Solving Procedure Research Articles

Uncertain dynamical system-based decision making with application to production-inventory problems

• Firstly introduce uncertainty theory into constrained production-inventory problem. • A critical value model of uncertain optimal control is constructed for the problem. • A solving procedure for handling uncertain model is proposed. • The behavior of the value function is characterized. Uncertainty theory is a new methodology to describe subjective indeterminacy. This paper discusses an infinite-horizon production-inventory problem with constraints that the production rates shall be restricted to an appropriate interval, and the indeterminacy of the decision system is extracted and analyzed through uncertainty theory. To solve such a problem, an uncertain linear quadratic control model is investigated with a critical value criterion. Applying the equation of optimality, it is shown that an optimal feedback control exists. In addition, the behavior of the value function that is characterized benefits from numerical illustrations. Furthermore, we compare these optimal solutions with the solutions of an unconstrained problem. Then some economic interpretations are provided to reveal the significance of the model to practical applications.

A flexible programming approach based on intuitionistic fuzzy optimization and geometric programming for solving multi-objective nonlinear programming problems

In this paper, a novel method is proposed to support the process of solving multi-objective nonlinear programming problems subject to strict or flexible constraints. This method assumes that the practical problems are expressed in the form of geometric programming problems. Integrating the concept of intuitionistic fuzzy sets into the solving procedure, a rich structure is provided which can include the inevitable uncertainties into the model regarding different objectives and constraints. Another important feature of the proposed method is that it continuously interacts with the decision maker. Thus, the decision maker could learn about the problem, thereby a compromise solution satisfying his/hers preferences could be obtained. Further, a new two-step geometric programming approach is introduced to determine Pareto-optimal compromise solutions for the problems defined during different iterative steps. Employing the compensatory operator of “weighted geometric mean”, the first step concentrates on finding an intuitionistic fuzzy efficient compromise solution. In the cases where one or more intuitionistic fuzzy objectives are fully achieved, a second geometric programming model is developed to improve the resulting compromise solution. Otherwise, it is concluded that the resulting solution vectors simultaneously satisfy both of the conditions of intuitionistic fuzzy efficiency and Pareto-optimality. The models forming the proposed solving method are developed in a way such that, the posynomiality of the defined problem is not affected. This property is of great importance when solving nonlinear programming problems. A numerical example of multi-objective nonlinear programming problem is also used to provide a better understanding of the proposed solving method.

An interface approach based on moving mesh and cohesive modeling in Z-pinned composite laminates

Abstract An FE approach based Arbitrary Lagrangian-Eulerian (ALE) and cohesive fracture mechanics is implemented to investigate the effects of debonding mechanisms on the behavior of z-pinned composite laminates. The model is based on the combination of moving and discrete cohesive interface elements, which allow the simulation of interfacial damage or strengthening mechanisms produced by debonding phenomena or z-pinned techniques, respectively. Moreover, complex phenomena such as crack initiation, coalescence mechanisms are easily implemented in both static and dynamic frameworks. Despite existing approaches, available from the literature, the computational procedure is able to overcome difficulties concerning mesh dependence of the solution, numerical complexities and costs involved in the solving procedure. The numerical implementation of the model and its capability to predict debonding mechanisms are discussed with respect different laminate configurations and onset conditions. Moreover, comparisons with existing experimental results available from the literature are developed to investigate the relationship between strengthened and unstrengthened composite laminates.

Calculation of Multiphase Chemical Equilibrium by the Modified RAND Method

A robust and efficient algorithm for simultaneous chemical and phase equilibrium calculations is proposed. It combines two individual nonstoichiometric solving procedures: a nested-loop method with successive substitution for the first steps and final convergence with the second-order modified RAND method. The modified RAND extends the classical RAND method from single-phase chemical reaction equilibrium of ideal systems to multiphase chemical equilibrium of nonideal systems. All components in all phases are treated in the same manner and the system Gibbs energy can be used to monitor convergence. This is the first time that modified RAND was applied to multiphase chemical equilibrium systems. The combined algorithm was tested using nine examples covering vapor–liquid (VLE) and vapor–liquid–liquid equilibria (VLLE) of ideal and nonideal reaction systems. Successive substitution provided good initial estimates for the accelerated computation with modified RAND, to ultimately converge to the equilibrium sol...

