Alternative Solution Techniques Research Articles

On a New Method of Quasi-static and Dynamic Analysis of Viscoelastic Plate on Elastic Foundation

In the present work, an alternative solution technique based on mixed finite element (MFE) formulation in the Laplace-Carson domain is proposed for quasi-static and dynamic analyses of viscoelastic plate (VEP) resting on an elastic foundation (EF). This work contributed a numerical solution to the problem of a viscoelastic Kirchhoff plate supported on a Winkler foundation. VEP-EF interaction problems are taken into account under different wave-type loadings. The viscoelastic material behavior of the plate is modeled by the Zener rheological solid model. A four-nodded linear isoparametric element containing sixteen degrees of freedom is used to model the VEP. Developed functional in the Laplace-Carson domain based on the Gâteaux differential method is transformed to the real time domain by utilizing the Dubner and Abate (D&A) inverse Laplace transform technique (ILTT). To evaluate the applicability of the results, five numerical samples are considered. Further analyzes are performed on different wave type loadings to offer a new perspective on the time-dependent behavior of VEP on EF.

Development of IoT Smart Greenhouse System for Hydroponic Gardens

This study focused on the development of a smart greenhouse system for hydroponic gardens with the adaptation of the Internet of Things and monitored through mobile as one of the solutions towards the negative effects of the worlds booming population, never ending - shrinking of arable lands, and the effect of climate change drastically in our environments. To achieve the goal of the study, the researchers created an actual hydroponic greenhouse system with completely developing plants, and automation in examining and monitoring the water pH level, light, water, and greenhouse temperature, as well as humidity which is linked to ThingSpeak. The developed SMART Greenhouse monitoring system was tested and evaluated to confirm its reliability, functions, and usability under ISO 9126 evaluation criteria. The respondents who include casual plant owners and experts in hydroponic gardening able to test and evaluate the prototype, and the mobile application to monitor the parameters with the results of 7.77 for pH level, 83 for light, 27.94 deg C for water temperature, 27 deg C for greenhouse temperature, and 75% for humidity with a descriptive result in both software and hardware as Very Good with a mean average of 4.06 which means that the developed technology is useful and recommended. The SMART Greenhouse System for Hydroponic Garden is used as an alternative tool, solution, and innovation technique towards food shortages due to climate change, land shortages, and low farming environments. The proponents highly suggest the use of solar energy for the pump power, prototype wiring should be improved, the usage of a high-end model of Arduino to address more sensors and devices for a larger arsenal of data collected, enclosures of the device to ensure safety, and mobile application updates such as bug fixes and have an e-manual of the whole systems.

Exact Inverse Operator on Field Equations

Differential equations of electromagnetic and similar physical fields are generally solved via antiderivative Green’s functions involving integration over a region and its boundary. Research on the Kasner metric reveals a variable boundary deemed inappropriate for standard anti-derivatives, suggesting the need for an alternative solution technique. In this work I derive such a solution and prove its existence, based on circulation equations in which the curl of the field is induced by source current density and possibly changes in associated fields. We present an anti-curl operator that is believed novel and we prove that it solves for the field without integration required.

Sustainable energy selection based on interval-valued intuitionistic fuzzy and neutrosophic aggregation operators

Sustainable energy selection has been a very popular problem among the researchers and various models including deterministic, probabilistic and fuzzy approaches have been developed for the solution of this problem. Fuzzy approaches to sustainable energy selection problems have been often handled in the literature. Aggregation operators for multi-expert decision making problems are an alternative solution technique for multi criteria decision making problems. Since neutrosophic and intuitionistic fuzzy aggregation operators are comparable extensions of ordinary fuzzy sets, they have been employed to aggregate multi-expert judgments. An illustrative energy selection problem is presented, solved by two approaches, and results are compared. The same linguistic data have been used for the comparison purpose.

Comparison of various solution techniques in dispatching coupled electricity‐heat system with independent thermal energy storage

Notable benefit can be brought by combined operation of coupled electricity-heat system (CEHS) and be enhanced by introducing independent thermal energy storage (ITES). With prevalent constant-flow variable temperature (CF-VT) control strategy of heat network, explicitly formulating CEHS with ITES leads to mixed-integer non-convex programming. Although the problem can be reformulated as a mixed integer second-order cone programming (MISOCP) problem and solved by commercial solvers, improving the computation efficiency still needs more effort. Here, several alternative solution techniques, based on either reformulation or approximation methods, are studied and compared with the original MISOCP formulation. The computation efficiencies as well as on the solution accuracies of various solution techniques or a combination of them are investigated and analysed based on two constructed systems. Simulation results reveal that appropriately selecting formulations of electric and heat networks can effectively improve the performance of solving the original problem.

