Mathematics

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12 pages, 1635 KiB

Open AccessArticle

An Adaptive Controller Design for Nonlinear Active Air Suspension Systems with Uncertainties

by Jinhua Zhang, Yi Yang and Cheng Hu

Mathematics 2023, 11(12), 2626; https://doi.org/10.3390/math11122626 - 8 Jun 2023

Cited by 5 | Viewed by 1814

Abstract

Active air spring suspensions can improve the vehicle ride comfort and meanwhile realize the vehicle height regulation, and therefore, they have been widely used and studied. However, to achieve better ride comfort and a satisfactory vehicle body height adjustment, the active air suspension [...] Read more.

Active air spring suspensions can improve the vehicle ride comfort and meanwhile realize the vehicle height regulation, and therefore, they have been widely used and studied. However, to achieve better ride comfort and a satisfactory vehicle body height adjustment, the active air suspension controller becomes an indispensable and significant part of the system. Since the nonlinear suspension system possesses uncertainties, it is difficult to take into account both ride comfort and height regulation. This study innovatively proposes an adaptive control algorithm to specifically address the problem of vehicle height regulation and ride comfort for nonlinear active air suspension systems with uncertainties. The accurate tracking to reference vehicle body height curves is realized, and the ride comfort is also improved. Through simulations with two scenarios, it is illustrated that the active air suspension controller owns better control effectiveness than the PID controller. Compared with the PID controller, the designed controller can track the reference vehicle body height curves faster and more accurately. The result also verifies the priority of the designed controller. Full article

(This article belongs to the Special Issue Modeling and Simulation in Engineering, 2nd Edition)

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19 pages, 4875 KiB

Open AccessArticle

Simulation of Light Scattering in Automotive Paints: Role of Particle Size

by Sergey Ershov, Alexey Voloboy and Vladimir Galaktionov

Mathematics 2023, 11(11), 2429; https://doi.org/10.3390/math11112429 - 24 May 2023

Viewed by 1051

Abstract

Nowadays, computer simulation is being used to develop new materials. Many of them are dispersed media (e.g., paints, and 3D printer inks). Modern automotive paints are of great interest in research works. They contain colorant particles and thin flat metallic or pearlescent flakes [...] Read more.

Nowadays, computer simulation is being used to develop new materials. Many of them are dispersed media (e.g., paints, and 3D printer inks). Modern automotive paints are of great interest in research works. They contain colorant particles and thin flat metallic or pearlescent flakes distributed in a clear varnish. There are two main approaches to simulation of light scattering in a dispersed media. The first one is based on the continuous medium model. This model is faster but less accurate. The second approach is the simulation of light propagation through an ensemble of paint flakes and particles represented as an explicit geometry. This model correctly calculates light scattering but is rather time-consuming. In our study, we investigated the dependence of the painted surface luminance on particle size and compared both the approaches. We prove that the effect of coarse particles can emerge even in a model where positions of these particles are not correlated; this is different from the mainstream studies which have only concentrated on the role of these correlations. Then, we suggest a semi-analytical model of dependence on particle size. This model not only allows to more accurately simulate visual appearance but also admits intuitive comprehension of how it is affected by various medium parameters. In case of the divergence between the results of LTE and accurate approaches, we propose a simple approximation that allows to improve the accuracy of the LTE results for coarse particles. Full article

(This article belongs to the Special Issue Modeling and Simulation in Engineering, 2nd Edition)

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15 pages, 6325 KiB

Open AccessArticle

Estimation of the Spatial and Temporal Distribution of Magnetic Fields around Overhead Power Lines—A Case Study

by Ionel Pavel, Camelia Petrescu, Valeriu David and Eduard Lunca

Mathematics 2023, 11(10), 2292; https://doi.org/10.3390/math11102292 - 15 May 2023

Cited by 4 | Viewed by 1162

Abstract

Due to the growing number, diversity and spreading of magnetic field sources, an increasing need to determine the field levels of human exposure has arisen. Some of the most encountered sources are the overhead power lines (OPL) and the determination of spatial and [...] Read more.

