Topic Editors

School of Electrical and Electronic Engineering, University College Dublin, D04 V1W8 Dublin, Ireland
Section of Mathematics, International Telematic University Uninettuno, 00186 Roma, Italy

Engineering Mathematics

Abstract submission deadline
closed (31 December 2022)
Manuscript submission deadline
closed (30 April 2023)
Viewed by
83837

Topic Information

Dear Colleagues,

The purpose of “Engineering Mathematics” is to bring together mathematicians and engineers, as well as other scientists. The Topic will accept high-quality papers with original research results. This Topic aims to include the latest results related to Dynamical Systems (Continuous and Discrete), Mathematics of Networks, Optimization, Numerical Analysis, etc., in the field of engineering. “Engineering Mathematics” also aims to bring new insights in the mathematical modeling of several real-world applications in engineering, including electrical power systems, materials, energy, chemical engineering, etc. Finaly, articles that propose and construct new mathematical models in engineering are also very welcome.

Topics to be covered included but are not limited to:

  • differential/difference equations; 
  • partial differential equations; 
  • dynamical systems; 
  • control systems;
  • mathematical modeling; 
  • computational modeling and simulation; 
  • fractional calculus;
  • mathematics of networks;
  • modelling and stability analysis of signal models;
  • discrete calculus; 
  • circuits theory;
  • signal processing; 
  • materials; 
  • energy;
  • engineering

Dr. Ioannis Dassios
Prof. Dr. Clemente Cesarano
Topic Editors

Keywords

  • dynamical systems
  • control systems
  • mathematical modeling
  • fractional calculus
  • mathematics of networks
  • engineering

Participating Journals

Journal Name Impact Factor CiteScore Launched Year First Decision (median) APC
Applied Sciences
applsci
2.7 4.5 2011 16.9 Days CHF 2400
Energies
energies
3.2 5.5 2008 16.1 Days CHF 2600
Mathematics
mathematics
2.4 3.5 2013 16.9 Days CHF 2600
Signals
signals
- - 2020 35.1 Days CHF 1000
Symmetry
symmetry
2.7 4.9 2009 16.2 Days CHF 2400

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Published Papers (46 papers)