The numerical investigation of angle of attack of inclined rectangular rib on the turbulent heat transfer of Water-Al2O3 nanofluid in a tube

In present research, the flow and heat transfer characteristics of the turbulent flow in the tube have been numerically investigated. The main purpose of this study is investigating the effect of attack angle of ribs and Al2O3 nanoparticle on the heat transfer enhancement. The flow has been simulated in Reynolds numbers of 24000, 36000, 48000 and 60000 in volume fractions of 0, 2 and 4% of nanoparticles. In present study, in order to ensure from the accuracy of numerical solving procedure, the obtained results have been compared with others empirical and numerical results and proper coincidence has been obtained. The mean Nusselt number, pressure drop and performance coefficient are presented results. In addition to the mentioned quantitative results, in order to investigate of physics of flow, the stream lines, are also presented. The obtained results demonstrate that, the existence of ribs with the creation of eddy on the direction of flow causes better mixture of flow and consequently, heat transfer increases and adding nanoparticles to the base flow causes more augment of heat transfer. According to the obtained results, in order to improve the heat transfer without considering the applied pressure drop, using rib with angle of attack 90° inside the tube is suggested. However, the investigation of fluid- thermal performance coefficient indicates that, the ratio of heat transfer enhancement to the applied pressure drop in the rib with attack angle of 60° is maximum.

An automated procedure for the generation and conformal discretization of 3D woven composites RVEs

A generation tool is developed for complex three dimensional textile reinforced composites Representative Volume Elements (RVEs). This integrated methodology takes into account contact conditions between yarns with polygonal convex cross sections by means of an iterative geometry generation scheme. The tensioning of the yarns is applied in an implicit geometrical manner resulting in their movement leading to contacts between them. The non-circular shape of their cross sections requires the use of a rotational degree of freedom to describe their movement. This rotational degree of freedom is managed during the contact solving procedure. A level set-based post-processing is then used at the end of RVE the generation to automatically supress any residual interpenetration, that further enables controlling the volume fraction (Vyarn) of each family of yarns in the RVE. A thin clearance can also be inserted between yarns during the post processing phase in order to ease the subsequent conforming mesh generation. An implicit geometry-based meshing procedure is subsequently used to produce a high quality discretization of the obtained RVEs. This integrated procedure is used for various woven and 3D RVEs to illustrate its versatility, showing that the discretized RVEs can be used for parametric studies based on computational homogenisation.

A generalized solution procedure for in-plane free vibration of rectangular plates and annular sectorial plates.

A generalized solution procedure is developed for in-plane free vibration of rectangular and annular sectorial plates with general boundary conditions. For the annular sectorial plate, the introduction of a logarithmic radial variable simplifies the basic theory and the expression of the total energy. The coordinates, geometric parameters and potential energy for the two different shapes are organized in a unified framework such that a generalized solving procedure becomes feasible. By using the improved Fourier–Ritz approach, the admissible functions are formulated in trigonometric form, which allows the explicit assembly of global mass and stiffness matrices for both rectangular and annular sectorial plates, thereby making the method computationally effective, especially when analysing annular sectorial plates. Moreover, the improved Fourier expansion eliminates the potential discontinuity of the original normal and tangential displacement functions and their derivatives in the entire domain, and accelerates the convergence. The generalized Fourier–Ritz approach for both shapes has the characteristics of generality, accuracy and efficiency. These features are demonstrated via a few numerical examples.

Proces sušenja oraha

U ovom radu analiziran je postupak tretmana oraha koji se izlažu sušenju. Sugerisani su dijagrami tokova, kako za ceo proces koji uključuje i pripremne operacije, tako i za numeričku analizu posmatranog problema, koja je neophodna da bi se dobili preliminarni rezultati matematičkog modela procesa sušenja oraha. Detaljnije je objašnjena numerička strategija, kao i različiti metodi sušenja i skladištenja. Ovakva analiza problema pruža uopštenu sliku procesa sušenja, što može da omogući bolji uvid u partikularne probleme i pouzdanije planiranje procesa.