Group-invariant solutions for one dimensional, inviscid hydrodynamics

In this paper, the results of the Lie group method carried out by Ovsiannikov are utilized to study the one-dimensional hydrodynamic equations governing compressible, inviscid fluid flow in the absence of heat conduction. One-parameter subgroups of the admissible R-parameter Lie group of point transformations of the system are applied to reduce the first-order, non-linear system of partial differential equations (PDE)s to a first-order system of ordinary differential equations (ODE)s. Closed-form solutions to the reduced ODE systems are subsequently determined using a linear velocity profile ansatz. These solutions are valid in one-dimensional (1D) planar, cylindrical and spherical geometries and are connected to solutions of the governing system of PDEs through an inverse map. The linear velocity type solutions were first considered by Sedov in 1953 and constitute a subclass of all possible similarity solutions of the compressible hydrodynamics equations. They further serve as illustrative examples of using solutions obtained for the reduced ODEs to find solutions of the associated system of PDEs. Consequently, the reduced systems of ODEs are provided in their entirety inviting additional solutions to be determined via alternative explicit or numerical solution techniques.

A New Solution Approach for Non-Linear Equation Systems with Grey Wolf Optimizer

The aim of this study is to bring a new perspective for the solutions of non-linear equation systems. So this study handles the non-linear equation systems as a constrained optimization problem, while generally is handled unconstrained optimization problem or multi objective optimization problem. The object is to minimize the sum of the squares of nonlinear equations under the nonlinear equality constraints. A recently developed heuristic optimization algorithm called Grey Wolf Optimizer (GWO) is proposed for the solution of nonlinear equation systems. Two results were obtained. Firstly, it has been seen that GWO can be an alternative solution technique for the solution of nonlinear equation systems. Secondly, modelling the systems of nonlinear equations as constrained optimization gives better results.

Dynamic optimization of constrained semi-batch processes using Pontryagin’s minimum principle—An effective quasi-Newton approach

Abstract This work considers the numerical optimization of constrained batch and semi-batch processes, for which direct as well as indirect methods exist. Direct methods are often the methods of choice, but they exhibit certain limitations related to the compromise between feasibility and computational burden. Indirect methods, such as Pontryagin’s Minimum Principle (PMP), reformulate the optimization problem. The main solution technique is the shooting method, which however often leads to convergence problems and instabilities caused by the integration of the co-state equations forward in time. This study presents an alternative indirect solution technique. Instead of integrating the states and co-states simultaneously forward in time, the proposed algorithm parameterizes the inputs, and integrates the state equations forward in time and the co-state equations backward in time, thereby leading to a gradient-based optimization approach. Constraints are handled by indirect adjoining to the Hamiltonian function, which allows meeting the active constraints explicitly at every iteration step. The performance of the solution strategy is compared to direct methods through three different case studies. The results show that the proposed PMP-based quasi-Newton strategy is effective in dealing with complicated constraints and is quite competitive computationally.

Robust Pricing of Fixed Income Securities

We analyze a dynamic investment problem with interest rate risk and ambiguity. After deriving the optimal terminal wealth and investment policy, we expand our model into a robust general equilibrium model and calibrate it to U.S. data. We confirm the bond premium puzzle, i.e., we need an unreasonably high relative risk-aversion parameter to explain excess returns on long-term bonds. Our model with robust investors reduces this risk-aversion parameter substantially: a relative risk aversion of less than four suffices to match market data. Additionally we provide a novel formulation of robust dynamic investment problems together with an alternative solution technique: the robust version of the martingale method.

Global solutions to folded concave penalized nonconvex learning

This paper is concerned with solving nonconvex learning problems with folded concave penalty. Despite that their global solutions entail desirable statistical properties, there lack optimization techniques that guarantee global optimality in a general setting. In this paper, we show that a class of nonconvex learning problems are equivalent to general quadratic programs. This equivalence facilitates us in developing mixed integer linear programming reformulations, which admit finite algorithms that find a provably global optimal solution. We refer to this reformulation-based technique as the mixed integer programming-based global optimization (MIPGO). To our knowledge, this is the first global optimization scheme with a theoretical guarantee for folded concave penalized nonconvex learning with the SCAD penalty (Fan and Li, 2001) and the MCP penalty (Zhang, 2010). Numerical results indicate a significant outperformance of MIPGO over the state-of-the-art solution scheme, local linear approximation, and other alternative solution techniques in literature in terms of solution quality.

