Antônio José da Silva Neto

An Introduction to Inverse Problems with Applications

Computational engineering/science uses a blend of applications, mathematical models and computations. Mathematical models require accurate approximations of their parameters, which are often viewed as solutions to inverse problems. Thus, the study of inverse problems is an integral part of computational engineering/science. This book presents several aspects of inverse problems along with needed prerequisite topics in numerical analysis and matrix algebra. If the reader has previously studied these prerequisites, then one can rapidly move to the inverse problems in chapters 4-8 on image restoration, thermal radiation, thermal characterization and heat transfer. This text does provide a comprehensive introduction to inverse problems and fills a void in the literature. Robert E White, Professor of Mathematics, North Carolina State University

A SOURCE-DETECTOR METHODOLOGY FOR THE CONSTRUCTION AND SOLUTION OF THE ONE-DIMENSIONAL INVERSE TRANSPORT EQUATION

A source-detector methodology is presented for the construction of an inverse transport equation that once solved provides estimates for radiative properties and/or internally distributed sources in participating media. From the proper combination of source and detector pairs, a system of non-linear equations is assembled, taking also in consideration experimental data on the exit radiation from the medium. Test case results are also presented.

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.

A hybrid approach with artificial neural networks, Levenberg–Marquardt and simulated annealing methods for the solution of gas–liquid adsorption inverse problems

In the present work the inverse problem of gas–liquid interface adsorption isotherm identification is investigated using a combination of an artificial neural network (ANN), and the Levenberg–Marquardt (LM) and the simulated annealing (SA) methods.

Absorption coefficient estimation in heterogeneous media using a domain partition consistent with divergent beams

An inverse radiative transfer problem is solved for the estimation of the absorption coefficient in a purely absorbing two-dimensional heterogeneous medium. A natural base built with a domain partition that takes into account the possibility of having divergent radiation beams originated at external sources is used in combination with a family of action by line reconstruction algorithms, built within the framework of Lebesgue measure, with Bregman distances based on a q-discrepancy functional. The domain partition and the assembly of the corresponding system of linear algebraic equations, whose unknowns are the absorption coefficients for each element of the partition, are described in detail. Results are presented for test cases using synthetic experimental data generated with a Monte Carlo simple integration technique.

An Inverse Mass Transfer Problem in Solid-Liquid Adsorption Systems

The basic phenomena in solid-liquid adsorption systems involves the movement of macromolecules from a liquid solution to the active sites located in the interior of the pores of the adsorbent. Therefore, the phenomenon is controlled by mass transfer mechanisms. These mechanisms consist of external diffusion, the effective diffusion in the pores and the velocity of the adsorption on the active site of the adsorbent. In this work, the mass transfer coefficients and the coefficients of the adsorption isotherm are estimated using an implicit formulation with the cost function of the squared residues, between calculated and measured concentrations, being minimized with the Levenberg-Marquardt method. One configuration was considered: the transient experimental data on the solute concentration is obtained in a stirred-bath system. In the implicit formulation considered here, the direct problem is solved several times along the iterative procedure used for the solution of the inverse problem. The solutions of the direct problems were obtained using a combination of finite volume method and finite difference method, and were validated with real experimental data of the concentration for the protein Bovine Serum Albumin (BSA) on Accell Plus QMA® macro porous adsorbent resin using Tris-HCL buffer solution.

Application of a GEO + SA hybrid optimization algorithm to the solution of an inverse radiative transfer problem

In a former study (F.L. de Sousa, F.M. Ramos, F.J.C.P. Soeiro, and A.J. Silva Neto, Application of the generalized extremal optimization algorithm to an inverse radiative transfer problem, Inverse Probl. Sci. Eng. 15 (2007), pp. 699–714), a new evolutionary optimization metaheuristic–the generalized extremal optimization (GEO) algorithm (F.L. de Sousa, F.M. Ramos, P.Paglione, and R.M. Girardi, A new stochastic algorithm for design optimization, AIAA J. 41 (2003), pp. 1808–1818)–was applied to the solution of an inverse problem of radiative properties estimation. A comparison with two other stochastic methods; simulated annealing (SA) and genetic algorithms (GA), was also performed, demonstrating GEOs competitiveness for that problem. In the present article, a recently developed hybrid version of GEO and SA (R.L. Galski, Development of improved, hybrid, parallel, and multiobjective versions of the generalized extremal optimization method and its application to the design of spatial systems, D.Sc. Thesis, Instituto Nacional de Pequisas Espaciais, Brazil, 2006, p. 279. INPE-14795-TDI/1238 (in Portuguese)) is applied to the same radiative transfer problem and the results obtained are compared with those from the previous study. The present approach was already foreseen (e.g. in F.L. de Sousa, F.M. Ramos, F.J.C.P. Soeiro, and A.J. Silva Neto, Application of the generalized extremal optimization algorithm to an inverse radiative transfer problem, Inverse Probl. Sci. Eng. 15 (2007), pp. 699–714) as a technique that could significantly improve the performance of GEO for this problem. The idea is to make use of a scheduling for GEOs free parameter γ in a similar way to the cooling rate of SA. The main objective of this approach is to combine the good exploration properties of GEO during the early stages of the search with the good convergence properties of SA at the end of the search.

An approach for Fault Diagnosis based on bio-inspired strategies

In this work we present a study on the application of bio-inspired strategies for optimization to Fault Diagnosis in industrial systems. The principal aim is to establish a basis for the development of new and viable model-based Fault Diagnosis Methods which improve some difficulties that the current methods cannot avoid. These difficulties are related with fault sensitivity and robustness to external disturbances. To get start the study, we consider the Differential Evolution and the Ant Colony Optimization algorithms. This application is illustrated using simulation data of the Two Tanks System benchmark. In order to analyze the merits of these algorithms to obtain a diagnosis which needs to be sensitive to faults and robust to external disturbances, some experiments with incipient faults and noisy data have been simulated. The results indicate that the proposed approach, basically the combination of the two algorithms, characterizes a promising methodology for Fault Diagnosis.

Reconstruction of a combination of the absorption and scattering coefficients with a discrete ordinates method consistent with the source–detector system

In the present work a combination of the absorption and scattering coefficients in heterogeneous two-dimensional media is estimated using the source–detector methodology and a discrete ordinates method whose directions of radiation propagation are taken in a way that is consistent with the source–detector system for parallel beams of radiation. The domain partition, the solution of the direct problem, and the source–detector methodology are described. Test case results are also presented.In the present work a combination of the absorption and scattering coefficients in heterogeneous two-dimensional media is estimated using the source–detector methodology and a discrete ordinates method whose directions of radiation propagation are taken in a way that is consistent with the source–detector system for parallel beams of radiation. The domain partition, the solution of the direct problem, and the source–detector methodology are described. Test case results are also presented.

An approach to parameters estimation of a chromatography model using a clustering genetic algorithm based inverse model

Genetic algorithms are tools for searching in complex spaces and they have been used successfully in the system identification solution that is an inverse problem. Chromatography models are represented by systems of partial differential equations with non-linear parameters which are, in general, difficult to estimate many times. In this work a genetic algorithm is used to solve the inverse problem of parameters estimation in a model of protein adsorption by batch chromatography process. Each population individual represents a supposed condition to the direct solution of the partial differential equation system, so the computation of the fitness can be time consuming if the population is large. To avoid this difficulty, the implemented genetic algorithm divides the population into clusters, whose representatives are evaluated, while the fitness of the remaining individuals is calculated in function of their distances from the representatives. Simulation and practical studies illustrate the computational time saving of the proposed genetic algorithm and show that it is an effective solution method for this type of application.