Design of energy-Efficient timetables in two-way railway rapid transit lines

A methodology to design energy-efficient timetables in Rapid Railway Transit Networks is presented. Using an empirical description of the train energy consumption as a function of running times, the timetable design problem is modelled as a Mixed Integer Non-Linear optimization problem (MINLP) for a complete two-way line. In doing so, all the services in both directions along a certain planning horizon are considered while attending a known passengers’ demand. The MINLP formulation, which depends on train loads, is fully linearised supposing train loads are fixed. A sequential Mixed Integer Linear solving procedure is then used to solve the timetabling optimization problem with unknown train loads. The proposed methodology emphasizes the need of considering all the services running during the planning horizon when designing energy-efficient timetables, as consequence of the relationship among train speeds, frequency and fleet size of each line. Moreover, the convenience of considering the energy consumption as part of a broad objective function that includes other relevant costs is pointed out. Otherwise, passengers and operators could face up to an increase in the whole cost and a decrease in the quality of service. A real data scenario, based on the C-2 Line of the Madrid Metropolitan Railways, is used to illustrate the proposed methodology and to discuss the differences between the energy-efficient solutions and those obtained when considering operation and acquisition costs.

Beyond court digitalization with ODR

“I felt so sorry for you, such a lovely tool, and then you have no users!” This was one of the comments after my presentation of the eKantonrechter at ODR2016, organized by HIIL in the Hague in May 2016. ODR, online dispute resolution, was presented as a tool to solve all problems in the 4th Trend Report by HIIL after the conference. A weblog, however, commented that ODR had raised hopes in its early promoters, but had not really taken off. ODR is a tool to help parties in de dispute resolve their problem. There are various examples of ODR tool: supporting double blind bidding to determine a sum of money, working out divorce settlements, negotiating a solution and taking a case to court. Interesting research questions abound in the area of ODR and its users: What paths do people take when trying to resolve a problem? How can people have ownership of their court procedure? How can solutions, ODR and court procedures, best be tailored to the type of problem? The article describes the development of the e-Kantonrechter, a digital small claims procedure, as an example. ODR and its users is a field in which law and society researchers can effectively contribute to improving digital problem solving and dispute resolution procedures in court.

Uncertain Optimal Control Approach for CO2 Mitigation Problem

AbstractThe new types of uncertain control approaches based on the critical value criterion and chance criterion are respectively introduced to deal with multi‐stage dynamic optimization problems in the presence of target constraints. Integrating the method of dynamic programming with the viability approach, the solving procedure of the optimal control sequence is provided. As a case study, a cost‐effectiveness problem of mitigation policies for uncertain carbon dioxide emissions is analyzed and numerically computed to illustrate the proposed approaches.

The impact of particular components of the PSO-based algorithm solving the Dynamic Vehicle Routing Problem

This paper presents and analyzes a Two-Phase Multi-Swarm Particle Swarm Optimizer (2MPSO) solving the Dynamic Vehicle Routing Problem (DVRP). The research presented in this paper focuses on finding a configuration of several optimization improvement techniques, dedicated to solving dynamic optimization problems, within the 2MPSO framework. Techniques, whose impact on results achieved for DVRP is analyzed, include: solving the current state of a problem with a capacitated clustering and routing heuristic algorithms, solving requests-to-vehicles assignment by the PSO algorithm, route optimization by a separate instance of the PSO algorithm, and knowledge transfer between subsequent states of the problem. The results obtained by the best chosen configuration of the 2MPSO are compared with the state-of-the-art literature results on a popular set of benchmark instances.Our study shows that strong results achieved by 2MPSO should be attributed to three factors: generating initial solutions with a clustering heuristic, optimizing the requests-to-vehicle assignment with a metaheuristic approach, direct passing of solutions obtained in the previous stage (times step) of the problem solving procedure to the next stage. Additionally, 2MPSO outperforms the average results obtained by other algorithms presented in the literature, both in the time limited experiments, as well as those restricted by the number of fitness function evaluations.

