Mathematical Modeling in Industrial Engineering and Electrical Engineering

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Engineering Mathematics".

Deadline for manuscript submissions: closed (31 August 2021) | Viewed by 57048

Special Issue Editor


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Dipartimento di Ingegneria Civile Energia Ambiente e Materiali (DICEAM), “Mediterranea” University, 89122 Reggio Calabria, Italy
Interests: magnetorheological fluids; theoretical models for magnetorheological fluids; experimental models for magnetorheological fluids; magnetorheological fluids for industrial applications
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

It is clear that the cooperation among universities and industries determines the progress of social, cultural, technological, and economic innovation. The cooperation between these two worlds is an essential tool for the development of knowledge, guaranteeing greater competitiveness. The conditions for a virtuous exchange of knowledge among universities and industries are set in motion by cooperating to find ways, languages, and opportunities to achieve the necessary coordination: requests and offers from the industries and offer of knowledge and skills from the universities. Thus, the need in the university world in general, and in particular in the fields of electrical and industrial engineering, matures to realize research projects shared with the industry world. There is no doubt that mathematical modeling is the first important step in managing industrial problems. However, such models are often complex, requiring numerical techniques to obtain solutions, especially when the enormous amount of input data is affected by uncertainty.

This Special Issue aims to explore, from a broad perspective, the most recent developments in the field of mathematical modeling for problems of interest in electrical and industrial engineering. Topics of interest range from analytical, numerical, and soft computing modeling techniques to solving industrial problems.

Prof. Dr. Mario Versaci
Guest Editor

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Keywords

  • Artificial Intelligence
  • Complex systems
  • Delayed systems
  • Dynamical systems
  • Machine learning
  • Mathematical modeling
  • Neural networks
  • Numerical techniques
  • Physics-based modeling
  • Soft computing techniques
  • Stability
  • Uncertain systems
  • Application in industrial and electrical engineering

Published Papers (22 papers)

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Editorial

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5 pages, 188 KiB  
Editorial
Preface to the Special Issue “Mathematical Modeling in Industrial Engineering and Electrical Engineering”—Special Issue Book
by Mario Versaci
Mathematics 2022, 10(21), 3965; https://doi.org/10.3390/math10213965 - 25 Oct 2022
Viewed by 976
Abstract
It is now clear that cooperation between academia and industries is crucial for social, cultural, technological and economic progress and innovation [...] Full article