Due to the growing number, diversity and spreading of magnetic field sources, an increasing need to determine the field levels of human exposure has arisen. Some of the most encountered sources are the overhead power lines (OPL) and the determination of spatial and temporal variation of the magnetic fields produced by OPLs is a challenge. In this paper a hybrid method for the estimation of the temporal and spatial distribution of the magnetic flux density B caused by OPLs, based on experimental measurements and on numerical and analytical simulations, is presented. Thus, using a small number of simultaneous spot measurements correlated with a long-term survey, maps of the magnetic flux density distribution on extended areas are established, for several time instances. The proposed method is verified using two sets of different measurements and the results obtained through simulation. The difference between the estimated and simulated values of B is under 5.5%, which is considered acceptable considering that B spans over a large set of values (724 nT ÷ 1375 nT) in the location of the long-term survey procedure. The possibilities and limitations of the proposed method are discussed. Full article

(This article belongs to the Special Issue Modeling and Simulation in Engineering, 2nd Edition)

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17 pages, 4627 KiB

Open AccessArticle

Upper Limb Joint Angle Estimation Using Wearable IMUs and Personalized Calibration Algorithm

by Md. Mahmudur Rahman, Kok Beng Gan, Noor Azah Abd Aziz, Audrey Huong and Huay Woon You

Mathematics 2023, 11(4), 970; https://doi.org/10.3390/math11040970 - 14 Feb 2023

Cited by 6 | Viewed by 2917

Abstract

In physical therapy, exercises improve range of motion, muscle strength, and flexibility, where motion-tracking devices record motion data during exercises to improve treatment outcomes. Cameras and inertial measurement units (IMUs) are the basis of these devices. However, issues such as occlusion, privacy, and [...] Read more.

In physical therapy, exercises improve range of motion, muscle strength, and flexibility, where motion-tracking devices record motion data during exercises to improve treatment outcomes. Cameras and inertial measurement units (IMUs) are the basis of these devices. However, issues such as occlusion, privacy, and illumination can restrict vision-based systems. In these circumstances, IMUs may be employed to focus on a patient’s progress quantitatively during their rehabilitation. In this study, a 3D rigid body that can substitute a human arm was developed, and a two-stage algorithm was designed, implemented, and validated to estimate the elbow joint angle of that rigid body using three IMUs and incorporating the Madgwick filter to fuse multiple sensor data. Two electro-goniometers (EGs) were linked to the rigid body to verify the accuracy of the joint angle measuring algorithm. Additionally, the algorithm’s stability was confirmed even in the presence of external acceleration. Multiple trials using the proposed algorithm estimated the elbow joint angle of the rigid body with a maximum RMSE of 0.46°. Using the IMU manufacturer’s (WitMotion) algorithm (Kalman filter), the maximum RMSE was 1.97°. For the fourth trial, joint angles were also calculated with external acceleration, and the RMSE was 0.996°. In all cases, the joint angles were within therapeutic limits. Full article

(This article belongs to the Special Issue Modeling and Simulation in Engineering, 2nd Edition)

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18 pages, 6860 KiB

Open AccessArticle

Exploration of Multiple Transfer Phenomena within Viscous Fluid Flows over a Curved Stretching Sheet in the Co-Existence of Gyrotactic Micro-Organisms and Tiny Particles

by Pachiyappan Ragupathi, N. Ameer Ahammad, Abderrahim Wakif, Nehad Ali Shah and Yongseok Jeon

Mathematics 2022, 10(21), 4133; https://doi.org/10.3390/math10214133 - 5 Nov 2022

Cited by 56 | Viewed by 2256

Abstract

In the present study, the magnetohydrodynamics (MHD) bio-convective flow and heat transfer of nanofluid, due to the swimming of the gyrotactic micro-organisms over a curved stretched sheet, is examined. In addition, thermophoresis and Brownian motion behaviors are also investigated by assuming slip conditions [...] Read more.

