Journal articles on the topic 'Linear systems; Mathematical optimization; Reliability (Engineering) – Mathematical models'
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Bogdanov, Sergey. "Application of Neural Networks in the Construction of Nonlinear Models of Field-Effect Transistors." Infocommunications and Radio Technologies 5, no. 1 (March 25, 2022): 45–53. http://dx.doi.org/10.29039/2587-9936.2022.05.1.03.
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The nonlinear model of a field-effect transistor based on the mathematical apparatus of the theory of artificial neural networks was developed. The main feature of this model is the possibility of training neural networks used to approximate the current-voltage characteristic and the gate-drain and gate-source capacitances of a nonlinear transistor model by using optimization algorithms built into popular microwave CAD systems. This makes it possible to use the well-known advantages of neural networks in the problems of function approximation to increase the reliability of the results of non-linear modeling of microwave devices based on field-effect transistors.
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Andriy Viktorovich, Goncharenko. "Hybrid-Optional Effectiveness Functions Entropy Conditional Extremization Doctrine Contributions into Engineering Systems Reliability Assessments." Transactions on Aerospace Research 2019, no. 2 (June 1, 2019): 90–100. http://dx.doi.org/10.2478/tar-2019-0012.
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Abstract In this publication a Doctrine for the Conditional Extremization of the Hybrid-Optional Effectiveness Functions Entropy is discussed as a tool for the Reliability Assessments of Engineering Systems. Traditionally, most of the problems having been dealt with in this area relate with the probabilistic problem settings. Regularly, the optimal solutions are obtained through the probability extremizations. It is shown a possibility of the optimal solutions “derivation”, with the help of a model implementing a variational principle which takes into account objectively existing parameters and components of the Markovian process. The presence of an extremum of the objective state probability is observed and determined on the basis of the proposed Doctrine with taking into account the measure of uncertainty of the hybrid-optional effectiveness functions in the view of their entropy. Such approach resembles the well known Jaynes’ Entropy Maximum Principle from theoretical statistical physics adopted in subjective analysis of active systems as the subjective entropy maximum principle postulating the subjective entropy conditional optimization. The developed herewith Doctrine implies objective characteristics of the process rather than subjective individual’s preferences or choices, as well as the states probabilities maximums are being found without solving a system of ordinary linear differential equations of the first order by Erlang corresponding to the graph of the process. Conducted numerical simulation for the proposed mathematical models is illustrated with the plotted diagrams.
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Larrahondo, Diego, Ricardo Moreno, Harold R. Chamorro, and Francisco Gonzalez-Longatt. "Comparative Performance of Multi-Period ACOPF and Multi-Period DCOPF under High Integration of Wind Power." Energies 14, no. 15 (July 27, 2021): 4540. http://dx.doi.org/10.3390/en14154540.
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Today, the power system operation represents a challenge given the security and reliability requirements. Mathematical models are used to represent and solve operational and planning issues related with electric systems. Specifically, the AC optimal power flow (ACOPF) and the DC optimal power flow (DCOPF) are tools used for operational and planning purposes. The DCOPF versions correspond to lineal versions of the ACOPF. This is due to the fact that the power flow solution is often hard to obtain with the ACOPF considering all constraints. However, the simplifications use only active power without considering reactive power, voltage values and losses on transmission lines, which are crucial factors for power system operation, potentially leading to inaccurate results. This paper develops a detailed formulation for both DCOPF and ACOPF with multiple generation sources to provide a 24-h dispatching in order to compare the differences between the solutions with different scenarios under high penetration of wind power. The results indicate the DCOPF inaccuracies with respect to the complete solution provided by the ACOPF.
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Al-Subhi, Ahmad. "Dynamic Economic Load Dispatch Using Linear Programming and Mathematical-Based Models." Mathematical Modelling of Engineering Problems 9, no. 3 (June 30, 2022): 606–14. http://dx.doi.org/10.18280/mmep.090307.
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Economic dispatch (ED) is one of the most important topics in power system operation and planning. The main purpose of this paper is to develop simple and effective mathematical models for the ED problem. Two stages were considered to solve this problem. First, the ED problem is formulated using linear piecewise functions and then optimally solved using the LP technique at various load values. The effectiveness of the LP in optimally solving the ED problem is verified by applying it to two different test systems. The results are compared with those obtained using other ED optimization techniques. The LP optimization performance of the proposed method is found to be similar to those of the reported techniques. In the second stage, the data collected from the optimization process in the first stage are transferred to TuringBot software. This software is adopted to build efficient mathematical models for the optimal power generation (output parameters) as functions of the load values (input parameters). The main objective of these models is to easily evaluate the optimal power sharing of the generators in an online fashion under rapid variable loading conditions without the need to solve the ED-LP based problem. Optimization techniques, including the LP, generally require considerable simulation times for linearization and optimization code execution, particularly under fast load variations. Thus, the main features of the developed models in this paper are simplicity, accessibility, as well as the ability in obtaining an efficient and optimal solution with a faster execution time.
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Stetsyuk, Petro, Oleksii Lykhovyd, Volodymyr Zhydkov, and Anton Suprun. "OPTIMIZATION PROBLEMS OF MODERNIZATION OF THE CAPACITY OF ARCS OF FAULT-TOLERANT NETWORKS." Journal of Automation and Information sciences 5 (September 1, 2021): 5–20. http://dx.doi.org/10.34229/1028-0979-2021-5-1.
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Mathematical models of two classes of problems of modernization of the capacity of arcs of fault-tolerant oriented networks are considered. A network is considered to be fault-tolerant for which it is possible to satisfy all the demands for the transmission of flows when there will be one, but any failure, from all possible single network failures. For the first class of problems (problem A), all possible paths in the network can be used for the transmission of flows. For the second class of problems (problem P), only paths from a predetermined set of paths are used to transfer flows. Mathematical models are represented by linear, Boolean and nonlinear programming problems with a block structure of the constraint matrix.The material of the article is presented in five sections. The first section describes the concepts of a single failure and the scenario of network failures, the content of optimization problems A and P for modernization of capacity of arcs of a fault-tolerant network, a test network (6 vertices and 19 arcs) to test algorithms for solving the problems of modernization of fault-tolerant networks. In the second section, basic models of linear programming problems for finding the capacities of arcs of the fault-tolerant physical structure of a network (problem A) and the fault-tolerant logical structure of a network (problem P) are described, and their properties are considered. The third section describes problems A and P in the form of mixed Boolean linear programming models. Optimal solutions of problem A for various failure scenarios are given for the example of the test network. The solutions were found using the Gurobi program from the NEOS server, where the mathematical model of problem A is described in the AMPL modeling language.The fourth section describes nonlinear convex programming models for problems A and P, developed to find the optimal capacities of fault-tolerant networks according to the selected criterion, and a decomposition algorithm for their solution. The fifth section describes software in the FORTRAN programming language for the decomposition algorithm based on efficient implementations of Shor’s r-algorithms. The decomposition algorithm is compared with the IPOPT program based on the results of solving test problems.
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Velmisov, Petr A., and Andrey V. Ankilov. "Mathematical modeling in problems about dynamics and stability of elastic elements of wing profiles." Cybernetics and Physics, Volume 10, 2021, Number 3 (November 30, 2021): 201–12. http://dx.doi.org/10.35470/2226-4116-2021-10-3-201-212.
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The mathematical models describing the dynamics of elastic elements of wing structures and representing the initial-boundary value problems for systems of partial differential equations are proposed. The dynamics and stability of elastic elements of wings, flown around by a gas or liquid stream in a model of an incompressible medium, are investigated. To study the dynamics of elastic elements and a gas-liquid medium, both linear and nonlinear models of the mechanics of a solid deformable body and linear models of the mechanics of liquid and gas are used. On the basis of the constructed functionals for partial differential equations, the sufficient stability conditions are obtained in analytical form. The conditions impose restrictions on the parameters of mechanical systems. The obtained stability conditions are necessary for solving the problems of controlling the parameters of the aeroelastic system. On the basis of the Galerkin method, a numerical study of the dynamics of elastic elements was carried out, the reliability of which is confirmed by the obtained analytical results.
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Cevikcan, Emre. "A mathematical programming approach for walking-worker assembly systems." Assembly Automation 34, no. 1 (January 28, 2014): 56–68. http://dx.doi.org/10.1108/aa-07-2013-067.
