Mathematical Solution Methods Research Articles

Redundancy allocation problem in repairable systems with variegated components: a simulation-based optimization approach

The redundancy allocation problem (RAP) is one of the most commonly used approaches for improving the reliability of systems. In previous studies, to simplify the problem model and mathematical solution methods, some real conditions were not emphasized in analysing the issue of RAP. But the present study, while considering these conditions, enables considering multiple goals, analysing repairable systems and examining the failure rate and repair rate appropriate to the type of components. Two goals of this purpose are maximizing the Mean Time To First Failure (MTTFF) and minimizing the total cost of the system, considering the weight and volume limitations and number of plugin components. To solve the problem model four Multi-objective meta-heuristic algorithms have been used: NSGA-II, MOPSO, PESA-II and MALO. In addition, the simulation method is used to estimate the first objective function of the problem.

A Systematic Review of Sustainable Supply Chain Network Design: Optimization Approaches and Research Trends

In response to the ever-increasing pursuit of competitiveness among organizations in today’s global business landscape, the subject of supply chain management has become a vital domain encompassing a wide range of sectors and industries across the economy. The growing concern about sustainable development has prompted public and private supply chain players to incorporate the three pillars of sustainability, namely, economic, environmental, and social, into the design of their supply chain networks. This study reviews and examines the content of 102 relevant papers to discuss the mathematical models, modeling approaches, and solutions that have been explored in the existing literature on forward sustainable supply chain network design. This paper also investigates the sustainability elements and supply chain network peculiarities including design factors and decision levels. In this review, several limitations in the current literature on sustainable supply chain network design optimization models are highlighted. According to the analysis, it was found that a better understanding of the industry and its sustainability requirements and priorities is essential for designing sustainable supply chain networks that are tailored to the needs of a specific industry rather than achieving general sustainability objectives. In addition, integrating strategic, tactical, and operational decision levels in the design of supply chain networks is critical for evaluating their impact on each other in terms of sustainability. More sophisticated mathematical solution methods for dealing with real-life scenarios including nonlinearity and uncertainty sources are required. The paper concludes with new prospects of research to promote a better integration of sustainability into supply chain networks.

Cognitive Improvement in Thermodynamic Functions With Calculus Chain Rule

This research was motivated by the low ability of students to apply mathematical solution methods to thermodynamic functions. Thermodynamic functions are functions that consist of pressure, temperature, volume and enthalpy functions where changes in one function can occur due to changes in other functions. The aim of this research was to show the implementation of chain rules in thermodynamic function problems by relying on a process technique to improve students' cognitive awareness of thermodynamic functions. The place of this research was at the TD Pardede Institute of Science and Technology. The process of understanding chain rules is very impactful for understanding thermodynamic state functions. Differential decomposition of functions within functions is also described in the chain rule method. Thermodynamic functions which consist of pressure, temperature, volume and enthalpy functions can depend on each other so that the chain rule analysis method can be clearly used. With this method students will also be given the opportunity to connect one concept with other thermodynamic concepts. Apart from that, this method can be used anywhere. This shows a cognitive increase in terms of cognitive elements, cognitive structure and cognitive function.

Exploring Gaussian elimination based solution methods of electric systems using circuit principles

AbstractIn power system simulation, the mathematical solution methods are typically regarded as pure numerical operations, which are independent of the circuit principles. In this letter, it is demonstrated that the computational procedures in the commonly used numerical solution methods for circuit equations are essentially equivalent to the basic principles of electricity. The computational procedures of the representative Gaussian elimination based solution methods (including GE and pivoting method for sparsity of GE/LU) are comprehensively analyzed and their deep relationships with the circuit principles are revealed: the computation process of these mathematics based numerical solution methods can be completely explained using circuit principles. The interesting findings could help understand the computational process of solution methods from the circuit perspective, which may also guide the design of new circuit solution methods.

Research Progresses of Wavelet Methods and Their Applications in Mechanics

The wavelet theory shows very unique time-frequency localization and multi-resolution analysis ability in signal processing and function approximation. The wavelet basis function has excellent mathematical properties such as orthogonality, compactness, low-pass filtering and interpolation, which endows the wavelet analysis theory with great application potential in the fields of computational mathematics and computational mechanics, and creates new opportunities for breakthrough development in these fields. Since the 1990s, a large number of studies have proved that the numerical method based on the wavelet theory has very obvious advantages in solving differential equations, but at the same time, have exposed some limitations of numerical calculation application caused by the wavelet basis function itself and its unique approximation method. In order to promote the innovative application of the wavelet theory in the fields of computational mathematics and mechanics and provide researchers with a new research perspective, the development background of the wavelet analysis and the research history of methods based on the wavelet theory were reviewed, and the numerical method problems were emphasized and the research progresses made in recent years discussed. The conclusions and comments may provide a meaningful reference for the further development and improvement of quantitative mathematical solution methods based on the wavelet theory and applications in mechanics as well as solutions of a wide range of engineering problems.