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26 pages, 5797 KiB  
Article
Upper Bound Solution Analysis of the Ultimate Bearing Capacity of Two–Layered Strip Foundation Based on Improved Radial Movement Optimization
by Liangxing Jin, Tian Qin and Pingting Liu
Appl. Sci. 2023, 13(12), 7299; https://doi.org/10.3390/app13127299 - 19 Jun 2023
Viewed by 879
Abstract
Considering the change of different soil layer parameters of a two–layered strip foundation, a planar kinematically permissible multi–block failure mechanism of a two–layered strip foundation under vertical uniform load is formulated. Based on upper–bound limit analysis theorem, the solution process of ultimate bearing [...] Read more.
Considering the change of different soil layer parameters of a two–layered strip foundation, a planar kinematically permissible multi–block failure mechanism of a two–layered strip foundation under vertical uniform load is formulated. Based on upper–bound limit analysis theorem, the solution process of ultimate bearing capacity of a two–layered strip foundation is proposed. The improved radial movement optimization (IRMO) could search the critical slip surface of the foundation and calculate associated ultimate bearing capacity. On this basis, analyze the influence parameters. The results show that the IRMO algorithm is feasible, stable, and efficient in solving the ultimate bearing capacity. With the increase in the internal friction angle and cohesion of the two–layered strip foundation, the critical slip surface will expand more deeply, and the ultimate bearing capacity will increase. The influence of upper soil parameters on the calculation results is greater than that of lower soil. For the case with upper–hard soil, the ultimate bearing capacity of it increases gradually with the increase in the H/B ratio. For the upper–soft case, the ultimate bearing capacity of it decreases gradually with the increase in the H/B ratio. Moreover, the increase of ground overload will also cause a linear–increasing in the ultimate bearing capacity. Full article
(This article belongs to the Topic Engineering Mathematics)
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19 pages, 4641 KiB  
Article
Intelligent Health Care and Diseases Management System: Multi-Day-Ahead Predictions of COVID-19
by Ahed Abugabah and Farah Shahid
Mathematics 2023, 11(4), 1051; https://doi.org/10.3390/math11041051 - 19 Feb 2023
Viewed by 1106
Abstract
The rapidly growing number of COVID-19 infected and death cases has had a catastrophic worldwide impact. As a case study, the total number of death cases in Algeria is over two thousand people (increased with time), which drives us to search its possible [...] Read more.
The rapidly growing number of COVID-19 infected and death cases has had a catastrophic worldwide impact. As a case study, the total number of death cases in Algeria is over two thousand people (increased with time), which drives us to search its possible trend for early warning and control. In this paper, the proposed model for making a time-series forecast for daily and total infected cases, death cases, and recovered cases for the countrywide Algeria COVID-19 dataset is a two-layer dropout gated recurrent unit (TDGRU). Four performance parameters were used to assess the model’s performance: mean absolute error (MAE), root mean squared error (RMSE), R2, and mean absolute percentage error (MAPE). The results generated with TDGRU are compared with actual numbers as well as predictions with conventional time-series techniques, such as autoregressive integrated moving average (ARIMA), machine learning model of linear regression (LR), and the time series-based deep learning method of long short-term memory (LSTM). The experiment results on different time horizons show that the TDGRU model outperforms the other forecasting methods that deliver correct predictions with lower prediction errors. Furthermore, since this TDGRU is based on a relatively simpler architecture than the LSTM, in comparison to LSTM-based models, it features a significantly reduced number of parameters, a shorter training period, a lower memory storage need, and a more straightforward hardware implementation. Full article
(This article belongs to the Topic Engineering Mathematics)
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17 pages, 888 KiB  
Article
Delayed Impulsive Control for μ-Synchronization of Nonlinear Multi-Weighted Complex Networks with Uncertain Parameter Perturbation and Unbounded Delays
by Hongguang Fan, Jiahui Tang, Kaibo Shi, Yi Zhao and Hui Wen
Mathematics 2023, 11(1), 250; https://doi.org/10.3390/math11010250 - 03 Jan 2023
Cited by 5 | Viewed by 1271
Abstract
The global μ-synchronization problem for nonlinear multi-weighted complex dynamical networks with uncertain parameter perturbation and mixed time-varying delays is investigated in this paper. Unlike other existing works, all delays, including sampling and internal and coupling delays, are assumed to be unbounded, making [...] Read more.
The global μ-synchronization problem for nonlinear multi-weighted complex dynamical networks with uncertain parameter perturbation and mixed time-varying delays is investigated in this paper. Unlike other existing works, all delays, including sampling and internal and coupling delays, are assumed to be unbounded, making the considered model more general and practical. Based on the generalized impulsive comparison principles, a time-varying impulsive controller with sampling delays is designed, and some new sufficient conditions are obtained to make drive–response multi-weighted networks reach μ-synchronization. In addition, the external coupling matrices do not need to meet the requirement of zero-row sum, and the limitation of time delay on pulse interval is weakened. The results obtained in this article can be seen as extensions of previous related research. Full article
(This article belongs to the Topic Engineering Mathematics)
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33 pages, 10620 KiB  
Article
Quasi-Static and Dynamic Tensile Behavior of Water-Bearing Sandstone Subjected to Microwave Irradiation
by Pin Wang, Tubing Yin, Xibing Li and Heinz Konietzky
Mathematics 2023, 11(1), 203; https://doi.org/10.3390/math11010203 - 30 Dec 2022
Cited by 3 | Viewed by 1478
Abstract
Microwave irradiation on rocks before excavation is an effective method to reduce equipment wear and energy consumption during mechanical cutting. Rock mass excavation is usually carried out in a water-rich environment and exposed to dynamic loads, thus understanding the coupled effects of water [...] Read more.
Microwave irradiation on rocks before excavation is an effective method to reduce equipment wear and energy consumption during mechanical cutting. Rock mass excavation is usually carried out in a water-rich environment and exposed to dynamic loads, thus understanding the coupled effects of water content and loading rate on the mechanical behavior of rocks under microwave radiation is essential. In this study, sandstone samples with five levels of water content (from oven-dried to water-saturated) were exposed to microwave irradiation at a power of 700 W for 10 min. Brazilian disc tests were conducted on sandstone samples after microwave radiation under both quasi-static and dynamic loading conditions. Test results revealed that, with the increase of the initial water content, the microwave heating capacity of the rock is significantly improved. The surface temperature of the saturated samples is approximately 1.38 times higher than that of the dry ones. Moreover, weight, P-wave velocity, quasi-static and dynamic tensile strength of the rock decrease, while porosity and damage factor exhibit a similar growth law. Before microwave irradiation, the average value of the P-wave velocity and the quasi-static tensile strength of sandstone were about 2521.3 m·s−1 and 4.65 MPa. However, after microwave treatment, when the initial water content was 2%, 3%, 4% and 5.4%, the P-wave velocity decreased by 6.1%, 9.8%, 16.4% and 30.2%, while that quasi-static tensile strength reduced by 9.2%, 16.7%, 30.6% and 48.9%, respectively. For water-saturated samples under microwave irradiation, the porosity increases from 13.02% to 18.12% (showing an increase of 39.2%), and the damage value rises to 0.51. In addition, the dynamic tensile strength shows a significant loading rate dependence, and as the initial water content increases, also the dynamic increase factor (DIF) increases. At a given loading rate, the energy dissipation decreases with the increase of the initial water content, which indicates that the presence of water cause more significant damage to the rock when subjected to microwave radiation. Scanning electron microscopy (SEM) results indicate that the internal damage of the rock after microwave radiation is dominated by intergranular cracks, and crack density increases with increasing initial water content of the samples. The underlying damage mechanisms of microwave radiation on water-bearing sandstone were interpreted with the theory of pore water pressure and structural thermal stresses. Full article
(This article belongs to the Topic Engineering Mathematics)
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15 pages, 302 KiB  
Article
Repdigits as Sums of Four Tribonacci Numbers
by Yuetong Zhou, Peng Yang, Shaonan Zhang and Kaiqiang Zhang
Symmetry 2022, 14(9), 1931; https://doi.org/10.3390/sym14091931 - 16 Sep 2022
Viewed by 1112
Abstract
In this paper, we show that 66666 is the largest repdigit expressible as the sum of four tribonacci numbers. We used Binet’s formula, Baker’s theory, and a reduction method during the proving procedure. We also used the periodic properties of tribonacci number modulo [...] Read more.
In this paper, we show that 66666 is the largest repdigit expressible as the sum of four tribonacci numbers. We used Binet’s formula, Baker’s theory, and a reduction method during the proving procedure. We also used the periodic properties of tribonacci number modulo 9 to deal with three individual cases. Full article
(This article belongs to the Topic Engineering Mathematics)
16 pages, 748 KiB  
Article
A Numerical Algorithm for Self-Learning Model Predictive Control in Servo Systems
by Hengzhan Yang, Dian Xi, Xu Weng, Fucai Qian and Bo Tan
Mathematics 2022, 10(17), 3152; https://doi.org/10.3390/math10173152 - 02 Sep 2022
Cited by 2 | Viewed by 1093
Abstract
Model predictive control (MPC) is one of the most effective methods of dealing with constrained control problems. Nevertheless, the uncertainty of the control system poses many problems in its performance optimization. For high-precision servo systems, friction is typically the main factor in uncertainty [...] Read more.
Model predictive control (MPC) is one of the most effective methods of dealing with constrained control problems. Nevertheless, the uncertainty of the control system poses many problems in its performance optimization. For high-precision servo systems, friction is typically the main factor in uncertainty affecting the accuracy of the system. Our work focuses on stochastic systems with unknown parameters and proposes a model predictive control strategy with machine learning characteristics that utilizes pre-estimated information to reduce uncertainty. Within this model, the parameters are obtained using the estimator. The uncertainty caused by the parameter estimation error in the system is parameterized, serving as a learning control component to reduce future uncertainty. Then, the estimated parameters and the current state of the system are used to predict the future p-step state. The control sequence is calculated under the MPC’s rolling optimization mechanism. After the system output is obtained, the new parameter value at the next moment is re-estimated. Finally, MPC is carried out to realize the dual rolling optimization mechanism. In general, the proposed strategy optimizes the control objective while reducing the system uncertainty of the future parameter and achieving better system performance. Simulation results demonstrate the effectiveness of the algorithm. Full article
(This article belongs to the Topic Engineering Mathematics)
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21 pages, 4429 KiB  
Article
Research on Vibration Propagation Law and Dynamic Effect of Bench Blasting
by Lu He, Dezhong Kong and Zhen Lei
Mathematics 2022, 10(16), 2951; https://doi.org/10.3390/math10162951 - 16 Aug 2022
Cited by 4 | Viewed by 2068
Abstract
To address the problem of damage to adjacent buildings (structures) caused by bench blasting construction, blasting in a sand and gravel mine in Guizhou Province was used as the background. Through on-site monitoring and numerical simulation, the blasting vibration propagation law and dynamic [...] Read more.