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Purpose – It has become increasingly critical to design and maintain flexible and rapid assembly systems due to unpredictable and varying market conditions. The first stage of developing such systems is to restructure the existing assembly system. After designing the manufacturing system, efforts should be made for capacity adjustments to meet the demand in terms of allocating tasks to workers. Walking-worker assembly systems can be regarded as an effective method to achieve flexibility and agility via rabbit chase (RC) approach in which workers follow each other around the assembly cell or line and perform each task in sequence. In this paper, a novel mathematical programming approach is developed with the aim of integrating RC in assembly processes. Therefore, this study is thought to add value to industrial assembly systems in terms of effectively raising engineering control for task allocation activities. Design/methodology/approach – Two consecutive mathematical models are developed, since such a hierarchical approach provides computational convenience for the problem. The initial mathematical programming model determines the number of workers in each RC loop for each segment. In addition, the number of stations and the distribution of station times in the segments is essential. Therefore, the succeeding mathematical programming model generates stations in each segment and provides convenience for the workflow in RC loops. The output of mathematical programming models are the parameters of simulation model for performance assessment. Findings – The effectiveness of the proposed approach was validated by an application in a real-life chair production system. The application resulted in performance improvements for labour requirement (12.5 per cent) and production lead time (9.6 per cent) when compared to a classical assembly system design (CASD) where one stationary worker exists in each station. In addition, it is worth to note that RC leads to a reduced number of workers for a considerable number (39.4 per cent) of test problems. What is more, input as well as output factors have been determined via discriminant analysis and their impacts to the utilization of RC were analyzed for different levels. Practical implications – This study is thought to add value to the industry in terms of effectively providing convenience during production planning and task allocation in assembly lines and cells. Originality/value – To the best knowledge of the author, optimization models for RC considering a real industrial application have not yet been developed. In this context, this paper presents an approach which models RC by the use of mathematical programming in manual assembly processes to address this research gap. The contribution of the paper to the relevant literature is the development of hierarchical mixed integer linear programming models to solve RC problem for the first time.
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Eliwa, M. S., Medhat EL-Damcese, A. H. El-Bassiouny, Abhishek Tyag, and M. El-Morshedy. "The Weibull Distribution: Reliability Characterization Based on Linear and Circular Consecutive Systems." Statistics, Optimization & Information Computing 9, no. 4 (September 24, 2021): 974–83. http://dx.doi.org/10.19139/soic-2310-5070-1132.
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Linear and circular consecutive models play a vital role to study the mechanical systems emerging in various fields including survival analysis, reliability theory, biological disciplines, and other lifetime sciences. As a result, analysis of reliability properties of consecutive k − out − of − n : F systems has gained a lot of attention in recent years from a theoretical and practical point of view. In the present article, we have studied some important stochastic and aging properties of residual lifetime of consecutive k − out − of − n : F systems under the condition n − k + 1, k ≤ n and all components of the system are working at time t. The mean residual lifetime (MRL) and its hazard rate function are proposed for the linear consecutive k − out − of − n : F (lin/con/k/n:F) and circular consecutive k − out − of − n : F (cir/con/k/n:F) systems. Furthermore, several mathematical properties of the proposed MRL are examined. Finally, the Weibull distribution with two parameters is used as an example to explain the theoretical results.
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Lixandru, Bianca Andreea, and Vlad Monescu. "LAPACK library for mathematical modeling used in 3D object reconstruction." SERIES III - MATEMATICS, INFORMATICS, PHYSICS 13(62), no. 2 (January 20, 2021): 715–22. http://dx.doi.org/10.31926/but.mif.2020.13.62.2.27.
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Over time, multiple solutions have been sought for building 3D models in the fastest and most accurate way possible. For this reason, this article proposes the use of LAPACK library for a quick solution of linear systems generated by least square method calculation. A mathematical and physical component used in the reconstruction of models consists in the use of Spherical Harmonics which represent some special functions often used in solving partial differential equations in different scientific areas. This problem finds its place in multiple domains such as medicine, engineering, programming. The target of the work described by this paper is to achieve optimization in the reconstruction of 3D models. We aim to perform real-time model reconstruction for large data sets by using Spherical Harmonics functions.
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Colina, Eliezer, Mario Peña, Villie Morocho, and Lorena Siguenza-Guzman. "Mathematical modeling to standardize times in assembly processes: Application to four case studies." Journal of Industrial Engineering and Management 14, no. 2 (March 5, 2021): 294. http://dx.doi.org/10.3926/jiem.3192.
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Purpose: This paper proposes model-based standard times estimates, using multiple linear regression, nonlinear optimization, and fuzzy systems in four real cases assembly lines. The work includes a description of the models and a comparison of their performance with values obtained using the conventional chronometer method. These models allow estimating standard times without reconducting field studies.Design/methodology/approach: For the development of the time study, the methodology applied by the International Labour Organization (ILO) was used as a baseline. This methodology is structured in three phases: selection of the case study, registration of the process by direct observation, and calculation/estimation of the standard time. The selected case studies belong to real assembly lines of motorcycles, television sets, printed circuit boards, and bicycles.Findings: In the motorcycle’s assembly case, the study allowed constructing seven linear regression models to estimate standard times for assembling the front parts, and seven linear regression models to predict standard times for the rear parts of the different motorcycle types. Compared to the classical chronometer method, the results obtained never exceeded 10%. Regarding the case studies of assembling TV sets and PCBs, the study considered the construction of nonlinear optimization models that allow making appropriate predictions of the standard times in their assembly lines. Finally, for the bicycle assembly line, a fuzzy logic model to represent the standard time was constructed and validated.Research limitations/implications: For reasons of confidentiality of information, this work omitted the names of companies, services, and models of manufactured products.Originality/value: The literature consulted does not refer to the representation of standard time on assembly lines using mathematical models. The construction of these models with empirical data from actual assembly lines was a valuable aid to the companies involved in supporting activity planning.
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González-Hernández, José Genaro, and Rubén Salas-Cabrera. "Wind Power Extraction Optimization by Dynamic Gain Scheduling Approximation Based on Non-Linear Functions for a WECS Based on a PMSG." Mathematics 9, no. 17 (August 24, 2021): 2028. http://dx.doi.org/10.3390/math9172028.
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Mathematical models and algorithms for maximizing power extraction have become an essential topic in renewable energies in the last years, especially in wind energy conversion systems. This study proposes maximum power point tracking using gain scheduling approximations for an emulated wind system in a direct-drive connection. Power extraction is obtained by controlling the duty cycle of a Multilevel Boost Converter, which directly varies the rotational speed of a permanent magnet synchronous generator directly coupled to a three-phase induction motor that emulates the wind turbine. The system’s complexity is linked to the inherent non-linearities associated with the diverse electrical, mechanical, and power electronic elements. In order to present a synthesized model without losing the system dynamic richness, several physical tests were made to obtain parameters for building several mathematical approaches, resulting in non-linear dynamic equations for the controller gains, which are dependant on wind speed. Thirty real operational wind speeds considering typical variations were used in several tests to demonstrate the mathematical models’ performance. Results among these gain scheduling approaches and a typical controller constant gains mathematical model were compared based on standard deviations, absolute error, and the time for reaching the optimum generator angular speed related to every wind speed.
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Cevikcan, Emre. "An optimization methodology for multi model walking-worker assembly systems: an application from busbar energy distribution systems." Assembly Automation 36, no. 4 (September 5, 2016): 439–59. http://dx.doi.org/10.1108/aa-09-2015-072.
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Purpose Walking-worker assembly lines can be regarded as an effective method to achieve the above-mentioned characteristics. In such systems, workers, following each other, travel workstations in sequence by performing all of the required tasks of their own product. As the eventual stage of assembly line design, efforts should be made for capacity adjustments to meet the demand in terms of allocating tasks to workers via assembly line balancing. In this context, the purpose of this study is to address the balancing problem for multi-model walking-worker assembly systems, with the aim of improving planning capability for such systems by means of developing an optimization methodology. Design/methodology/approach Two linear integer programming models are proposed to balance a multi-model walking-worker assembly line optimally in a sequential manner. The first mathematical programming model attempts to determine number of workers in each segment (i.e. rabbit chase loop) for each model. The second model generates stations in each segment to smooth workflow. What is more, heuristic algorithms are provided due to computational burden of mathematical programming models. Two segment generation heuristic algorithms and a station generation heuristic algorithm are provided for the addressed problem. Findings The application of the mathematical programming approach improved the performance of a tap-off box assembly line in terms of number of workers (9.1 per cent) and non-value-added time ratio (between 27.9 and 26.1 per cent for different models) when compared to a classical assembly system design. In addition, the proposed approach (i.e. segmented walking-worker assembly line) provided a more convenient working environment (28.1 and 40.8 per cent shorter walking distance for different models) in contrast with the overall walking-worker assembly line. Meanwhile, segment generation heuristics yielded reduction in labour requirement for a considerable number (43.7 and 49.1 per cent) of test problems. Finally, gaps between the objective values and the lower bounds have been observed as 8.3 per cent (Segment Generation Heuristic 1) and 6.1 (Segment Generation Heuristic 2). Practical implications The proposed study presents a decision support for walking-worker line balancing with high level of solution quality and computational performance for even large-sized assembly systems. That being the case, it contributes to the management of real-life assembly systems in terms of labour planning and ergonomics. Owing to the fact that the methodology has the potential of reducing labour requirement, it will present the opportunity of utilizing freed-up capacity for new lines in the start-up period or other bottleneck processes. In addition, this study offers a working environment where skill of the workers can be improved within reasonable walking distances. Originality/value To the best knowledge of the author, workload balancing on multi-model walking-worker assembly lines with rabbit chase loop(s) has not yet been handled. Addressing this research gap, this paper presents a methodology including mathematical programming models and heuristic algorithms to solve the multi-model walking-worker assembly line balancing problem for the first time.
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Aboura, Khalid, Johnson I. Agbinya, and Ali Eskandarian. "Weibull Decision Support Systems in Maintenance." Organizacija 47, no. 2 (May 1, 2014): 81–89. http://dx.doi.org/10.2478/orga-2014-0008.