Influences of Elastic Foundations and Material Gradient on the Dynamic Response of Polymer Cylindrical Pipes Patterned by Carbon Nanotube Subjected to Moving Pressures.

Composite materials are frequently used in the construction of rail, tunnels, and pipelines as well as in the construction of aircraft, ships, and chemical pipelines. When such structural elements are formed from new-generation composites, such as CNT-reinforced composites, and their interaction with the ground, there is a need to renew the dynamic response calculations under moving pressures and to create new mathematical solution methods during their design. The aim of this study was to analyze the influences of elastic foundations (EFs) and material gradient on the dynamic response of infinitely long carbon nanotube (CNT)-based polymer pipes under combined static and moving pressures. The CNT-based polymer pipes resting on the EFs were exposed to the axial and moving pressures. The uniform and heterogeneous reinforcement distributions of CNTs, which varied linearly throughout the thickness of polymer pipes, were considered. After setting the problem, the fundamental equations derived to find new analytical expressions for dynamic coefficients and critical velocity, which are dynamic characteristics of cylindrical pipes reinforced by the uniform and linear distributions of CNTs, were solved in the framework of the vibration theory. Finally, numerical computations were performed to examine the effects of EFs on the critical parameters depending on the characteristics of the pipes, the speed of moving pressures, the shape of the distribution of CNTs, and the change in volume fractions.

Interaction energy between two identical hemispherical surfaces with uniform surface charge density

Obtaining the interaction energy between two uniformly charged hemispherical surfaces in compact analytical form seems to be an impossible task to achieve under arbitrary conditions. However, we show in this work that one can obtain the interaction energy between two identical hemispherical surfaces with uniform surface charge density for the special condition of them touching each other along the ‘equator’. The mathematical solution method that we apply is remarkable in that the bulk of the treatment is analytic with the only drawback of having to rely on knowledge of certain special functions and their properties.

Mathematical Apparatus for Selection of Optimal Parameters of Technical, Technological Systems and Materials Based on Vector Optimization

We presented Mathematical apparatus of the choice of optimum parameters of technical, technological systems and materials on the basis of vector optimization. We have considered the formulation and solution of three types of tasks presented below. First, the problem of selecting the optimal parameters of technical systems depending on the functional characteristics of the system. Secondly, the problem of selecting the optimal parameters of the process depending on the technological characteristics of the process. Third, the problem of choosing the optimal structure of the material depending on the functional characteristics of this material. The statement of all problems is made in the form of vector problems of mathematical (nonlinear) programming. The theory and the principle of optimality of the solution of vector tasks it is explained in work of https://rdcu.be/bhZ8i. The implementation of the methodology is shown on a numerical example of the choice of optimum parameters of the technical, technological systems and materials. On the basis of mathematical methods of solution of vector problems we developed the software in the MATLAB system. The numerical example includes: input data (requirement specification) for modeling; transformation of mathematical models with uncertainty to the model under certainty; acceptance of an optimal solution with equivalent criteria (the solution of numerical model); acceptance of an optimal solution with the given priority of criterion.

Mathematical modeling method based on genetic algorithm and its applications

In many spheres of human activity are having challenges and amounted to an identification of the most rational solution, taking into account the prevailing conditions and limitations, that is, the optimization problem. Such areas could include not only socio-economic activities, but many of the engineering industry. To date, invited and actively used a large number of mathematical methods of solution of optimization tasks. The success of the solution of practical tasks depends on the quality and efficiency of applied mathematical methods and models. A very important consequence of mathematical modeling is to implement a synthesized model in the form of algorithms and programs for electronic computing machines. Describes a way of formalizing the various kinds of information security threats and vulnerabilities of the information system of enterprises and institutions. Because of the complexity of ensuring the protection of the information of any organized system should apply new concepts and solutions in the field of information security. One such approach is a method of genetic algorithm. For enterprises of all spheres of activity is an actual question of integrated evaluation of level of security of information systems, taking into account the quantitative and qualitative factors that characterize the components of information security.

Reduction of terms of demolition works of fully assembled residential buildings in Moscow

As of the end of 2017, in Moscow, there are 286 mapped five-story fully-assembled residential buildings of K-7, II-32, II-35, 1605-AM, 1MG-300 series with total area of 1046,7 thousand square meters. They were built at the beginning of the era of mass construction, in 1959 - 1962 years, and were distinguished by thin outer walls of lightweight ribbed expanded clay panels with unstable thermal protection properties. The technologies used in the construction of such buildings do not allow reconstructing them. Nowadays, the task of demolition of the neighborhood of five-storey houses in Moscow with the maximum possible reduction in terms of production of works and the maximum quality of work is very important. It is also necessary to ensure safe work and compliance with all sanitary standards. The order of execution of the works has a mathematical solution method. It identifies issues that arise in the alternating sections performing the process of demolition.