In the present study, the magnetohydrodynamics (MHD) bio-convective flow and heat transfer of nanofluid, due to the swimming of the gyrotactic micro-organisms over a curved stretched sheet, is examined. In addition, thermophoresis and Brownian motion behaviors are also investigated by assuming slip conditions at the boundary. A non-linear system of partial differential equations (PDEs) is reduced to a system of ordinary differential equations (ODEs). For convergent solutions, the obtained ODE system is solved by the use of the BVP4C routine integrated MATLAB package. In addition, the impacts of different influential parameters on motile micro-organisms, temperature, velocity, and concentration profiles are deliberated. The velocity field is observed to be reduced when the slip parameter increases. As the main results, it is demonstrated that the distribution of motile microorganisms against the curvature parameter decreases significantly. Similarly, it is found that the nanofluid parameters (i.e., Brownian motion and thermophoresis parameters) and the Peclet number reduce the motile micro-organisms’ number. On the other hand, it is evidenced that the motile micro-organisms’ distribution can be improved with an increase in bio-convective Schmidt number. Full article

(This article belongs to the Special Issue Modeling and Simulation in Engineering, 2nd Edition)

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18 pages, 11582 KiB

Open AccessFeature PaperArticle

Inspection Interval Optimization for Aircraft Composite Tail Wing Structure Using Numerical-Analysis-Based Approach

by Salman Khalid, Hee-Seong Kim, Heung Soo Kim and Joo-Ho Choi

Mathematics 2022, 10(20), 3836; https://doi.org/10.3390/math10203836 - 17 Oct 2022

Cited by 4 | Viewed by 2735

Abstract

Recently, there has been a tremendous increase in the use of fiber-reinforced composite (FRCP) in the aviation and aerospace industries due to its superior properties of high strength, stiffness, and low weight. The most important feature of implementing composite materials in aviation is [...] Read more.

Recently, there has been a tremendous increase in the use of fiber-reinforced composite (FRCP) in the aviation and aerospace industries due to its superior properties of high strength, stiffness, and low weight. The most important feature of implementing composite materials in aviation is their behavior under dynamic loads and resistance to fatigue. To predict the life of composite structures and optimize the inspection interval, it is essential to predict the damage behavior of composites. In this study, a model of fatigue delamination damage of composite specimens was first constructed using a finite element analysis (FEA)-based approach. The FEA modeling was verified through comparison with experimental specimen data, and the verified FEA model was applied to the composite material aircraft tail wing structure. In this case, a Monte Carlo simulation (MCS) was performed by building a response surface model while considering the uncertainty of the mechanical parameters. Through this process, the risk as a function of flight time could be quantitatively evaluated, and the inspection interval was optimized by selecting the combination with the lowest number of repeated inspections that met the permitted risk criteria. Full article

(This article belongs to the Special Issue Modeling and Simulation in Engineering, 2nd Edition)

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16 pages, 6396 KiB

Open AccessArticle

Analysis and Performance Evaluation of a Novel Adjustable Speed Drive with a Homopolar-Type Rotor

by Songlin Guo, Zhengkang Yi, Pan Liu, Guoshuai Wang, Houchuan Lai, Kexun Yu and Xianfei Xie

Mathematics 2022, 10(19), 3712; https://doi.org/10.3390/math10193712 - 10 Oct 2022

Cited by 3 | Viewed by 1718

Abstract

The use of a magnetic adjustable speed drive is a popular choice in industrial settings due to its efficient operation, vibration isolation, low maintenance, and overload protection. Most conventional magnetic adjustable speed drives use various forms of the permanent magnets (PMs). Due to [...] Read more.

