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3 pages, 168 KiB

Open AccessEditorial

Preface to the Special Issue on “Modelling and Simulation in Engineering”

by Camelia Petrescu and Valeriu David

Mathematics 2022, 10(14), 2387; https://doi.org/10.3390/math10142387 - 7 Jul 2022

Viewed by 839

Abstract

The continuing achievements in Information Technology and Computer science in recent decades provide new tools for engineers in the design of devices and systems, with significant advances both in numerical and in analytical methods of analysis [...] Full article

(This article belongs to the Special Issue Modeling and Simulation in Engineering)

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17 pages, 6074 KiB

Open AccessArticle

Effects of Magnetic Fields, Coupled Stefan Blowing and Thermodiffusion on Ferrofluid Transport Phenomena

by Rohana Abdul Hamid, Roslinda Nazar, Kohilavani Naganthran and Ioan Pop

Mathematics 2022, 10(10), 1646; https://doi.org/10.3390/math10101646 - 12 May 2022

Cited by 7 | Viewed by 1074

Abstract

The paramagnetic feature of ferrofluid allows it to be utilised in electronic devices and improvise fluid circulation in transformer windings. Hence, the present article aims to conduct the numerical study of ferrofluid boundary layer flow along with the Stefan blowing, velocity and thermal [...] Read more.

The paramagnetic feature of ferrofluid allows it to be utilised in electronic devices and improvise fluid circulation in transformer windings. Hence, the present article aims to conduct the numerical study of ferrofluid boundary layer flow along with the Stefan blowing, velocity and thermal slip, and Soret effects within the stagnation region over a stretching/shrinking surface. The governing equations were solved numerically using the bvp4c function in the MATLAB computing package. Based on the results, a stronger magnetic field of ferrofluid was needed to identify the numerical solutions past the shrinking surface, while the Stefan blowing diminished the solution’s availability. More than one solution is acquired for some specific values of the shrinking parameter, and the stability analysis validated that only one solution is reliable and stable. Full article

(This article belongs to the Special Issue Modeling and Simulation in Engineering)

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26 pages, 1726 KiB

Open AccessArticle

Estimation of the Hurst Parameter in Spot Volatility

by Yicun Li and Yuanyang Teng

Mathematics 2022, 10(10), 1619; https://doi.org/10.3390/math10101619 - 10 May 2022

Cited by 3 | Viewed by 1567

Abstract

This paper contributes in three stages in a logic of the cognitive process: we firstly propose a new estimation of Hurst exponent by changing frequency method which is purely mathematical. Then we want to check if the new Hurst is efficient, so we [...] Read more.

This paper contributes in three stages in a logic of the cognitive process: we firstly propose a new estimation of Hurst exponent by changing frequency method which is purely mathematical. Then we want to check if the new Hurst is efficient, so we prove the advantages of this new Hurst in asymptotic variance in the perspective compared with other two Hurst estimator. However, a purely mathematical game is not enough, a good estimation should be proven by reality, so we apply the new Hurst estimator into truncated and non-truncated spot volatility which fills the gap of previous literatures using 5-min price data (Source: Wind Financial Terminal) of 10 Chinese A-share industry indices from 1 January 2005 until 31 December 2020. Full article

(This article belongs to the Special Issue Modeling and Simulation in Engineering)

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17 pages, 2700 KiB

Open AccessArticle

Roughness Scaling Extraction Accelerated by Dichotomy-Binary Strategy and Its Application to Milling Vibration Signal

by Feng Feng, Meng Yuan, Yousheng Xia, Haoming Xu, Pingfa Feng and Xinghui Li

Mathematics 2022, 10(7), 1105; https://doi.org/10.3390/math10071105 - 29 Mar 2022

Cited by 2 | Viewed by 1509

Abstract

Fractal algorithms for signal analysis are developed from geometric fractals and can be used to describe various complex signals in nature. A roughness scaling extraction algorithm with first-order flattening (RSE-f1) was shown in our previous studies to have a high accuracy, strong noise [...] Read more.