Predictions of aneurysm formation in distensible tubes: Part A—Theoretical background to alternative approaches

Pressurised distensible tubes are subject to aneurysms. Aneurysm inception will take place at a location along the tube when a critical pressure, relative to tube wall thickness at that location, is reached. Parents will recognise the existence of critical pressure when endeavouring to inflate a party balloon. Another example of aneurysm is the thoracic aortic aneurysm corresponding to permanent dilation of the aorta in such proportions that it can be life threatening. Corrective procedures for aortic aneurysms involve the introduction of stiff materials to prevent aneurysm. Similarly in a proposed distensible tube based wave energy device aneurysm inception is partially controlled through the use of alternative longitudinal strips of inextensible material and appropriate rubber strips. Here we consider distensible tubes made of one material.Having reviewed the aneurysm based literature some inconsistencies were observed between the material properties used in a non-linear finite element analysis and the material properties of the specimen used to provide experimental measurements for comparison. To appreciate the inconsistencies the authors decided to investigate aneurysm development using both non-linear finite element analyses and distinct alternative formulations and solution techniques. Rather than restrict strain-energy function to a subset of Neo-Hookean, Mooney–Rivlin and Ogden forms, the authors have implemented several alternative strain-energy models in parallel, also exploring for the first time the impact of using different combinations of uniaxial, equi-biaxial and pure shear experimental data for different rubbers.This paper addresses the needs (necessary considerations, such as the Valanis–Landel hypothesis, Maxwell equal area rule and data selection criteria) for a realistic approach to modelling a distensible tube to provide predictions of critical pressure. In common with all other cited references a static analysis is used.

Resource-Driven Mission-Phasing Techniques for Constrained Agents in Stochastic Environments

Because an agent's resources dictate what actions it can possibly take, it should plan which resources it holds over time carefully, considering its inherent limitations (such as power or payload restrictions), the competing needs of other agents for the same resources, and the stochastic nature of the environment. Such agents can, in general, achieve more of their objectives if they can use --- and even create --- opportunities to change which resources they hold at various times. Driven by resource constraints, the agents could break their overall missions into an optimal series of phases, optimally reconfiguring their resources at each phase, and optimally using their assigned resources in each phase, given their knowledge of the stochastic environment. In this paper, we formally define and analyze this constrained, sequential optimization problem in both the single-agent and multi-agent contexts. We present a family of mixed integer linear programming (MILP) formulations of this problem that can optimally create phases (when phases are not predefined) accounting for costs and limitations in phase creation. Because our formulations multaneously also find the optimal allocations of resources at each phase and the optimal policies for using the allocated resources at each phase, they exploit structure across these coupled problems. This allows them to find solutions significantly faster(orders of magnitude faster in larger problems) than alternative solution techniques, as we demonstrate empirically.

Analytical heat diffusion models for heat sinks with circular micro-channels

This study explores the prediction of temperature distribution in a heat sink containing an array of circular micro-channels, which is found mostly in electronic cooling applications. The analytical heat diffusion models for most common micro-channel shapes are based on one-dimensional fin models with varying degrees of complexity. Because of a singularity in the governing one-dimensional heat diffusion equation for a fin with circular profile, no exact solution is possible for the circular heat sink geometry. In this paper, an alternative analytical power series solution technique is presented in which the differential equation is recast in polynomial form. Predictions of the power series solution are validated for different channel diameters and spacings and both one-sided and two-sided heating conditions using one-dimensional and two-dimensional numerical simulations. Overall, maximum percent differences in temperature and heat transfer rate between the analytical and two-dimensional numerical results of 0.23% and 1.33%, respectively, prove that the present analytical models are very accurate and effective tools for the design and thermal resistance prediction of micro-channel heat sinks found in electronic cooling applications.

An alternative simple solution algorithm of an inventory model with fixed and variable lead time crash costs under unknown demand distribution

Inventory models with controllable lead time both for known and unknown demand distributions have been proposed in the literature. A model is useless unless it is formulated correctly and feasible. A simple solution procedure of a model also plays an important role in its application. This article highlights an erroneous formulation of an inventory model developed with fixed and variable lead time crash costs under unknown demand distribution, and also demonstrates its infeasibility. To attain feasibility we extend the model to include a constraint. Then, we present an alternative simple solution technique of the modified model and carry out a comparative study on a numerical example to show its potential significance.

Forecasting the transport energy demand based on PLSR method in China

Abstract Transportation sector accounts for a major share of energy consumption in China, especially the petroleum products, which experienced rapid increases in energy demand. The purpose of this study is to forecast transport energy demand for 2010, 2015 and 2020 based on partial least square regression (PLSR) method under two scenarios. Transport energy demand is analyzed for the period of 1990–2006 based on gross domestic product (GDP), urbanization rate, passenger-turnover and freight-turnover. This method suggests that transport energy demand for 2020 will reach to a level of around 433.13 Mtce and 468.26 Mtce, respectively. Those figures are very close to the estimation obtained by Energy Research Institute of China. Thus this study provides an effective tool, which can be used as an alternative solution and estimation techniques for the transport energy demand.