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Abstract Background: The Weibull distribution is one of the most important lifetime distributions in applied statistics. Weibull analysis is the leading method in the world for fitting and analyzing lifetime data. We discuss one of the earliest decision support system for the assessment of a distribution for the parameters of the Weibull reliability model using expert information. We then present a different approach to assess the parameters distribution. Objectives: The studies mentioned in this paper aimed to construct a distribution of the parameters of the Weibull reliability model and apply it in the domain of Maintenance Optimization. Method: The parameters of the Weibull reliability model are considered random variables and a distribution for the parameters is assessed using informed judgment in the form of reliability estimates from vendor information, engineering knowledge or experience in the field. Results: The results are the development of modern maintenance optimization models that can be embodied in decision support systems. Conclusion: While the information management part is important in the building of maintenance optimization decision systems, the accuracy of the mathematical and statistical algorithms determines the level of success of the maintenance solution.
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Li, S. C., and A. Nassirharand. "Non-linear proportional–integral–derivative synthesis for unstable non-linear systems using describing function inversion with experimental verification." Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering 226, no. 2 (August 25, 2011): 145–53. http://dx.doi.org/10.1177/0959651811417767.
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This paper demonstrates a new non-linear proportional–integral–derivative (PID) controller synthesis approach using a describing function inversion technique for unstable systems where a mathematical model may not be available. The approach is applied to an inverted pendulum experimental set-up whose dynamic behaviour is very sensitive to the amplitude level of excitation. The procedure involves stabilization of the unstable system followed by generation of the describing function models of the stabilized closed-loop system. Then, the corresponding unstable open-loop frequency domain models at various operating regimes are extracted. A controller at nominal conditions is designed, followed by obtaining the corresponding desired open-loop frequency domain model. A set of controllers that force the open-loop behaviour of the system mimic, which is desired at various operating regimes, is designed by optimization. Finally, the controller gains are inverted using a describing function inversion technique followed by experimental verification. The non-linear PID design is compared with two other alternative designs. The experimental results indicate that the proposed approach is a viable and effective non-linear controller synthesis technique for use with unstable non-linear systems.
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Dec, Grzegorz, Grzegorz Drałus, Damian Mazur, and Bogdan Kwiatkowski. "Forecasting Models of Daily Energy Generation by PV Panels Using Fuzzy Logic." Energies 14, no. 6 (March 17, 2021): 1676. http://dx.doi.org/10.3390/en14061676.
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This paper contains studies of daily energy production forecasting methods for photovoltaic solar panels (PV panel) by using mathematical methods and fuzzy logic models. Mathematical models are based on analytic equations that bind PV panel power with temperature and solar radiation. In models based on fuzzy logic, we use Adaptive-network-based Fuzzy Inference Systems (ANFIS) and the zero-order Takagi-Sugeno model (TS) with specially selected linear and non-linear membership functions. The use of mentioned membership functions causes that the TS system is equivalent to a polynomial and its properties can be compared to other analytical models of PV panels found in the literature. The developed models are based on data from a real system. The accuracy of developed prognostic models is compared, and a prototype software implementing the best-performing models is presented. The software is written for a generic programmable logic controller (PLC) compliant to the IEC 61131-3 standard.
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Chen, Jiqing, Shaorong Xie, Jun Luo, and Hengyu Li. "Wind-driven land-yacht robot mathematical modeling and verification." Industrial Robot: An International Journal 43, no. 1 (January 18, 2016): 77–90. http://dx.doi.org/10.1108/ir-03-2015-0052.
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Purpose – The purpose of this paper was to solve the shortage of carrying energy in probing robot and make full use of wind resources in the Antarctic expedition by designing a four-wheel land-yacht. Land-yacht is a new kind of mobile robot powered by the wind using a sail. The mathematical model and trajectory of the land-yacht are presented in this paper. Design/methodology/approach – The mechanism analysis method and experimental modeling method are used to establish a dual-input and dual-output mathematical model for the motion of land-yacht. First, the land-yacht’s model structure is obtained by using mechanism analysis. Then, the models of steering gear, servomotors and force of wing sail are analyzed and validated. Finally, the motion of land-yacht is simulated according to the mathematical model. Findings – The mathematical model is used to analyze linear motion and steering motion. Compared with the simulation results and the actual experimental tests, the feasibility and reliability of the proposed land-yacht modeling are verified. It can travel according to the given signal. Practical implications – This land-yacht can be used in the Antarctic, outer planet or for harsh environment exploration. Originality/value – A land-yacht is designed, and the contribution of this research is the development of a mathematical model for land-yacht robot. It provides a theoretical basis for analysis of the land-yacht’s motion.
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Necoara, Ion, and Tudor-Corneliu Ionescu. "Optimal H2 Moment Matching-Based Model Reduction for Linear Systems through (Non)convex Optimization." Mathematics 10, no. 10 (May 22, 2022): 1765. http://dx.doi.org/10.3390/math10101765.
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In this paper, we compute a (local) optimal reduced order model that matches a prescribed set of moments of a stable linear time-invariant system of high dimension. We fix the interpolation points and parametrize the models achieving moment-matching in a set of free parameters. Based on the parametrization and using the H2-norm of the approximation error as the objective function, we derive a nonconvex optimization problem, i.e., we search for the optimal free parameters to determine the model yielding the minimal H2-norm of the approximation error. Furthermore, we provide the necessary first-order optimality conditions in terms of the controllability and the observability Gramians of a minimal realization of the error system. We then propose two gradient-type algorithms to compute the (local) optimal models, with mathematical guarantees on the convergence. We also derive convex semidefinite programming relaxations for the nonconvex Problem, under the assumption that the error system admits block-diagonal Gramians, and derive sufficient conditions to guarantee the block diagonalization. The solutions resulting at each step of the proposed algorithms guarantee the achievement of the imposed moment matching conditions. The second gradient-based algorithm exhibits the additional property that, when stopped, yields a stable approximation with a reduced H2-error norm. We illustrate the theory on a CD-player and on a discretized heat equation.
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Eryiğit, Miraç. "Cost optimization of water distribution networks by using artificial immune systems." Journal of Water Supply: Research and Technology-Aqua 64, no. 1 (July 19, 2014): 47–63. http://dx.doi.org/10.2166/aqua.2014.031.
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This study aims at the development of an optimization model based on artificial immune systems (AIS) to minimize cost designs of water distribution networks (WDNs). Clonal selection algorithm (Clonalg), a class of AIS, was used as an optimization technique in the model, and its mutation operation was modified to increase the diversity (search capability). EPANET, a widely known WDN simulator, was used in conjunction with the proposed model. The model was applied to four WDNs of Two-loop, Hanoi, Go Yang, New York City, and the results obtained were compared with other heuristic and mathematical optimization models in the related literature, such as harmony search, genetic algorithm, immune algorithm, shuffled complex evolution, differential evolution, and non-linear programming-Lagrangian algorithm. Furthermore, the modified Clonalg was compared with the classic Clonalg in order to demonstrate the impact of the modification on the diversity. The proposed model appeared to be promising in terms of cost designs of WDNs.
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Melero, Valdir, Estevao Dos Santos Gedraite, Leo Kunigk, Patricia Angelica Vieira, Ricardo Amâncio Malagoni, Rodrigo Sislian, Ubirajara Coutinho Filho, Rubens Gedraite, and Sergio Ribeiro Augusto. "Experimental Investigation about Rinse Water Consumption of a CIP Process Applied to a Shell and Tube Exchanger." Advanced Materials Research 785-786 (September 2013): 1294–98. http://dx.doi.org/10.4028/www.scientific.net/amr.785-786.1294.
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This paper focused the CIP (clean in place) rinse stage, typically applied to the food industry. The dynamic behavior of residuals removal kinetics was studied, to obtain mathematical models that describe adequately the system. The optimization of water, detergent, etc., is the next goal. The obtained results show that the temperature influence can be neglected in comparison with the rinse water flow rate considering the cleaning process. The systems dynamics are non linear and were adequately represented by 1st order plus dead time transfer functions. The flow models obtained with this paper were validated versus experimental data and the results were close with respect to the last ones.
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Lyashenko, B. A., Z. A. Stotsko, O. A. Kuzin, M. O. Kuzin, and V. A. Mechnik. "Analysis of friction interaction and optimisation of detail surface hardening technologies using non-local mathematical models." Journal of Achievements in Materials and Manufacturing Engineering 1, no. 100 (May 1, 2020): 20–25. http://dx.doi.org/10.5604/01.3001.0014.1960.
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Purpose: The aim of the work is to build physically sound engineering and design schemes that take into account the behaviour of polycrystalline metal systems under intense loads and allow optimization of surface treatment technologies to increase the operational reliability parameters of products. Design/methodology/approach: Using the approaches of thermodynamics, a methodological scheme is proposed, on the basis of which it is possible to optimize surface engineering technologies to increase the contact durability of details. Findings: It was found that the maximum increase in the durability of steel 40X13 (AISI 420) is achieved with thermocyclic ion nitriding in a cycle of ± 50°C, and the minimum with isothermal nitriding. Research limitations/implications: In this paper, the optimization of technological solutions to increase the contact durability of structural elements operating under prevailing power loads is given. Practical implications: Using the proposed mathematical relationships, optimal technological regimes of ion-plasma nitriding were established for various operating conditions, under which the maximum durability and wear resistance of 40X13 (AISI 420) steel are ensured. Originality/value: The paper proposes an approach to the formation of functionally gradient surface layers of steel with specified operational parameters when choosing optimal nitriding technology modes based on nonlocal mathematical models.