To address the problem of damage to adjacent buildings (structures) caused by bench blasting construction, blasting in a sand and gravel mine in Guizhou Province was used as the background. Through on-site monitoring and numerical simulation, the blasting vibration propagation law and dynamic effect characteristics under the joint action of different bench heights and horizontal distances were studied. The regression model was established. The results show that: the peak vibration speed in all three directions with the increase in the horizontal distance of the burst center is a decaying trend, and the field measurements are basically consistent with the safe vibration speed and do not exceed 1.5 cm/s, so the house is in a safe state; shear stress with the increase in the horizontal distance of the burst center strictly decays, so the source of the shear stress and vibration speed decay faster in the near zone, with the slow decay in the far zone; analysis found that the shear stress and vibration speed are quadratic and exponential. Through the analysis of the regression model, it is obtained that there is no co-linearity among the influencing factors, which has a significant effect on the regression equation and regression coefficient, and so the multiple linear regression equation fits well. The model can predict the blast vibration intensity, which can be used as a safety criterion for buildings under the action of blasting, and provides a reference for blast vibration control, hole network parameters, and the design index. Full article
(This article belongs to the Topic Engineering Mathematics)
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25 pages, 7103 KiB  
Article
The Kinematics of a Bipod R2RR Coupling between Two Non-Coplanar Shafts
by Stelian Alaci, Ioan Doroftei, Florina-Carmen Ciornei, Ionut-Cristian Romanu and Ioan Alexandru Doroftei
Mathematics 2022, 10(16), 2898; https://doi.org/10.3390/math10162898 - 12 Aug 2022
Viewed by 1341
Abstract
The paper presents a new solution for motion transmission between two shafts with non-intersecting axes. The structural considerations fundament the existence in the structure of the mechanism of three revolute pairs and a bipod contact. Compared to classical solutions, where linkages with cylindrical [...] Read more.
The paper presents a new solution for motion transmission between two shafts with non-intersecting axes. The structural considerations fundament the existence in the structure of the mechanism of three revolute pairs and a bipod contact. Compared to classical solutions, where linkages with cylindrical pairs are used, our solution proposes a kinematical chain also containing higher pairs. Due to the presence of a higher pair, the transmission is much simpler, the number of elements decreases, and as a consequence, the kinematical study is straightforward. Regardless, the classical analysis of linkages cannot be applied because of the presence of the higher pair. For the proposed spatial coupling, the transmission ratio is expressed as a function of constructive parameters. The positional analysis of the mechanism cannot be performed using the Hartenberg–Denavit method due to the presence of a bipod contact, and instead, the geometrical conditions of existence for the bipod contact are applied. The Hartenberg–Denavit method requires the replacement of the bipodic coupling with a kinematic linkage with cylindrical (revolute and prismatic) pairs, resulting in complicated analytical calculus. To avoid this aspect, the geometrical conditions required by the bipod coupling were expressed in vector form, and thus, the calculus is significantly reduced. The kinematical solution for the proposed transmission can be obtained in two ways: first, by considering the equivalent transmission containing only cylindrical pairs and applying the classical analysis methods; second, by directly expressing the condition of definition for the higher pairs (bipodic pair) in vector form. The last method arrives at a simpler solution for which analytical relations for the positional parameters are obtained, with one exception where numerical calculus is needed (but the precision of this parameter is controlled). The analytical kinematics results show two possibilities of building the actual mechanism with the same constructive parameters. The rotation motions from the revolute pairs, internal and driven, and the motions from the bipod joint were obtained through numerical methods since the equations are very intricate and cannot be solved analytically. The excellent agreement validates the theoretical solutions obtained and the possibility of applying such mechanisms in technical applications. The constructive solution exemplified here is simple and robust. Full article
(This article belongs to the Topic Engineering Mathematics)
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15 pages, 2389 KiB  
Article
Simultaneous State and Kinetic Observation of Class-Controllable Bioprocesses
by Velislava Noreva Lyubenova, Maya Naydenova Ignatova, Vesela Nevelinova Shopska, Georgi Atanasov Kostov and Olympia Nikolaeva Roeva
Mathematics 2022, 10(15), 2665; https://doi.org/10.3390/math10152665 - 28 Jul 2022
Viewed by 947
Abstract
Monitoring of bioprocesses is a challenge in designing modern systems for control. In the biotechnology industry, the lack of reliable hardware sensors for key variables related to the metabolism of microorganisms is a topical problem. This predetermines the progress of a scientific field [...] Read more.
Monitoring of bioprocesses is a challenge in designing modern systems for control. In the biotechnology industry, the lack of reliable hardware sensors for key variables related to the metabolism of microorganisms is a topical problem. This predetermines the progress of a scientific field that relies on the development of software sensors for immeasurable variables. In this paper, a new approach for the monitoring of class-controllable bioprocesses that evolve through various physiological states (metabolic regimes) is proposed. At the core of the approach is the potential to present total biomass as a sum of the biomass concentrations obtained during each of the metabolic regimes. Algorithms for estimation of immeasurable variables and their kinetics are here derived and applied using real experimental data. As a case-study, a fed-batch process for phytase production by E. coli is considered. Effectiveness of the method is proven by using two sets of real experiments. One is used to tune the software sensors and the other to verify the approach. The stability analyses are provided, as well. The obtained results and successful verification confirm the adaptive properties of the approach. The considered software sensors will be further built into an interactive system for training specialists/students of biotechnology. Full article
(This article belongs to the Topic Engineering Mathematics)
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16 pages, 2863 KiB  
Article
Modified Interaction Method for Response of Group Piles Considering Pile–Soil Slip
by Shifan Qiao, Changrui Dong, Guyang Li, Hao Zhou and Gang Wang
Mathematics 2022, 10(15), 2616; https://doi.org/10.3390/math10152616 - 26 Jul 2022
Cited by 2 | Viewed by 1832
Abstract
The existing model for calculating the settlements of group piles is based on the principle of superposition, which fails to calculate the interaction between piles more comprehensively and to take into consideration the influence of slip between pile and soil. In this paper, [...] Read more.
The existing model for calculating the settlements of group piles is based on the principle of superposition, which fails to calculate the interaction between piles more comprehensively and to take into consideration the influence of slip between pile and soil. In this paper, the interaction between group piles is analyzed from a novel perspective. It is assumed that the interaction between piles is a dynamic equilibrium process, i.e., additional shear forces and additional displacements are continuously transferred between piles until a state of equilibrium is reached. On this basis, we propose a new model for calculating the settlements of group piles considering pile–soil slip. First, a calculation method for pile–side resistance is developed considering the influence of slip. Based on experience with the pile–soil interface, pile–side soils can be categorized as near–pile soil and far–pile soil, and different load–transfer models are applied to describe their mechanical states. By equating pile–side soils into a nonlinear spring and connecting them in series to determine the overall equivalent stiffness considering the effect of pile–soil slip, the pile–side resistance under different loading conditions can be accurately determined. Secondly, equilibrium analysis of the pile unit is carried out when the equilibrium condition is reached, and the stiffness matrix for load transfer is derived. Therefore, in this paper, the interaction between piles is concentrated in this matrix, which makes the proposed model for pile settlement calculation clearer and more concise. Compared with measured data, the proposed method can capture the main features of the load–settlement behavior of group piles. Full article
(This article belongs to the Topic Engineering Mathematics)
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16 pages, 2910 KiB  
Article
Handwriting Recognition Based on 3D Accelerometer Data by Deep Learning
by Pedro Lopez-Rodriguez, Juan Gabriel Avina-Cervantes, Jose Luis Contreras-Hernandez, Rodrigo Correa and Jose Ruiz-Pinales
Appl. Sci. 2022, 12(13), 6707; https://doi.org/10.3390/app12136707 - 02 Jul 2022
Cited by 4 | Viewed by 2194
Abstract
Online handwriting recognition has been the subject of research for many years. Despite that, a limited number of practical applications are currently available. The widespread use of devices such as smartphones, smartwatches, and tablets has not been enough to convince the user to [...] Read more.
Online handwriting recognition has been the subject of research for many years. Despite that, a limited number of practical applications are currently available. The widespread use of devices such as smartphones, smartwatches, and tablets has not been enough to convince the user to use pen-based interfaces. This implies that more research on the pen interface and recognition methods is still necessary. This paper proposes a handwritten character recognition system based on 3D accelerometer signal processing using Convolutional Neural Networks (CNN) and Long Short-Term Memory (LSTM). First, a user wearing an MYO armband on the forearm writes a multi-stroke freestyle character on a touchpad by using the finger or a pen. Next, the 3D accelerometer signals generated during the writing process are fed into a CNN, LSTM, or CNN-LSTM network for recognition. The convolutional backbone obtains spatial features in order to feed an LSTM that extracts short-term temporal information. The system was evaluated on a proprietary dataset of 3D accelerometer data collected from multiple users with an armband device, corresponding to handwritten English lowercase letters (a–z) and digits (0–9) in a freestyle. The results show that the proposed system overcomes other systems from the state of the art by 0.53%. Full article
(This article belongs to the Topic Engineering Mathematics)
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23 pages, 464 KiB  
Article
The Estimation of Bent Line Expectile Regression Model Based on a Smoothing Technique
by Jie Liu, Jiaqing Chen and Yangxin Huang
Symmetry 2022, 14(7), 1320; https://doi.org/10.3390/sym14071320 - 26 Jun 2022
Viewed by 1058
Abstract
A bent line expectile regression model can describe the effect of a covariate on the response variable with two different straight lines, which intersect at an unknown change-point. Due to the existence of the change-point, the objective function of the model is not [...] Read more.
A bent line expectile regression model can describe the effect of a covariate on the response variable with two different straight lines, which intersect at an unknown change-point. Due to the existence of the change-point, the objective function of the model is not differentiable with respect to the change-point, so it cannot be solved by the method of the traditional linear expectile regression model. For this model, a new estimation method is proposed by a smoothing technique, that is, using Gaussian kernel function to approximate the indicator function in the objective function. It can not only estimate the regression coefficients and change-point location simultaneously, but also have better estimation effect, which compensates for the insufficiency of the previous estimation methods. Under the given regularity conditions, the theoretical proofs of the consistency and asymptotic normality of the proposed estimators are derived. There are two parts of numerical simulations in this paper. Simulation 1 discusses various error distributions at different expectile levels under different conditions, the results show that the mean values of the biases of the estimation method in this paper, and other indicators, are very small, which indicates the robust property of the new method. Simulation 2 considers the symmetric and asymmetric bent lien expectile regression models, the results show that the estimated values of the estimation method in this paper are similar to the true values, which indicates the estimation effect and large sample performance of the proposed method are excellent. In the application research, the method in this paper is applied to the Arctic annual average temperature data and the Nile annual average flow data. The research shows that the standard errors of the estimation method in this paper are very similar to 0, indicating that the parameter estimation accuracy of the new method is very high, and the location of the change-point can be accurately estimated, which further confirms that the new method is effective and feasible. Full article
