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This book brings together a rich selection of studies in mathematical modeling and computational intelligence, with application in several fields of engineering, like automation, biomedical, chemical, civil, electrical, electronic, geophysical and mechanical engineering, on a multidisciplinary approach. Authors from five countries and 16 different research centers contribute with their expertise in both the fundamentals and real problems applications based upon their strong background on modeling and computational intelligence. The reader will find a wide variety of applications, mathematical and computational tools and original results, all presented with rigorous mathematical procedures.

This work is intended for use in graduate courses of engineering, applied mathematics and applied computation where tools as mathematical and computational modeling, numerical methods and computational intelligence are applied to the solution of real problems.



Chapter 1. Preliminary Correlations for Characterizing the Morphology of Abdominal Aortic Aneurysms as Predictor of Rupture

The morphology of abdominal aortic aneurysms (AAA) has been recognized as a factor that may predispose their rupture. The time variation of the AAA morphology induces hemodynamic changes in morphological behavior that, in turn, alters the distribution of hemodynamic stress on the arterial wall. This behavior can influence the phenomenon of rupture. In order to evaluate the relationship between the main geometric parameters characterizing the AAA and the hemodynamic stresses, 6 AAA models were reconstructed and characterized. The models were characterized using thirteen geometrical factors based on the lumen center line: eight 1D indices, three 3D indices, and two 0D indices. The temporal and spatial distributions of hemodynamic stresses were computed using computational fluid dynamics. The results showed that the hemodynamic stresses are modified by the time variations of the AAA morphology, and therefore, the hemodynamic stresses, in combination with other parameters, could be a criterion for improved rupture risk prediction. Statistical correlations between hemodynamic stresses and geometric indices have confirmed the influence by the AAA morphometry on the prediction of the rupture risks, although higher reliability of these correlations is required.

Guillermo Vilalta Alonso, Eduardo Soudah, José A. Vilalta Alonso, Laurentiu Lipsa, Félix Nieto, Marı́a Ángeles Pérez, Carlos Vaquero

Chapter 2. Mathematical-Computational Simulation of Cytoskeletal Dynamics

Actin and microtubules are components of the cytoskeleton, and are key mediators of neuron growth and maintenance. Knowing how they are regulated enhances our understanding of neural development, ageing, degeneration, and regeneration. However, biological investigation alone will not unravel the complex cytoskeletal machinery. We expect that inquiries about the cytoskeleton can be significantly enhanced if their physico-chemical behavior is concealed and summarized in mathematical and computational models that can be coupled to concepts of biological regulation. Our computational modeling concerns the mechanical aspects associated with the dynamics of relatively simple, finger-like membrane protrusions called filopodia. Here we propose an alternative approach for representing the displacement of molecules and cytoplasmic fluid in the extremely narrow and long filopodia and discuss strategies to couple the particle-in-cell method with algorithms for laminar flow to model the two phases of actin dynamics: polymerization into filaments which are pulled back into the cell and compensatory G-actin drift towards its tip to supply polymerization. We use nerve cells of the fruit fly Drosophila as an effective, genetically amenable biological system to generate experimental data as the basis for the abstract models and their validation.

Carlos A. de Moura, Mauricio V. Kritz, Thiago F. Leal, Andreas Prokop

Chapter 3. Fault Diagnosis with Missing Data Based on Hopfield Neural Networks

Most of the existing artificial neural network models use a significant amount of information for their training. The need for such information could be an inconvenience for its application in fault diagnosis in industrial systems, where the information, due to different factors such as data losses in the data acquisition systems, is scarce or not verified. In this chapter, a diagnostic system based on a Hopfield neural network is proposed to overcome this inconvenience. The proposal is tested using the development and application of methods for the actuator diagnostic in industrial control systems (DAMADICS) benchmark, with successful performance.

Raquelita Torres Cabeza, Egly Barrero Viciedo, Alberto Prieto-Moreno, Valery Moreno Vega

Chapter 4. Diagnosing Time-Dependent Incipient Faults

This chapter focuses on a formulation for fault diagnosis (FDI) using an inverse problem methodology. It has been shown that this approach allows for diagnoses with adequate balance between robustness and sensitivity. The main contribution of this chapter is the expansion of this approach to include the diagnosis of time-dependent incipient faults. The FDI inverse problem is formulated as an optimization problem that is then solved with two metaheuristics: Differential Evolution and its variation Differential Evolution with Particle Collision. The proposed methodology is tested using simulated data from the Two Tanks system, which is recognized as benchmark for control and diagnosis. The results indicate that this proposal is suitable for the aforementioned diagnosis.