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Lenz, Wagner B., Mauricio A. Ribeiro, Rodrigo T. Rocha, Jose M. Balthazar, and Angelo M. Tusset. "Numerical Simulations and Control of Offshore Energy Harvesting Using Piezoelectric Materials in a Portal Frame Structure." Shock and Vibration 2021 (June 2, 2021): 1–11. http://dx.doi.org/10.1155/2021/6651999.
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Buoy systems are an alternative for micropowering small devices in remote locations. Portal frames are very useful to harvest the energy of the waves into usable energy. Thus, using the current models for a portal frame in the literature and the spectrum of available energy in sea waves, a nonlinear mathematical model accounting for the coupling of a nonlinear piezoelectric material is considered. The neighbour of selected variables is analyzed and then optimized by a process utilizing the particle swarm optimization (PSO) algorithm. Furthermore, an optimal control using the linear-quadratic regulator (LQR) controller is applied to control the load resistance of the piezoelectric circuit. The optimization process and the LQR show to be effective. The results show a general gain due to optimization and a relatively small gain using the controller.
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Ohrimenko, Olga I., Igor M. Maltsev, Violetta V. Rokotyanskaya, and Maria L. Vilisova. "The theory of nonlinear systems as an instrument for solving engineering problems." MATEC Web of Conferences 226 (2018): 04040. http://dx.doi.org/10.1051/matecconf/201822604040.
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The article outlines theoretical, methodological and practical issues of modern control and optimization theory, as well as the problems of nonlinear systems theory. Theoretical conclusions and results allowed to build mathematical models applicable to the management of objects of different nature with different principles of action, in particular, to the management of complex technical and technological objects that can be considered as nonlinear dynamic systems. The authors find it appropriate to consider nonlinear dynamic integral models as Volterra integro-power series from many functional arguments with multidimensional weight functions and a certain finite set of inputs to the system. The set of multidimensional kernels of integral Volterra operators completely characterizes the nonlinear and dynamic properties, and, consequently, the technical state of the initial system. The application of Volterra series based models allows to take into account the nonlinear and inertial properties of the initial nonlinear dynamic system more fully and accurately, it also makes the model diagnostic of a technical system more universal, raises the reliability of the forecast. The diagnostic procedure in this case is aimed at defining Volterra kernels based on the data of “input-output” experiment and building the diagnostic system of attribute in the space of which the decisive rule of optimal classification is created.
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Kaczmarczyk, Robert, and Sebastian Gurgul. "A Thermodynamic Analysis of Heavy Hydrocarbons Reforming for Solid Oxide Fuel Cell Application as a Part of Hybrid Energy Systems." Energies 14, no. 2 (January 9, 2021): 337. http://dx.doi.org/10.3390/en14020337.
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A thermodynamical analysis of steam reforming of Associated Petroleum Gas (APG) was conducted in the presented research. The reforming process of heavy hydrocarbons for small scale power generation is a complex issue. One of the main issues is that a set of undesired chemical reactions deposit solid carbon and, consequently, block the reactor’s catalytic property. The experimental investigation is crucial to design an APG reforming reactor. However, a numerical simulation is a key tool to design a safe operating condition. Designing the next generation of reactors requires a complex coupling of mathematical models, kinetics, and thermodynamic analysis. In practice, the thermodynamic analysis should be applied in each control volume to assure realistic results. This is not easy to apply in practice since both thermodynamic analysis and CFD modeling can be time-consuming. In this paper, the authors suggest using a mathematical formalism called Parametric Equation Formalism to calculate the equilibrium composition. The novelty lies in the mathematical approach in which any complex system at equilibrium can be reduced to the problem of solving one non-linear equation at a time. This approach allows implementing a thermodynamic analysis easily into CFD models to assure the reasonability of obtained results and can be used for research and development of solid oxide fuel cells as a part of hybrid energy systems.
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Bao, Zhe, Ye Xu, Wei Li, Xu Wang, Meng R. Li, Ji H. Li, and Han S. Yang. "A Birandom Chance-Constrained Linear Programming Model for CCHP System Operation Management: A Case Study of Hotel in Shanghai, China." Mathematical Problems in Engineering 2020 (November 19, 2020): 1–16. http://dx.doi.org/10.1155/2020/1589415.
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Due to its capability to reduce fuel consumption and increase energy efficiency, the combined cooling, heating, and power (CCHP) system has obtained great concern during the last decade. A large number of deterministic and stochastic optimization models were proposed for supporting the operation management of the CCHP system, but few studies noticed that users’ demands in the real world may be subjected to twofold randomness with incomplete or uncertain information. In this study, a birandom chance-constrained linear programming (BCCLP) model is developed for identifying optimal operation strategies under random uncertainties. Compared with traditional stochastic programming models, the BCCLP model made the improvement through describing the energy demands as the birandom variables firstly, instead of traditional random variables. This way effectively avoided potential imbalance between energy supply and demand caused by oversimplified expression of uncertain parameters. A gas-fired CCHP system of a hotel in Shanghai, China, was used as a study case for demonstration. A variety of operation strategies are obtained under specific constraints-satisfaction conditions. It is concluded that the BCCLP model was capable of generating the cost-effective operation strategies and evaluating the tradeoffs between system economy and reliability. The influence imposed by some critical parameters on the system performance was examined through the sensitivity analysis, which provided the important guidance to the design and operational management of other similar CCHP systems in the future.
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Tran, Huu Khoa, Juing-Shian Chiou, and Viet-Hung Dang. "New Fusion Algorithm-Reinforced Pilot Control for an Agricultural Tricopter UAV." Mathematics 8, no. 9 (September 4, 2020): 1499. http://dx.doi.org/10.3390/math8091499.
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Currently, fuzzy proportional integral derivative (PID) controller schemes, which include simplified fuzzy reasoning decision methodologies and PID parameters, are broadly and efficaciously practiced in various fields from industrial applications, military service, to rescue operations, civilian information and also horticultural observation and agricultural surveillance. A fusion particle swarm optimization (PSO)–evolutionary programming (EP) algorithm, which is an improved version of the stochastic optimization strategy PSO, was presented for designing and optimizing controller gains in this study. The mathematical calculations of this study include the reproduction of EP with PSO. By minimizing the integral of the absolute error (IAE) criterion that is used for estimating the system response as a fitness function, the obtained integrated design of the fusion PSO–EP algorithm generated and updated the new elite parameters for proposed controller schemes. This progression was used for the complicated non-linear systems of the attitude-control pilot models of a tricopter unmanned aerial vehicle (UAV) to demonstrate an improvement on the performance in terms of rapid response, precision, reliability, and stability.
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Soliman, Hisham M., Farag A. El-Sheikhi, Ehab H. E. Bayoumi, and Michele De Santis. "Ellipsoidal Design of Robust Stabilization for Markov Jump Power Systems under Normal and Contingency Conditions." Energies 15, no. 19 (October 2, 2022): 7249. http://dx.doi.org/10.3390/en15197249.
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The essential prerequisites for secure customer service are power system stability and reliability. This work shows how to construct a robust switching control for studying power system load changes using an invariant ellipsoid method. Furthermore, the suggested control ensures stability when the system is subjected to random stochastic external disturbances, and functions randomly in two conditions: normal and contingency. The extreme (least) reliability state is chosen as the most severe scenario (corresponding to a transmission line outage). As a two-state Markov random chain, the transition probabilities are utilized to simulate the switching between normal and contingency modes (or processes). To characterize the dynamics of the studied system, a stochastic mathematical model is developed. The effect of stochastic disturbances and random normal/contingency operations is taken into account during the design stage. For a stochastic power system, a novel excitation control is designed. The attractive ellipsoid approach and linear matrix inequalities (LMIs) optimization are used to build the best two-controller gains. Therefore, the proposed modeling/design technique can be employed for the power system under load changes, stochastic topological changes, and random disturbances. Finally, the system’s random dynamics simulation indicates the effectiveness of the designed control law.
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Dasari, Siva Krishna, Abbas Cheddad, and Petter Andersson. "Predictive modelling to support sensitivity analysis for robust design in aerospace engineering." Structural and Multidisciplinary Optimization 61, no. 5 (January 3, 2020): 2177–92. http://dx.doi.org/10.1007/s00158-019-02467-5.