Research

Jump to: Editorial

11 pages, 279 KiB  
Article
Hermite B-Splines: n-Refinability and Mask Factorization
by Mariantonia Cotronei and Caroline Moosmüller
Mathematics 2021, 9(19), 2458; https://doi.org/10.3390/math9192458 - 02 Oct 2021
Cited by 4 | Viewed by 1657
Abstract
This paper deals with polynomial Hermite splines. In the first part, we provide a simple and fast procedure to compute the refinement mask of the Hermite B-splines of any order and in the case of a general scaling factor. Our procedure is solely [...] Read more.
This paper deals with polynomial Hermite splines. In the first part, we provide a simple and fast procedure to compute the refinement mask of the Hermite B-splines of any order and in the case of a general scaling factor. Our procedure is solely derived from the polynomial reproduction properties satisfied by Hermite splines and it does not require the explicit construction or evaluation of the basis functions. The second part of the paper discusses the factorization properties of the Hermite B-spline masks in terms of the augmented Taylor operator, which is shown to be the minimal annihilator for the space of discrete monomial Hermite sequences of a fixed degree. All our results can be of use, in particular, in the context of Hermite subdivision schemes and multi-wavelets. Full article
22 pages, 2137 KiB  
Article
Localization of Rolling Element Faults Using Improved Binary Particle Swarm Optimization Algorithm for Feature Selection Task
by Chun-Yao Lee and Guang-Lin Zhuo
Mathematics 2021, 9(18), 2302; https://doi.org/10.3390/math9182302 - 18 Sep 2021
Cited by 3 | Viewed by 1334
Abstract
The accurate localization of the rolling element failure is very important to ensure the reliability of rotating machinery. This paper proposes an efficient and anti-noise fault diagnosis model for rolling elements. The proposed model is composed of feature extraction, feature selection and fault [...] Read more.
The accurate localization of the rolling element failure is very important to ensure the reliability of rotating machinery. This paper proposes an efficient and anti-noise fault diagnosis model for rolling elements. The proposed model is composed of feature extraction, feature selection and fault classification. Feature extraction is composed of signal processing and signal noise reduction. Signal processing is carried out by local mean decomposition (LMD), and signal noise reduction is performed by product function (PF) selection and wavelet packet decomposition (WPD). Through the steps of signal noise reduction, high-frequency noise can be effectively removed, and the fault information hidden under the noise can be extracted. To further improve the effectiveness of the diagnostic model, an improved binary particle swarm optimization (IBPSO) is proposed to find the most important features from the feature space. In IBPSO, cycling time-varying inertia weight is introduced to balance exploitation and exploration and improve the capability to escape from local solutions, and crossover and mutation operations are also introduced to improve exploration and exploitation capabilities, respectively. The main contributions of this research are briefly described as follows: (1) The feature extraction process applied in this research can effectively remove noise and establish a high-accuracy feature set. (2) The proposed feature selection algorithm has higher accuracy than the other state-of-the-art feature selection algorithms. (3) In a strong noise environment, the proposed rolling element fault diagnosis model is compared with the state-of-the-art fault diagnosis model in terms of classification accuracy. Experimental results show that the model can maintain high classification accuracy in a strong noise environment. Therefore, it can be proved that the fault diagnosis model proposed in this paper can be effectively applied to the fault diagnosis of rotating machinery. Full article
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20 pages, 3885 KiB  
Article
A Real-Time Harmonic Extraction Approach for Distorted Grid
by Po Li, Xiang Li, Jinghui Li, Yimin You and Zhongqing Sang
Mathematics 2021, 9(18), 2245; https://doi.org/10.3390/math9182245 - 12 Sep 2021
Cited by 1 | Viewed by 2011
Abstract
Harmonic interference is a major hazard in the current power system that affects power quality. How to extract harmonics quickly and accurately is the premise to ensure the sustainable operation of power system, which is particularly important in the field of new energy [...] Read more.
Harmonic interference is a major hazard in the current power system that affects power quality. How to extract harmonics quickly and accurately is the premise to ensure the sustainable operation of power system, which is particularly important in the field of new energy power generation. In this paper, a harmonic extraction method based on a time-varying observer is proposed. Firstly, a frequency estimation algorithm is used to estimate the power grid current frequency, which can estimate the frequency in real time. Then, applying the zero-crossing detection method to convert the frequency into a phase variable. Finally, using the phase variable and integral current signal as input, a observer is modeled to extract each order harmonic component. The proposed method is evaluated on a FGPA test platform, which shows that the method can extract the harmonic components of the grid current and converge within 80 ms even in the presence of grid distortions. In the verification case, the relative errors of the 1st, 5th, 7th and 11th harmonics are 0.005%, −0.003%, 0.251% and 0.620%, respectively, which are sufficiently small. Full article
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11 pages, 3373 KiB  
Article
Hierarchical Transfer Learning for Cycle Time Forecasting for Semiconductor Wafer Lot under Different Work in Process Levels
by Junliang Wang, Pengjie Gao, Zhe Li and Wei Bai