Mental arithmetic in the bilingual brain: Language matters

How do bilinguals solve arithmetic problems in each of their languages? We investigated this question by exploring the neural substrates of mental arithmetic in bilinguals. Critically, our population was composed of a homogeneous group of adults who were fluent in both of their instruction languages (i.e., German as first instruction language and French as second instruction language). Twenty bilinguals were scanned with fMRI (3T) while performing mental arithmetic. Both simple and complex problems were presented to disentangle memory retrieval occuring in very simple problems from arithmetic computation occuring in more complex problems. In simple additions, the left temporal regions were more activated in German than in French, whereas no brain regions showed additional activity in the reverse constrast. Complex additions revealed the reverse pattern, since the activations of regions for French surpassed the same computations in German and the extra regions were located predominantly in occipital regions. Our results thus highlight that highly proficient bilinguals rely on differential activation patterns to solve simple and complex additions in each of their languages, suggesting different solving procedures. The present study confirms the critical role of language in arithmetic problem solving and provides novel insights into how highly proficient bilinguals solve arithmetic problems.

A nonlinear magnetic circuit model for periodic eddy current problems using T,ϕ-ϕ formulation

PurposeA transformer model is used as a benchmark for testing various methods to solve 3D nonlinear periodic eddy current problems. This paper aims to set up a nonlinear magnetic circuit problem to assess the solving procedure of the nonlinear equation system for determining the influence of various special techniques on the convergence of nonlinear iterations and hence the computational time.Design/methodology/approachUsing the T,ϕ-ϕ formulation and the harmonic balance fixed-point approach, two techniques are investigated: the so-called “separate method” and the “combined method” for solving the equation system. When using the finite element method (FEM), the elapsed time for solving a problem is dominated by the conjugate gradient (CG) iteration process. The motivation for treating the equations of the voltage excitations separately from the rest of the equation system is to achieve a better-conditioned matrix system to determine the field quantities and hence a faster convergence of the CG process.FindingsIn fact, both methods are suitable for nonlinear computation, and for comparing the final results, the methods are equally good. Applying the combined method, the number of iterations to be executed to achieve a meaningful result is considerably less than using the separated method.Originality/valueTo facilitate a quick analysis, a simplified magnetic circuit model of the 3D problem was generated to assess how the different ways of solutions will affect the full 3D solving process. This investigation of a simple magnetic circuit problem to evaluate the benefits of computational methods provides the basis for considering this formulation in a 3D-FEM code for further investigation.

Generalized Primitive Stamps for Nonlinear Circuit-Field Coupling in the Transient Case

The simultaneous solution of circuit and field equations is often required in the analysis of magnetic devices. Although schemes for the solution of this coupled problem have been proposed, the existing formulations are usually tied to specific time discretization or nonlinear iteration expressions and therefore lack generality. In this paper, a highly systematized approach is proposed for strong circuit-field coupling in a transient finite element context, by identifying primitive stamps for field elements, circuit elements, and circuit-field couplings. The filamentary and solid conductors of the field model are the key elements for systematic interconnection using generalized stamps and modified nodal analysis. As a result, the coupling equations are treated just as any other circuit element, simplifying the implementation and providing a unified framework for circuit-field analysis. Both circuit and field stamps are independent of the time discretization and nonlinear solving procedure. With the proposed scheme, the finite element equations can be linked to circuits of arbitrary topology. The theory is developed for the axisymmetric and Cartesian 2-D cases and several examples are then solved to show the effectiveness of our new approach. Solutions are compared with those produced by well-known and validated commercial software packages which implement different, proprietary, and/or undisclosed circuit-field coupling methods.