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AbstractThe design of aircraft engines involves computationally expensive engineering simulations. One way to solve this problem is the use of response surface models to approximate the high-fidelity time-consuming simulations while reducing computational time. For a robust design, sensitivity analysis based on these models allows for the efficient study of uncertain variables’ effect on system performance. The aim of this study is to support sensitivity analysis for a robust design in aerospace engineering. For this, an approach is presented in which random forests (RF) and multivariate adaptive regression splines (MARS) are explored to handle linear and non-linear response types for response surface modelling. Quantitative experiments are conducted to evaluate the predictive performance of these methods with Turbine Rear Structure (a component of aircraft) case study datasets for response surface modelling. Furthermore, to test these models’ applicability to perform sensitivity analysis, experiments are conducted using mathematical test problems (linear and non-linear functions) and their results are presented. From the experimental investigations, it appears that RF fits better on non-linear functions compared with MARS, whereas MARS fits well on linear functions.
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Hussein, Mohammed A., Ekhlas H. Karam, and Rokaia S. Habeeb. "CANCER GROWTH TREATMENT USING IMMUNE LINEAR QUADRATIC REGULATOR BASED ON CROW SEARCH OPTIMIZATION ALGORITHM." Applied Computer Science 17, no. 2 (June 30, 2021): 56–69. http://dx.doi.org/10.35784/acs-2021-13.
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The rapid and uncontrollable cell division that spreads to surrounding tissues medically termed as malignant neoplasm, cancer is one of the most common diseases worldwide. The need for effective cancer treatment arises due to the increase in the number of cases and the anticipation of higher levels in the coming years. Oncolytic virotherapy is a promising technique that has shown encouraging results in several cases. Mathematical models of virotherapy have been widely developed, and one such model is the interaction between tumor cells and oncolytic virus. In this paper an artificially optimized Immune- Linear Quadratic Regulator (LQR) is introduced to improve the outcome of oncolytic virotherapy. The control strategy has been evaluated in silico on number of subjects. The crow search algorithm is used to tune immune and LQR parameters. The study is conducted on two subjects, S1 and S3, with LQR and Immune-LQR. The experimental results reveal a decrease in the number of tumor cells and remain in the treatment area from day ten onwards, this indicates the robustness of treatment strategies that can achieve tumor reduction regardless of the uncertainty in the biological parameters.
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Adnan, Aliaa, Ekhlas H. Karam, and Muaayed F. Al-Rawi. "Model based adaptive controller with grasshopper optimization algorithm for upper-limb rehabilitation robot." Indonesian Journal of Electrical Engineering and Computer Science 26, no. 2 (May 1, 2022): 723. http://dx.doi.org/10.11591/ijeecs.v26.i2.pp723-731.
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<span>Model based adaptive controllers (MBACs) are considered one of the most common adaptive controllers that are used with robotic systems due to their ensuring nonlinear robust scheme with global asymptotic stability for controlling nonlinear systems. However, this controller requires precise mathematical models of the controlled systems. In this paper, an optimal model-based adaptive controller (OMBAC) is suggested for controlling a two-link upper limb rehabilitation robot. This controller, in the presence of model uncertainties, can guarantee the robustness of the rehabilitation robot. Although the OMBAC is an adaptive and model-based controller, some of its parameters need to be determined precisely. In this paper, these parameters are determined by the grasshopper optimization algorithm (GOA). The Lyapunov method is used to analyze the stability assurance of controlled rehabilitation. The results of the simulation for two tested trajectories (linear and nonlinear trajectories) demonstrate the efficiency of the suggested OMBAC with fast settling time, minimum error steady state, and very small overshoot.</span>
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Puspita, Fitri Maya, Bella Juwita Rezky, Arden Naser Yustian Simarmata, Evi Yuliza, and Yusuf Hartono. "Improved incentive pricing-based quasi-linear utility function of wireless networks." Indonesian Journal of Electrical Engineering and Computer Science 22, no. 3 (June 1, 2021): 1467. http://dx.doi.org/10.11591/ijeecs.v22.i3.pp1467-1475.
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The model of the incentive pricing scheme-based quasi-linear utility function in wireless network was designed. Previous research seldom focusses on user’s satisfaction while using network. Therefore, the model is then attempted to be set up that is derived from the modification of bundling and models of reverse charging and maintain the quality of service to users by utilizing quasi-linear utility function. The pricing schemes then are applied to local data server traffic. The model used is known as mathematical programming problem that can be solved by LINGO 13.0 program as optimization tool to get the optimal solution. The optimal results show that the improved incentive pricing can achieve better solution compared to original reverse charging where the models will be obtained in flat fee, usage-based, and two-part tariff strategies for homogeneous consumers.
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Czyżewicz, Jacek, Piotr Jaskólski, Paweł Ziemiański, Marian Piwowarski, Mateusz Bortkiewicz, Krzysztof Laszuk, Ireneusz Galara, Marta Pawłowska, and Karol Cybulski. "Towards Designing an Innovative Industrial Fan: Developing Regression and Neural Models Based on Remote Mass Measurements." Energies 15, no. 7 (March 25, 2022): 2425. http://dx.doi.org/10.3390/en15072425.
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This article presents the process of the construction and testing a remote, fully autonomous system for measuring the operational parameters of fans. The measurement results obtained made it possible to create and verify mathematical models using linear regression and neural networks. The process was implemented as part of the first stage of an innovative project. The article presents detailed steps of constructing a system to collect and process measurement data from fans installed in actual operating conditions and the results of analysis of this data. In particular, a measurement infrastructure was developed, defined, and implemented. Measuring equipment was mounted on selected ventilation systems with relevant fans. Systems were implemented that allowed continuous measurement of ventilation system parameters and remote transmission of data to a server where it was regularly analysed and selected for use in the process of modelling and diagnostics. Pearson’s correlation analysis for p < 0.05 indicated that all seven parameters (suction temperature, discharge temperature, suction pressure, current consumption, rotational speed, humidity, and flow) were significantly correlated with efficiency (p < 0.001). A satisfactory level of correlation between the selected parameters measured in actual conditions and the characteristics of the fan and the ventilation system was experimentally verified. This was determined by finding 4 statistically significant parameters at a confidence level of 95%. This allowed the creation of two mathematical models of the fan system and the ventilation system using linear regression and neural networks. The linear regression model showed that the suction temperature, discharge temperature, and air humidity did not affect the fan efficiency (they are statistically insignificant, p > 0.05). The neural model, which considered all measured parameters, achieved the same accuracy as the model based on four significant parameters: suction pressure, current consumption, rotational speed, and flow.
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Popkov, Yuri S. "Controlled Positive Dynamic Systems with an Entropy Operator: Fundamentals of the Theory and Applications." Mathematics 9, no. 20 (October 14, 2021): 2585. http://dx.doi.org/10.3390/math9202585.
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Controlled dynamic systems with an entropy operator (DSEO) are considered. Mathematical models of such systems were used to study the dynamic properties in demo-economic systems, the spatiotemporal evolution of traffic flows, recurrent procedures for restoring images from projections, etc. Three problems of the study of DSEO are considered: the existence and uniqueness of singular points and the influence of control on them; stability in “large” of the singular points; and optimization of program control with linear feedback. The theorems of existence, uniqueness, and localization of singular points are proved using the properties of equations with monotone operators and the method of linear majorants of the entropy operator. The theorem on asymptotic stability of the DSEO in “large” is proven using differential inequalities. Methods for the synthesis of quasi-optimal program control and linear feedback control with integral quadratic quality functional, and ensuring the existence of a nonzero equilibrium, were developed. A recursive method for solving the integral equations of the DSEO using the multidimensional functional power series and the multidimensional Laplace transform was developed. The problem of managing regional foreign direct investment is considered, the distribution of flows is modeled by the corresponding DSEO. It is shown that linear feedback control is a more effective tool than program control.
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Schütz, Arwed, Sönke Maeter, and Tamara Bechtold. "System-Level Modelling and Simulation of a Multiphysical Kick and Catch Actuator System." Actuators 10, no. 11 (October 21, 2021): 279. http://dx.doi.org/10.3390/act10110279.
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This paper presents a system-level model of a microsystem architecture deploying cooperating microactuators. An assembly of a piezoelectric kick-actuator and an electromagnetic catch-actuator manipulates a structurally unconnected, magnetized micromirror. The absence of mechanical connections allows for large deflections and multistability. Closed-loop feedback control allows this setup to achieve high accuracy, but requires fast and precise system-level models of each component. Such models can be generated directly from large-scale finite element (FE) models via mathematical methods of model order reduction (MOR). A special challenge lies in reducing a nonlinear multiphysical FE model of a piezoelectric kick-actuator and its mechanical contact to a micromirror, which is modeled as a rigid body. We propose to separate the actuator–micromirror system into two single-body systems. This step allows us to apply the contact-induced forces as inputs to each sub-system and, thus, avoid the nonlinear FE model. Rather, we have the linear model with nonlinear input, to which established linear MOR methods can be applied. Comparisons between the reference FE model and the reduced order model demonstrate the feasibility of the proposed methodology. Finally, a system-level simulation of the whole assembly, including two actuators, a micromirror and a simple control circuitry, is presented.
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Huang, Tao, and Chih-Chiang Fang. "Optimization of Software Test Scheduling under Development of Modular Software Systems." Symmetry 15, no. 1 (January 9, 2023): 195. http://dx.doi.org/10.3390/sym15010195.
