are in millimetres).</p>
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<p>Experiment with fixed support.</p>
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<p>Schematic indicating points of displacement measurements (all dimensions are in millimetres).</p>
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<p>Schematic indicating points of rotation measurements (all dimensions are in millimetres).</p>
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<p>Schematic indicating points of strain measurements (all dimensions are in millimetres).</p>
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<p>Deflected shape of the beam during the loading phase.</p>
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<p>Experimental beam load–deflection curve (midspan).</p>
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<p>Experimental beam load–tilt diagram.</p>
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<p>Graphical summary of experimental beam flange longitudinal strain gauge results.</p>
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<p>Graphical summary of experimental beam flange transverse strain gauge results.</p>
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<p>Graphical summary of experimental beam 45° web strain gauge results.</p>
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<p>Load–deflection graph displaying experimental deflection results, FE results, and results obtained with the analytical formula.</p>
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<p>Load–rotation graph displaying experimental, FE, and the M/R analytical formula results.</p>
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<p>Correlation matrix of (<b>a</b>) midspan deflection dataset and (<b>b</b>) failure load dataset.</p>
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<p>Correlation between the deflection determined using FEM and the deflection estimated using LR (<b>a</b>) on the training dataset and (<b>b</b>) on the testing dataset.</p>
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<p>Correlation between the deflection determined using FEM and the deflection estimated using POLYREG-HYT (<b>a</b>) on the training dataset and (<b>b</b>) on the testing dataset.</p>
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<p>Correlation between the deflection determined using FEM and the deflection estimated using the DANN-MPIH-HYT algorithm (<b>a</b>) on the training dataset (<b>b</b>) on the testing.</p>
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<p>Correlation between the deflection determined using FEM and the deflection estimated using the XGBoost-HYT-CV algorithm (<b>a</b>) on the training dataset (<b>b</b>) on the testing dataset.</p>
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<p>Summary of sensitivity analysis findings (XGBoost-HYT-CV).</p>
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<p>Case of deflection. Tuned cross-validation history for the case of (<b>a</b>) DANN-MPIH-HYT and (<b>b</b>) XGBoost-HYT-CV.</p>
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<p>Correlation between the failure load determined using FEM and the failure load estimated using LR (<b>a</b>) on the training dataset (<b>b</b>) on the testing dataset.</p>
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<p>Correlation between the failure load determined using FEM and the failure load estimated using POLYREG-HYT (<b>a</b>) on the training dataset (<b>b</b>) on the testing dataset.</p>
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<p>Correlation between the failure load determined using FEM and the failure load estimated using the DANN-MPIH-HYT algorithm (<b>a</b>) on the training dataset (<b>b</b>) on the testing dataset.</p>
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<p>Correlation between the failure load determined using FEM and the failure load estimated using the XGBoost-HYT-CV algorithm (<b>a</b>) on the training dataset (<b>b</b>) on the testing dataset.</p>
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<p>Results of sensitivity analysis (XGBoost-HYT-CV).</p>
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<p>Case of ultimate load. Tuned cross-validation history for the case of (<b>a</b>) DANN-MPIH-HYT and (<b>b</b>) XGBoost-HYT-CV.</p>
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<p>Correlation between the deflection determined using FEM and the deflection estimated using DANN-MPIH-HYT on the validation dataset.</p>
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<p>Correlation between the deflection determined using FEM and the deflection estimated using XGBoost-HYT-CV on the validation dataset.</p>
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<p>Correlation between the deflection determined using FEM and the deflection estimated using Castigliano’s theorem on the validation dataset.</p>
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<p>Correlation between the failure load determined using FEM and the failure load estimated using DANN-MPIH-HYT on the validation dataset.</p>
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<p>Correlation between the failure load determined using FEM and the failure load estimated using XGBoost-HYT-CV on the validation dataset.</p>
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