The use of a magnetic adjustable speed drive is a popular choice in industrial settings due to its efficient operation, vibration isolation, low maintenance, and overload protection. Most conventional magnetic adjustable speed drives use various forms of the permanent magnets (PMs). Due to the PMs, this type of machine has continuous free-wheeling losses in the form of hysteresis and induced eddy currents. In recent years, the homopolar-type rotor has been widely used in high-speed machines, superconducting machines, and in the application of flywheel energy storage. This study proposes a new application of the homopolar-type rotor. A novel adjustable speed drive with a homopolar-type rotor (HTR-ASD), which has obvious advantages (no brush, no permanent magnet, and no mechanical flux regulation device), is designed and analyzed in this study. Its speed and torque can be adjusted only by adjusting the excitation current. Firstly, in this study, the structure, operation principles, and flux-modulated mechanism of the HTR-ASD are studied. The homopolar-type rotor has a special three-dimensional magnetic circuit structure with the same pole. The 3D-FEM is usually used to calculate its parameters, which is time consuming. In this study, an analytical method is developed to solve this issue. To analytically calculate the torque characteristics, the air gap magnetic flux density, and the winding inductance parameter, the equivalent circuit and the air gap permeance are researched to simplify the analysis. Then, the key parameters of the HTR-ASD are calculated. Finally, the performance of the HTR-ASD is comparatively studied using the analytical method and finite element method, and a comparison of the results is carried out. The comparison indicates that the analytical method is in good agreement with simulation results, and that it is very helpful for designing homopolar-type rotor machines. According to the analysis, the proposed adjustable speed drive displays a great performance in relation to the operating characteristics of a flexible mechanical speed drive. Full article

(This article belongs to the Special Issue Modeling and Simulation in Engineering, 2nd Edition)

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15 pages, 6277 KiB

Open AccessArticle

Prediction and Optimization of Pile Bearing Capacity Considering Effects of Time

by Mohammadreza Khanmohammadi, Danial Jahed Armaghani and Mohanad Muayad Sabri Sabri

Mathematics 2022, 10(19), 3563; https://doi.org/10.3390/math10193563 - 29 Sep 2022

Cited by 8 | Viewed by 1761

Abstract

Prediction of pile bearing capacity has been considered an unsolved problem for years. This study presents a practical solution for the preparation and maximization of pile bearing capacity, considering the effects of time after the end of pile driving. The prediction phase proposes [...] Read more.

Prediction of pile bearing capacity has been considered an unsolved problem for years. This study presents a practical solution for the preparation and maximization of pile bearing capacity, considering the effects of time after the end of pile driving. The prediction phase proposes an intelligent equation using a genetic programming (GP) model. Thus, pile geometry, soil properties, initial pile capacity, and time after the end of driving were considered predictors to predict pile bearing capacity. The developed GP equation provided an acceptable level of accuracy in estimating pile bearing capacity. In the optimization phase, the developed GP equation was used as input in two powerful optimization algorithms, namely, the artificial bee colony (ABC) and the grey wolf optimization (GWO), in order to obtain the highest bearing capacity of the pile, which corresponds to the optimum values for input parameters. Among these two algorithms, GWO obtained a higher value for pile capacity compared to the ABC algorithm. The introduced models and their modeling procedure in this study can be used to predict the ultimate capacity of piles in such projects. Full article

(This article belongs to the Special Issue Modeling and Simulation in Engineering, 2nd Edition)

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14 pages, 2139 KiB

Open AccessArticle

Power-Law Nanofluid Flow over a Stretchable Surface Due to Gyrotactic Microorganisms

by Hossam A. Nabwey, Waqar A. Khan, A. M. Rashad, Fazal Mabood and Taha Salah

Mathematics 2022, 10(18), 3285; https://doi.org/10.3390/math10183285 - 9 Sep 2022

Cited by 3 | Viewed by 1660

Abstract

This study aims to learn more about how the flow of a power-law nanofluid’s mixed bio-convective stagnation point flow approaching a stretchable surface behaves with the presence of a passively controlled boundary condition. The governing equations incorporate the motile bacterium and nanoparticles, and [...] Read more.