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Software testing and debugging is a crucial part of the software development process since defective software not only incurs customer dissatisfaction but also might incur legal issues. However, the managers of a software development company cannot arbitrarily prolong their software debugging period due to their software testing budget and opportunity in the market. Accordingly, in order to propose an advantageous testing project, the managers should be aware of the influence of the testing project on cost, quality, and time to make the best decision. In this study, a new software reliability growth model (SRGM) with consideration of the testing staff’s learning effect is proposed to achieve better prediction. The methods of estimating the model’s parameters and the symmetric confidence intervals are also proposed in the study. Moreover, in the past, most of the SRGMs focused on a single software system. However, in practice, some software systems were developed using modular-based system engineering approaches. Therefore, traditional software testing work can be changed to multiple modular testing work in this scenario. Therefore, the manager can use this to dispatch multiple staff groups to perform the individual testing work simultaneously. The study proposes two mathematical programming models to handle the scheduling of modular testing work. Additionally, the design of a computerized decision support system is also proposed in the study for the application in practice.
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Khan, Akhlaque Ahmad, Ahmad Faiz Minai, Rupendra Kumar Pachauri, and Hasmat Malik. "Optimal Sizing, Control, and Management Strategies for Hybrid Renewable Energy Systems: A Comprehensive Review." Energies 15, no. 17 (August 27, 2022): 6249. http://dx.doi.org/10.3390/en15176249.
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To meet the expanding energy demand, all available energy sources must be utilized. Renewable energies are both eternal and natural, but their major downside is their inconsistency. Due to the rising costs of fossil fuels and the CO2 they emit, hybrid renewable energy (HRE) sources have gained popularity as an alternative in remote and rural areas. To address this issue, a hybrid renewable energy system (HRES) can be developed by combining several energy sources. In order to build modern electrical grids that have advantages for the economy, environment, and society, the hybrid system is preferable. A summary of various optimization methods (modeling techniques) of an HRES is presented in this paper. This study offers an in-depth analysis of the best sizing, control methodologies, and energy management strategies, along with the incorporation of various renewable energy sources to form a hybrid system. Modern hybrid renewable energy system utilities rely more on an optimal design to reduce the cost function. Reviews of several mathematical models put out by various academicians are presented in this work. These models were created based on reliability analyses incorporating design factors, objective functions, and economics. The reader will get familiar with numerous system modelling optimization strategies after reading this study, and they will be able to compare different models based on their cost functions. Numerous modeling approaches and software simulation tools have been created to aid stakeholders in the planning, research, and development of HRES. The optimal use of renewable energy potential and the meticulous creation of applicable designs are closely tied to the full analysis of these undoubtedly complicated systems. In this field, as well, several optimization restrictions and objectives have been applied. Overall, the optimization, sizing, and control of HRES are covered in this paper with the energy management strategies.
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Cacuci, Dan Gabriel. "The nth-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Response-Coupled Forward/Adjoint Linear Systems (nth-CASAM-L): I. Mathematical Framework." Energies 14, no. 24 (December 10, 2021): 8314. http://dx.doi.org/10.3390/en14248314.
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This work presents the mathematical framework of the nth-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Response-Coupled Forward/Adjoint Linear Systems (abbreviated as “nth-CASAM-L”), which is conceived for obtaining the exact expressions of arbitrarily-high-order (nth-order) sensitivities of a generic system response with respect to all of the parameters (including boundary and initial conditions) underlying the respective forward/adjoint systems. Since many of the most important responses for linear systems involve the solutions of both the forward and the adjoint linear models that correspond to the respective physical system, the sensitivity analysis of such responses makes it necessary to treat linear systems in their own right, rather than treating them as particular cases of nonlinear systems. This is in contradistinction to responses for nonlinear systems, which can depend only on the forward functions, since nonlinear operators do not admit bona-fide adjoint operators (only a linearized form of a nonlinear operator admits an adjoint operator). The nth-CASAM-L determines the exact expression of arbitrarily-high order sensitivities of responses to the parameters underlying both the forward and adjoint models of a nonlinear system, thus enable the most efficient and accurate computation of such sensitivities. The mathematical framework underlying the nth-CASAM is developed in linearly increasing higher-dimensional Hilbert spaces, as opposed to the exponentially increasing “parameter-dimensional” spaces in which response sensitivities are computed by other methods, thus providing the basis for overcoming the “curse of dimensionality” in sensitivity analysis and all other fields (uncertainty quantification, predictive modeling, etc.) which need such sensitivities. In particular, for a scalar-valued valued response associated with a nonlinear model comprising TP parameters, the 1st-−CASAM-L requires 1 additional large-scale adjoint computation (as opposed to TP large-scale computations, as required by other methods) for computing exactly all of the 1st-−order response sensitivities. All of the (mixed) 2nd-order sensitivities are computed exactly by the 2nd-CASAM-L in at most TP computations, as opposed to TP(TP + 1)/2 computations required by all other methods, and so on. For every lower-order sensitivity of interest, the nth-CASAM-L computes the “TP next-higher-order” sensitivities in one adjoint computation performed in a linearly increasing higher-dimensional Hilbert space. Very importantly, the nth-CASAM-L computes the higher-level adjoint functions using the same forward and adjoint solvers (i.e., computer codes) as used for solving the original forward and adjoint systems, thus requiring relatively minor additional software development for computing the various-order sensitivities.
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Zhang, J. H., Z. X. Yi, C. Y. Peng, and Shahid Hussain. "An Energy-Aware Data Transmission Scheme under the Guarantee of Reliability for 3D WSNs." Journal of Sensors 2020 (September 27, 2020): 1–16. http://dx.doi.org/10.1155/2020/8855073.
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Three-dimensional wireless sensor networks (3D WSNs) play an important role to provide data collection services for Internet of things (IoT) in the real applications. However, many of the existing WSN data collection researches are based on a relatively simple linear or plane network model. The three-dimensional space problems are simplified to two-dimensional plane, which limits the applicability. In this paper, the data collection in 3D WSN is studied. In the three-dimensional space, we firstly analyze the data loads, energy consumption, and end-to-end (E2E) delay of each node when the network is following the shortest path routing. The mathematical analysis of data loads and E2E delay of each node are presented. Based on the analysis of data loads and energy consumption, an energy-ware data transmission scheme is proposed to achieve the trade-off optimization between the E2E delay and network lifetime under the guarantee of the transmission reliability. The key point of the proposed scheme is to make fully use of the unbalanced energy consumption of the 3D WSN. The performance of the proposed scheme is discussed, analyzed, and evaluated. The theoretical analysis and simulation results show that the E2E network delay and energy efficiency can be improved under the constraint of transmission reliability.
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Reinbold, Vincent, Van-Binh Dinh, Daniel Tenfen, Benoit Delinchant, and Dirk Saelens. "Optimal operation of building microgrids – comparison with mixed-integer linear and continuous non-linear programming approaches." COMPEL - The international journal for computation and mathematics in electrical and electronic engineering 37, no. 2 (March 5, 2018): 603–16. http://dx.doi.org/10.1108/compel-11-2016-0489.
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PurposeThis paper aims to present two mathematical models to solve the Energy Management problem of a building microgrid (MG). In particular, it proposes a deterministic mixed integer linear programming (MILP) and non-linear programming (NLP) formulations. This paper focuses on the modelling process and the optimization performances for both approaches regarding optimal operation of near-zero energy buildings connected to an electric MG with a 24-h time horizon. Design/methodology/approachA general architecture of a MG is detailed, involving energy storage systems, distributed generation and a thermal reduced model of the grid-connected building. A continuous non-linear model is detailed along with linearizations for the mixed-integer liner formulation. Multi-physic, non-linear and non-convex phenomena are detailed, such as ventilation and air quality models. FindingsResults show that both approaches are relevant for solving the energy management problem of the building MG. Originality/valueIntroduction and modelling of the thermal loads within the MG. The resulting linear program handles the mutli-objective trade-off between discomfort and the cost of use taking into account air quality criterion. Linearization and modelling of the ventilation system behaviour, which is generally non-linear and non-convex equality constraints, involving air quality model, heat transfer and ventilation power. Comparison of both MILP and NLP methods on a general use case provides a solution that can be interpreted for implementation.
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Fernández del Castillo, Alberto, Marycarmen Verduzco Garibay, Carolina Senés-Guerrero, Carlos Yebra-Montes, José de Anda, and Misael Sebastián Gradilla-Hernández. "Mathematical Modeling of a Domestic Wastewater Treatment System Combining a Septic Tank, an Up Flow Anaerobic Filter, and a Constructed Wetland." Water 12, no. 11 (October 27, 2020): 3019. http://dx.doi.org/10.3390/w12113019.
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Systems combining anaerobic bioreactors with constructed wetlands (CW) have proven to be adequate and efficient for wastewater treatment. Detailed knowledge of removal dynamics of contaminants can ensure positive results for engineering and design. Mathematical modeling is a useful approach to studying the dynamics of contaminant removal in wastewater. In this study, water quality monitoring was performed in a system composed of a septic tank (ST), an up flow anaerobic filter (UAF), and a horizontal flow constructed wetland (HFCW). Biological oxygen demand (BOD5), chemical oxygen demand (COD), total Kjeldahl nitrogen (TKN), NH3, organic nitrogen (ON), total suspended solids (TSS), NO2−, and NO3− were measured biweekly during a 3-month period. First-order kinetics, multiple linear regression, and mass balance models were applied for data adjustment. First-order models were useful to predict the outlet concentration of pollutants (R2 > 0.87). Relevant multiple linear regression models were found, which could be applied to facilitate the system’s monitoring and provide valuable information to control and improve biological and physical processes necessary for wastewater treatment. Finally, the values of important parameters (μmax, Ks, and Yx/s) in mass-balance models were determined with the aid of a differential neural network (DNN) and an optimization algorithm. The estimated parameters indicated the high robustness of the treatment system since performance stability was found despite variations in wastewater composition.