(This article belongs to the Topic Engineering Mathematics)
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19 pages, 4906 KiB  
Article
Bond Graph-Based Approach to Modeling Variable-Speed Gearboxes with Multi-Type Clutches
by Jiangming Wu, Hongzhi Yan, Shuangqi Liu, Yin Zhang and Wuzhong Tan
Appl. Sci. 2022, 12(12), 6181; https://doi.org/10.3390/app12126181 - 17 Jun 2022
Cited by 5 | Viewed by 1743
Abstract
The modeling and simulation of gearboxes is important for analyzing the dynamic characteristics and designing control strategies of transmission systems. Variable-speed gearboxes include compound planetary gear trains and clutches, which complicates dynamic modeling. Here, a procedural bond graph-based modeling method that considers many [...] Read more.
The modeling and simulation of gearboxes is important for analyzing the dynamic characteristics and designing control strategies of transmission systems. Variable-speed gearboxes include compound planetary gear trains and clutches, which complicates dynamic modeling. Here, a procedural bond graph-based modeling method that considers many uncertainties is proposed. The proposed method yields a constant system–structure model. First, bond graph models of the two most common planetary gears were summarized, and were used as sub-models of a compound planetary gear train. Then, the Karnopp friction sub-model of the friction clutch and a relative angular displacement sub-model of the one-way clutch were constructed. Based on the dynamic coupling between the sub-models, the modeling steps of the gearbox, including the compound planetary gear train friction clutch one-way clutch coupling system, are described in detail. Next, the main sources of uncertainties of gearbox were analyzed and the simulation methods were given. Finally, the novel uncertain bond graph model was used to simulate the double planetary gearbox; the transmission ratio before and after the shift was 2.42 and 1.72, compared with the design values of 2.41 and 1.71, respectively; the deviation is within 5.8%; The average rotating speeds of the output shaft fluctuated by 6 and 2.5% respectively, which was within a reasonable range, so the effectiveness of the method is verified. Full article
(This article belongs to the Topic Engineering Mathematics)
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26 pages, 5499 KiB  
Article
Moving Spatial Turbulence Model for High-Fidelity Rotorcraft Maneuvering Simulation
by Honglei Ji, Linghai Lu and Renliang Chen
Mathematics 2022, 10(12), 2093; https://doi.org/10.3390/math10122093 - 16 Jun 2022
Viewed by 1644
Abstract
A moving spatial turbulence model is developed for rotorcraft maneuvering simulation under different flight conditions. The recursive algorithms are adopted to model its distributed longitudinal turbulence components, which are correlated with the lateral and vertical axes to form a local spatial turbulence field. [...] Read more.
A moving spatial turbulence model is developed for rotorcraft maneuvering simulation under different flight conditions. The recursive algorithms are adopted to model its distributed longitudinal turbulence components, which are correlated with the lateral and vertical axes to form a local spatial turbulence field. The flow field is constrained around the rotorcraft by following its movement, and the corresponding turbulence components are updated at a constant spatial interval. The statistical properties along the longitudinal, lateral, and vertical directions have been validated against the von Kármán theory. A synthetic simulation environment consisting of a flight dynamics model and a pilot model is constructed to demonstrate the effectiveness of the turbulence model. Its performance is validated by comparing the power spectral densities of both rotorcraft responses and pilot controls in turbulence against flight test data. The piloted simulation results on an Approach-to-Hovering task show that the handling qualities ratings are susceptive to the level of turbulence and significantly increase when performing aggressive controls. The simulation also accurately predicts the expected effect of varied aircraft speed, wind speed, turbulence intensity, and stability augmentation system on piloted handling qualities rating for rotorcraft flight in turbulence. Full article
(This article belongs to the Topic Engineering Mathematics)
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13 pages, 2919 KiB  
Article
Bright, Dark, and Rogue Wave Soliton Solutions of the Quadratic Nonlinear Klein–Gordon Equation
by Alrazi Abdeljabbar, Harun-Or Roshid and Abdullah Aldurayhim
Symmetry 2022, 14(6), 1223; https://doi.org/10.3390/sym14061223 - 13 Jun 2022
Cited by 18 | Viewed by 2000
Abstract
This article reflects on the Klein–Gordon model, which frequently arises in the fields of solid-state physics and quantum field theories. We analytically delve into solitons and composite rogue-type wave propagation solutions of the model via the generalized Kudryashov and the extended Sinh Gordon [...] Read more.
This article reflects on the Klein–Gordon model, which frequently arises in the fields of solid-state physics and quantum field theories. We analytically delve into solitons and composite rogue-type wave propagation solutions of the model via the generalized Kudryashov and the extended Sinh Gordon expansion approaches. We obtain a class of analytically exact solutions in the forms of exponential and hyperbolic functions involving some arbitrary parameters with the help of Maple, which included comparing symmetric and non-symmetric solutions with other methods. After analyzing the dynamical behaviors, we caught distinct conditions on the accessible parameters of the solutions for the model. By applying conditions to the existing parameters, we obtained various types of rogue waves, bright and dark bells, combing bright–dark, combined dark–bright bells, kink and anti-kink solitons, and multi-soliton solutions. The nature of the solitons is geometrically explained for particular choices of the arbitrary parameters. It is indicated that the nonlinear rogue-type wave packets are restricted in two dimensions that characterized the rogue-type wave envelopes. Full article
(This article belongs to the Topic Engineering Mathematics)
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16 pages, 2856 KiB  
Article
Non-Similarity Solutions of Non-Newtonian Brinkman–Viscoelastic Fluid
by Siti Farah Haryatie Mohd Kanafiah, Abdul Rahman Mohd Kasim, Syazwani Mohd Zokri and Nur Syamilah Arifin
Mathematics 2022, 10(12), 2023; https://doi.org/10.3390/math10122023 - 11 Jun 2022
Cited by 2 | Viewed by 1269
Abstract
The exploration of heat transference in relation to fluid flow problems is important especially for non-Newtonian type of fluid. The use of the particular fluid can be found in many industrial applications such as oil and gas industries, automotives and manufacturing processes. Since [...] Read more.
The exploration of heat transference in relation to fluid flow problems is important especially for non-Newtonian type of fluid. The use of the particular fluid can be found in many industrial applications such as oil and gas industries, automotives and manufacturing processes. Since the experimental works are costly and high-risk procedures, the mathematical study is proposed to counter the limitations. Therefore, this work aims to study the characteristics of a fluid that combines the properties of viscosity and elasticity, together with the porosity conditions, called the Brinkman–viscoelastic model. The flow is assumed to move over a horizontal circular cylinder (HCC) under consideration of the convective thermal boundary condition. The mathematical model is transformed to the less complex form by utilising a non-dimensionless and non-similarity variable. The resulting equations are in the partial differential equation (PDE) form. Subsequently, the equations are required to be solved by employing the Keller-box method (KBM). The solutions were conveniently evaluated by observing the plotted graphs in order to capture the propensity of the fluid’s behavior in response to the adjusting parameters. The study discovered that the viscoelastic and Brinkman variables had the impact of decreasing the fluid’s velocity and increasing the temperature distribution. Nevertheless, when mixed convection and Biot numbers increased, the velocity profile exhibited the opposite pattern. Furthermore, increasing the Biot number raises the Nusselt number while decreasing the skin friction coefficient. These numerical results are critical for assisting engineers in making heat transfer process decisions and accurately verifying experimental investigations. Full article
(This article belongs to the Topic Engineering Mathematics)
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13 pages, 2149 KiB  
Article
Numerical Study on Dynamics of Blood Cell Migration and Deformation in Atherosclerotic Vessels
by Yihao Wu, Hui Xing, Qingyu Zhang and Dongke Sun
Mathematics 2022, 10(12), 2022; https://doi.org/10.3390/math10122022 - 11 Jun 2022
Viewed by 1824
Abstract
A phase field model is used to study the effect of atherosclerotic plaque on hemodynamics. The migration of cells in blood flows is described by a set of multiple phase field equations, which incorporate elastic energies and the interacting effects of cells. Several [...] Read more.
A phase field model is used to study the effect of atherosclerotic plaque on hemodynamics. The migration of cells in blood flows is described by a set of multiple phase field equations, which incorporate elastic energies and the interacting effects of cells. Several simulations are carried out to reveal the influences of initial velocities of blood cells, cellular elasticity and block rates of hemodynamic vessels. The results show that the cell deformation increases with the growth of the initial active velocity and block rate but with the decrease of the cellular elasticity. The atherosclerotic plaque not only affects the deformation and migration of cells but also can promote the variation in hemodynamic properties. The atherosclerotic plaque causes a burst in cell velocity, and the greater the block rate and cellular elasticity, the more dramatic the variation of instantaneous velocity. The present work demonstrates that the phase field method could be extended to reveal formation atherosclerosis at the microscopic level from the perspective of hemodynamics. Full article
(This article belongs to the Topic Engineering Mathematics)
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22 pages, 350 KiB  
Article
The Landweber Iterative Regularization Method for Solving the Cauchy Problem of the Modified Helmholtz Equation
by Yong-Gang Chen, Fan Yang and Qian Ding
Symmetry 2022, 14(6), 1209; https://doi.org/10.3390/sym14061209 - 11 Jun 2022
Cited by 1 | Viewed by 1234
Abstract
In this manuscript, the Cauchy problem of the modified Helmholtz equation is researched. This inverse problem is a serious ill-posed problem. The classical Landweber iterative regularization method is designed to find the regularized solution of this inverse problem. The error estimations between the [...] Read more.
In this manuscript, the Cauchy problem of the modified Helmholtz equation is researched. This inverse problem is a serious ill-posed problem. The classical Landweber iterative regularization method is designed to find the regularized solution of this inverse problem. The error estimations between the exact solution and the regularization solution are all obtained under the a priori and the a posteriori regularization parameter selection rule. The Landweber iterative regularization method can also be applied to solve the Cauchy problem of the modified Helmholtz equation on the spherically symmetric and cylindrically symmetric regions. Full article
(This article belongs to the Topic Engineering Mathematics)
21 pages, 1488 KiB  
Article
The Numerical Investigation of a Fractional-Order Multi-Dimensional Model of Navier–Stokes Equation via Novel Techniques
