Haroldo Fraga de Campos Velho

A comparison of some inverse methods for estimating the initial condition of the heat equation

In this work we analyze two explicit methods for the solution of an inverse heat conduction problem and we confront them with the least-squares method, using for the solution of the associated direct problem a classical finite difference method and a method based on an integral formulation. Finally, the Tikhonov regularization connected to the least-squares criterion is examined. We show that the explicit approaches to this inverse heat conduction problem will present disastrous results unless some kind of regularization is used.

Different approaches for the solution of a backward heat conduction problem

This work presents a comparison of three different techniques to solve the inverse heat conduction problem involving the estimation of the unknown initial condition for a one-dimensional slab, whose solution is obtained through minimization of a known functional form. The following techniques are employed to solve the inverse problem: the conjugate gradient method with the adjoint equation, regularized solution using a quasi-Newton method, and regularized solution via genetic algorithm (GA) method. For the first one, a general form to compute the gradient of the functional form (considering the time and space domains) is presented, and for the GA method a new genetic operator named epidemical is applied.

Novel approaches to entropic regularization

In this work, two new entropic regularization techniques are introduced. They represent a generalization of the standard MaxEnt regularization method, and allow for a greater flexibility for introducing any prior information about the expected structure of the true physical model, or its derivatives, into the inversion procedure. The first technique is based on the minimization of the entropy of the vector of first-differences of unknown parameters. Adopting standard terminology, it is known as the minimum first-order entropy method (MinEnt-1). To illustrate the essential feature of the method, MinEnt-1 is applied to the reconstruction of two-dimensional geoelectric conductivity distributions from magnetotelluric data. The second technique is based on the maximization of the entropy of the vector of second-differences of the unknown parameters, and is denoted as the MaxEnt-2 method. The MaxEnt-2 method is applied to the retrieval of vertical profiles of temperature in the atmosphere from remote sensing data.

Linear and Nonlinear Statistical Downscaling for Rainfall Forecasting over Southeastern Brazil

Abstract In this work linear and nonlinear downscaling are developed to establish empirical relationships between the synoptic-scale circulation and observed rainfall over southeastern Brazil. The methodology uses outputs from the regional Eta Model; prognostic equations for local forecasting were developed using an artificial neural network (ANN) and multiple linear regression (MLR). The final objective is the application of such prognostic equations to Eta Model output to generate rainfall forecasts. In the first experiment the predictors were obtained from the Eta Model and the predictand was rainfall data from meteorological stations in southeastern Brazil. In the second experiment the observed rainfall on the day prior to the forecast was included as a predictor. The threat score (TS) and bias, used to quantify the performance of the forecasts, showed that the ANN was superior to MLR in most seasons. When compared with Eta Model forecasts, it was observed that the ANN has a tendency to forecast moder...

Non-extensive statistics and three-dimensional fully developed turbulence

In this paper, we present further evidence, based on new data from the Large Scale Biosphere Atmosphere Experiment in Amazonia (LBA), that the generalized thermostatistics provides a simple and accurate framework for modeling the statistical behavior of fully developed turbulence.

Estimation of initial condition in heat conduction by neural network

This article describes a methodology for using neural networks in an inverse heat conduction problem. Three neural network (NN) models are used to determine the initial temperature profile on a slab with adiabatic boundary condition, given a transient temperature distribution at a given time. This is an ill-posed one-dimensional parabolic inverse problem, where the initial condition has to be estimated. Three neural network models addressed the problem: a feedforward network with backpropagation, radial basis functions (RBF), and cascade correlation. The input for the NN is the temperature profile obtained from a set of probes equally spaced in the one-dimensional domain. The NNs were trained considering a 5% of noise in the experimental data. The training was performed considering 500 similar test-functions and 500 different test-functions. Good reconstructions have been obtained with the proposed methodology.

Apparent-density mapping using entropic regularization

We present a new apparent-density mapping method on the horizontal plane that combines the minimization of the first-orderentropywiththemaximizationofthezeroth-order entropyoftheestimateddensitycontrasts.Theinterpretation modelconsistsofagridofvertical,juxtaposedprismsinboth horizontal directions. We assume that the top and the bottom of the gravity sources areflat and horizontal and estimate the prisms’densitycontrasts.Theminimizationofthefirst-order entropy favors solutions presenting sharp borders, and the maximization of the zeroth-order entropy prevents the tendency of the source estimate to become a single prism.Thus, ajudiciouscombinationofbothconstraintsmayleadtosolutions characterized by regions with virtually constant estimated density contrasts separated by sharp discontinuities. We apply our method to synthetic data from simulated intrusive bodies in sediments that presentflat and horizontal tops. By comparing our results with those obtained with the smoothness constraint, we show that both methods produce good and equivalent locations of the sources’ central positions. However, the entropic regularization delineates the boundaries of the bodies with greater resolution, even in the case of 100-m-wide bodies separated by a distance as small as 50 m. Both the proposed and the global smoothness constraints are applied to real anomalies from the eastern Alps and from the Matsitama intrusive complex, northeastern Botswana. In the first case, the entropic regularization delineates two sources, with a horizontal and nearly flat top being consistent with the known geologic information. In the second case, both constraints produce virtually the same estimate, indicating, in agreement with results of synthetic tests, thatthetopsofthesourcesareneitherflatnorhorizontal.

Inverse problems in space science and technology

Solutions for inverse problems appearing in space applications and space technology are described. The inverse problem is formulated as a nonlinear optimization problem. Usually some additional information must be added from our previous knowledge about the physical phenomenon. In general this a priori information means smoothness, in other words, regularized solutions are searched for. The methodology is applied to geophysics (magneto-telluric inversion), meteorology (temperature retrieval from satellite data), and oceanography (inverse hydrologic optics), as examples of space applications. The scheme is also employed for solving an inverse problem emerging from technology: the inverse design of a space radiator.

A variational approach for solving an inverse vibration problem

The present investigation is focused on the solution of a dynamic inverse problem which is concerned with the assessment of damage in structures by means of measured vibration data. This inverse problem has been presented as an optimization problem and has been solved through the use of the Variational Approach, i.e. the conjugate gradient method (CGM) coupled with the adjoint equation. The results have been presented in a satisfactory form when a small structure with few degrees of freedom (DOF) is considered, however, when a higher DOF structure is studied, the simple application of the variational approach is not any more satisfactory, being necessary the application of an additional methodology. In order to solve this difficulty, a new approach based on the use of the genetic algorithm (GA) method has been proposed. The GA method is used to generate a primary solution which is employed as the initial guess for the CGM. The application of this new approach has shown that better results can be achieved, although the computational time for the application analyzed here could be increased. The damage estimation has been evaluated using noiseless and noisy synthetic experimental data, and the reported results are concerned with both truss and beam-like structures, which have been modeled through a finite element technique. Moreover, in order to take into account the reduced set of experimental data to be employed in the optimization algorithm, a Guyan reduction technique has been adopted on the finite element formulation. ¶Selected paper from Inverse Problems, Design and Optimization Symposium, 2004.

Multifractal model for eddy diffusivity and counter-gradient term in atmospheric turbulence

A new approach for eddy diffusivity and counter-gradient term in atmospheric turbulent fluxes is developed. This scheme is based on the Taylor statistical theory of turbulence and on a multifractal approach to the turbulent spectrum of energy. The non-extensive thermodynamics description is used to obtain a multifractal model.