Comprehensive review on structure and operation of virtual power plant in electrical system

Constrained by low capacity and volatility, the rapid growth of distributed energy resources are obviously slowdown resulting in consumption difficulty and investment obstacle. As an effective integration and management technology, virtual power plant (VPP) becomes a suitable cornerstone of renewable energy future development. Based on current scientific research, this study intends to provide a detailed review of VPP from an internal perspective (e.g. energy resources' integration and operation) to the external aspect including participation in electricity market. In accordance with market diversity, different bidding strategy optimisation problems of VPP are formulated and their corresponding mathematical solution methods are literately reviewed. To extract characteristics of VPP, a comparison between energy management techniques (e.g. VPP, microgrid, active distribution network, and load aggregator) is conducted, where advantages and defects of VPP are also concluded. Meanwhile, realistic deployments of VPP in European electricity markets are elaborated to verify its feasibility and applicability. To better accommodate future development of renewable energy, a flexible structure and effective management mechanism of VPP should be built leading to its technical innovation and management reform. Possessed with the threefold development orientation, VPP will undoubtedly improve the utilisation and management of renewable energy sources as a coordinated and operational entity.

Thermodynamic Property Calculations for Equilibrium Mixtures

Modeling of chemical equilibrium is fundamental to the analysis of rocket motors. Related modeling supports performance calculations, combustion gas properties, and important interactions between reactive gases and ablative insulators. Available computer programs for providing these types of calculations were primarily developed decades ago and are known to have solution instabilities and limited capabilities. The authors have previously presented mathematical solution methods for determining compositions of systems in chemical equilibrium. Here, the methodology is extended to include calculations for thermodynamic properties. This requires certain modeling assumptions and complex calculations to determine composition derivatives. Detailed derivations are provided so that modeling assumptions and property definitions are clear, and all mathematics are presented in matrix–vector form to support program implementation using modern programming methods. This methodology has been implemented into a computer program named Chemics, and verification of this approach and implementation is presented here by demonstrating accuracy against property data for air over a wide range of temperatures and by comparing thermodynamic property calculations for the combustion products of an aluminized propellant against results using a legacy modeling program. The Chemics program provides a modern platform for equilibrium calculations, extends applicability, and improves stability over legacy programs. Continued development is underway to provide advanced implementation into rocket performance and ablation heat transfer modeling programs.

Modelling an articulated raft wave energy converter

In this paper we develop an efficient mathematical solution method for an articulated raft wave energy converter. Representative of Pelamis and the Cockerell raft design, it is comprised of a series of floating pontoons connected via hinges. Power is generated through the relative motions of adjacent elements which are excited by the incident wave as it passes along the length of the device. Using an efficient semi-analytic solution we are able to generate results more quickly than would be possible using a panel-based numerical code such as WAMIT. This allows us to explore the parameter space quickly and thus to develop an understanding as to what elements of raft-type wave energy converter design allow it to generate power so successfully. We find that the capture factor increases proportionately to the number of pontoons, a focusing effect that allows the device to absorb far more power than that which is directly incident upon its frontage. Hinge position and device proportions are also significant with results favouring long, narrow rafts made up of pontoons of increasing length from fore to aft.

A multi-objective multi-echelon green supply chain network design problem with risk-averse retailers in an uncertain environment

In this paper, the multi-objective multi-echelon supply chain network design problem is investigated. The resulted problem considers uncertainty of single product demand and the downstream risk attitude simultaneously and integrate it into the greenness concept. That is, makes the model more realistic in comparison with the others. According to the related literature study, there is no specific study to design the green supply chain network based on the risk attitude of the retailer. This paper aims to deal with this research gap by formulating robust counterpart of the main proposed uncertain problem. To do this, the conditional value at risk (CVaR) method through the data-driven approach is applied to deal with demand uncertainty to makes the model to be convex and sensitive to the risk averseness level in a robust manner. In addition, uncertainty sets approach is employed to deal with the uncertainty of other three parameters according to CO2 emission. The augmented e-constraint method is used to transform the resulted multi-objective mathematical programming problem into the single objective one, to obtain the global optimal solution through the exact mathematical solution method. Finally, the model is successfully simulated and its results are illustrated through a numerical example.