by Safyan Mukhtar, Rasool Shah and Saima Noor
Symmetry 2022, 14(6), 1102; https://doi.org/10.3390/sym14061102 - 27 May 2022
Cited by 50 | Viewed by 2429
Abstract
In this study, numerical results of a fractional-order multi-dimensional model of the Navier–Stokes equations will be achieved via adoption of two analytical methods, i.e., the Adomian decomposition transform method and the q-Homotopy analysis transform method. The Caputo–Fabrizio operator will be used to define [...] Read more.
In this study, numerical results of a fractional-order multi-dimensional model of the Navier–Stokes equations will be achieved via adoption of two analytical methods, i.e., the Adomian decomposition transform method and the q-Homotopy analysis transform method. The Caputo–Fabrizio operator will be used to define the fractional derivative. The proposed methods will be implemented to provide the series form results of the given models. The series form results of proposed techniques will be validated with the exact results available in the literature. The proposed techniques will be investigated to be efficient, straightforward, and reliable for application to many other scientific and engineering problems. Full article
(This article belongs to the Topic Engineering Mathematics)
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13 pages, 3185 KiB  
Article
Using Python for the Simulation of a Closed-Loop PI Controller for a Buck Converter
by Acacio M. R. Amaral and Antonio J. Marques Cardoso
Signals 2022, 3(2), 313-325; https://doi.org/10.3390/signals3020020 - 20 May 2022
Cited by 2 | Viewed by 3640
Abstract
This paper presents a Python-based simulation technique that can be used to predict the behavior of switch-mode non-isolated (SMNI) DC-DC converters operating in closed loop. The proposed technique can be implemented in an open-source numerical computation software, such as Scilab, Octave or Python, [...] Read more.
This paper presents a Python-based simulation technique that can be used to predict the behavior of switch-mode non-isolated (SMNI) DC-DC converters operating in closed loop. The proposed technique can be implemented in an open-source numerical computation software, such as Scilab, Octave or Python, which makes it versatile and portable. The software that will be used to implement the proposed technique is Python, since it is an open-source programming language, unlike MATLAB, which is one of most-used programming and numeric computing platforms to simulate this type of system. The proposed technique requires the discretization of the equations that govern the open-loop operation of the converter, as well as the discretization of the transfer function of the controller. To simplify the implementation of the simulation technique, the code must be subdivided into different modules, which together form a package. The converter under analysis will be a buck converter operating in CCM. The proposed technique can be extended to any other SMNI DC-DC converter. The validation of the proposed technique will be carried out by comparing it with the results obtained in LTspice. Full article
(This article belongs to the Topic Engineering Mathematics)
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16 pages, 556 KiB  
Article
Surface Wave Propagation in a Rotating Doubly Coated Nonhomogeneous Half Space with Application
by Ali M. Mubaraki, Maha M. Helmi and Rahmatullah Ibrahim Nuruddeen
Symmetry 2022, 14(5), 1000; https://doi.org/10.3390/sym14051000 - 13 May 2022
Cited by 9 | Viewed by 1251
Abstract
The current study examines the propagation of surface waves in an asymmetric rotating doubly coated nonhomogeneous half space. The coating layers are assumed to be made of different homogeneous isotropic materials, while the overlaying nonhomogeneous half space layer is considered to be of [...] Read more.
The current study examines the propagation of surface waves in an asymmetric rotating doubly coated nonhomogeneous half space. The coating layers are assumed to be made of different homogeneous isotropic materials, while the overlaying nonhomogeneous half space layer is considered to be of exponentially varying material properties. The consequential exact vibrational displacements and dispersion relation are determined analytically, in addition to the approximate validation of the dispersion relation via the application of an asymptotic procedure within the long wave limit. Two cases of unloaded and loaded end surface scenarios are analyzed by examining the posed fundamental modes. More precisely, an elastic Winkler foundation was considered in the case of a mechanically loaded end surface condition and was found to proliferate the transition between having a fundamental mode over the frequency axis to the wave number axis as the angular velocity increased. Moreover, the rotational effect was found to have a direct impact on the surface wave propagation with a long wave and low frequency. Aside from that, an increase in the nonhomogeneity parameter resulted in propagation with a relatively long frequency. Full article
(This article belongs to the Topic Engineering Mathematics)
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12 pages, 1015 KiB  
Article
Dynamic Parameters Identification Method of 6-DOF Industrial Robot Based on Quaternion
by Jun Cheng, Shusheng Bi and Chang Yuan
Mathematics 2022, 10(9), 1513; https://doi.org/10.3390/math10091513 - 02 May 2022
Viewed by 1880
Abstract
Identifying accurate dynamic parameters is of great significance to improving the control accuracy of industrial robots, but this area is relatively unexplored in the research. In this paper, a new algorithm for accurately identifying the dynamic parameters of a 6-degrees-of-freedom (DOF) robot is [...] Read more.
Identifying accurate dynamic parameters is of great significance to improving the control accuracy of industrial robots, but this area is relatively unexplored in the research. In this paper, a new algorithm for accurately identifying the dynamic parameters of a 6-degrees-of-freedom (DOF) robot is proposed by establishing a dynamic model. First, a multibody dynamic model of the robot is established, which can decouple the dynamic parameters of the rigid bodies that make up the robot. Decoupling is the basis of parameters identification. In order to ensure that the model is suitable for large-angle range motion and has good real-time performance, quaternion is used as the angle coordinate, and the model established thereby eliminates the singularity and improves the calculation efficiency. Second, the dynamic model is rewritten, and the dynamic parameters are separated as the parameters to be identified; thus, the parameters identification model is obtained. Furthermore, an identification algorithm based on the least-squares method is proposed, which can realize the accurate identification of dynamic parameters. The algorithm is verified by a simulation example. The results show that the value of the maximum absolute error of the identified parameters is −0.0264, and the maximum relative error is 0.031%, which proves the correctness and accuracy of the algorithm. Full article
(This article belongs to the Topic Engineering Mathematics)
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16 pages, 4299 KiB  
Article
Driver Response Time and Age Impact on the Reaction Time of Drivers: A Driving Simulator Study among Professional-Truck Drivers
by Milos Poliak, Lucia Svabova, Jan Benus and Ebru Demirci
Mathematics 2022, 10(9), 1489; https://doi.org/10.3390/math10091489 - 29 Apr 2022
Cited by 8 | Viewed by 3023
Abstract
Drivers’ response time means that drivers act after a judgment is made when an emergency action signal is needed. Drivers have different feelings while driving, and the response time to sudden situations differs. The main purpose of this study was to verify whether [...] Read more.
Drivers’ response time means that drivers act after a judgment is made when an emergency action signal is needed. Drivers have different feelings while driving, and the response time to sudden situations differs. The main purpose of this study was to verify whether the mean reaction time of professional drivers is at the level of one second, which is the value usually used for practical purposes, and to verify the impact of age on the reaction times of drivers. Two different studies with a total of 120 participants—professional drivers—were conducted on the simulator, with 116 drivers participating in the first experiment and four drivers participating in the second experiment using eye-tracking technology. The determination of the mean reaction time was realized using statistical tests. The evaluation of the impact of age on the reaction time of professional drivers was carried out using statistical testing, a regression model, and clustering. The results of this study can be immediately used in practice for professional drivers, as the mean reaction time is usually used as a benchmark in several calculations in transport, for forensic and educational purposes, and for planning traffic and modelling different traffic situations. Full article
(This article belongs to the Topic Engineering Mathematics)
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18 pages, 3798 KiB  
Article
Variable Step Block Hybrid Method for Stiff Chemical Kinetics Problems
by Hira Soomro, Nooraini Zainuddin, Hanita Daud, Joshua Sunday, Noraini Jamaludin, Abdullah Abdullah, Mulono Apriyanto and Evizal Abdul Kadir
Appl. Sci. 2022, 12(9), 4484; https://doi.org/10.3390/app12094484 - 28 Apr 2022
Cited by 8 | Viewed by 1816
Abstract
Integration of a larger stiff system of initial value problems emerging from chemical kinetics models requires a method that is both efficient and accurate, with a large absolute stability region. To determine the solutions of the stiff chemical kinetics ordinary differential equations that [...] Read more.
Integration of a larger stiff system of initial value problems emerging from chemical kinetics models requires a method that is both efficient and accurate, with a large absolute stability region. To determine the solutions of the stiff chemical kinetics ordinary differential equations that help in explaining chemically reactive flows, a numerical integration methodology known as the 3-point variable step block hybrid method has been devised. An appropriate time step is automatically chosen to give accurate results. To check the efficiency of the new method, the numerical integration of a few renowned stiff chemical problems is evaluated such as Belousov–Zhabotinskii reaction and Hires, which are widely used in numerical studies. The results generated are then compared with the MATLAB stiff solver, ode15s. Full article
(This article belongs to the Topic Engineering Mathematics)
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25 pages, 913 KiB  
Article
Load-Carrying Capacity of Ultra-Thin Shells with and without CNTs Reinforcement
by Tan N. Nguyen, L. Minh Dang, Jaehong Lee and Pho Van Nguyen
Mathematics 2022, 10(9), 1481; https://doi.org/10.3390/math10091481 - 28 Apr 2022
Cited by 10 | Viewed by 1823
Abstract
Isotropic ultra-thin shells or membranes, as well as cable–membrane structures, cannot resist loads at the initial state and always require a form-finding process to reach the steady state. After this stage, they can work in a pure membrane state and quickly experience large [...] Read more.
Isotropic ultra-thin shells or membranes, as well as cable–membrane structures, cannot resist loads at the initial state and always require a form-finding process to reach the steady state. After this stage, they can work in a pure membrane state and quickly experience large deflection behavior, even with a small amplitude of load. This paper aims to improve the load-carrying capacity and strength of membrane structures via exploiting the advantages of functionally graded carbon-nanotube-reinforced composite (FG-CNTRC) material. In this work, the load-carrying capacity and nonlinear behavior of membrane structures with and without CNTs reinforcement are first investigated using a unified adaptive approach (UAA). As an advantage of UAA, both form finding and postbuckling analysis are performed conveniently and simultaneously based on a modified Riks method. Different from the classical membrane theory, the present theory (first-order shear deformation theory) simultaneously takes into account the membrane, shear and bending strains/stiffnesses of structures. Accordingly, the present formulation can be applied adaptively and naturally to various types of FG-CNTRC structures: plates, shells and membranes. A verification study is conducted to show the high accuracy of the present approach and formulation. Effects of CNTs distribution, volume fraction, thickness, curvature, radius-to-thickness and length-to-radius ratios on the form-finding and postbuckling behavior of FG-CNTRC membranes are particularly investigated. In particular, equilibrium paths of FG-CNTRC membrane structures are first provided in this paper. Full article