Fractal algorithms for signal analysis are developed from geometric fractals and can be used to describe various complex signals in nature. A roughness scaling extraction algorithm with first-order flattening (RSE-f1) was shown in our previous studies to have a high accuracy, strong noise resistance, and a unique capacity to recognize the complexity of non-fractals that are common in signals. In this study, its disadvantage of a long calculation duration was addressed by using a dichotomy-binary strategy. The accelerated RSE-f1 algorithm (A-RSE-f1) retains the three above-mentioned advantages of the original algorithm according to theoretical analysis and artificial signal testing, while its calculation speed is significantly accelerated by 13 fold, which also makes it faster than the typical Higuchi algorithm. Afterwards, the vibration signals of the milling process are analyzed using the A-RSE-f1 algorithm, demonstrating the ability to distinguish different machining statuses (idle, stable, and chatter) effectively. The results of this study demonstrate that the RSE algorithm has been improved to meet the requirements of practical engineering with both a fast speed and a high performance. Full article

(This article belongs to the Special Issue Modeling and Simulation in Engineering)

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19 pages, 539 KiB

Open AccessArticle

Numerical Method for Solving of the Anomalous Diffusion Equation Based on a Local Estimate of the Monte Carlo Method

by Viacheslav V. Saenko, Vladislav N. Kovalnogov, Ruslan V. Fedorov, Dmitry A. Generalov and Ekaterina V. Tsvetova

Mathematics 2022, 10(3), 511; https://doi.org/10.3390/math10030511 - 5 Feb 2022

Cited by 1 | Viewed by 1709

Abstract

This paper considers a method of stochastic solution to the anomalous diffusion equation with a fractional derivative with respect to both time and coordinates. To this end, the process of a random walk of a particle is considered, and a master equation describing [...] Read more.

This paper considers a method of stochastic solution to the anomalous diffusion equation with a fractional derivative with respect to both time and coordinates. To this end, the process of a random walk of a particle is considered, and a master equation describing the distribution of particles is obtained. It has been shown that in the asymptotics of large times, this process is described by the equation of anomalous diffusion, with a fractional derivative in both time and coordinates. The method has been proposed for local estimation of the solution to the anomalous diffusion equation based on the simulation of random walk trajectories of a particle. The advantage of the proposed method is the opportunity to estimate the solution directly at a given point. This excludes the systematic component of the error from the calculation results and allows constructing the solution as a smooth function of the coordinate. Full article

(This article belongs to the Special Issue Modeling and Simulation in Engineering)

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29 pages, 5759 KiB

Open AccessArticle

Modeling and Optimization of a Compression Ignition Engine Fueled with Biodiesel Blends for Performance Improvement

by Ali Alahmer, Hegazy Rezk, Wail Aladayleh, Ahmad O. Mostafa, Mahmoud Abu-Zaid, Hussein Alahmer, Mohamed R. Gomaa, Amel A. Alhussan and Rania M. Ghoniem

Mathematics 2022, 10(3), 420; https://doi.org/10.3390/math10030420 - 28 Jan 2022

Cited by 24 | Viewed by 2626

Abstract

Biodiesel is considered to be a promising alternative option to diesel fuel. The main contribution of the current work is to improve compression ignition engine performance, fueled by several biodiesel blends. Three metrics were used to evaluate the output performance of the compression [...] Read more.