Lı́dice Camps-Echevarrı́a, Orestes Llanes-Santiago, Haroldo Fraga de Campos Velho, Antônio José da Silva Neto

Chapter 5. An Indirect Kernel Optimization Approach to Fault Detection with KPCA

This chapter discusses a new indirect kernel optimization criterion for the adjustment of a fault detection process that is based on the dimension–reduction technique known as kernel principal component analysis. The kernel parameter optimization proposed here involves the computation of the false alarm rate and false detection rate indicators that are combined in a single indicator: the area under the ROC curve. This approach was tested on the Tennessee Eastman (TE) process, where a significant decrease in false and missing alarms was observed.

José M. Bernal de Lázaro, Orestes Llanes-Santiago, Alberto Prieto-Moreno, Diego Campos Knupp

Chapter 6. Uncertainty Quantification in Chromatography Process Identification Based on Markov Chain Monte Carlo

Modeling and simulation of chromatography systems leads to better understanding of the mass transfer mechanisms and operational conditions that can be used to improve molecular separation/purification. In this chapter, parameter uncertainty produced by the model and measurement errors in a front velocity chromatography model is quantified by means of a Bayesian method, the delayed rejection adaptive metropolis algorithm, which is a variant of the Markov Chain Monte Carlo (MCMC) method. The model is also evaluated for a random sample of parameters, being then determined the uncertainty in the prediction.

Mirtha Irizar Mesa, Leôncio D. Tavares Câmara, Diego Campos-Knupp, Antônio José da Silva Neto

Chapter 7. Inverse Analysis of a New Anomalous Diffusion Model Employing Maximum Likelihood and Bayesian Estimation

The classical diffusion equation models the behavior of several physical phenomena related to dispersion processes quite successfully; however, in some cases, this approach fails to represent the actual physical behavior. In most published works dealing with this situation, the well-known second order parabolic equation is assumed as the basic governing equation of the dispersion process, but the anomalous diffusion effect is modeled with the introduction of fractional derivatives or the imposition of a convenient variation of the diffusion coefficient with time or concentration. Alternatively, Bevilacqua and coauthors developed a new analytical formulation for the simulation of the phenomena of diffusion with retention. Its purpose is to reduce all diffusion processes with retention to a unifying phenomenon that can adequately simulate the retention effect. This model may have relevant applications in different areas, such as population spreading with partial hold up of the population to guarantee territorial domain, chemical reactions inducing adsorption processes, and multiphase flow through porous media. In the new formulation, a discrete approach is first formulated with regard to a control parameter that represents the fraction of particles allowed to diffuse, and the governing equation for the modeling of diffusion with retention in a continuum medium requires a fourth order differential term. In order to apply this new formulation to the modeling of practical problems, the newly introduced parameters need to be accurately determined through an inverse problem analysis. Hence, this chapter provides an overview of the inverse analysis of anomalous diffusion problems as modeled through this new formulation, and a summary is also presented on the inverse problem formulation and related solution through three different approaches: (1) the maximum likelihood estimation, (2) the Bayesian approach through the Maximum a Posteriori objective function, and (3) Markov Chain Monte Carlo methods.

Diego Campos-Knupp, Luciano G. da Silva, Luiz Bevilacqua, Augusto C. N. R. Galeão, Antônio José da Silva Neto

Chapter 8. Accelerated Direct-Problem Solution: A Complementary Method for Computational Time Reduction

This paper presents a proposal designed to reduce the time required by the process to estimate the parameters of a system by accelerating the direct-problem solution as the slow phase in any estimation method. This proposal is considered a complement to existing procedures, such as the combination of different optimization methods for the purpose of reducing the number of calls to the objective function. The proposal consists of a procedure that helps study the relation between the direct-problem solution step and the time required for this solution, as well as the influence of the direct solution’s built-in error on the accuracy of the estimated parameters. Consequently, the extent in which the estimation process can be accelerated without impairing estimation accuracy can be determined. For the purpose of testing its viability, this proposal was applied to the estimation problem of the kinetic parameters of a chromatography column process, as modeled using the front-velocity method. The results from this test show that, by accelerating the direct-problem solution, the estimation time can be reduced significantly, without affecting the accuracy of the estimation.