(This article belongs to the Topic Engineering Mathematics)
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8 pages, 285 KiB  
Article
Inverse Problem for a Time Fractional Parabolic Equation with Nonlocal Boundary Conditions
by Ebru Ozbilge, Fatma Kanca and Emre Özbilge
Mathematics 2022, 10(9), 1479; https://doi.org/10.3390/math10091479 - 28 Apr 2022
Cited by 4 | Viewed by 1854
Abstract
This article considers an inverse problem of time fractional parabolic partial differential equations with the nonlocal boundary condition. Dirichlet-measured output data are used to distinguish the unknown coefficient. A finite difference scheme is constructed and a numerical approximation is made. Examples and numerical [...] Read more.
This article considers an inverse problem of time fractional parabolic partial differential equations with the nonlocal boundary condition. Dirichlet-measured output data are used to distinguish the unknown coefficient. A finite difference scheme is constructed and a numerical approximation is made. Examples and numerical experiments, such as man-made noise, are provided to show the stability and efficiency of this numerical method. Full article
(This article belongs to the Topic Engineering Mathematics)
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14 pages, 407 KiB  
Article
A Biorthogonal Hermite Cubic Spline Galerkin Method for Solving Fractional Riccati Equation
by Haifa Bin Jebreen and Ioannis Dassios
Mathematics 2022, 10(9), 1461; https://doi.org/10.3390/math10091461 - 27 Apr 2022
Cited by 6 | Viewed by 1474
Abstract
This paper is devoted to the wavelet Galerkin method to solve the Fractional Riccati equation. To this end, biorthogonal Hermite cubic Spline scaling bases and their properties are introduced, and the fractional integral is represented based on these bases as an operational matrix. [...] Read more.
This paper is devoted to the wavelet Galerkin method to solve the Fractional Riccati equation. To this end, biorthogonal Hermite cubic Spline scaling bases and their properties are introduced, and the fractional integral is represented based on these bases as an operational matrix. Firstly, we obtain the Volterra integral equation with a weakly singular kernel corresponding to the desired equation. Then, using the operational matrix of fractional integration and the Galerkin method, the corresponding integral equation is reduced to a system of algebraic equations. Solving this system via Newton’s iterative method gives the unknown solution. The convergence analysis is investigated and shows that the convergence rate is O(2s). To demonstrate the efficiency and accuracy of the method, some numerical simulations are provided. Full article
(This article belongs to the Topic Engineering Mathematics)
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22 pages, 10948 KiB  
Article
An Efficient Parallel Implementation of the Runge–Kutta Discontinuous Galerkin Method with Weighted Essentially Non-Oscillatory Limiters on Three-Dimensional Unstructured Meshes
by Weicheng Pei, Yuyan Jiang and Shu Li
Appl. Sci. 2022, 12(9), 4228; https://doi.org/10.3390/app12094228 - 22 Apr 2022
Cited by 3 | Viewed by 1357
Abstract
In computational fluid dynamics, high-order solvers suitable for three-dimensional unstructured meshes are attractive but are less developed than other methods. In this article, we provide the formulation and a parallel implementation of the Runge–Kutta discontinuous Galerkin finite element method with weighted essentially non-oscillatory [...] Read more.
In computational fluid dynamics, high-order solvers suitable for three-dimensional unstructured meshes are attractive but are less developed than other methods. In this article, we provide the formulation and a parallel implementation of the Runge–Kutta discontinuous Galerkin finite element method with weighted essentially non-oscillatory limiters, which are compact and effective for suppressing numerical oscillations near discontinuities. In our experiments, high-order solvers do outperform their low-order counterparts in accuracy and the efficient parallel implementation makes the time cost affordable for large problems. Such high-order parallel solvers are efficient tools for solving conservative laws including the Euler system that models inviscid compressible flows. Full article
(This article belongs to the Topic Engineering Mathematics)
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17 pages, 1040 KiB  
Article
Geometric Algebra Applied to Multiphase Electrical Circuits in Mixed Time–Frequency Domain by Means of Hypercomplex Hilbert Transform
by Francisco G. Montoya, Raúl Baños, Alfredo Alcayde, Francisco M. Arrabal-Campos and Javier Roldán-Pérez
Mathematics 2022, 10(9), 1419; https://doi.org/10.3390/math10091419 - 22 Apr 2022
Cited by 4 | Viewed by 1700
Abstract
In this paper, power flows in electrical circuits are modelled in a mixed time-frequency domain by using geometric algebra and the Hilbert transform for the first time. The use of this mathematical framework overcomes some of the limitations of some of the existing [...] Read more.
In this paper, power flows in electrical circuits are modelled in a mixed time-frequency domain by using geometric algebra and the Hilbert transform for the first time. The use of this mathematical framework overcomes some of the limitations of some of the existing methodologies, in which the so-called “active current” may not lead to the lowest Root Mean Square (RMS) current under distorted supply or unbalanced load. Moreover, this current may contain higher levels of harmonic distortion compared to the supply voltage. The proposed method can be used for sinusoidal and non-sinusoidal power supplies, non-linear loads and single- and multi-phase electrical circuits, and it provides meaningful engineering results with a compact formulation. It can also serve as an advanced tool for developing algorithms in the power electronics field. Several examples have been included to verify the validity of the proposed theory. Full article
(This article belongs to the Topic Engineering Mathematics)
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34 pages, 17364 KiB  
Article
Stress State in an Eccentric Elastic Ring Loaded Symmetrically by Concentrated Forces
by Stelian Alaci, Florina-Carmen Ciornei and Ionut-Cristian Romanu
Mathematics 2022, 10(8), 1314; https://doi.org/10.3390/math10081314 - 14 Apr 2022
Cited by 1 | Viewed by 1901
Abstract
The stress state from an eccentric ring made of an elastic material symmetrically loaded on the outer boundary by concentrated forces is deduced. The analytical results are obtained using the Airy stress function expressed in bipolar coordinates. The elastic potential corresponding to the [...] Read more.
The stress state from an eccentric ring made of an elastic material symmetrically loaded on the outer boundary by concentrated forces is deduced. The analytical results are obtained using the Airy stress function expressed in bipolar coordinates. The elastic potential corresponding to the same loading but for a compact disk is first written in bipolar coordinates, then expanded in Fourier series, and after that, an auxiliary potential of a convenient form is added to it in order to impose boundary conditions. Since the inner boundary is unloaded, boundary conditions may be applied directly to the total potential. A special focus is on the number of terms from Fourier expansion of the potential in bipolar coordinates corresponding to the compact disk as this number influences the sudden increase if the coefficients from the final form of the total potential. Theoretical results are validated both by using finite element software and experimentally through the photoelastic method, for which a device for sample loading was designed and constructed. Isochromatic fields were considered for the photoelastic method. Six loading cases for two different geometries of the ring were studied. For all the analysed cases, an excellent agreement between the analytical, numerical and experimental results was achieved. Finally, for all the situations considered, the stress concentration effect of the inner hole was analytically determined. It should be mentioned that as the eccentricity of the inner hole decreases, the integrals from the relations of the total elastic potential present a diminishing convergence in the vicinity of the inner boundary. Full article
(This article belongs to the Topic Engineering Mathematics)
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18 pages, 2967 KiB  
Article
Robust Self-Learning PID Control of an Aircraft Anti-Skid Braking System
by Fengrui Xu, Xuelin Liang, Mengqiao Chen and Wensheng Liu
Mathematics 2022, 10(8), 1290; https://doi.org/10.3390/math10081290 - 13 Apr 2022
Cited by 4 | Viewed by 2223
Abstract
In order to deal with strong nonlinearity and external interference in the braking process, this paper proposes a robust self-learning PID algorithm based on particle swarm optimization, which does not depend on a precise mathematical model of the controlled object. The self-learning function [...] Read more.
In order to deal with strong nonlinearity and external interference in the braking process, this paper proposes a robust self-learning PID algorithm based on particle swarm optimization, which does not depend on a precise mathematical model of the controlled object. The self-learning function is used to adapt to the diversity of the runway road surface friction, the particle swarm algorithm is used to optimize the rate of self-learning, and robust control is used to deal with the modeling uncertainty and external disturbance of the system. The convergence of the control strategy is proved by theoretical analysis and simulation experiments. The superiority and accuracy of the method are verified by NASA ground test results. The simulation results shows that the adverse effect of the external disturbance is suppressed, and the ideal trajectory is tracked. Full article
(This article belongs to the Topic Engineering Mathematics)
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18 pages, 3798 KiB  
Article
Physical Modeling and Structural Properties of Small-Scale Mine Ventilation Networks
by David-Fernando Novella-Rodriguez, Emmanuel Witrant and Christian Commault
Mathematics 2022, 10(8), 1253; https://doi.org/10.3390/math10081253 - 11 Apr 2022
Cited by 2 | Viewed by 1356
Abstract
This work is devoted to the modeling and structural analysis of ventilation networks in small-scale mines using a physically oriented modeling method that ensures power conservation. Small-scale mines are common in the mineral extraction industry of underdeveloped countries and their physical characteristics are [...] Read more.
This work is devoted to the modeling and structural analysis of ventilation networks in small-scale mines using a physically oriented modeling method that ensures power conservation. Small-scale mines are common in the mineral extraction industry of underdeveloped countries and their physical characteristics are taken into account in the modeling process. The geometrical topology of the ventilation network in addition with the conservation laws of the fluid distribution along the network are considered in order to obtain a simple modeling methodology. Non-linear characteristics of the interconnected fluid dynamics represent a challenge to determine significant features of the system from a control point of view. Observability and controllability properties are analyzed by considering the structural systems approach. An structural analysis provides information based on the network topology independently of the mine parameters allowing the number of sensors and actuators to be reduced while also preserving the observability and controllability of the ventilation system. Experimental results are provided by building a small-scale ventilation network benchmark to evaluate the proposed model and its properties. Full article
(This article belongs to the Topic Engineering Mathematics)
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13 pages, 263 KiB  
Article
Carlitz’s Equations on Generalized Fibonacci Numbers
by Min Wang, Peng Yang and Yining Yang
Symmetry 2022, 14(4), 764; https://doi.org/10.3390/sym14040764 - 07 Apr 2022
Cited by 1 | Viewed by 1325
Abstract
Carlitz solved some Diophantine equations on Fibonacci or Lucas numbers. We extend his results to the sequence of generalized Fibonacci and Lucas numbers. In this paper, we solve the Diophantine equations of the form [...] Read more.
Carlitz solved some Diophantine equations on Fibonacci or Lucas numbers. We extend his results to the sequence of generalized Fibonacci and Lucas numbers. In this paper, we solve the Diophantine equations of the form An1Ank=Bm1BmrCt1Cts, where (An), (Bm), and (Ct) are generalized Fibonacci or Lucas numbers. Especially, we also find all solutions of symmetric Diophantine equations Ua1Ua2Uam=Ub1Ub2Ubn, where 1<a1a2am, and 1<b1b2bn. Full article