This study aims to learn more about how the flow of a power-law nanofluid’s mixed bio-convective stagnation point flow approaching a stretchable surface behaves with the presence of a passively controlled boundary condition. The governing equations incorporate the motile bacterium and nanoparticles, and the current model includes Brownian motion and thermophoresis effects. The governing equations are transformed into ordinary differential equations, which are then numerically solved using the Runge–KuttaFehlberg (RKF) with the shooting technique. The controlling parameters are chosen as follows: the velocity ratio parameter, ε, is taken between 0.1 and 1.5; the mixed convection parameter, λ, is considered in the range 0–3; the buoyancy ratio parameter is considered in the range between 0.1 and 4; the bio-convection parameter, Rb, is taken in the range 0–1; nanofluid parameters are taken in the range 0.1–0.7; the bioconvection Schmidt number is considered in the range 0.1–3; the Prandtl number is taken between 1–4; and the Schmidt number is taken between 1 and 3. The Nusselt number, skin friction, and nanoparticle volume fraction profiles are shown graphically to observe the impact of several parameters under consideration. Both the Schmidt number and the Brownian motion parameter are shown to significantly increase the Sherwood number. Thermophoresis, however, has been proven to lower the Sherwood number. Furthermore, the bioconvection constant and Peclet number both help to slow down the rate of mass transfer. The presented theoretical investigation has a considerable role in engineering, where nanofluid flow is applied to organize a bioconvection process to develop power generation and mechanical energy. One of the more essential features of bioconvection is the aggregation of nanoparticles with motile microorganisms requested to augment the stability, heat, and mass transmission. Full article

(This article belongs to the Special Issue Modeling and Simulation in Engineering, 2nd Edition)

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14 pages, 1987 KiB

Open AccessArticle

Activation Energy Performance through Magnetized Hybrid Fe₃O₄–PP Nanofluids Flow with Impact of the Cluster Interfacial Nanolayer

by M. Zubair Akbar Qureshi, Qadeer Raza, Aroosa Ramzan, M. Faisal, Bagh Ali, Nehad Ali Shah and Wajaree Weera

Mathematics 2022, 10(18), 3277; https://doi.org/10.3390/math10183277 - 9 Sep 2022

Cited by 11 | Viewed by 1647

Abstract

The current work investigated the mass and heat transfer of the MHD hybrid nanofluid flow subject to the impact of activation energy and cluster interfacial nanolayer. The heat transport processes related to the interfacial nanolayer between nanoparticles and base fluids enhanced the base [...] Read more.

The current work investigated the mass and heat transfer of the MHD hybrid nanofluid flow subject to the impact of activation energy and cluster interfacial nanolayer. The heat transport processes related to the interfacial nanolayer between nanoparticles and base fluids enhanced the base fluid’s thermal conductivity. The tiny particles of

F e_{3} O_{4}

and

P P y

were considered due to the extraordinary thermal conductivity which is of remarkable significance in nanotechnology, electronic devices, and modern shaped heat exchangers. Using the similarity approach, the governing higher-order nonlinear coupled partial differential equation was reduced to a system of ordinary differential equations (ODEs). Fe₃O₄–PPy hybrid nanoparticles have a considerable influence on thermal performance, and when compared to non-interfacial nanolayer thermal conductivity, the interfacial nanolayer thermal conductivity model produced substantial findings. The increase in nanolayer thickness from level 1 to level 5 had a significant influence on thermal performance improvement. Further, the heat and mass transfer rate was enhanced with higher input values of interfacial nanolayer thickness. Full article

(This article belongs to the Special Issue Modeling and Simulation in Engineering, 2nd Edition)

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26 pages, 8521 KiB

Open AccessArticle

A Novel Surrogate Model-Based Solving Framework for the Black-Box Dynamic Co-Design and Optimization Problem in the Dynamic System

by Qi Zhang, Yizhong Wu and Li Lu

Mathematics 2022, 10(18), 3239; https://doi.org/10.3390/math10183239 - 6 Sep 2022

Cited by 7 | Viewed by 1704

Abstract

When encountering the black-box dynamic co-design and optimization (BDCDO) problem in the multidisciplinary dynamic system, the finite difference technique is inefficient or even infeasible to provide approximate numerical gradient information for the optimization algorithm since it requires numerous original expensive evaluations. Therefore, a [...] Read more.