Nonlocal size dependency in nonlinear instability of axially loaded exponential shear deformable FG-CNT reinforced nanoshells under heat conduction

The present study deals with size-dependent nonlinear instability characteristics of functionally graded carbon nanotube (FG-CNT) reinforced composite shells at nanoscale subjected to axial compression combined with through-thickness heat conduction. To take size dependency into account, Eringen’s nonlocal continuum elasticity is incorporated to a novel shear deformation shell theory including a refined exponential distribution for transverse shear strain. In addition to the uniform distribution (UD) of CNT reinforcements, three FG patterns are also considered, namely FG-A, FG-V and FG-X. Also, on the basis of polynomial series, the temperature variation due to the through-thickness heat conduction is estimated. Via a perturbation-based boundary layer-type solving procedure, explicit expressions for nonlocal equilibrium curves are proposed relevant to the prebuckling and postbuckling regimes of FG-CNT exponential shear deformable nanoshells with temperature-dependent and temperature-independent material properties. It is observed that by taking the nonlocality size effect into consideration, the influence of the through-thickness heat conduction on the nonlinear axial instability response of FG-CNT reinforced nanoshells becomes more significant.

Approximate solutions of time and time-space fractional wave equations with variable coefficients

We consider the Cauchy problem for fractional evolution equations with time fractional derivative as Caputo fractional derivative of order and space variable coefficients on an unbounded domain. The space derivatives that appear in the equations are of integer or fractional order such as the left and the right Liouville fractional derivative as well as the Riesz fractional derivative. In order to solve this problem we introduce and develop generalized uniformly continuous solution operators and use them to obtain the unique solution on a certain Colombeau space. In our solving procedure, instead of the originate problem we solve a certain approximate problem, but therefore we also prove that the solutions of these two problems are associated. At the end, we illustrate the applications of the developed theory by giving some appropriate examples.

Thermodynamic analysis and optimization of a gas turbine and cascade CO2 combined cycle

This paper describes a novel gas turbine and cascade CO2 combined cycle which composes of a gas turbine, a supercritical CO2 Brayton cycle and a transcritical CO2 cycle. To show its thermodynamic potential, a new solving procedure for performance evaluation and optimization of this combined cycle was proposed. Genetic algorithm (GA) was introduced for parameter optimization in order to get better combined cycle performance. Simulation results showed that the GT-cascade CO2 combined cycle did have better thermodynamic performance than conventional GT-steam Rankine combined cycles. And this GT-cascade CO2 combined cycle could have an efficiency increase of more than 17.03% from singe gas turbine cycles. Moreover, this combined configuration could be applied to gas turbines of different power levels. Through GA optimization, the thermal efficiency could achieve 52.53% for the Taurus 60 GT-cascade CO2 combined cycle. Sensitivity simulation results indicated that the proposed cascade CO2 cycle was favorable to counteract the influence of ambient temperature on the combined cycle performance.

A stochastic programming approach to integrated water supply and wastewater collection network design problem

In this paper, a mixed scenario-based and probabilistic two-stage stochastic programming model is proposed for the design of integrated water supply and wastewater collection systems. None of the existing models simultaneously takes into account both business-as-usual and hazard uncertainties. To explore suitable solutions in a reasonable time, a solving procedure comprised of the (1) sample average approximation method, (2) Bezdek fuzzy clustering method and (3) Benders decomposition algorithm is developed. In order to expedite the convergence of the applied Benders decomposition algorithm, different acceleration techniques especially the local branching method are utilized. The performance of the proposed mathematical model and solution procedure is analyzed computationally through a real case study which the results show the usefulness of the developed stochastic programming model as well as the efficiency of the solution approach.

Kinematic accuracy and dynamic performance of a simple planar space deployable mechanism with joint clearance considering parameter uncertainty

Joint clearance and the uncertainty of geometric and physical parameters significantly influence the kinematic accuracy and dynamic response of space deployable mechanisms. Such mechanisms have been widely employed in astronautic missions to improve the capabilities of launchers. This paper proposes a methodology to investigate the kinematic accuracy and dynamic performance of space deployable mechanism with joint clearance while considering parameter uncertainty. The model of space deployable mechanism with a planar revolute joint is provided. With consideration of several uncertain parameters, the solving procedure of the dynamic equations is presented based on the Monte Carlo method. A case study is conducted to reveal the effect of parameter uncertainty on its kinematic accuracy and dynamic performance. The results indicate that parameter uncertainty should be considered to accurately evaluate the performance of long-term operating space deployable mechanisms, especially for such systems with clearance joints. According to the results, brief suggestions for design and evaluation of the mechanisms are provided.