(This article belongs to the Topic Engineering Mathematics)
21 pages, 4051 KiB  
Article
MHD Mixed Convection Hybrid Nanofluids Flow over a Permeable Moving Inclined Flat Plate in the Presence of Thermophoretic and Radiative Heat Flux Effects
by Umair Khan, Iskandar Waini, Aurang Zaib, Anuar Ishak and Ioan Pop
Mathematics 2022, 10(7), 1164; https://doi.org/10.3390/math10071164 - 03 Apr 2022
Cited by 14 | Viewed by 2061
Abstract
Recent nanotech advancements have created a tremendous platform for the development of a superior ultrahigh performance coolant referred to as nanofluid for several industrial and engineering technologies. In this research, the impact of thermophoretic and viscous dissipation on the radiative mixed convective flow [...] Read more.
Recent nanotech advancements have created a tremendous platform for the development of a superior ultrahigh performance coolant referred to as nanofluid for several industrial and engineering technologies. In this research, the impact of thermophoretic and viscous dissipation on the radiative mixed convective flow comprising hybrid nanofluid through an inclined permeable moving flat plate with a magnetic field is examined numerically. A model of non-linear differential equations is derived based on some realistic assumptions and tackled numerically using the bvp4c technique. The impact of the specific set of distinguished parameters on the velocity profiles, shear stress, temperature distribution profiles, heat transfer, concentration distribution profile, and mass transfer for the two dissimilar branch solutions are discussed in detail. In addition, it has been discovered that double solutions exist in the case of an opposing flow, while a single solution is observed in the case of an assisting flow. The temperature distribution profile escalates with the radiation parameter, while decelerating the velocity and concentration profiles. Full article
(This article belongs to the Topic Engineering Mathematics)
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16 pages, 385 KiB  
Article
A Boundary Element Procedure for 3D Electromagnetic Transmission Problems with Large Conductivity
by Jorge Eliécer Ospino Portillo, Matthias Maischak and Zouhair Nezhi
Mathematics 2022, 10(7), 1148; https://doi.org/10.3390/math10071148 - 02 Apr 2022
Viewed by 1215
Abstract
We consider the scattering of time-periodic electromagnetic fields by metallic obstacles, or the eddy current problem. In this interface problem, different sets of Maxwell equations must be solved both in the obstacle and outside it, while the tangential components of both electric and [...] Read more.
We consider the scattering of time-periodic electromagnetic fields by metallic obstacles, or the eddy current problem. In this interface problem, different sets of Maxwell equations must be solved both in the obstacle and outside it, while the tangential components of both electric and magnetic fields are continuous across the interface. We describe an asymptotic procedure, applied for large conductivity, which reflects the skin effect in metals. The key to our method is a special integral equation procedure for the exterior boundary value problems corresponding to perfect conductors. The asymptotic procedure leads to a great reduction in complexity for the numerical solution, since it involves solving only the exterior boundary value problems. Furthermore, we introduce a FEM/BEM coupling procedure for the transmission problem and consider the implementation of Galerkin’s elements for the perfect conductor problem, and present numerical experiments. Full article
(This article belongs to the Topic Engineering Mathematics)
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20 pages, 5184 KiB  
Article
Analytical Solution on Ground Deformation Caused by Parallel Construction of Rectangular Pipe Jacking
by Yazheng Wang, Dingli Zhang, Qian Fang, Xiang Liu and Jianchen Wang
Appl. Sci. 2022, 12(7), 3298; https://doi.org/10.3390/app12073298 - 24 Mar 2022
Cited by 9 | Viewed by 2265
Abstract
Pipe jacking has been widely used in urban underground engineering construction in recent years. Prediction of ground deformation caused by pipe jacking is particularly important for the safety of construction. With regard to the densely arranged pipes used in the pipe roof structure [...] Read more.
Pipe jacking has been widely used in urban underground engineering construction in recent years. Prediction of ground deformation caused by pipe jacking is particularly important for the safety of construction. With regard to the densely arranged pipes used in the pipe roof structure method, an analytical model of stratum disturbance caused by jacking of parallel rectangular pipes is proposed on the basis of Mindlin’s displacement solution and the stochastic medium theory. The influencing factors such as soil loss, additional thrust on the excavation face, friction between pipe jacking machine and soil, friction between subsequent pipes and soil, and the grouting pressure were comprehensively considered. Then, a 3D numerical simulation and a case study were conducted. The results showed consistent agreement with the analytical solution, and the proposed method can take into account the asymmetry of surface settlement curve induced by construction. A discussion of the ground deformation law shows that the proposed approach can reasonably predict the ground deformation and provide a reference for relevant pipe jacking construction. Full article
(This article belongs to the Topic Engineering Mathematics)
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25 pages, 358 KiB  
Article
Improved Allocation and Reallocation Approaches for Software Trustworthiness Based on Mathematical Programming
by Hongwei Tao, Lianyou Fu, Yixiang Chen, Lin Han and Xiao Wang
Symmetry 2022, 14(3), 628; https://doi.org/10.3390/sym14030628 - 21 Mar 2022
Cited by 5 | Viewed by 1548
Abstract
Software trustworthiness allocation and reallocation are the symmetry of software trustworthiness measure. They can provide the optimization scheme for trustworthiness development and improvement, according to the requirements. The existing allocation and reallocation models do not consider the absolute majority of software trustworthiness classification; [...] Read more.
Software trustworthiness allocation and reallocation are the symmetry of software trustworthiness measure. They can provide the optimization scheme for trustworthiness development and improvement, according to the requirements. The existing allocation and reallocation models do not consider the absolute majority of software trustworthiness classification; therefore, they cannot be very accurate in the allocation and reallocation of software trustworthiness. In this paper, improved allocation and reallocation models are constructed, which can resolve the above problem, and their polynomial solving algorithms are designed. At the same time, a demonstration application of the improved models and algorithms is given, and the trustworthiness enhancement specification of spacecraft software, based on factory reports, is established, including trustworthiness development specification and trustworthiness improvement specification. This enhancement specification provides a scientific and reasonable theory and method for the delivery acceptance of spacecraft software, from qualitative to quantitative grading acceptance, and furnishes a standard guarantee for the trustworthy development and improvement of such software. Full article
(This article belongs to the Topic Engineering Mathematics)
14 pages, 4527 KiB  
Communication
Modified Elliptic Integral Approach for the Forced Vibration and Sound Transmission Analysis of a Nonlinear Panel Backed by a Partitioned Cavity
by Yiu-Yin Lee
Mathematics 2022, 10(6), 984; https://doi.org/10.3390/math10060984 - 18 Mar 2022
Cited by 2 | Viewed by 1342
Abstract
This article is the further work of previous papers and also the first study to adopt the elliptic integral approach to solve the forced nonlinear structural acoustic problem. A previous elliptic integral approach, which was only used for the free vibration analyses of [...] Read more.
This article is the further work of previous papers and also the first study to adopt the elliptic integral approach to solve the forced nonlinear structural acoustic problem. A previous elliptic integral approach, which was only used for the free vibration analyses of various nonlinear structural acoustic problems, is modified and custom designed for conducting this forced vibration analysis. The main advantage of the proposed approach is that one elliptic cosine contains various harmonic components, while one simple cosine term only carries one particular harmonic component. That is why the proposed solution form can be more concise than those in the harmonic balance procedures. This is the first study to employ the proposed elliptic cosine solution form for the forced vibration and sound transmission of a nonlinear panel backed by a partitioned cavity. This study has two focuses: (1) the development of elliptic integral approach for solving the nonlinear structural acoustic governing equations, and (2) the effect of partitioned cavities on the forced vibration response and sound transmission loss. Moreover, a set of elliptic cosine solutions is verified by that from the modified residue harmonic balance method. A mode convergence study and a harmonic contribution analysis are also conducted. Full article
(This article belongs to the Topic Engineering Mathematics)
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16 pages, 3744 KiB  
Article
The Consistent Couple Stress Theory-Based Vibration and Post-Buckling Analysis of Bi-directional Functionally Graded Microbeam
by Rong Zhang, Hongbai Bai and Xiaochao Chen
Symmetry 2022, 14(3), 602; https://doi.org/10.3390/sym14030602 - 17 Mar 2022
Cited by 6 | Viewed by 1797
Abstract
The present work aims to study the free vibration, buckling and post-buckling behaviors of bidirectional functionally graded (BDFG) microbeams. The material properties of a BDFG microbeam were varied continuously in both thickness and axial directions. Furthermore, four different kinds of material distribution function [...] Read more.
The present work aims to study the free vibration, buckling and post-buckling behaviors of bidirectional functionally graded (BDFG) microbeams. The material properties of a BDFG microbeam were varied continuously in both thickness and axial directions. Furthermore, four different kinds of material distribution function were taken into consideration, two of which were symmetrical in the thickness direction, and the remaining two were asymmetrical. Employing the Timoshenko beam theory and the consistent couple stress theory (CCST), the governing equations and associated boundary conditions of BDFG microbeams were formulated by Hamilton’s principle. The differential quadrature method (DQM) and Newton’s method were applied to solve the eigenvalue problems and buckling path, respectively. Finally, several parametric investigations were carried out to probe the influence of material distribution functions, length to thickness ratio, gradient indexes and size effect on the vibration and buckling behaviors of BDFG microbeam under different boundary conditions. Full article
(This article belongs to the Topic Engineering Mathematics)
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19 pages, 8108 KiB  
Article
Cross-Channel Dynamic Weighting RPCA: A De-Noising Algorithm for Multi-Channel Arterial Pulse Signal
by Bo Peng, Kaifeng Gong, Zhendong Chen, Chao Chen, Zhan Zhang, Xiaohua Xie, Xihong Chen and Cheng-Chi Tai
Appl. Sci. 2022, 12(6), 2931; https://doi.org/10.3390/app12062931 - 13 Mar 2022
Cited by 3 | Viewed by 1872
Abstract
Pulse wave analysis (PWA) has been widely used in the medical field. A novel multi-channel sensor is employed in arterial pulse acquisition and brings richer physiological information to PWA. However, the noise of this sensor is distributed in the main frequency band of [...] Read more.
Pulse wave analysis (PWA) has been widely used in the medical field. A novel multi-channel sensor is employed in arterial pulse acquisition and brings richer physiological information to PWA. However, the noise of this sensor is distributed in the main frequency band of the pulse signal, which seriously interferes with subsequent analyses and is difficult to eliminate by existing methods. This study proposes a cross-channel dynamic weighting robust principal component analysis algorithm. A channel-scaled factor technique is used to manipulate the weighting factors in the nuclear norm. This factor can adaptively adjust the weights among the channels according to the signal pattern of each channel, optimizing the feature extraction in multi-channel signals. A series of performance evaluations were conducted, and four well-known de-noising algorithms were used for comparison. The results reveal that the proposed algorithm achieved one of the best de-noising performances in the time and frequency domains. The mean of h1 in the amplitude relative error (ARE) was 23.4% smaller than for the WRPCA algorithm. Moreover, our algorithm could accelerate convergence and reduce the computational time complexity by approximately 34.6%. These results demonstrate the performance and efficiency of the algorithm. Meanwhile, the idea can be extended to other multi-channel physiological signal de-noising and feature extraction fields. Full article