Mathematics 2021, 9(17), 2039; https://doi.org/10.3390/math9172039 - 25 Aug 2021
Cited by 2 | Viewed by 1999
Abstract
The accurate cycle time (CT) prediction of the wafer fabrication remains a tough task, as the system level of work in process (WIP) is fluctuant. Aiming to construct one unified CT forecasting model under dynamic WIP levels, this paper proposes a transfer learning [...] Read more.
The accurate cycle time (CT) prediction of the wafer fabrication remains a tough task, as the system level of work in process (WIP) is fluctuant. Aiming to construct one unified CT forecasting model under dynamic WIP levels, this paper proposes a transfer learning method for finetuning the predicted neural network hierarchically. First, a two-dimensional (2D) convolutional neural network was constructed to predict the CT under a primary WIP level with the input of spatial-temporal characteristics by reorganizing the input parameters. Then, to predict the CT under another WIP level, a hierarchical optimization transfer learning strategy was designed to finetune the prediction model so as to improve the accuracy of the CT forecasting. The experimental results demonstrated that the hierarchically transfer learning approach outperforms the compared methods in the CT forecasting with the fluctuation of WIP levels. Full article
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20 pages, 1165 KiB  
Article
Altruistic Preference Models of Low-Carbon E-Commerce Supply Chain
by Jianfeng Liu, Liguo Zhou and Yuyan Wang
Mathematics 2021, 9(14), 1682; https://doi.org/10.3390/math9141682 - 17 Jul 2021
Cited by 14 | Viewed by 2417
Abstract
With the gradual popularity of online sales and the enhancement of consumers’ low-carbon awareness, the low-carbon e-commerce supply chain (LCECSC) has developed rapidly. However, most of the current research on LCECSC assumes that the decision-making body is rational, and there is less research [...] Read more.
With the gradual popularity of online sales and the enhancement of consumers’ low-carbon awareness, the low-carbon e-commerce supply chain (LCECSC) has developed rapidly. However, most of the current research on LCECSC assumes that the decision-making body is rational, and there is less research on the irrational behavior of the e-platform altruistic preference. Therefore, aiming at the LCECSC composed of a single e-platform and a single manufacturer, this paper establishes two basic models with or without altruistic preference. Additionally, this paper combines the characteristics of online sales and assumes that altruistic preference is a proportional function of commission, then establishes a commission-based extended model with altruistic preference to further explore the influence of commission on its altruistic preference. The current literature does not consider this point, nor does it analyze the influence of other parameters on the degree of altruism preference. By comparing the optimal decisions and numerical analysis among the models, the following conclusions can be drawn that: (1) different from the traditional offline supply chain, the profit of the dominator e-platform is lower than the profit of the follower manufacturer; (2) when the consumers’ carbon emission reduction elasticity coefficient increases, service level, sales price, carbon emission reduction, sales, supply chain members profits, and system profit increase, ultimately improving economic and environmental performances; (3) the altruistic preference behavior of the e-platform is a behavior of ‘profit transferring’. The moderate altruistic preference is conducive to the stable operation and long-term development of LCECSC. Full article
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15 pages, 5863 KiB  
Article
A Real Time Bolometer Tomographic Reconstruction Algorithm in Nuclear Fusion Reactors
by Augusto Montisci, Sara Carcangiu, Giuliana Sias, Barbara Cannas and Alessandra Fanni
Mathematics 2021, 9(11), 1186; https://doi.org/10.3390/math9111186 - 24 May 2021
Cited by 2 | Viewed by 1783
Abstract
In tokamak nuclear fusion reactors, one of the main issues is to know the total emission of radiation, which is mandatory to understand the plasma physics and is very useful to monitor and control the plasma evolution. This radiation can be measured by [...] Read more.
In tokamak nuclear fusion reactors, one of the main issues is to know the total emission of radiation, which is mandatory to understand the plasma physics and is very useful to monitor and control the plasma evolution. This radiation can be measured by means of a bolometer system that consists in a certain number of elements sensitive to the integral of the radiation along straight lines crossing the plasma. By placing the sensors in such a way to have families of crossing lines, sophisticated tomographic inversion algorithms allow to reconstruct the radiation tomography in the 2D poloidal cross-section of the plasma. In tokamaks, the number of projection cameras is often quite limited resulting in an inversion mathematic problem very ill conditioned so that, usually, it is solved by means of a grid-based, iterative constrained optimization procedure, whose convergence time is not suitable for the real time requirements. In this paper, to illustrate the method, an assumption not valid in general is made on the correlation among the grid elements, based on the statistical distribution of the radiation emissivity over a set of tomographic reconstructions, performed off-line. Then, a regularization procedure is carried out, which merge highly correlated grid elements providing a squared coefficients matrix with an enough low condition number. This matrix, which is inverted offline once for all, can be multiplied by the actual bolometer measures returning the tomographic reconstruction, with calculations suitable for real time application. The proposed algorithm is applied, in this paper, to a synthetic case study. Full article
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13 pages, 683 KiB  
