Fran Sérgio Lobato

Solution of inverse radiative transfer problems in two-layer participating media with differential evolution

In the present work the differential evolution approach (DE) is used for the estimation of radiative properties in two-layer participating media. This physical phenomenon is modelled by an integro-differential equation known as the Boltzmann equation. A review of the optimization technique used is presented. The direct radiative transfer problem is solved by using the collocation method. Then, case studies are presented aimed at illustrating the efficiency of the methodology used in the treatment of an inverse problem of radiative transfer. The results obtained from the solution of the inverse problem are compared with those obtained from a hybridization of simulated annealing and Levenberg–Marquardt methods. The preliminary results indicate that the proposed approach characterizes a promising methodology for the present type of inverse problem.

A comparative study of the application of differential evolution and simulated annealing in radiative transfer problems

The radiative transfer phenomenon is modeled by an integro-differential equation known as Boltzmann equation. This equation describes mathematically the interaction of the radiation with the participating medium, i.e., a medium that may absorb, scatter and emit radiation. In this sense, this work presents a study regarding the estimation of radiative properties in a one-dimensional participating medium by using two optimization heuristic methods, namely Simulated Annealing and Differential Evolution. First, a review of these two optimization techniques is presented. The direct radiative transfer problem solution, which is required for both optimization techniques, is obtained by using the Collocation Method. Finally, case-studies are presented aiming at illustrating the efficiency of these methodologies in the treatment of inverse radiative transfer problems.

Model updating of a rotating machine using the self-adaptive differential evolution algorithm

Despite the good accuracy of finite element (FE) models to represent the dynamic behaviour of mechanical systems, practical applications show significant discrepancies between analytical predictions and experimental results, which are mostly due to uncertainties on the geometry configuration, imprecise material parameters and vague boundary conditions. Thereby, different approaches have been proposed to solve the inverse problems associated with the updating of FE models. Among them, the techniques based on minimization processes have shown to be some of the most promising ones. In this paper, a self-adaptive heuristic optimization method, namely the self-adaptive differential evolution (SADE), is evaluated. Differently from the canonical differential evolution (DE) algorithm, the SADE strategy is able to update dynamically the required parameters such as population size, crossover parameter and perturbation rate. This is done by considering a defined convergence rate on the evolution process of the algorithm in order to reduce the number of evaluations of the objective function. For illustration purposes, the SADE strategy is applied to the solution of typical mathematical functions. Additionally, the strategy is equally used to update the FE model of a rotating machine composed by a horizontal flexible shaft, two rigid discs and two unsymmetrical bearings. For comparison purposes, the canonical DE is also used. The results indicate that the SADE algorithm is a recommended technique for dealing with this kind of inverse problem.

A Comparative Study using Bio-Inspired Optimization Methods Applied to Controllers Tuning

The evolution of process control techniques have increased in a significant way during last years. Even so, in the industry, the Proportional-Integral-Derivative (PID) controller is frequently used in closed loops due to its simplicity, applicability, and easy implementation (Astrom & Hagglund, 1995); Shinskey, 1998; (Desbourough & Miller, 2002). An extensive research concerning regulatory control of loops used in refinery, chemical, and pulp and paper processes reveals that 97% of the applications make use of classical PID structure even though sophisticated control techniques, like advanced control strategies, are also based on PID algorithms with lower hierarchy level (Desbourough & Miller, 2002).

Estimation of space-dependent single scattering albedo in a radiative transfer problem using differential evolution

This work presents the differential evolution algorithm applied to an inverse radiative transfer problem formulated as a finite dimensional optimization problem. It is considered a one-dimensional isotropically-scattering medium with finite optical thickness, space-dependent scattering albedo and plane-parallel geometry. The direct radiative transfer problem models the transmission of radiation through this medium by a linear version of the Boltzmann equation with azimuthal symmetry. The direct radiative transfer problem solution, which is required for the optimization techniques, is obtained by using the collocation method. Some test cases are presented, aiming at illustrating the efficiency of the methodologies used in the treatment of an inverse problem of radiative transfer. The results are compared with other approaches and indicate that the proposed methodology characterizes a promising methodology for dealing with this type of inverse problem.

