Economic, environmental and mixed objective functions in non-linear process optimization using simulated annealing and tabu search

Screening of topologies developed by hierarchical heuristic procedures can be carried out by comparing their optimal performance. In this work we will be exploiting mono-objective process optimization using two algorithms, simulated annealing and tabu search, and four different objective functions: two of the net present value type, one of them including environmental costs and two of the global potential impact type. The hydrodealkylation of toluene to produce benzene was used as case study, considering five topologies with different complexities mainly obtained by including or not liquid recycling and heat integration. The performance of the algorithms together with the objective functions was observed, analyzed and discussed from various perspectives: average deviation of results for each algorithm, capacity for producing high purity product, screening of topologies, objective functions robustness in screening of topologies, trade-offs between economic and environmental type objective functions and variability of optimum solutions.

An introduction to the fractional continuous-time linear systems

A brief introduction to the fractional continuous-time linear systems is presented. It will be done without needing a deep study of the fractional derivatives. We will show that the computation of the impulse and step responses is very similar to the classic. The main difference lies in the substitution of the exponential by the Mittag-Leffler function. We will present also the main formulae defining the fractional derivatives.

Optimal tuning of fractional controllers using genetic algorithms

This study addresses the optimization of fractional algorithms for the discrete-time control of linear and non-linear systems. The paper starts by analyzing the fundamentals of fractional control systems and genetic algorithms. In a second phase the paper evaluates the problem in an optimization perspective. The results demonstrate the feasibility of the evolutionary strategy and the adaptability to distinct types of systems.

Combining global tabu search with local search for solving systems of equalities and inequalities

This papers aims at providing a combined strategy for solving systems of equalities and inequalities. The combined strategy uses two types of steps: a global search step and a local search step. The global step relies on a tabu search heuristic and the local step uses a deterministic search known as Hooke and Jeeves. The choice of step, at each iteration, is based on the level of reduction of the l2-norm of the error function observed in the equivalent system of equations, compared with the previous iteration.

An introduction to the fractional continuous- time linear systems: the 21st century systems

IEEE CIRCUITS AND SYSTEMS MAGAZINE, Third Quarter

On the initial conditions in continuous-time fractional linear systems

Signal Processing, Vol. 83, nº 11

Design of New Materials for Passive Vibration Control

The aim of this contribution is to extend the techniques of composite materials design to non-linear material behaviour and apply it for design of new materials for passive vibration control. As a first step a computational tool allowing determination of macroscopic optimized one-dimensional isolator behaviour was developed. Voigt, Maxwell, standard and more complex material models can be implemented. Objective function considers minimization of the initial reaction and/or displacement peak as well as minimization of the steady-state amplitude of reaction and/or displacement. The complex stiffness approach is used to formulate the governing equations in an efficient way. Material stiffness parameters are assumed as non-linear functions of the displacement. The numerical solution is performed in the complex space. The steady-state solution in the complex space is obtained by an iterative process based on the shooting method which imposes the conditions of periodicity with respect to the known value of the period. Extension of the shooting method to the complex space is presented and verified. Non-linear behaviour of material parameters is then optimized by generic probabilistic meta-algorithm, simulated annealing. Dependence of the global optimum on several combinations of leading parameters of the simulated annealing procedure, like neighbourhood definition and annealing schedule, is also studied and analyzed. Procedure is programmed in MATLAB environment.

Modeling Vegetable Fractals by means of Fractional-order Equations

This paper characterizes four ‘fractal vegetables’: (i) cauliflower (brassica oleracea var. Botrytis); (ii) broccoli (brassica oleracea var. italica); (iii) round cabbage (brassica oleracea var. capitata) and (iv) Brussels sprout (brassica oleracea var. gemmifera), by means of electrical impedance spectroscopy and fractional calculus tools. Experimental data is approximated using fractional-order models and the corresponding parameters are determined with a genetic algorithm. The Havriliak-Negami five-parameter model fits well into the data, demonstrating that classical formulae can constitute simple and reliable models to characterize biological structures.

A Review of Operational Matrices and Spectral Techniques for Fractional Calculus

Recently, operational matrices were adapted for solving several kinds of fractional differential equations (FDEs). The use of numerical techniques in conjunction with operational matrices of some orthogonal polynomials, for the solution of FDEs on finite and infinite intervals, produced highly accurate solutions for such equations. This article discusses spectral techniques based on operational matrices of fractional derivatives and integrals for solving several kinds of linear and nonlinear FDEs. More precisely, we present the operational matrices of fractional derivatives and integrals, for several polynomials on bounded domains, such as the Legendre, Chebyshev, Jacobi and Bernstein polynomials, and we use them with different spectral techniques for solving the aforementioned equations on bounded domains. The operational matrices of fractional derivatives and integrals are also presented for orthogonal Laguerre and modified generalized Laguerre polynomials, and their use with numerical techniques for solving FDEs on a semi-infinite interval is discussed. Several examples are presented to illustrate the numerical and theoretical properties of various spectral techniques for solving FDEs on finite and semi-infinite intervals.

