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Inverse approach to drying of thin bodies with significant shrinkage effects was studied. It was concluded that, based on a single thermocouple temperature response, it is possible to estimate simultaneously the two moisture diffusivity parameters, the convection heat and mass transfer coefficients and the relative humidity of drying air.

This paper deals with the Bayesian estimation of flow parameters in a porous material based on the measurements of local temperature at selected points inside the packed-bed. The unknown probability distribution function of estimated parameters was sampled using a Markov Chain Monte Carlo (MCMC) method. The MCMC method is efficient in sampling unknown distributions, but it is extremely time-consuming. The Proper Orthogonal Decomposition was used to construct off-line, low order approximation of the porous media flow problem. This model was further incorporated into the Metropolis-Hastings algorithm to retrieve the posterior distribution of the unknown parameters. This approach allowed us to decrease the computational time necessary to generate an ergodic Markov Chain. The efficiency of the proposed approach was tested on the simulated data generated with commercial CFD tools, and finally, it was applied to the real data acquired on the dedicated experimental stand. • Research highlight are summarized as follows: • Development of the mathematical model of biomass drying process. • Development of the coupled POD-MCMC inverse methodology estimate unknown parameters of the model. • Analysis of the accuracy of the developed approach. • Application of the inverse method to estimate model parameters for a real measurement data. [ABSTRACT FROM AUTHOR]

In vitro experiments were conducted in this work to analyze the proliferation of tumor (DU-145) and normal (macrophage RAW 264.7) cells under the influence of a chemotherapeutic drug (doxorubicin). Approximate Bayesian Computation (ABC) was used to select among four competing models to represent the number of cells and to estimate the model parameters, based on the experimental data. For one case, the selected model was validated in a replicated experiment, through the solution of a state estimation problem with a particle filter algorithm, thus demonstrating the robustness of the ABC procedure used in this work. [ABSTRACT FROM AUTHOR]

In this paper, the use of Bayesian inference is explored for estimating both the thermal conductivity and the internal convective heat transfer coefficient of an old historic building wall. The room air temperature, as well as the temperatures at the surface and within the wall have been monitored during one year and then used to solve the identification problem. With Bayesian inference, the posterior distributions of the unknown parameters are explored based on their prior distributions and on the likelihood function that models the measurement errors. In this work, the Markov Chain Monte Carlo method is used to explore the posterior distribution. The error of the inadequacy of mathematical model are considered using the approximation error model. The distribution of the estimated parameters have a small standard deviation, which illustrates the accuracy of the method. The parameters have been compared to the standard values from the French thermal regulations. The heat flux at the internal surface has been calculated with the estimated parameters and the standard values. It is shown that the standard values underestimate the heat flux of an order by 10%. This study also illustrates the importance of the preliminary diagnosis of a building with the estimation of the thermal properties of the wall for model calibration. [ABSTRACT FROM AUTHOR]

Cancer is characterized by the uncontrolled growth of cells with the ability of invading local organs and/or tissues and of spreading to other sites. Several kinds of mathematical models have been proposed in the literature, involving different levels of refinement, for the evolution of tumors and their interactions with chemotherapy drugs. In this article, we present the solution of a state estimation problem for tumor size evolution. A system of nonlinear ordinary differential equations is used as the state evolution model, which involves as state variables the numbers of tumor, normal and angiogenic cells, as well as the masses of the chemotherapy and anti-angiogenic drugs in the body. Measurements of the numbers of tumor and normal cells are considered available for the inverse analysis. Parameters appearing in the formulation of the state evolution model are treated as Gaussian random variables and their uncertainties are taken into account in the estimation of the state variables, by using an algorithm based on the auxiliary sampling importance resampling particle filter. Test cases are examined in the article dealing with a chemotherapy protocol for pancreatic cancer. [ABSTRACT FROM AUTHOR]

Thermal contact resistance/conductance is very important in many heat transfer applications, such as electronic packaging, nuclear reactors, aerospace and biomedicine, among others. The determination of the thermal contact resistance/conductance is often a very difficult task. Previously, the authors presented a computationally fast inverse problem methodology to estimate thermal contact conductance without intrusive measurements, in steady-state heat conduction problems. This paper is an extension of such methodology, applied to transient problems. The methodology presented is formulated in terms of a reciprocity functional approach, together with the method of fundamental solutions. The solution is composed of two steps. In the first step, two steady-state auxiliary problems, which do not depend on the thermal conductance, are solved. With the results of the first step, different thermal conductances can then be recovered through an integration process of the boundary data. Thus, the methodology is fast and can be used to detect contact flaws in different materials with small computational effort. Test cases with simulated measurements containing measurement errors are presented in order to illustrate the robustness of the proposed technique. [ABSTRACT FROM PUBLISHER]