Article
Short-Term Scheduling Model of Cluster Tool in Wafer Fabrication
by Ying-Mei Tu
Mathematics 2021, 9(9), 1029; https://doi.org/10.3390/math9091029 - 01 May 2021
Cited by 3 | Viewed by 2057
Abstract
Since last decade, the cluster tool has been mainstream in modern semiconductor manufacturing factories. In general, the cluster tool occupies 60% to 70% of production machines for advanced technology factories. The most characteristic feature of this kind of equipment is to integrate the [...] Read more.
Since last decade, the cluster tool has been mainstream in modern semiconductor manufacturing factories. In general, the cluster tool occupies 60% to 70% of production machines for advanced technology factories. The most characteristic feature of this kind of equipment is to integrate the relevant processes into one single machine to reduce wafer transportation time and prevent wafer contaminations as well. Nevertheless, cluster tools also increase the difficulty of production planning significantly, particularly for shop floor control due to complicated machine configurations. The main objective of this study is to propose a short-term scheduling model. The noteworthy goal of scheduling is to maximize the throughput within time constraints. There are two modules included in this scheduling model—arrival time estimation and short-term scheduling. The concept of the dynamic cycle time of the product’s step is applied to estimate the arrival time of the work in process (WIP) in front of machine. Furthermore, in order to avoid violating the time constraint of the WIP, an algorithm to calculate the latest time of the WIP to process on the machine is developed. Based on the latest process time of the WIP and the combination efficiency table, the production schedule of the cluster tools can be re-arranged to fulfill the production goal. The scheduling process will be renewed every three hours to make sure of the effectiveness and good performance of the schedule. Full article
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13 pages, 566 KiB  
Article
Modeling and Semi-Analytic Stability Analysis for Dynamics of AC Machines
by Mohamed El-Borhamy, Essam Eddin M. Rashad, Ismail Sobhy and M. Kamel El-Sayed
Mathematics 2021, 9(6), 644; https://doi.org/10.3390/math9060644 - 18 Mar 2021
Cited by 4 | Viewed by 2629
Abstract
In this article, a semi-analytical technique is proposed to predict stable sustained periodic responses of AC electrical machines. Based on such desired outputs, the proper selections of machine variables are captured, such as the perturbation parameter arisen from the relative movement between the [...] Read more.
In this article, a semi-analytical technique is proposed to predict stable sustained periodic responses of AC electrical machines. Based on such desired outputs, the proper selections of machine variables are captured, such as the perturbation parameter arisen from the relative movement between the stationary and rotating parts. Compared to the experimental results, the derived analytical results are relatively well-fitted with the studied practical cases. Full article
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18 pages, 838 KiB  
Article
Linearly Decoupled Control of a Dynamic Voltage Restorer without Energy Storage
by Luis Ramon Merchan-Villalba, Jose Merced Lozano-Garcia, Juan Gabriel Avina-Cervantes, Hector Javier Estrada-Garcia, Alejandro Pizano-Martinez and Cristian Andres Carreno-Meneses
Mathematics 2020, 8(10), 1794; https://doi.org/10.3390/math8101794 - 15 Oct 2020
Cited by 7 | Viewed by 1833
Abstract
This paper presents the design of a decoupled linear control strategy for a Dynamic Voltage Restorer (DVR) that utilizes a Matrix Converter (MC) as its core element and obtains the compensation energy directly from the power system. This DVR is intended to cope [...] Read more.
This paper presents the design of a decoupled linear control strategy for a Dynamic Voltage Restorer (DVR) that utilizes a Matrix Converter (MC) as its core element and obtains the compensation energy directly from the power system. This DVR is intended to cope with power quality problems present in supply system voltages such as balanced and unbalanced variations (sags and swells), and harmonic distortion. The dynamic model of the complete system that includes the Matrix Converter, the input filters and the electrical grid, is performed in the synchronous reference frame (dq0), to have constant signals at the fundamental frequency, in order to design the proposed linear control strategy. The coupling in the dq components of the system output signals caused by the Park Transformation, is eliminated by a change of variable proposed for the controller design, giving rise to a decoupled linear control. In this way, the strategy developed makes it possible to establish an adequate transient response for the converter in terms of convergence speed and overshoot magnitude, in addition to ensuring closed-loop system stability under bounded operating conditions. Unlike other proposals that utilize complex modulation strategies to control the MC under adverse conditions at the input terminals, in this case, the ability to generate fully controllable output voltages, regardless of the condition of the input signals, is provided by the designed linear controller. This allows the development of a multifunctional compensator with a simple control that could be of easy implementation. In order to verify the performance of the control strategy developed, and the effectiveness of the proposed DVR to mitigate the power quality problems already mentioned, several case studies are presented. The operational capacity of the MC is demonstrated by the obtained simulation results, which clearly reveals the capability of the DVR to eliminate voltage swells up to 50% and sags less than 50%. The compensation limit reached for sags is 37%. In relation to compensation for unbalanced voltage variations, the DVR manages to reduce the voltage imbalance from 11.11% to 0.37%. Finally, with regard to the operation of the DVR as an active voltage filter, the compensator is capable of reducing a THD of 20% calculated on the supply voltage, to a value of 1.53% measured at the load terminals. In the last two cases, the DVR mitigates disturbances to a level below the criteria established in the IEEE standard for power quality. Results obtained from numerical simulations performed in MATLAB/Simulink serve to validate the proposal, given that for each condition analyzed, the MC had succesfully generated the adequate compensation voltages, thus corroborating the robustness and effectiveness of the control strategy developed in this proposal. Full article
