Francisco Duarte Moura Neto

Joint economic model for totally adaptive and R charts

Recent studies have shown that the amount of cost savings produced by a Vp X chart designed economically is higher than the fixed parameter X chart. This paper extends these studies for processes that are monitored jointly by X and R charts having all design parameters varying adaptively. We develop a joint expected cost model for a process whose mean is controlled by a Vp X chart and whose variance is controlled by a Vp R chart. The cost function due to controlling the process quality through these Vp charts is derived. This model provides a tool for optimal selection of the design parameters, in this way the minimum cost can be obtained. The possible savings provided by the developed model can be assessed.

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

Function estimation with Alifanov’s iterative regularization method in linear and nonlinear heat conduction problems

Abstract Various aspects of a methodology to determine unknown functions representing source terms in inverse heat conduction problems are presented. The methodology is centered on gradient based iterative procedures for optimization problems and we consider specifically Landweber iteration and the conjugate gradient method. The formulation is given for inverse problems with both linear and nonlinear direct heat conduction problems. Test case results are presented and the performance of the estimation results of a nonlinear equation, using linear and nonlinear models, are compared.

Evaluation of dispersion parameters for River São Pedro, Brazil, by the simulated annealing method

The dispersion coefficient parameterizes different and complex phenomena that control substance transport in water bodies. This article presents an inverse problem approach solved by the simulated annealing (SA) algorithm to estimate dispersion coefficient and other parameters that can model dispersion in rivers with non-uniform geometry. The method is compared with two other classical methods, the peak concentration and Chatwin. The SA algorithm, peak and Chatwin methods were applied to the advection–dispersion model, whereas the SA was tested in the dispersion dead zone model (DDZM) as well. The methods are assessed in the study of a tracer transport achieved in a small mountain river. Comparing with observations, the best performance was obtained conjugating SA and the DDZM. The classical methods showed high sensitivity to the river discharge determination method, being more precise when the sections method was adopted. Considering this restriction, the inverse problem formulation solved by the SA approach showed to be a promising alternative, given that it can be built in a way that the river discharge itself can be estimated.

Economic-statistical design of variable parameters non-central chi-square control chart

Production processes are monitored by control charts since their inception by Shewhart (1924). This surveillance is useful in improving the production process due to increased stabilization of the process, and consequently standardization of the output. Control charts keep track of a few key quality characteristics of the outcome of the production process. This is done by means of univariate or multivariate charts. Small improvements in control chart methodology can have significant economic impact in the production process. In this investigation, we propose the monitoring of a single variable by means of a variable parameter non-central chi-square control chart. The design of the chart is accomplished by means of optimizing a cost function. We use here a simulated annealing optimization tool, due to the difficulty of classical gradient based optimization techniques to handle the optimization of the cost function. The results show some of the drawbacks of using this model.

Multi-q pattern classification of polarization curves

Several experimental measurements are expressed in the form of one-dimensional profiles, for which there is a scarcity of methodologies able to classify the pertinence of a given result to a specific group. The polarization curves that evaluate the corrosion kinetics of electrodes in corrosive media are applications where the behavior is chiefly analyzed from profiles. Polarization curves are indeed a classic method to determine the global kinetics of metallic electrodes, but the strong nonlinearity from different metals and alloys can overlap and the discrimination becomes a challenging problem. Moreover, even finding a typical curve from replicated tests requires subjective judgment. In this paper, we used the so-called multi-q approach based on the Tsallis statistics in a classification engine to separate the multiple polarization curve profiles of two stainless steels. We collected 48 experimental polarization curves in an aqueous chloride medium of two stainless steel types, with different resistance against localized corrosion. Multi-q pattern analysis was then carried out on a wide potential range, from cathodic up to anodic regions. An excellent classification rate was obtained, at a success rate of 90%, 80%, and 83% for low (cathodic), high (anodic), and both potential ranges, respectively, using only 2% of the original profile data. These results show the potential of the proposed approach towards efficient, robust, systematic and automatic classification of highly nonlinear profile curves.

Double azeotropy: calculations with Newton-like methods and continuous GRASP (C-GRASP)

Azeotropy is a thermodynamic phenomenon where a boiling liquid produces a vapour with identical composition. This situation is a challenge for separation engineering, since distillation processes explore the differences among relative volatilities and, thus, an azeotrope can be a barrier for the separation. In binary mixtures, the azeotropy calculation problem is characterised by a 2 × 2 non-linear system with pressure or temperature and a molar fraction as unknowns. An interesting and rare case is the so-called double azeotropy, when this non-linear system has two solutions, corresponding to two distinct azeotropes. In this paper, we present some numerical aspects of double azeotropy using classical approaches (Newton’s methods with globalisation techniques) and a new non-linear optimisation algorithm (the C-GRASP method).

Second-Order Inverse Reliability Analysis: A New Methodology to the Treatment of Reliability in Engineering System

Reliability-based methods have been established to take into account, in a rigorous manner, the uncertainties involved in analysis of engineering systems. The failure probability and reliability index are used to quantify risks and therefore evaluate the consequences of failure. First/second-order reliability method (FORM/SORM) is considered to be one of the most reliable computational methods to deal with reliability in engineering systems. Basically, the idea is to overcome the computational difficulties in determination of the reliability index and approximating the constraints. In this contribution, a new methodology to deal with uncertainties in engineering systems is proposed. This approach, called Second-Order Inverse Reliability Analysis (SOIRA), consists in the use of first and second order derivatives to find the solution associated with the highest probability value (inverse reliability analysis). In order to evaluate the proposed methodology, three reliability approaches (FORM, SORM and IRA - Inverse Reliability Analysis) are applied in two test cases: (i) W16X31 steel beam problem and (ii) beam problem. The obtained results demonstrated that the proposed strategy represents an interesting alternative to reliability design of engineering systems.

Acoplamento de algoritmos de otimização e agrupamento para resolução de problemas globalmente multimodais

Um problema de otimizacao globalmente multimodal e aquele que possui mais de um ponto de otimo global. Algoritmos deterministicos e evolucionarios sao metodos comumente utilizados para resolucao de problemas de otimizacao, mas enfrentam dificuldades para obtencao das solucoes de um problema globalmente multimodal. Os metodos de agrupamento utilizam relacoes de similaridade entre os dados para encontrar padroes dentro do conjunto e realizar o agrupamento dos dados. O objetivo deste trabalho e empregar conjuntamente algoritmos de otimizacao e tecnicas de agrupamento para obter simultaneamente todas as solucoes de um problema globalmente multimodal. Para tal, utiliza-se inicialmente o algoritmo evolucionario, denominado Busca Harmonica, para identificar pequenos grupos em torno de pontos de otimo global do problema. Em seguida, usa-se o algoritmo de agrupamento espectral para mapear os grupos; entao, os pontos sao classificados conforme o grupo ao qual pertencem e retorna-se uma estimativa de cada uma das solucoes, utilizando o metodo k-means. Por fim, com o auxilio de um metodo deterministico, calcula-se cada uma das solucoes. A metodologia proposta foi aplicada a duas funcoes teste, ambas bidimensionais. Nota-se que para as funcoes utilizadas a metodologia obteve exito, ao encontrar todas as solucoes globais e com pequeno erro relativo.

Radiative Transfer and Heat Conduction

We show in this chapter how to estimate the value of several material properties, such as single scattering albedo and thermal conductivity, present in the heating process of a material with thermal radiation.