Biodiesel is considered to be a promising alternative option to diesel fuel. The main contribution of the current work is to improve compression ignition engine performance, fueled by several biodiesel blends. Three metrics were used to evaluate the output performance of the compression ignition engine, as follows: brake torque (BT), brake specific fuel consumption (BSFC), and brake thermal efficiency (BTE), by varying two input parameters (engine speed and fuel type). The engine speeds were in the 1200–2400 rpm range. Three biodiesel blends, containing 20 vol.% of vegetable oil and 80 vol.% of pure diesel fuel, were prepared and tested. In all the experiments, pure diesel fuel was employed as a reference for all biodiesel blends. The experimental results revealed the following findings: although all types of biodiesel blends have low calorific value and slightly high viscosity, as compared to pure diesel fuel, there was an improvement in both BT and brake power (BP) outputs. An increase in BSFC by 7.4%, 4.9%, and 2.5% was obtained for palm, sunflower, and corn biodiesel blends, respectively, as compared to that of pure diesel. The BTE of the palm oil biodiesel blend was the lowest among other biodiesel blends. The suggested work strategy includes two stages (modeling and parameter optimization). In the first stage, a robust fuzzy model is created, depending on the experimental results, to simulate the output performance of the compression ignition engine. The particle swarm optimization (PSO) algorithm is used in the second stage to determine the optimal operating parameters. To confirm the distinction of the proposed strategy, the obtained outcomes were compared to those attained by response surface methodology (RSM). The coefficient of determination (R²) and the root-mean-square-error (RMSE) were used as comparison metrics. The average R² was increased by 27.7% and 29.3% for training and testing, respectively, based on the fuzzy model. Using the proposed strategy in this work (integration between fuzzy logic and PSO) may increase the overall performance of the compression ignition engine by 2.065% and 8.256%, as concluded from the experimental tests and RSM. Full article

(This article belongs to the Special Issue Modeling and Simulation in Engineering)

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14 pages, 23773 KiB

Open AccessArticle

Inverse Modeling of Grout Curtain Hydraulic Conductivity Evolution Considering the Calcium Leaching Effect

by Kailai Zhang, Zhenzhong Shen, Liqun Xu, Yongkang Shu and Chao Yang

Mathematics 2022, 10(3), 381; https://doi.org/10.3390/math10030381 - 26 Jan 2022

Cited by 5 | Viewed by 2140

Abstract

The calcium leaching effect inevitably increases the grout curtain hydraulic conductivity. It is diffucult to sample and obtain the leaching-related calculation parameters for deep-buried grout curtains. This study introduced the inversion method into the calcium leaching analysis to get proper leaching-related calculation parameters [...] Read more.

The calcium leaching effect inevitably increases the grout curtain hydraulic conductivity. It is diffucult to sample and obtain the leaching-related calculation parameters for deep-buried grout curtains. This study introduced the inversion method into the calcium leaching analysis to get proper leaching-related calculation parameters and accurate results. An inverse analysis model was proposed using the genetic algorithm (GA) and finite element analysis technology to solve the calcium leaching problems. The objective function is constructed using the hydraulic head and leakage quantity time-series measurements, which improves the uniqueness and reliability of the inverse results. The proposed method was applied to the inverse analysis of the hydraulic conductivity evolution of the grout curtain in a concrete dam foundation. The predicted water heads and leakage quantity are consistent with the monitored data, indicating the rationality of this simulation. The grout curtain hydraulic conductivity prediction in 100 years is also presented. The results illustrate the feasibility of the proposed method for determining leaching-related parameters and the hydraulic conductivity prediction in the leaching process. Full article

(This article belongs to the Special Issue Modeling and Simulation in Engineering)

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14 pages, 2785 KiB

Open AccessArticle

Unsteady Three-Dimensional Flow in a Rotating Hybrid Nanofluid over a Stretching Sheet

by Noor Farizza Haniem Mohd Sohut, Siti Khuzaimah Soid, Sakhinah Abu Bakar and Anuar Ishak

Mathematics 2022, 10(3), 348; https://doi.org/10.3390/math10030348 - 24 Jan 2022

Cited by 11 | Viewed by 2789

Abstract

The problem of an unsteady 3D boundary layer flow induced by a stretching sheet in a rotating hybrid nanofluid is studied. A dimensionless set of variables is employed to transform the system of partial differential equations (PDEs) to a set of nonlinear ordinary [...] Read more.