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37 pages, 1125 KiB  
Article
Electrostatic Capacity of a Metallic Cylinder: Effect of the Moment Method Discretization Process on the Performances of the Krylov Subspace Techniques
by Mario Versaci and Giovanni Angiulli
Mathematics 2020, 8(9), 1431; https://doi.org/10.3390/math8091431 - 26 Aug 2020
Cited by 3 | Viewed by 1832
Abstract
When a straight cylindrical conductor of finite length is electrostatically charged, its electrostatic potential ϕ depends on the electrostatic charge qe, as expressed by the equation L(qe)=ϕ, where L is an integral operator. Method [...] Read more.
When a straight cylindrical conductor of finite length is electrostatically charged, its electrostatic potential ϕ depends on the electrostatic charge qe, as expressed by the equation L(qe)=ϕ, where L is an integral operator. Method of moments (MoM) is an excellent candidate for solving L(qe)=ϕ numerically. In fact, considering qe as a piece-wise constant over the length of the conductor, it can be expressed as a finite series of weighted basis functions, qe=n=1Nαnfn (with weights αn and N, number of the subsections of the conductor) defined in the L domain so that ϕ becomes a finite sum of integrals from which, considering testing functions suitably combined with the basis functions, one obtains an algebraic system Lmnαn=gm with dense matrix, equivalent to L(qe)=ϕ. Once solved, the linear algebraic system gets αn and therefore qe is obtainable so that the electrostatic capacitance C=qe/V, where V is the external electrical tension applied, can give the corresponding electrostatic capacitance. In this paper, a comparison was made among some Krylov subspace method-based procedures to solve Lmnαn=gm. These methods have, as a basic idea, the projection of a problem related to a matrix ARn×n, having a number of non-null elements of the order of n, in a subspace of lower order. This reduces the computational complexity of the algorithms for solving linear algebraic systems in which the matrix is dense. Five cases were identified to determine Lmn according to the type of basis-testing functions pair used. In particular: (1) pulse function as the basis function and delta function as the testing function; (2) pulse function as the basis function as well as testing function; (3) triangular function as the basis function and delta function as the testing function; (4) triangular function as the basis function and pulse function as the testing function; (5) triangular function as the basis function with the Galerkin Procedure. Therefore, five Lmn and five pair qe and C were computed. For each case, for the resolution of Lmnαn=gm obtained, GMRES, CGS, and BicGStab algorithms (based on Krylov subspaces approach) were implemented in the MatLab® Toolbox to evaluate qe and C as N increases, highlighting asymptotical behaviors of the procedures. Then, a particular value for N is obtained, exploiting both the conditioning number of Lmn and considerations on C, to avoid instability phenomena. The performances of the exploited procedures have been evaluated in terms of convergence speed and CPU-times as the length/diameter and N increase. The results show the superiority of BcGStab, compared to the other procedures used, since even if the number of iterations increases significantly, the CPU-time decreases (more than 50%) when the asymptotic behavior of all the procedures is in place. This superiority is much more evident when the CPU-time of BicGStab is compared with that achieved by exploiting Gauss elimination and Gauss–Seidel approaches. Full article
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12 pages, 787 KiB  
Article
A Lévy-Driven Stochastic Queueing System with Server Breakdowns and Vacations
by Yi Peng and Jinbiao Wu
Mathematics 2020, 8(8), 1239; https://doi.org/10.3390/math8081239 - 29 Jul 2020
Cited by 2 | Viewed by 1418
Abstract
Motivated by modelling the data transmission in computer communication networks, we study a Lévy-driven stochastic fluid queueing system where the server may subject to breakdowns and repairs. In addition, the server will leave for a vacation each time when the system is empty. [...] Read more.
Motivated by modelling the data transmission in computer communication networks, we study a Lévy-driven stochastic fluid queueing system where the server may subject to breakdowns and repairs. In addition, the server will leave for a vacation each time when the system is empty. We cast the workload process as a Lévy process modified to have random jumps at two classes of stopping times. By using the properties of Lévy processes and Kella–Whitt martingale method, we derive the limiting distribution of the workload process. Moreover, we investigate the busy period and the correlation structure. Finally, we prove that the stochastic decomposition properties also hold for fluid queues with Lévy input. Full article
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15 pages, 397 KiB  
Article
The Loss-Averse Newsvendor Problem with Random Yield and Reference Dependence
by Wei Liu, Shiji Song, Ying Qiao, Han Zhao and Huachang Wang
Mathematics 2020, 8(8), 1231; https://doi.org/10.3390/math8081231 - 27 Jul 2020
Cited by 5 | Viewed by 1971