System Modeling and Control Through Fractional-Order Algorithms

The theory of fractional calculus goes back to the beginning of thr throry of differential calculus but its inherent complexity postponed the applications of the associated concepts. In the last decade the progress in the areas of chaos and fractals revealed subtle relationships with the fractional calculus leading to an increasing interest in the development of the new paradigm. In the area of automaticcontrol preliminary work has already been carried out but the proposed algorithms are restricted to the frequency domain. The paper discusses the design of fractional-order discrete-time controllers. The algorithms studied adopt the time domein, which makes them suited for z-transform analusis and discrete-time implementation. The performance of discrete-time fractional-order controllers with linear and non-linear systems is also investigated.

Malaria outbreaks in a non-endemic area of Brazil, 2005

In March 2005, a resident of the municipality of Monte Alegre de Minas, State of Minas Gerais, without any history of traveling to endemic areas for malaria, was diagnosed with Plasmodium vivax infection and local mosquito-borne transmission was suspected. The epidemiological investigation identified another 10 cases with local transmission and all of them were related to the imported malaria case that was detected in this region. The potential exposure site was the banks of the river Tejuco, an area frequented by mineral prospectors. Some of these prospectors were known to have come from states with malaria transmission. In the autochthonous cases, Plasmodium vivax and Plasmodium falciparum were diagnosed. Entomological investigation identified Anopheles (Nyssorhynchus) darlingi, Anopheles (Nyssorhynchus) albitarsis, Anopheles (Nyssorhynchus) triannulatus and Anopheles (Nyssorhynchus) parvus. After the first outbreak, another three autochthonous cases were notified in municipality of Monte Alegre de Minas, in the same year. The occurrence of these outbreaks highlights the importance of surveillance systems in areas that are nonendemic for malaria.

Modeling and simulation of population balances for particulate processes

This work focuses on the modeling and numerical approximations of population balance equations (PBEs) for the simulation of different phenomena occurring in process engineering. The population balance equation (PBE) is considered to be a statement of continuity. It tracks the change in particle size distribution as particles are born, die, grow or leave a given control volume. In the population balance models the one independent variable represents the time, the other(s) are property coordinate(s), e.g., the particle volume (size) in the present case. They typically describe the temporal evolution of the number density functions and have been used to model various processes such as granulation, crystallization, polymerization, emulsion and cell dynamics. The semi-discrete high resolution schemes are proposed for solving PBEs modeling one and two-dimensional batch crystallization models. The schemes are discrete in property coordinates but continuous in time. The resulting ordinary differential equations can be solved by any standard ODE solver. To improve the numerical accuracy of the schemes a moving mesh technique is introduced in both one and two-dimensional cases ...

Contractive probability metrics and asymptotic behavior of dissipative kinetic equations

The present notes are intended to present a detailed review of the existing results in dissipative kinetic theory which make use of the contraction properties of two main families of probability metrics: optimal mass transport and Fourier-based metrics. The first part of the notes is devoted to a self-consistent summary and presentation of the properties of both probability metrics, including new aspects on the relationships between them and other metrics of wide use in probability theory. These results are of independent interest with potential use in other contexts in Partial Differential Equations and Probability Theory. The second part of the notes makes a different presentation of the asymptotic behavior of Inelastic Maxwell Models than the one presented in the literature and it shows a new example of application: particle's bath heating. We show how starting from the contraction properties in probability metrics, one can deduce the existence, uniqueness and asymptotic stability in classical spaces. A global strategy with this aim is set up and applied in two dissipative models.

Predicting trabecular bone microdamage initiation and accumulation using a non-linear perfect damage model

Studies evaluating the mechanical behavior of the trabecular microstructure play an important role in our understanding of pathologies such as osteoporosis, and in increasing our understanding of bone fracture and bone adaptation. Understanding of such behavior in bone is important for predicting and providing early treatment of fractures. The objective of this study is to present a numerical model for studying the initiation and accumulation of trabecular bone microdamage in both the pre- and post-yield regions. A sub-region of human vertebral trabecular bone was analyzed using a uniformly loaded anatomically accurate microstructural three-dimensional finite element model. The evolution of trabecular bone microdamage was governed using a non-linear, modulus reduction, perfect damage approach derived from a generalized plasticity stress-strain law. The model introduced in this paper establishes a history of microdamage evolution in both the pre- and post-yield regions

Validity of impedance-based equations for the prediction of total body water as measured by deuterium dilution in African women.

BACKGROUND: Little information is available on the validity of simple and indirect body-composition methods in non-Western populations. Equations for predicting body composition are population-specific, and body composition differs between blacks and whites. OBJECTIVE: We tested the hypothesis that the validity of equations for predicting total body water (TBW) from bioelectrical impedance analysis measurements is likely to depend on the racial background of the group from which the equations were derived. DESIGN: The hypothesis was tested by comparing, in 36 African women, TBW values measured by deuterium dilution with those predicted by 23 equations developed in white, African American, or African subjects. These cross-validations in our African sample were also compared, whenever possible, with results from other studies in black subjects. RESULTS: Errors in predicting TBW showed acceptable values (1.3-1.9 kg) in all cases, whereas a large range of bias (0.2-6.1 kg) was observed independently of the ethnic origin of the sample from which the equations were derived. Three equations (2 from whites and 1 from blacks) showed nonsignificant bias and could be used in Africans. In all other cases, we observed either an overestimation or underestimation of TBW with variable bias values, regardless of racial background, yielding no clear trend for validity as a function of ethnic origin. CONCLUSIONS: The findings of this cross-validation study emphasize the need for further fundamental research to explore the causes of the poor validity of TBW prediction equations across populations rather than the need to develop new prediction equations for use in Africa.