Abstract: In this paper, we apply the Markov Chain Monte Carlo method, within the Bayesian framework, for the estimation of parameters appearing in the heat conduction model in metals under the condition of thermal non-equilibrium between electrons and lattice. Such non-equilibrium can be experimentally observed in a time scale of up to few picoseconds, during the heating of thin metal films with laser pulses of the order of femtoseconds. Simulated measurements containing random errors are used for the solution of the inverse problem. Results are presented for the simultaneous estimation of the electron–phonon coupling factor, the thermal conductivity and the heat capacity of the electron gas. [Copyright &y& Elsevier]

This work considers the detection of the spatial source term distribution in a multidimensional linear diffusion problem with constant (and known) thermal conductivity. This work can be physically associated with the detection of non-homogeneities in a material that are inclusion sources in a heat conduction problem. The uniqueness of the inverse problem is discussed in terms of classes of identifiable sources. Numerically, we propose to solve these inverse source problems using fundamental solution-based methods, namely an extension of the method of fundamental solutions to domain problems. Several examples are presented and the numerical reconstructions are discussed. [ABSTRACT FROM AUTHOR]

This work deals with the use of radial basis functions for the interpolation of the likelihood function in parameter estimation problems. The focus is on the use of Bayesian techniques based on Markov Chain Monte Carlo (MCMC) methods. The proposed interpolation of the likelihood function is applied to test cases of inverse problems in heat and mass transfer, solved with the Metropolis-Hastings algorithm. The use of the interpolated likelihood function reduces significantly the computational cost associated with the implementation of such Markov Chain Monte Carlo method without loss of accuracy in the estimated parameters. [ABSTRACT FROM AUTHOR]

In this article, the conjugate gradient method with adjoint problem is applied for the identification of the heat flux at the surface of ablating materials, by assuming no a priori information regarding the functional form of the unknown. Simulated measurements of the position of the ablating surface are used in the inverse analysis, together with simulated temperature measurements. The accuracy of the conjugate gradient method with adjoint problem is examined for functions containing sharp corners, by using different regularization approaches. Three different versions of the conjugate gradient method are compared, as applied to the inverse problem under observation. [ABSTRACT FROM AUTHOR]

In this article, the conjugate gradient method with adjoint problem is applied for the identification of the heat and mass transfer coefficients at the surface of drying capillary-porous bodies. The unknown functions are supposed to vary along the surface open to the surrounding environment. The effects of temperature and moisture content measurements on the inverse analysis are examined. The inverse problem is solved by considering either the heat or the mass transfer coefficients as unknown, as well as by considering simultaneously both functions as unknown. [ABSTRACT FROM AUTHOR]

Thermogenesis results from the cellular metabolism and has a fundamental role for body thermoregulation in endothermic species. The motivation for this work is the analysis of the kidneys' contribution for thermoregulation. An inverse problem is solved for the estimation of the heat generation rate that results from the metabolic activities in the kidney, by using transient temperature measurements of the urine. The Markov chain Monte Carlo (MCMC) method is applied for the solution of the inverse problem, which presents inherent difficulties associated with low sensitivity of the parameters of main interest that represent the transient heat source term and strong correlation of the remaining model parameters. Such difficulties are dealt with in this work by using a version of the Metropolis‐Hastings algorithm that samples the parameters in blocks. Simulated temperature measurements are used for the inverse problem solution, and the convergence of the Markov chains is verified with two different techniques. [ABSTRACT FROM AUTHOR]

A foreword to the April 2009 issue of the journal "Inverse Problems in Science and Engineering" is presented.

In this paper, the authors proposed an inverse analysis using an in–house three-dimensional finite element method for the extraction of thermal conductivity tensor components of carbon-fiber/epoxy composite, based on the recorded thermographic data in the form of laser-induced temperature field. The core of the computational algorithm used for determining the thermal conductivity values (tensor components) consists of finite element solver, which operates in a hybrid mode with an analytical model. The presented method evaluates the thermal conductivity values by matching the calculated spatial and temporal temperature fields to the experimental data. Due to the specific nature of the measurement process and computational algorithm, the proposed technique is very efficient and allows for relatively rapid obtainment of the thermal conductivity values. For considered in this work composite material with 34% fiber volume fraction the experimental thermal conductivity values in transverse and parallel to the fiber directions were equal to 0.32 W/mK and 6.80 W/mK, respectively. Additionally, in order to verify the reliability of the presented methodology, the selected isotropic reference material was investigated, using the same testing procedure. The results obtained by using this novel approach are in good agreement with data measured using the conventional testing techniques. [ABSTRACT FROM AUTHOR]