Abstract
This paper studies a loss-averse newsvendor problem with reference dependence, where both demand and yield rate are stochastic. We obtain the loss-averse newsvendor’s optimal ordering policy and analyze the effects of loss aversion, reference dependence, random demand and yield on it. It is [...] Read more.
This paper studies a loss-averse newsvendor problem with reference dependence, where both demand and yield rate are stochastic. We obtain the loss-averse newsvendor’s optimal ordering policy and analyze the effects of loss aversion, reference dependence, random demand and yield on it. It is shown that the loss-averse newsvendor’s optimal order quantity and expected utility decreases in loss aversion level and reference point. Then, that this order quantity may be larger than the risk-neutral one’s if the reference point is less than a negative threshold. In addition, although the effect of random yield leads to an increase in the order quantity, the loss-averse newsvendor may order more than, equal to or less than the classical one, which significantly depends on loss aversion level and reference point. Numerical experiments were conducted to demonstrate our theoretical results. Full article
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23 pages, 6530 KiB  
Article
A Computational Model for Determining Levels of Factors in Inventory Management Using Response Surface Methodology
by Chia-Nan Wang, Thanh-Tuan Dang and Ngoc-Ai-Thy Nguyen
Mathematics 2020, 8(8), 1210; https://doi.org/10.3390/math8081210 - 22 Jul 2020
Cited by 20 | Viewed by 6375
Abstract
Inventory management plays a critical role in balancing supply availability with customer requirements and significantly contributes to the performance of the whole supply chain. It involves many different features, such as controlling and managing purchases from suppliers to consumers, keeping safety stock, examining [...] Read more.
Inventory management plays a critical role in balancing supply availability with customer requirements and significantly contributes to the performance of the whole supply chain. It involves many different features, such as controlling and managing purchases from suppliers to consumers, keeping safety stock, examining the amount of product for sale, and order fulfillment. This paper involves the development of computational modeling for the inventory control problem in Thailand. The problem focuses on determining levels of factors, which are order quantity, reorder point, target stock, and inventory review policy, using a heuristic approach. The objective is to determine the best levels of factors that are significantly affected by their responses to optimize them using the response surface methodology. Values of the quantity of backlog and the average inventory amount, as well as their corresponding total costs, are simulated using the Arena software to gain statistical power. Then, the Minitab-response surface methodology is used to find the feasible solutions of the responses, which consist of test power and sample size, full factorial design, and Box–Behnken design. For a numerical example, the computational model is tested with real data to show the efficacy of the model. The result suggests that the effects from the reorder point, target stock, and inventory review policy are significant to the minimum total cost if their levels are set appropriately. The managerial implications of this model’s results not only suggest the best levels of factors for a case study of the leading air compressor manufacturers in Thailand, but also provide a guideline for decision-makers to satisfy customer demand at the minimum possible total inventory cost. Therefore, this paper can be a useful reference for warehouse supervisors, managers, and policymakers to determine the best levels of factors to improve warehouse performance. Full article
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20 pages, 3688 KiB  
Article
A Hybrid Predictive Approach for Chromium Layer Thickness in the Hard Chromium Plating Process Based on the Differential Evolution/Gradient Boosted Regression Tree Methodology
by Paulino José Garcia Nieto, Esperanza García Gonzalo, Fernando Sanchez Lasheras and Antonio Bernardo Sánchez
Mathematics 2020, 8(6), 959; https://doi.org/10.3390/math8060959 - 11 Jun 2020
Cited by 3 | Viewed by 2585
Abstract
The purpose of the industrial process of chromium plating is the creation of a hard and wear-resistant layer of chromium over a metallic surface. One of the main properties of chromium plating is its resistance to both wear and corrosion. This research presents [...] Read more.
The purpose of the industrial process of chromium plating is the creation of a hard and wear-resistant layer of chromium over a metallic surface. One of the main properties of chromium plating is its resistance to both wear and corrosion. This research presents an innovative nonparametric machine learning approach that makes use of a hybrid gradient boosted regression tree (GBRT) methodology for hard chromium layer thickness prediction. GBRT is a non-parametric statistical learning technique that produces a prediction model in the form of an ensemble of weak prediction models. The motivation for boosting is a procedure that combines the output of many weak classifiers to produce a powerful committee. In this study, the GBRT hyperparameters were optimized with the help of differential evolution (DE). DE is an optimization technique within evolutionary computing. The results found that this model was able to predict the thickness of the chromium layer formed in this industrial process with a determination coefficient equal to 0.9842 and a root-mean-square error value of 0.01590. The two most important variables of the model were the time of the hard-chromium process and the thickness of the layer removed by electropolishing. Thus, these results provide a foundation for an accurate predictive model of hard chromium layer thickness. The derived model also allowed the ranking of the importance of the independent input variables that were examined. Finally, the high performance and simplicity of the model make the DE/GBRT method attractive compared to conventional forecasting techniques. Full article