(This article belongs to the Topic Engineering Mathematics)
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15 pages, 795 KiB  
Article
A Novel Algorithm for Hydrostatic-Mechanical Mobile Machines with a Dual-Clutch Transmission
by Yusheng Xiang, Ruoyu Li, Christine Brach, Xiaole Liu and Marcus Geimer
Energies 2022, 15(6), 2095; https://doi.org/10.3390/en15062095 - 13 Mar 2022
Cited by 7 | Viewed by 1705
Abstract
Mobile machines using a hydrostatic transmission is highly efficient under lower working-speed condition but less capable at higher transport velocities. To enhance overall efficiency, we have improved the powertrain design by combining a hydrostatic transmission with a dual-clutch transmission (DCT). Compared with other [...] Read more.
Mobile machines using a hydrostatic transmission is highly efficient under lower working-speed condition but less capable at higher transport velocities. To enhance overall efficiency, we have improved the powertrain design by combining a hydrostatic transmission with a dual-clutch transmission (DCT). Compared with other mechanical gearboxes, the DCT avoids the interruption of torque transmission in the process of shifting without sacrificing more transmission efficiency. However, there are some problems of unstable torque transmission during the shifting process, and an excessive torque drop occurring at the end of the gear shift, which result in a poor drive comfort. To enhance the performance of the novel structural possibility of powertrain design, we designed a novel control strategy, which maintains the sliding in the torque phase and reduces the difference before and after the engagement, for the motor torque and the clutch torques during the shifting process, and then validated the control effect with model-based simulation. As a result, the control strategy employing clutch and motor torque control achieve a smooth shifting process since the drive torque is well tracked, and highly dynamical actuators are not required. As another benefit, only two calibration parameters are designed and actually needed to adjust the control performance systematically, even for any different sizes machines. Our research indicates the possibility to adopt dual-clutch in the field of construction machines. Full article
(This article belongs to the Topic Engineering Mathematics)
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14 pages, 1022 KiB  
Article
Online Frequency Estimation on a Building-like Structure Using a Nonlinear Flexible Dynamic Vibration Absorber
by Francisco Beltran-Carbajal, Hugo Francisco Abundis-Fong, Luis Gerardo Trujillo-Franco, Hugo Yañez-Badillo, Antonio Favela-Contreras and Eduardo Campos-Mercado
Mathematics 2022, 10(5), 708; https://doi.org/10.3390/math10050708 - 24 Feb 2022
Cited by 8 | Viewed by 1694
Abstract
The online frequency estimation of forced harmonic vibrations on a building-like structure, using a nonlinear flexible vibration absorber in a cantilever beam configuration, is addressed in this article. Algebraic formulae to compute online the harmonic excitation frequency on the nonlinear vibrating mechanical system [...] Read more.
The online frequency estimation of forced harmonic vibrations on a building-like structure, using a nonlinear flexible vibration absorber in a cantilever beam configuration, is addressed in this article. Algebraic formulae to compute online the harmonic excitation frequency on the nonlinear vibrating mechanical system using solely available measurement signals of position, velocity, or acceleration are presented. Fast algebraic frequency estimation can, thus, be implemented to tune online a semi-active dynamic vibration absorber to obtain a high attenuation level of undesirable vibrations affecting the main mechanical system. A semi-active vibration absorber can be tuned for application where variations of the excitation frequency can be expected. Adaptive vibration absorption for forced harmonic vibration suppression for operational scenarios with variable excitation frequency can be then performed. Analytical, numerical, and experimental results to demonstrate the effectiveness and efficiency of the operating frequency estimation, as well as the acceptable attenuation level achieved by the tunable flexible vibration absorber, are presented. The algebraic parametric estimation approach can be extended to add capabilities of variable frequency vibration suppression for several configurations of dynamic vibration absorbers. Full article
(This article belongs to the Topic Engineering Mathematics)
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21 pages, 473 KiB  
Article
Multi-Stage Multi-Product Production and Inventory Planning for Cold Rolling under Random Yield
by Jing Wu, Dan Zhang, Yang Yang, Gongshu Wang and Lijie Su
Mathematics 2022, 10(4), 597; https://doi.org/10.3390/math10040597 - 15 Feb 2022
Cited by 2 | Viewed by 2481
Abstract
This paper studies a multi-stage multi-product production and inventory planning problem with random yield derived from the cold rolling process in the steel industry. The cold rolling process has multiple stages, and intermediate inventory buffers are kept between stages to ensure continuous operation. [...] Read more.
This paper studies a multi-stage multi-product production and inventory planning problem with random yield derived from the cold rolling process in the steel industry. The cold rolling process has multiple stages, and intermediate inventory buffers are kept between stages to ensure continuous operation. Switching products during the cold rolling process is typically very costly. Backorder costs are incurred for unsatisfied demand while inventory holding costs are incurred for excess inventory. The process also experiences random yield. The objective of the production and inventory planning problem is to minimize the total cost including the switching costs, inventory holding costs, and backorder costs. We propose a stochastic formulation with a nonlinear objective function. Two lower bounds are proposed, which are based on full information relaxation and Jensen’s inequality, respectively. Then, we develop two heuristics from the proposed lower bounds. In addition, we propose a two-stage procedure motivated by newsvendor logic. To verify the performance of the proposed bounds and heuristics, computational tests are conducted on synthetic instances. The results show the efficiency of the proposed bounds and heuristics. Full article
(This article belongs to the Topic Engineering Mathematics)
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19 pages, 4333 KiB  
Article
Intelligent Optimization Based Multi-Factor Deep Learning Stock Selection Model and Quantitative Trading Strategy
by Jujie Wang, Zhenzhen Zhuang and Liu Feng
Mathematics 2022, 10(4), 566; https://doi.org/10.3390/math10040566 - 12 Feb 2022
Cited by 5 | Viewed by 3748
Abstract
With the rapid development of financial research theory and artificial intelligence technology, quantitative investment has gradually entered people’s attention. Compared with traditional investment, the advantage of quantitative investment lies in quantification and refinement. In quantitative investment technology, quantitative stock selection is the foundation. [...] Read more.
With the rapid development of financial research theory and artificial intelligence technology, quantitative investment has gradually entered people’s attention. Compared with traditional investment, the advantage of quantitative investment lies in quantification and refinement. In quantitative investment technology, quantitative stock selection is the foundation. Without good stock selection ability, the effect of quantitative investment will be greatly reduced. Therefore, this paper builds an effective multi-factor stock selection model based on intelligent optimization algorithms and deep learning and proposes corresponding trading strategies based on this. First of all, this paper selects 26 effective factors of financial indicators, technical indicators and public opinion to construct the factor database. Secondly, a Gated Recurrent Unit (GRU) neural network based on the Cuckoo Search (CS) optimization algorithm is used to build a stock selection model. Finally, a quantitative investment strategy is designed, and the proposed multi-factor deep learning stock selection model based on intelligent optimization is applied to practice to test its effectiveness. The results show that the quantitative trading strategy based on this model achieved a Sharpe ratio of 127.08%, an annualized rate of return of 40.66%, an excess return of 13.13% and a maximum drawdown rate of −17.38% during the back test period. Compared with other benchmark models, the proposed stock selection model achieved better back test performance. Full article
(This article belongs to the Topic Engineering Mathematics)
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20 pages, 914 KiB  
Article
Buckling Response of Functionally Graded Porous Plates Due to a Quasi-3D Refined Theory
by Ashraf M. Zenkour and Maryam H. Aljadani
Mathematics 2022, 10(4), 565; https://doi.org/10.3390/math10040565 - 11 Feb 2022
Cited by 8 | Viewed by 1569
Abstract
A quasi-3D refined theory is used to investigate the buckling response of functionally graded (FG) porous plates. The present theory takes into consideration the effect of thickness stretching. Three models of FG porous plates are presented: an isotropic FG porous plate, FG skins [...] Read more.
A quasi-3D refined theory is used to investigate the buckling response of functionally graded (FG) porous plates. The present theory takes into consideration the effect of thickness stretching. Three models of FG porous plates are presented: an isotropic FG porous plate, FG skins with a homogenous core, and an FG core with homogenous skins. The FG porous material properties vary along with the thickness of the FG layer based on modified polynomial law. By using the principle of total potential energy, the equilibrium equations are obtained. The buckling response is determined for simply supported FG porous plates. Analytical investigations are verified to present the accuracy of the current quasi-3D refined theory in predicting the buckling response of FG porous plates. The effect of thickness stretching and several parameters such as porosity coefficients, mechanical loadings, geometric parameters, gradient indexes, and layer thickness ratios are discussed. It is observed that the current theory shows more accurate results for the buckling response of FG plates compared with other shear deformation theories. Full article
(This article belongs to the Topic Engineering Mathematics)
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28 pages, 3091 KiB  
Article
An Exact Solution to the Modified Winding Function for Eccentric Permanent Magnet Synchronous Machines
by Carsten Klein, Mira Pinter, Marco Palmieri, Matthias Nienhaus and Emanuele Grasso
Mathematics 2022, 10(3), 345; https://doi.org/10.3390/math10030345 - 24 Jan 2022
Cited by 2 | Viewed by 2174
Abstract
The Winding Function Approach has been used since 1965 to describe the inductance behavior of small air-gap electrical machines, and several works have contributed to its formulation in the presence of mechanical faults, such as eccentricity, leading to the Modified Winding Function Approach [...] Read more.
The Winding Function Approach has been used since 1965 to describe the inductance behavior of small air-gap electrical machines, and several works have contributed to its formulation in the presence of mechanical faults, such as eccentricity, leading to the Modified Winding Function Approach (MWFA). In order to use the MWFA, an integral over a full rotation period needs to be computed. Nevertheless, this typically requires the performance of numerical integration, and thus it is affected by integration error, requires relatively high computational effort and, at the same time, it does not easily allow for performance of the analysis of the inductance harmonics. In this work, an exact analytical solution to the MWFA equation is provided in a form that allows to highlight the harmonic content of the inductances. After a thorough mathematical derivation of the solution, a numerical investigation is proposed for verification purposes. Full article
(This article belongs to the Topic Engineering Mathematics)
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