The problem of an unsteady 3D boundary layer flow induced by a stretching sheet in a rotating hybrid nanofluid is studied. A dimensionless set of variables is employed to transform the system of partial differential equations (PDEs) to a set of nonlinear ordinary differential equations (ODEs). Then, the system of ODEs is solved numerically using the MATLAB software. The impacts of different parameters, such as copper nanoparticles volume fraction, radiation, rotation, unsteadiness, and stretching parameters are graphically displayed. It is found that two solutions exist for the flow induced by the stretching sheet. Furthermore, the increasing nanoparticle volume fraction enhances the skin friction coefficient. It is noticed that the skin friction coefficient, as well as the heat transfer rate at the surface, decrease as the rotating parameter increases. Additionally, the thermal radiation as well as the unsteadiness parameter stimulate the temperature. Full article

(This article belongs to the Special Issue Modeling and Simulation in Engineering)

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19 pages, 1307 KiB

Open AccessArticle

Solute Transport Control at Channel Junctions Using Adjoint Sensitivity

by Geovanny Gordillo, Mario Morales-Hernández and Pilar García-Navarro

Mathematics 2022, 10(1), 93; https://doi.org/10.3390/math10010093 - 28 Dec 2021

Cited by 2 | Viewed by 1281

Abstract

Water quality control and the control of contaminant spill in water in particular are becoming a primary need today. Gradient descent sensitivity methods based on the adjoint formulation have proved to be encouraging techniques in this context for river and channel flows. Taking [...] Read more.

Water quality control and the control of contaminant spill in water in particular are becoming a primary need today. Gradient descent sensitivity methods based on the adjoint formulation have proved to be encouraging techniques in this context for river and channel flows. Taking into account that most channels and rivers include junctions with other branches, the objective of this study is to explore the adjoint technique on a channel network to reconstruct the upstream boundary condition of the convection-reaction equation. For this purpose, the one-dimensional shallow water equations and the transport equation for a reactive solute are considered. The control is formulated through the gradient-descent technique supplied with a first-order iterative process. Both the physical and the adjoint equations are supplied with suitable internal boundary conditions at the junction and are numerically solved using a finite volume upwind scheme. The results reveal that the adjoint technique is capable of reconstructing the inlet solute concentration boundary condition in an acceptable number of iterations for both steady state and transient configurations using a downstream measurement location. It was also observed that the reconstruction of the boundary condition tends to be less effective the further away the measurement station is from the target. Full article

(This article belongs to the Special Issue Modeling and Simulation in Engineering)

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20 pages, 3845 KiB

Open AccessArticle

Rotating Flow in a Nanofluid with CNT Nanoparticles over a Stretching/Shrinking Surface

by Nor Azizah Yacob, Nor Fadhilah Dzulkifli, Siti Nur Alwani Salleh, Anuar Ishak and Ioan Pop

Mathematics 2022, 10(1), 7; https://doi.org/10.3390/math10010007 - 21 Dec 2021

Cited by 16 | Viewed by 2430

Abstract

The steady three-dimensional rotating flow past a stretching/shrinking surface in water and kerosene-based nanofluids containing single and multi-walled carbon nanotubes (CNTs) is investigated. The governing equations are converted to similarity equations, and then numerically solved using MATLAB software. The impacts of rotational, suction, [...] Read more.

The steady three-dimensional rotating flow past a stretching/shrinking surface in water and kerosene-based nanofluids containing single and multi-walled carbon nanotubes (CNTs) is investigated. The governing equations are converted to similarity equations, and then numerically solved using MATLAB software. The impacts of rotational, suction, and nanoparticle volume fraction on the flow and the thermal fields, as well as velocity and temperature gradients at the surface, are represented graphically and are analyzed. Further, the friction factor and the heat transfer rate for different parameters are presented in tables. It is found that the heat transfer rate increases with increasing nanoparticle volume fraction as well as suction parameter in water and kerosene-based nanofluids of single and multi-walled CNTs. However, the increment in the rotating flow parameter decreases the rate of heat transfer. Multi-walled carbon nanotubes and kerosene-based nanofluid contribute to heat transfer rates better than single-walled carbon nanotubes and water-based nanofluid, respectively. A unique solution exists for the stretching surface, while two solutions are obtained for the shrinking surface. Further analysis of their stabilities shows that only one of them is stable over time. Full article