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20 pages, 397 KiB  
Article
Supply Chain Coordination with a Loss-Averse Retailer and Combined Contract
by Wei Liu, Shiji Song, Ying Qiao and Han Zhao
Mathematics 2020, 8(4), 586; https://doi.org/10.3390/math8040586 - 16 Apr 2020
Cited by 9 | Viewed by 2254
Abstract
This paper studies the supply chain coordination where the retailer is loss-averse, and a combined buyback and quantity flexibility contract is introduced. The loss-averse retailer’s objective is to maximize the Conditional Value-at-Risk of utility. It is shown the combined contract can coordinate the [...] Read more.
This paper studies the supply chain coordination where the retailer is loss-averse, and a combined buyback and quantity flexibility contract is introduced. The loss-averse retailer’s objective is to maximize the Conditional Value-at-Risk of utility. It is shown the combined contract can coordinate the chain and a unique coordinating wholesale price exists if the confidence level is below a threshold. Moreover, the retailer’s optimal order quantity, expected utility and coordinating wholesale price are decreasing in loss aversion and confidence levels, respectively. We also find that when the contract parameters are restricted, the combined contract may coordinate the supply chain even though neither of its component contracts coordinate the chain. Full article
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19 pages, 2906 KiB  
Article
Computation of Analytical Zoom Locus Using Padé Approximation
by Kang Min Kim, Sun-Ho Choe, Jae-Myung Ryu and Hojong Choi
Mathematics 2020, 8(4), 581; https://doi.org/10.3390/math8040581 - 14 Apr 2020
Cited by 11 | Viewed by 2372
Abstract
When the number of lens groups is large, the zoom locus becomes complicated and thus cannot be determined by analytical means. By the conventional calculation method, it is possible to calculate the zoom locus only when a specific lens group is fixed or [...] Read more.
When the number of lens groups is large, the zoom locus becomes complicated and thus cannot be determined by analytical means. By the conventional calculation method, it is possible to calculate the zoom locus only when a specific lens group is fixed or the number of lens groups is small. To solve this problem, we employed the Padé approximation to find the locus of each group of zoom lenses as an analytic form of a rational function consisting of the ratio of polynomials, programmed in MATLAB. The Padé approximation is obtained from the initial data of the locus of each lens group. Subsequently, we verify that the obtained locus of lens groups satisfies the effective focal length (EFL) and the back focal length (BFL). Afterwards, the Padé approximation was applied again to confirm that the error of BFL is within the depth of focus for all zoom positions. In this way, the zoom locus for each lens group of the optical system with many moving lens groups was obtained as an analytical rational function. The practicality of this method was verified by application to a complicated zoom lens system with five or more lens groups using preset patents. Full article
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14 pages, 1372 KiB  
Article
Numerical Solutions of Fractional Differential Equations Arising in Engineering Sciences
by Alessandra Jannelli
Mathematics 2020, 8(2), 215; https://doi.org/10.3390/math8020215 - 08 Feb 2020
Cited by 21 | Viewed by 3835
Abstract
This paper deals with the numerical solutions of a class of fractional mathematical models arising in engineering sciences governed by time-fractional advection-diffusion-reaction (TF–ADR) equations, involving the Caputo derivative. In particular, we are interested in the models that link chemical and hydrodynamic processes. The [...] Read more.
This paper deals with the numerical solutions of a class of fractional mathematical models arising in engineering sciences governed by time-fractional advection-diffusion-reaction (TF–ADR) equations, involving the Caputo derivative. In particular, we are interested in the models that link chemical and hydrodynamic processes. The aim of this paper is to propose a simple and robust implicit unconditionally stable finite difference method for solving the TF–ADR equations. The numerical results show that the proposed method is efficient, reliable and easy to implement from a computational viewpoint and can be employed for engineering sciences problems. Full article
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21 pages, 32024 KiB  
Article
Second-Order Parabolic Equation to Model, Analyze, and Forecast Thermal-Stress Distribution in Aircraft Plate Attack Wing–Fuselage
by Giovanni Angiulli, Salvatore Calcagno, Domenico De Carlo, Filippo Laganá and Mario Versaci
Mathematics 2020, 8(1), 6; https://doi.org/10.3390/math8010006 - 18 Dec 2019
Cited by 3 | Viewed by 2550
Abstract
During a flight, the steel plate attack wing–fuselage of an aircraft is subjected to cyclical thermal stress caused by flight altitude variation that could compromise the functionality of the plate. Thus, it is compulsory after a sequence of flights to evaluate the state [...] Read more.