An alternative optimal solution technique for a single-vendor single-buyer integrated production inventory model

For the single-vendor single-buyer integrated production inventory problem, the lot is transferred by some researchers in shipments of equal and/or unequal sizes. For a given total number (n) of shipments, the minimal number (m) of unequal sized shipments is selected satisfying a constraint. Due to the complex dependence of m on n, there remained a conjecture about the convexity of the total cost (C) in n. Consequently, for a known n, lower and upper bounds on the minimal total cost are imposed and this cost is obtained through a search over n based on the convexity of C in the lot size (Q). Here it is demonstrated that m thus selected might not be the minimal and a method for obtaining the minimal m is developed. A formula for the minimal n based on the convexity of C in n (given m and Q) is also derived. Integrating the ways of finding the minimal m and n, along with the convexity of C in Q, an alternative minimal cost solution technique is presented. Finally, a comparative theoretical analysis of the methods along with numerical illustration is carried out to show the efficiency of our method.

An alternative heuristic solution technique for efficient management of the serial supply chain

The serial supply chain management has received considerable attention in the literature. A few years back, the literature had been enriched by the presentation of serial supply chain models, both for single and sequence dependent multicomponent supply chain management, and their heuristic solution procedures. This paper demonstrates that the sequencing rule applied to select the appropriate sequence of products in determining minimal total cost does not meet the purpose. In addition, it finds that though the author presented generalised models, the solution procedures are restricted to a particular case. In this paper, the models are reorganised and alternative generalised heuristic solution procedures are presented so that they can never be worse than the original one. Then, we carry out a comparative study of our methods with the original ones on two numerical problems (illustrated in the original paper) to show cost reductions with reduced cycle times by our method.

Single-Step Solid-State Synthesis of CeMgAl11O19:Tb Phosphor

The green-emitting CeMgAl 1 O 19 :Tb (CMAT) phosphor has been prepared at 1200 °C by the simple solid-state reaction using AlF 3 as a self-flux. This preparation temperature is much lower than those (1500-1700 °C) for conventional solid-state reaction and spray pyrolysis method. In particular, the complete process to produce high-quality phosphor particles was carried out through the single-step heat treatment of the mixture of corresponding oxide-type metal sources. An addition of A1F 3 as a self-flux significantly decreased the crystallization temperature of CMAT with plate-like shape. The particle morphology could be controlled from plate-like to spherical by using H 3 BO 3 as an additional flux. Thus, an optimal morphology and luminescence characteristics of CMAT were achieved when both AlF 3 and H 3 BO 3 fluxes were simultaneously used. Compared with conventional solid-state process, which is accompanied by the calcination step(s), and other alternative liquid solution techniques such as sol-gel method and spray pyrolysis, no use of active precursors and liquid media that are harmful to the environment is a distinctive advantage for the industrial purpose.

Modeling and Application of Genetic Algorithm (GA) Approach to Estimating the Future Total Energy Input Values

This study deals with the modeling and developing the energy input estimation equations in order to estimate the future projections based on genetic algorithm (GA) notion. In this regard, the GA future prediction of total energy input estimation model (GAFPTEIEM) is used to better estimate the future energy input demand based on the economic and social indicators of gross domestic product (GDP), population, import, export, house production, cement production, and basic house appliances consumption figures. The models proposed here can be used as an alternative solution and estimation techniques to available estimation techniques. It is also expected that this study will be helpful in developing highly applicable and productive planning for energy policies.

A flexible statistical and efficient computational approach to object location applied to electrical tomography

In electrical tomography, multiple measurements of voltage are taken between electrodes on the boundary of a region with the aim of investigating the electrical conductivity distribution within the region. The relationship between conductivity and voltage is governed by an elliptic partial differential equation derived from Maxwell's equations. Recent statistical approaches, combining Bayesian methods with Markov chain Monte Carlo (MCMC) algorithms, allow to greater flexibility than classical inverse solution approaches and require only the calculation of voltages from a conductivity distribution. However, solution of this forward problem still requires the use of the Finite Difference Method (FDM) or the Finite Element Method (FEM) and many thousands of forward solutions are needed which strains practical feasibility. Many tomographic applications involve locating the perimeter of some homogeneous conductivity objects embedded in a homogeneous background. It is possible to exploit this type of structure using the Boundary Element Method (BEM) to provide a computationally efficient alternative forward solution technique. A geometric model is then used to define the region boundary, with priors on boundary smoothness and on the range of feasible conductivity values. This paper investigates the use of a BEM/MCMC approach for electrical resistance tomography (ERT) data. The efficiency of the boundary-element method coupled with the flexibility of the MCMC technique gives a promising new approach to object identification in electrical tomography. Simulated ERT data are used to illustrate the procedures.