(This article belongs to the Special Issue Modeling and Simulation in Engineering)

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20 pages, 14170 KiB

Open AccessArticle

Application of a Pattern-Recognition Neural Network for Detecting Analog Electronic Circuit Faults

by M. Isabel Dieste-Velasco

Mathematics 2021, 9(24), 3247; https://doi.org/10.3390/math9243247 - 15 Dec 2021

Cited by 6 | Viewed by 2220

Abstract

In this study, machine learning techniques based on the development of a pattern–recognition neural network were used for fault diagnosis in an analog electronic circuit to detect the individual hard faults (open circuits and short circuits) that may arise in a circuit. The [...] Read more.

In this study, machine learning techniques based on the development of a pattern–recognition neural network were used for fault diagnosis in an analog electronic circuit to detect the individual hard faults (open circuits and short circuits) that may arise in a circuit. The ability to determine faults in the circuit was analyzed through the availability of a small number of measurements in the circuit, as test points are generally not accessible for verifying the behavior of all the components of an electronic circuit. It was shown that, despite the existence of a small number of measurements in the circuit that characterize the existing faults, the network based on pattern-recognition functioned adequately for the detection and classification of the hard faults. In addition, once the neural network has been trained, it can be used to analyze the behavior of the circuit versus variations in its components, with a wider range than that used to develop the neural network, in order to analyze the ability of the ANN to predict situations different from those used to train the ANN and to extract valuable information that may explain the behavior of the circuit. Full article

(This article belongs to the Special Issue Modeling and Simulation in Engineering)

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17 pages, 499 KiB

Open AccessArticle

Numerical Solution to Anomalous Diffusion Equations for Levy Walks

by Viacheslav V. Saenko, Vladislav N. Kovalnogov, Ruslan V. Fedorov and Yuri E. Chamchiyan

Mathematics 2021, 9(24), 3219; https://doi.org/10.3390/math9243219 - 13 Dec 2021

Cited by 2 | Viewed by 1655

Abstract

The process of Levy random walks is considered in view of the constant velocity of a particle. A kinetic equation is obtained that describes the process of walks, and fractional differential equations are obtained that describe the asymptotic behavior of the process. It [...] Read more.

The process of Levy random walks is considered in view of the constant velocity of a particle. A kinetic equation is obtained that describes the process of walks, and fractional differential equations are obtained that describe the asymptotic behavior of the process. It is shown that, in the case of finite and infinite mathematical expectation of paths, these equations have a completely different form. To solve the obtained equations, the method of local estimation of the Monte Carlo method is described. The solution algorithm is described and the advantages and disadvantages of the considered method are indicated. Full article

(This article belongs to the Special Issue Modeling and Simulation in Engineering)

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22 pages, 6771 KiB

Open AccessArticle

Trochoidal Milling Path with Variable Feed. Application to the Machining of a Ti-6Al-4V Part

by César García-Hernández, Juan-José Garde-Barace, Juan-Jesús Valdivia-Sánchez, Pedro Ubieto-Artur, José-Antonio Bueno-Pérez, Basilio Cano-Álvarez, Miguel-Ángel Alcázar-Sánchez, Francisco Valdivia-Calvo, Rubén Ponz-Cuenca, José-Luis Huertas-Talón and Panagiotis Kyratsis

Mathematics 2021, 9(21), 2701; https://doi.org/10.3390/math9212701 - 25 Oct 2021

Cited by 10 | Viewed by 2824

Abstract

Trochoidal milling is a well-stablished machining strategy which still allows for the introduction of new approaches. This strategy can be applied to any kind of material, although it is usually associated to advanced materials, such as titanium and nickel alloys. This study is [...] Read more.