During a flight, the steel plate attack wing–fuselage of an aircraft is subjected to cyclical thermal stress caused by flight altitude variation that could compromise the functionality of the plate. Thus, it is compulsory after a sequence of flights to evaluate the state of plate health. In this work, we propose a new dynamic model on the basis of the physical transmission of heat by conduction governed by a second-order parabolic partial differential equation with suitable initial and boundary conditions to analyze and forecast thermal stresses in the plate of a P64 OSCAR B airplane. Developing this model in the COMSOL Multi-Physics® environment, a finite-element technique was applied to achieve the thermal-stress map on the plate. The achieved results, equivalent to those obtained by a campaign of infrared thermographic experiment measurements (not yet used in the aeronautical industry), highlight the evolution of the thermal load of the steel plate attack wing–fuselage, adding evidence of possible incoming fatigue phenomena to identify in advance if the steel plate must be replaced. Full article
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18 pages, 472 KiB  
Article
A 2D Non-Linear Second-Order Differential Model for Electrostatic Circular Membrane MEMS Devices: A Result of Existence and Uniqueness
by Paolo Di Barba, Luisa Fattorusso and Mario Versaci
Mathematics 2019, 7(12), 1193; https://doi.org/10.3390/math7121193 - 05 Dec 2019
Cited by 19 | Viewed by 2502
Abstract
In the framework of 2D circular membrane Micro-Electric-Mechanical-Systems (MEMS), a new non-linear second-order differential model with singularity in the steady-state case is presented in this paper. In particular, starting from the fact that the electric field magnitude is locally proportional to the curvature [...] Read more.
In the framework of 2D circular membrane Micro-Electric-Mechanical-Systems (MEMS), a new non-linear second-order differential model with singularity in the steady-state case is presented in this paper. In particular, starting from the fact that the electric field magnitude is locally proportional to the curvature of the membrane, the problem is formalized in terms of the mean curvature. Then, a result of the existence of at least one solution is achieved. Finally, two different approaches prove that the uniqueness of the solutions is not ensured. Full article
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22 pages, 5013 KiB  
Article
Efficient Pipelined Broadcast with Monitoring Processing Node Status on a Multi-Core Processor
by Jongsu Park
Mathematics 2019, 7(12), 1159; https://doi.org/10.3390/math7121159 - 01 Dec 2019
Cited by 1 | Viewed by 2274
Abstract
This paper presents an efficient pipelined broadcasting algorithm with the inter-node transmission order change technique considering the communication status of processing nodes. The proposed method changes the transmission order for the broadcast operation based on the communication status of processing nodes. When a [...] Read more.
This paper presents an efficient pipelined broadcasting algorithm with the inter-node transmission order change technique considering the communication status of processing nodes. The proposed method changes the transmission order for the broadcast operation based on the communication status of processing nodes. When a broadcast operation is received, a local bus checks the remaining pre-existing transmission data size of each processing node; it then transmits data according to the changed transmission order using the status information. Therefore, the synchronization time can be hidden for the remaining time, until the pre-existing data transmissions finish; as a result, the overall broadcast completion time is reduced. The simulation results indicated that the speed-up ratio of the proposed algorithm was up to 1.423, compared to that of the previous algorithm. To demonstrate physical implementation feasibility, the message passing engine (MPE) with the proposed broadcast algorithm was designed by using Verilog-HDL, which supports four processing nodes. The logic synthesis results with TSMC 0.18 μm process cell libraries show that the logic area of the proposed MPE is 2288.1 equivalent NAND gates, which is approximately 2.1% of the entire chip area. Therefore, performance improvement in multi-core processors is expected with a small hardware area overhead. Full article
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14 pages, 1225 KiB  
Article
Using a Time Delay Neural Network Approach to Diagnose the Out-of-Control Signals for a Multivariate Normal Process with Variance Shifts
by Yuehjen E. Shao and Shih-Chieh Lin
Mathematics 2019, 7(10), 959; https://doi.org/10.3390/math7100959 - 13 Oct 2019
Cited by 24 | Viewed by 4621
Abstract
With the rapid development of advanced sensor technologies, it has become popular to monitor multiple quality variables for a manufacturing process. Consequently, multivariate statistical process control (MSPC) charts have been commonly used for monitoring multivariate processes. The primary function of MSPC charts is [...] Read more.
With the rapid development of advanced sensor technologies, it has become popular to monitor multiple quality variables for a manufacturing process. Consequently, multivariate statistical process control (MSPC) charts have been commonly used for monitoring multivariate processes. The primary function of MSPC charts is to trigger an out-of-control signal when faults occur in a process. However, because two or more quality variables are involved in a multivariate process, it is very difficult to diagnose which one or which combination of quality variables is responsible for the MSPC signal. Though some statistical decomposition methods may provide possible solutions, the mathematical difficulty could confine the applications. This study presents a time delay neural network (TDNN) classifier to diagnose the quality variables that cause out-of-control signals for a multivariate normal process (MNP) with variance shifts. To demonstrate the effectiveness of our proposed approach, a series of simulated experiments were conducted. The results were compared with artificial neural network (ANN), support vector machine (SVM) and multivariate adaptive regression splines (MARS) classifiers. It was found that the proposed TDNN classifier was able to accurately recognize the contributors of out-of-control signal for MNPs. Full article
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