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Cao, Yuyan, Ting Li, Yang Li, and Xinmin Wang. "Heterogeneous Multi-Agent-Based Fault Diagnosis Scheme for Actuation System." Actuators 11, no. 4 (April 18, 2022): 113. http://dx.doi.org/10.3390/act11040113.
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In this paper, a fault diagnosis method of a heterogeneous multi-agent is proposed that realizes the rapid and accurate fault diagnosis of a redundant multi-type actuation system of large aircraft. Firstly, the multi-agent model of a large aircraft actuation system is established, the composition of the actuation system and the relationship between each multi-agent are clarified and three different types of actuator mathematical models are established. Secondly, a fault detection and isolation (FDI) model is established and transformed into an optimization problem according to different performance index requirements. Aiming at the optimization problem, combined with the principle of linear matrix inequality (LMI), the fault diagnosis algorithm of a heterogeneous multi-agent system is designed. Moreover, the threshold judgment method based on the error signal is presented. Finally, the three actuator models of the aileron actuation system of large aircraft are combined to complete the fault diagnosis of a heterogeneous multi-agent system under the given model interference and model fault. The obtained results demonstrate and validate that the proposed method can accurately and effectively diagnose the faults of the actuator and its associated actuators.
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Ramadan, Abdelhady, Salah Kamel, Ibrahim B. M. Taha, and Marcos Tostado-Véliz. "Parameter Estimation of Modified Double-Diode and Triple-Diode Photovoltaic Models Based on Wild Horse Optimizer." Electronics 10, no. 18 (September 19, 2021): 2308. http://dx.doi.org/10.3390/electronics10182308.
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The increase in industrial and commercial applications of photovoltaic systems (PV) has a significant impact on the increase in interest in studying the improvement of the efficiency of these systems. Estimating the efficiency of PV is considered one of the most important problems facing those in charge of manufacturing these systems, which makes it interesting to many researchers. The difficulty in estimating the efficiency of PV is due to the high non-linear current–voltage characteristics and power–voltage characteristics. In addition, the absence of ample efficiency information in the manufacturers’ datasheets has led to the development of an effective electrical mathematical equivalent model necessary to simulate the PV module. In this paper, an application for an optimization algorithm named Wild Horse Optimizer (WHO) is proposed to extract the parameters of a double-diode PV model (DDM), modified double-diode PV model (MDDM), triple-diode PV model (TDM), and modified triple-diode PV model (MTDM). This study focuses on two main objectives. The first concerns comparing the original models (DDM and TDM) and their modification (MDDM and MTDM). The second concerns the algorithm behavior with the optimization problem and comparing this behavior with other recent algorithms. The evaluation process uses different methods, such as Root Mean Square Error (RMSE) for accuracy and statistical analysis for robustness. Based on the results obtained by the WHO, the estimated parameters using the WHO are more accurate than those obtained by the other studied optimization algorithms; furthermore, the MDDM and MTDM modifications enhanced the original DDM and TDM efficiencies.
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Amirteimoori, Alireza, Hossein Azizi, and Sohrab Kordrostami. "Double Frontier Two-Stage Fuzzy Data Envelopment Analysis." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 28, no. 01 (February 2020): 117–52. http://dx.doi.org/10.1142/s0218488520500063.
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Data envelopment analysis (DEA) is a mathematical programming approach with widespread applications in productivity and efficiency analysis. Compared with traditional DEA models, two-stage DEA models show the performance of each process and make available more information for decision making. In an article by Kao and Liu, models were proposed for combining a two-stage process to achieve overall fuzzy efficiency measures. Their method follows the simple geometric average approach and uses the product of two efficiencies. The present article applies a different angle for efficiency analysis in the two-stage fuzzy DEA. We suggest that the overall efficiency score of a decision-making unit (DMU) is defined as total weight of stage efficiencies, not as the simple product of their efficiency. Moreover, the proposed fuzzy DEA models are different from the model by Kao and Liu for fuzzy data in that our models are linear without the need for additional changes in variables and use the same set of constraints to measure the efficiency of DMUs with fuzzy input and output data. While the models by Kao and Liu are a nonlinear optimization problem that need additional changes in variables, and use different sets of constraints to measure fuzzy efficiencies. Additionally, our proposed approach evaluates the performance of DMUs from both optimistic and pessimistic viewpoints. Finally, using the proposed approach, the Taiwanese non-life insurance company problem will be investigated.
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Golovkov, A. A., and A. V. Fomin. "Parametrical Synthesis of Radio Devices with the Set Quantity of Identical Cascades for Inclusion Variants of Jet Two-port Networks between a Nonlinear Part and Loading." Journal of the Russian Universities. Radioelectronics 24, no. 6 (December 29, 2021): 27–37. http://dx.doi.org/10.32603/1993-8985-2021-24-6-27-37.
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Introduction. The ability to analytically determine some parameters of various radio devices, which are optimal according to the criterion of providing the set values of the modules and phases of transfer functions at the required number of frequencies, significantly reduces the time for numerical optimization of the rest of the parameters according to the criterion of forming the required frequency response and frequency response in the frequency band. Until now, such problems with respect to radio devices have been solved only for one stage of the "nonlinear part – matching device" or "matching device – nonlinear part" type. As a matching device, reactive, resistive, complex, or mixed quad-poles were used.Aim. Development of algorithms for parametric synthesis of radio devices with an arbitrary number of identical cascades of the "nonlinear part – matching reactive quadrupole" type according to the criterion of ensuring the specified frequency characteristics. Non-linear parts are represented as a non-linear element and parallel or serial current or voltage feedback.Materials and methods. Four-pole theory, matrix algebra, decomposition method, method of synthesis of microwave control devices, numerical optimization methods.Results. Systems of algebraic equations are formed and solved. Models of optimal quadrupole conductors are obtained in the form of mathematical expressions for determining the relationships between the elements of their classical transmission matrix and for finding the frequency dependences of the resistances of two-pole conductors.Conclusion. It is shown that the frequency characteristics of the studied radio devices from the same stages are identical or similar to the frequency characteristics of radio devices from the same stage, but with the signal source and load resistances changed in a certain way. Such schemes are called equivalent. A comparative analysis of the theoretical results (frequency response and frequency response of radio devices) obtained by mathematical modeling in the "MathCad" system, and the experimental results obtained by circuit modeling in the "OrCAD" and "MicroCap" systems, shows their satisfactory agreement.
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Rawa, Muhyaddin. "Towards Avoiding Cascading Failures in Transmission Expansion Planning of Modern Active Power Systems Using Hybrid Snake-Sine Cosine Optimization Algorithm." Mathematics 10, no. 8 (April 15, 2022): 1323. http://dx.doi.org/10.3390/math10081323.
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In this paper, a transmission expansion planning (TEP) model is proposed to guarantee the resilience of power systems and mitigate cascading failures’ impacts. The energy storage systems and fault current limiters’ planning models are integrated into the TEP problem to minimize cascading outages and comply with short-circuit current reliability constraints. Most studies in the literature adopt a single strategy to simulate power systems’ cascading failures that may not be enough to guarantee networks’ resilience. This work elaborates on two scenarios for initiating cascading failures to study the impact of various initiating events on the planned system’s strength and the projects required. The TEP problem is formulated as a non-linear, non-convex large-scale problem. To avoid linearization issues and enhance meta-heuristics performance, a hybridization of two meta-heuristic techniques, namely snake optimizer and sine cosine algorithm (SO-SCA), is proposed to solve the problem. Two hybridization strategies are suggested to improve the exploration and exploitation stages. Defining future loads growth is essential for TEP. Hence, a load forecasting technique based on SO-SCA is investigated and compared with some methods reported in the literature. The results obtained proved the efficiency of the proposed approach in predicting load growth. TEP’s calculations were carried out on the Garver and the IEEE 24-bus system. The results demonstrated the superiority of the hybrid SO-SCA in solving the TEP problem. Moreover, the projects required to expand networks differed according to the type of cascading failures’ initiating scenario.
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Rauh, Andreas, Johanna Minisini, and Eberhard Hofer. "Verification Techniques for Sensitivity Analysis and Design of Controllers for Nonlinear Dynamic Systems with Uncertainties." International Journal of Applied Mathematics and Computer Science 19, no. 3 (September 1, 2009): 425–39. http://dx.doi.org/10.2478/v10006-009-0035-1.