When encountering the black-box dynamic co-design and optimization (BDCDO) problem in the multidisciplinary dynamic system, the finite difference technique is inefficient or even infeasible to provide approximate numerical gradient information for the optimization algorithm since it requires numerous original expensive evaluations. Therefore, a solving framework based on the surrogate model of the state equation is introduced to optimize BDCDO. To efficiently construct the surrogate model, a sequential sampling method is presented on the basis of the successive relative improvement ratio. Meanwhile, a termination criterion is suggested to quantify the convergence of the solution. Ultimately, the newly proposed sampling strategy and termination criterion are incorporated into the BDCDO solving framework to optimize two numerical examples and two engineering examples. The results demonstrate that the framework integrating the proposed sampling strategy and termination criterion has the best performance in terms of the accuracy, efficiency, and computational budget compared to the existing methods. Full article

(This article belongs to the Special Issue Modeling and Simulation in Engineering, 2nd Edition)

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10 pages, 269 KiB

Open AccessArticle

The Dual Characterization of Structured and Skewed Structured Singular Values

by Mutti-Ur Rehman, Jehad Alzabut, Taqwa Ateeq, Jutarat Kongson and Weerawat Sudsutad

Mathematics 2022, 10(12), 2050; https://doi.org/10.3390/math10122050 - 13 Jun 2022

Cited by 3 | Viewed by 1687

Abstract

The structured singular values and skewed structured singular values are the well-known mathematical quantities and bridge the gap between linear algebra and system theory. It is well-known fact that an exact computation of these quantities is NP-hard. The NP-hard nature of structured singular [...] Read more.

The structured singular values and skewed structured singular values are the well-known mathematical quantities and bridge the gap between linear algebra and system theory. It is well-known fact that an exact computation of these quantities is NP-hard. The NP-hard nature of structured singular values and skewed structured singular values allow us to provide an estimations of lower and upper bounds which guarantee the stability and instability of feedback systems in control. In this paper, we present new results on the dual characterization of structured singular values and skewed structured singular values. The results on the estimation of upper bounds for these two quantities are also computed. Full article

(This article belongs to the Special Issue Modeling and Simulation in Engineering, 2nd Edition)

Review

Jump to: Research

48 pages, 6805 KiB

Open AccessReview

Role of Metaheuristic Approaches for Implementation of Integrated MPPT-PV Systems: A Comprehensive Study

by Amit Kumar Sharma, Rupendra Kumar Pachauri, Sushabhan Choudhury, Ahmad Faiz Minai, Majed A. Alotaibi, Hasmat Malik and Fausto Pedro García Márquez

Mathematics 2023, 11(2), 269; https://doi.org/10.3390/math11020269 - 4 Jan 2023

Cited by 18 | Viewed by 3900

Abstract

An effective MPPT approach plays a significant role in increasing the efficiency of a PV system. Solar energy is a rich renewable energy source that is supplied to the earth in surplus by the sun. Solar PV systems are designed to utilize sunlight [...] Read more.

An effective MPPT approach plays a significant role in increasing the efficiency of a PV system. Solar energy is a rich renewable energy source that is supplied to the earth in surplus by the sun. Solar PV systems are designed to utilize sunlight in order to meet the energy needs of the user. Due to unreliable climatic conditions, these PV frames have a non-linear characteristic that has a significant impact on their yield. Moreover, PSCs also affect the performance of PV systems in yielding maximum power. A significant progression in solar PV installations has resulted in rapid growth of MPPT techniques. As a result, a variety of MPPT approaches have been used to enhance the power yield of PV systems along with their advantages and disadvantages. Thus, it is essential for researchers to appraise developed MPPT strategies appropriately on regular basis. This study is novel because it provides an in-depth assessment of the current state of MPPT strategies for PV systems. On account of novelty, the authors analyzed the successive growth in MPPT strategies along with working principles, mathematical modeling, and simplified flow charts for better understanding by new learners. Moreover, the taxonomy and pro and cons of conventional and AI-based MPPT techniques are explored comprehensively. In addition, a comparative study based on key characteristics of PV system of all MPPT algorithms is depicted in a table, which can be used as a reference by various researchers while designing PV systems. Full article

(This article belongs to the Special Issue Modeling and Simulation in Engineering, 2nd Edition)

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