Trochoidal milling is a well-stablished machining strategy which still allows for the introduction of new approaches. This strategy can be applied to any kind of material, although it is usually associated to advanced materials, such as titanium and nickel alloys. This study is based on the adaptation of the feed speed of a milling tool with Ti-6Al-4V, so the chip width can be maintained constant without modifying the path geometry. A singularity in the experimental stage was to mill an Archimedes spiral groove instead of the conventional straight grooves. This made it possible to obtain a concave wall as well as a convex one and to optimize the amount of material used. The time efficiency compared to a constant feed, was slightly superior to 20%, reducing tool wear also. These techniques require milling machines with high mechanical and kinematic performance, as well as the absence of clearance between joints and a high acceleration capacity. Full article

(This article belongs to the Special Issue Modeling and Simulation in Engineering)

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18 pages, 2985 KiB

Open AccessArticle

An Improved High-Dimensional Kriging Surrogate Modeling Method through Principal Component Dimension Reduction

by Yaohui Li, Junjun Shi, Zhifeng Yin, Jingfang Shen, Yizhong Wu and Shuting Wang

Mathematics 2021, 9(16), 1985; https://doi.org/10.3390/math9161985 - 19 Aug 2021

Cited by 10 | Viewed by 2137

Abstract

The Kriging surrogate model in complex simulation problems uses as few expensive objectives as possible to establish a global or local approximate interpolation. However, due to the inversion of the covariance correlation matrix and the solving of Kriging-related parameters, the Kriging approximation process [...] Read more.

The Kriging surrogate model in complex simulation problems uses as few expensive objectives as possible to establish a global or local approximate interpolation. However, due to the inversion of the covariance correlation matrix and the solving of Kriging-related parameters, the Kriging approximation process for high-dimensional problems is time consuming and even impossible to construct. For this reason, a high-dimensional Kriging modeling method through principal component dimension reduction (HDKM-PCDR) is proposed by considering the correlation parameters and the design variables of a Kriging model. It uses PCDR to transform a high-dimensional correlation parameter vector in Kriging into low-dimensional one, which is used to reconstruct a new correlation function. In this way, time consumption of correlation parameter optimization and correlation function matrix construction in the Kriging modeling process is greatly reduced. Compared with the original Kriging method and the high-dimensional Kriging modeling method based on partial least squares, the proposed method can achieve faster modeling efficiency under the premise of meeting certain accuracy requirements. Full article

(This article belongs to the Special Issue Modeling and Simulation in Engineering)

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17 pages, 325 KiB

Open AccessArticle

Mathematical Modelling by Help of Category Theory: Models and Relations between Them

by Dmitrii Legatiuk

Mathematics 2021, 9(16), 1946; https://doi.org/10.3390/math9161946 - 15 Aug 2021

Cited by 7 | Viewed by 2986

Abstract

The growing complexity of modern practical problems puts high demand on mathematical modelling. Given that various models can be used for modelling one physical phenomenon, the role of model comparison and model choice is becoming particularly important. Methods for model comparison and model [...] Read more.

The growing complexity of modern practical problems puts high demand on mathematical modelling. Given that various models can be used for modelling one physical phenomenon, the role of model comparison and model choice is becoming particularly important. Methods for model comparison and model choice typically used in practical applications nowadays are computation-based, and thus time consuming and computationally costly. Therefore, it is necessary to develop other approaches to working abstractly, i.e., without computations, with mathematical models. An abstract description of mathematical models can be achieved by the help of abstract mathematics, implying formalisation of models and relations between them. In this paper, a category theory-based approach to mathematical modelling is proposed. In this way, mathematical models are formalised in the language of categories, relations between the models are formally defined and several practically relevant properties are introduced on the level of categories. Finally, an illustrative example is presented, underlying how the category-theory based approach can be used in practice. Further, all constructions presented in this paper are also discussed from a modelling point of view by making explicit the link to concrete modelling scenarios. Full article

(This article belongs to the Special Issue Modeling and Simulation in Engineering)

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