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Verification Techniques for Sensitivity Analysis and Design of Controllers for Nonlinear Dynamic Systems with UncertaintiesControl strategies for nonlinear dynamical systems often make use of special system properties, which are, for example, differential flatness or exact input-output as well as input-to-state linearizability. However, approaches using these properties are unavoidably limited to specific classes of mathematical models. To generalize design procedures and to account for parameter uncertainties as well as modeling errors, an interval arithmetic approach for verified simulation of continuoustime dynamical system models is extended. These extensions are the synthesis, sensitivity analysis, and optimization of open-loop and closed-loop controllers. In addition to the calculation of guaranteed enclosures of the sets of all reachable states, interval arithmetic routines have been developed which verify the controllability and observability of the states of uncertain dynamic systems. Furthermore, they assure asymptotic stability of controlled systems for all possible operating conditions. Based on these results, techniques for trajectory planning can be developed which determine reference signals for linear and nonlinear controllers. For that purpose, limitations of the control variables are taken into account as further constraints. Due to the use of interval techniques, issues of the functionality, robustness, and safety of dynamic systems can be treated in a unified design approach. The presented algorithms are demonstrated for a nonlinear uncertain model of biological wastewater treatment plants.
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Sitnikov, Ivan R., and Alexander V. Golikov. "Rationalization of the constructive form of towers with prestressed cables." Structural Mechanics of Engineering Constructions and Buildings 15, no. 3 (December 15, 2019): 182–92. http://dx.doi.org/10.22363/1815-5235-2019-15-3-182-192.
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Relevance. One of the main directions of development of mobile communication systems, radio engineering and telecommunication systems is the improvement of the structural form of the bearing supports, which will solve a number of practical tasks: to increase the coverage area, to ensure higher rates of data transmission speed and to ensure stable operation in an increasing number of users. These circumstances justify the relevance of research in this direction. Aims of research. Optimization of design solutions using parallel puffs, ensuring the possibility of erection and safe operation during the entire service life, which ensures that the requirements for strength, stability and deformations for such structures are met with minimal material consumption. Methods. For calculations, finite element methods are used for mathematical modeling using software and computing systems. To create linear models for numerical experiments, the method of mathematical planning of experiments was used. Results. The work of the towers of the proposed constructive solution is considered as supports for the placement of equipment of cellular operators using the example of a 42-meter tower. The method of mathematical planning of experiments was used to create a model line for numerical experiments. To establish the basic characteristics of the stress-strain state of the structures of the supports, a number of models were created and calculated in software packages, the basis of which is the finite element method. A comparative analysis of the effort in the delays determined by analytical calculation and the finite element method is performed. The analysis of changes in the stress-strain state of the towers from the influence of influencing factors, such as wind and icy-wind loads, the angle of deflection on the lower tier of the tower. By the criterion of minimum metal consumption and manufacturability of the construction of towers, rational overall dimensions of the tower were determined. The options for constructing the main junctions of the elements of the tower are proposed.
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Zhu, Guodong, Yong Wang, Guo-Niu Zhu, Minghao Weng, Jianhui Liu, Ji Zhou, and Bing Lu. "Parameter Optimization of Large-Size High-Speed Cam-Linkage Mechanism for Kinematic Performance." Actuators 12, no. 1 (December 21, 2022): 2. http://dx.doi.org/10.3390/act12010002.
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The cam-linkage mechanism is a typical transmission mechanism in mechanical science and is widely used in various automated production equipment. However, conventional modeling methods mainly focus on the design and dimensional synthesis of the cam-linkage mechanism in the slow-speed scenario. The influence of component dimensions is not taken into consideration. As a result, the model accuracy dramatically falls when analyzing large-size cam-linkage mechanisms, especially in high-speed environments. The kinematic aspects of cam design have been investigated, but there are few studies discussing the motion characteristic and accuracy analysis models of the large-size cam-linkage mechanism under high-speed scenarios. To handle such issues, this paper proposes a parameter optimization methodology for the design analysis of the large-size high-speed cam-linkage mechanism considering kinematic performance. Firstly, the mathematical model of the cam five-bar mechanism is presented. The cam curve and motion parameters are solved forward with linkage length and output speed. Then, a particle swarm-based multi-objective optimization method is developed to find the optimal structure parameters and output speed curve to minimize cam pressure angle and roller acceleration and maximize linkage mechanism drive angle. A Monte Carlo-based framework is put forward for the reliability and sensitivity analysis of kinematic accuracy. Finally, a transverse device of a sanitary product production line is provided to demonstrate the applicability of the proposed method. With the parameter optimization, the productivity of the transverse device is doubled, from 600 pieces per minute (PPM) to 1200 PPM.
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Geraskin, Mikhail. "Game-theoretic analysis of Stackelberg oligopoly with arbitrary rank reflexive behavior of agents." Kybernetes 46, no. 06 (June 5, 2017): 1052–67. http://dx.doi.org/10.1108/k-12-2016-0351.
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Purpose This paper aims to consider the problem of determining the equilibriums on oligopoly market in case of Stackelberg leader (leaders) and reflexive behavior of market agents. Design/methodology/approach This paper includes economic and mathematical modeling, optimization methods and game theory. Findings This paper explains models of reflexive games on oligopoly market, taking into account the diversity of agents’ reasoning about strategies of environing and equilibrium mechanisms for coincidence or opposition of agents’ reflexive reasoning on the same rank of reflection. Research limitations/implications This paper considers the oligopoly market with linear function of demand and costs of agents, the rational behavior of agents and the reflexive reasoning on the same rank of reflection. The set of agents’ reasoning about the environing strategies is considered as a set of market states for which the problem of agent’s optimal action choosing solves with the complete awareness. Practical implications Identification of reflexive behavior of environing allows agents to increase their market shares and profit. Social implications Oligopoly markets play a leading role in the world oil trade and reflexive behavior affects the market equilibrium. Originality/value In the paper, the mechanisms of equilibrium in reflexive games on the linear duopoly market for arbitrary rank reflection are developed.
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Lerner, Ilya M. "ON THE QUESTION OF CHOOSING A METHOD FOR ANALYZING TRANSIENT PROCESSES FOR DEVELOPING THE THEORY OF RESOLUTION TIME. RETROSPECTIVE ANALYTICAL REVIEW." T-Comm 15, no. 8 (2021): 62–70. http://dx.doi.org/10.36724/2072-8735-2021-15-8-62-70.
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One of the fundamental and central problems of radio engineering and communication theory was and remains the scientific problem of finding ways to potentially reduce the frequency band occupied by the signal, as well as reducing the power of transmitting devices, which provide the necessary speed and reliability of information transfer, that is, the problem of increasing the specific bandwidth. One of the key forms of solving this problem is the transition to the reception of information messages in conditions of strong intersymbol interference. Sufficiently encouraging results in this direction are shown by the theory of resolution time presented in the papers [1-5] for APSK-N- and PSK-n- signals. At the same time, as a mathematical apparatus in these works, it is used as a mathematical apparatus in the field of optimization and analysis of transient processes. At the same time, as shown in these papers, the correct choice of the mathematical apparatus for the analysis of transient processes is of paramount importance. At present, due to the constant growth of the volume of transmitted information, more and more attention is paid to the issues of the possibility of increasing the transmission speed due to the use of the transmission mode “above the Nyquist rate”. According to the theory of resolution time, which has been developing quite rapidly recently, it is required to analyze the transient processes in linear selective systems (LSS). In this case, LSS makes it possible to implement frequency selective properties of real communication channels in the channel model. At the same time, the question of choosing a method for analyzing the transient process is quite acute, since it primarily determines the complexity of estimating capacity procedure. This paper presents a retrospective, analytical review of methods for analyzing transient processes in LSS and substantiates the need to apply the method of slowly varying amplitudes S.I. Evtyanov and its developing. On its basis, the simplest and most convenient method for analyzing transient processes was chosen as applied to phase radio engineering systems for transmitting information.
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Liu, Dong, Feihong Yun, Wuchao Wang, Kefeng Jiao, Liquan Wang, Zheping Yan, Peng Jia, et al. "Sealing Contact Transient Thermal-Structural Coupling Analysis of the Subsea Connector." Machines 10, no. 3 (March 18, 2022): 213. http://dx.doi.org/10.3390/machines10030213.
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Taking the subsea collect connector as an example, the sealing characteristics of the sealing structure of the subsea connector under transient thermal–structural coupling were studied. Based on Airy’s thermal stress function, the mathematical model was established, the complex stress function was used to solve the problem, and a three-dimensional transient thermal stress model of the core sealing parts was obtained. The transient thermal–structural coupling stress model of the core seal was obtained by linear superposition principle. The transient temperature field of the subsea collet connector under different working conditions was analyzed. It was found that the larger the temperature difference between the components was, the greater the difference of expansion rate was, and the greater the impact on the sealing performance of LSG was in the process of temperature variation from transient to steady distribution. Numerical simulations of various working conditions under the transient temperature field were carried out. The results showed that sudden change of the temperature and oil–gas pressure will bring about large fluctuations of the maximum contact stress and equivalent stress of the seal, which was easy to fatigue wear, and thus affect the reliability of the sealing performance. Finally, the experiment proves that the sealing ring can maintain sealing performance under the conditions of temperature-cyclic loading. The coupled mathematical model proposed in this paper could be used for the transient thermal–structural coupling theoretical analysis of similar subsea equipment.