On the Equivalence between Static and Dynamic Railway Track Response and on the Euler-Bernoulli and Timoshenko Beams Analogy

The paper tries to clarify the problem of solution and interpretation of railway track dynamics equations for linear models. Set of theorems is introduced in the paper describing two types of equivalence: between static and dynamic track response under moving load and between the dynamic response of track described by both the Euler-Bernoulli and Timoshenko beams. The equivalence is clarified in terms of mathematical method of solution. It is shown that inertia element of rail equation for the Euler-Bernoulli beam and constant distributed load can be considered as a substitute axial force multiplied by second derivative of displacement. Damping properties can be treated as additional substitute load in the static case taking into account this substitute axial force. When one considers the Timoshenko beam, the substitute axial force depends additionally on shear properties of rail section, rail bending stiffness, and subgrade stiffness. It is also proved that Timoshenko beam, described by a single equation, from the point of view of solution, is an analogy of the Euler-Bernoulli beam for both constant and variable load. Certain numerical examples are presented and practical interpretation of proved theorems is shown.

An analytic solution of the static problem of inclined risers conveying fluid

We use the method of matched asymptotic expansion to develop an analytic solution to the static problem of clamped–clamped inclined risers conveying fluid. The inclined riser is modeled as an Euler–Bernoulli beam taking into account its self-weight, mid-plane stretching, an applied axial tension, and the internal fluid velocity. The solution consists of three parts: an outer solution valid away from the two boundaries and two inner solutions valid near the two ends. The three solutions are then matched and combined into a so-called composite expansion. A Newton–Raphson method is used to determine the value of the mid-plane stretching corresponding to each applied tension and internal velocity. The analytic solution is in good agreement with those obtained with other solution methods for large values of applied tensions. Therefore, it can be used to replace other mathematical solution methods that suffer numerical limitations and high computational cost.

A mathematical model of a solar air thermosyphon integrated with building envelope

A mathematical model comprising of analytical and two dimensional network procedures is proposed for predicting steady heat flow and heat transport in a solar heated thermosyphon integrated with building envelope. The detail mathematical solution method is presented for solving partial differential heat flow and transport equations by performing two dimensional energy balances at surface and air nodes through conjugate heat exchange and heat transport analysis of a solar thermosyphon. The mathematical solution procedure is devised for conduction and radiation heat exchange between surface nodes to improve the accuracy of traditional analytical solution for predicting buoyancy-induced mass flow rate of air flowing through a solar thermosyphon. The matrix inversion solution of mathematical model is unconditionally stable, with accuracy dependent on magnitude of conductance terms and number of nodes in the grid. Only Δy is chosen as aspect ratios (Δx = L, L/H and W/H) are defined by the geometry of the thermosyphon. The conduction and convection conductance terms are based on discretisation height Δy, thermal capacity conductance (mcp) is based on air-gap length Δx, whilst integrated radiation conductance terms are based on both height Δy and width Δx of the grid. The proposed model has compared the results obtained from analytical method, two dimensional network method for a single set of environmental condition with given geometry of thermosyphon. The proposed model is validated with experimental results obtained from outdoor experimental setup comprising of thermosyphon based photovoltaic solar wall system.

Bunker consumption optimization methods in shipping: A critical review and extensions

It is crucial nowadays for shipping companies to reduce bunker consumption while maintaining a certain level of shipping service in view of the high bunker price and concerned shipping emissions. After introducing the three bunker consumption optimization contexts: minimization of total operating cost, minimization of emission and collaborative mechanisms between port operators and shipping companies, this paper presents a critical and timely literature review on mathematical solution methods for bunker consumption optimization problems. Several novel bunker consumption optimization methods are subsequently proposed. The applicability, optimality, and efficiency of the existing and newly proposed methods are also analyzed. This paper provides technical guidelines and insights for researchers and practitioners dealing with the bunker consumption issues.

Decomposition of water Raman stretching band with a combination of optimization methods

In this study, an investigation of the behaviour of stretching bands of CH and OH groups of water–ethanol solutions at alcohol concentrations ranging from 0 to 96% by volume has been performed. A new approach to decomposition of the wide structureless water Raman band into spectral components based on modern mathematical methods of solution of inverse multi-parameter problems–combination of Genetic Algorithm and the method of Generalized Reduced Gradient–has been demonstrated. Application of this approach to decomposition of Raman stretching bands of water–ethanol solutions allowed obtaining new interesting results practically without a priori information. The behaviour of resolved spectral components of Raman stretching OH band in binary mixture with rising ethanol concentration is in a good agreement with the concept of clathrate-like structure of water–ethanol solutions. The results presented in this paper confirm existence of essential structural rearrangement in water–ethanol solutions at ethanol concentrations 20–30% by volume.

Photothermal microscopy: a step from thermal wave visualization to spatially localized thermal analysis

The calculation of photothermal response detected by a photothermal microscope is presented. By using a technique based on Green's functions and integral transforms, a model for laser-induced temperature distribution functions has been derived. The mathematical method for solution of inverse problem is proposed. It suggests that photothermal microscopy, besides imaging subsurface of solids, has the potential for quantitative thermal analysis of various samples.