Alberto Prieto-Moreno, Leôncio D. Tavares Câmara, Orestes Llanes-Santiago

Chapter 9. Effects of Antennas on Structural Behavior of Telecommunication Towers

The communication lattice towers must be designed to resist wind forces and support antennas under heavy working conditions. In the past few years, a number of communication lattice towers have collapsed in Cuba as a consequence of strong winds. Antennas modify the wind flow around their tower and act as a screen against wind loads and transmit strong efforts to its members. The aim of this chapter is to assess the effect of antenna locations on some structural parameters of the tower by means of physical and numerical experiments with computational applications. A physical experiment in a wind tunnel was conducted in order to obtain the drag coefficients of a tower holding dish antennas. Finite element method models of the tower with the implementation of SAP2000 code were generated to obtain forces and displacements on the members, and natural periods of the structure. The numerical experiment consisted of a 23 factorial experiment, where the independent variables were horizontal position, vertical position, and number of dishes on the tower. The results show that the vertical position of dish antennas has the greatest influence on the structural behavior of their supporting tower.

Patricia Martı́n Rodrı́guez, Vivian B. Elena Parnás, Angel Emilio Castañeda Hevia

Chapter 10. Comparing Two-Level Preconditioners for Solving Petroleum Reservoir Simulation Problems

Domain decomposition ideas (proven suitable for parallelization) are combined with incomplete factorizations (which are standard in reservoir simulation) at subdomain level, with the ultimate goal of designing a scalable parallel preconditioner for addressing reservoir simulation problems. An ILU(k)-based two-level domain decomposition preconditioner is introduced, and its performance is compared with a two-level ILU(k)-block Jacobi preconditioner.

José R. P. Rodrigues, Paulo Goldfeld, Luiz M. Carvalho

Chapter 11. Assessment of the Reliability of Electrical Power Systems

This chapter assesses the reliability of a generation system (HL-I) using the Monte Carlo Non-Sequential (MCNS) simulation method and probabilistic indicators, as well as the static sense of a secured generation–transmission system (HL-II) on the basis of its voltage stability. For the purpose of mathematically modeling the system’s adequacy, two-state generator models are applied; and for the purpose of the load curve, a relative cumulative frequency histogram, with polynomial interpolation among classes, is used. The security assessment discussed herein is based on the continued load flow charts obtained using the Newton–Raphson method that can monitor the voltage system’s behavior to load increases. A modal analysis is also conducted in order to identify, from an overall perspective, the nodes that most contribute to loss of voltage stability in the system. Both assessments take into account the performance of the system stability limits. These limits are established on the basis of certain state variables, such as voltage range at each node, thermal limits on the transmission lines, and the reactive power limits of the generating units.

Yorlandys Salgado Duarte, Alfredo M. del Castillo Serpa

Chapter 12. Polymeric Thin Film Transistors Modeling in the Presence of Non-Ohmic Contacts

This chapter discusses a model for polymeric thin film transistors, PTFTs, based on the unified model and parameter extraction method (UMEM), previously developed by these authors for thin film transistors, which includes specific features of OTFTs, as initial drain current and subthreshold behavior. In this case, the model shows the presence of non-ohmic contacts at drain and source. UMEM, has been previously used with a-Si:H, polysilicon and nanocrystalline TFTs and as compared with previous methods, it provides a more rigorous and accurate determination of the main electrical parameters of TFTs. Device parameters are extracted in a simple and direct way from the experimental measurements, with no need for assigning predetermined values to any model parameter or using optimization methods. In this case, the extraction procedure is complemented to include the extraction of the model parameters related to the non-ohmic contacts at drain and source. The model was implemented in Verilog-A and included for application in Spice simulators. Good consistency was found between the simulations in Spice using the model and the measured devices, as shown herein.

Magali Estrada del Cueto, Antonio Cerdeira Altuzarra, Benjamín Iñiguez Nicolau, Lluis F. Marsal Garvi, Josep Pallarés Marzal
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