Application of Simulated Annealing and Hybrid Methods in the Solution of Inverse Heat and Mass Transfer Problems

Antonio Jose da Silva Neto1, Jader Lugon Junior2,5, Francisco Jose da Cunha Pires Soeiro1, Luiz Biondi Neto1, Cesar Costapinto Santana3, Fran Sergio Lobato4 and Valder Steffen Junior4 Universidade do Estado do Rio de Janeiro1, Instituto Federal de Educacao, Ciencia e Tecnologia Fluminense2, Universidade Estadual de Campinas3, Universidade Federal de Uberlândia4, Centro de Tecnologia SENAI-RJ Ambiental5 Brazil

Reliability-Based Optimization Using Differential Evolution and Inverse Reliability Analysis for Engineering System Design

In this contribution, a new methodology based on a double-loop iteration process is proposed for the treatment of uncertainties in engineering system design. The inner optimization loop is used to find the solution associated with the highest probability value (inverse reliability analysis), and the outer loop is the regular optimization loop used to solve the considered reliability problem through differential evolution and multi-objective optimization differential evolution algorithms. The proposed methodology is applied to mathematical functions and to the design of classical engineering systems according to both mono- and multi-objective contexts. The obtained results are compared with those obtained by classical approaches and demonstrate that the proposed strategy represents an interesting alternative to reliability design of engineering systems.

Application of Three Bioinspired Optimization Methods for the Design of a Nonlinear Mechanical System

The present work focuses on the optimal design of nonlinear mechanical systems by using heuristic optimization methods. In this context, the nonlinear optimization problem is devoted to a two-degree-of-freedom nonlinear damped system, constituted of a primary mass attached to the ground by a linear spring and a secondary mass attached to the primary system by a nonlinear spring. This arrangement forms a nonlinear dynamic vibration absorber (nDVA), which is used in this contribution as a representative example of a nonlinear mechanical system. The sensitivity analysis of the suppression bandwidth, namely, the frequency range over which the ratio of the main mass displacement amplitude to the amplitude of the forcing function is less than unity, with respect to the design variables that characterize the nonlinear system based on the first order finite differences is presented. For illustration purposes the optimization problem is written as to maximize the suppression bandwidth by using three recent bioinspired optimization methods: Bees Colony Algorithm, Firefly Colony Algorithm, and Fish Swarm Algorithm. The results are compared with other evolutionary strategies.

Self-adaptive Multi-objective Optimization Differential Evolution

This chapter presents the development of the Self-adaptive Multi-objective Optimization Differential Evolution algorithm, as proposed to solve problems with multiple objectives. In this context, a brief review about the Differential Evolution algorithm both for the mono- and for the multi-objective contexts is presented. In addition, the strategies considered to update the DE parameters are discussed. Finally, to illustrate the performance of this new multi-objective optimization algorithm, a mathematical test case is evaluated.

ROBUST MULTI-OBJECTIVE OPTIMIZATION APPLIED TO ENGINEERING SYSTEMS DESIGN

IN ENGINEERING SYSTEMS DESIGN, THEORETICAL DETERMINISTIC SOLUTIONS CAN BE HARDLY APPLIED DIRECTLY TO REAL-WORLD SCENARIOS. BASICALLY, THIS IS DUE TO MANUFACTURING LIMITATIONS AND ENVIRONMENTAL CONDITIONS UNDER WHICH THE REAL SYSTEM WILL OPERATE. THEREFORE, A SMALL VARIA-TION IN THE DESIGN VARIABLES VECTOR CAN RESULT IN A MEANINGFUL CHANGE ON THE THEORETICAL OPTIMAL DESIGN AS REPRESENTED BY THE MINIMIZATION OF THE CORRESPONDING VECTOR OF OBJECTIVE FUNCTIONS. IN THIS CONTEXT, IT IS IMPORTANT TO DEVELOP METHODOLOGIES THAT ARE ABLE TO PRODUCE SOLUTIONS (EVEN SUBOPTIMAL) THAT ARE LESS SENSITIVE TO PERTURBATIONS IN THE DESIGN VARIABLE VECTOR AND, CONSEQUENTLY, LEADING TO A ROBUST OPTIMAL DESIGN. IN THIS CONTRIBUTION, FIRST THE PROPOSED APPROACH IS TESTED ON VARIOUS MATHEMATICAL FUNCTIONS. THEN, THE METHODOLOGY IS APPLIED TO THE DESIGN OF TWO REPRESENTATIVE ENGINEERING SYSTEMS THROUGH MULTI-OBJECTIVE OPTIMIZATION USING THE FIREFLY COLONY ALGORITHM IN ASSOCIATION WITH THE EFFECTIVE MEAN CONCEPT IS PRESENTED. THE RESULTS OBTAINED DEMONSTRATE THAT THE DESIGN STRATEGY CONVEYED REPRESENTS AN INTERESTING ALTERNATIVE APPROACH TO OBTAIN ROBUST DESIGN FOR A NUMBER OF ENGINEERING APPLICATIONS.