Wavelet-Galerkin method for one-dimensional elastoplasticity and damage problems: Constitutive modeling and computational aspects

This work presents an analysis of the wavelet-Galerkin method for one-dimensional elastoplastic-damage problems. Time-stepping algorithm for non-linear dynamics is presented. Numerical treatment of the constitutive models is developed by the use of return-mapping algorithm. For spacial discretization we can use wavelet-Galerkin method instead of standard finite element method. This approach allows to locate singularities. The discrete formulation developed can be applied to the simulation of one-dimensional problems for elastic-plastic-damage models. (C) 2007 Elsevier B.V. All rights reserved.

An inverse method to estimate the moving heat source in machining process

The present work propounds an inverse method to estimate the heat sources in the transient two-dimensional heat conduction problem in a rectangular domain with convective bounders. The non homogeneous partial differential equation (PDE) is solved using the Integral Transform Method. The test function for the heat generation term is obtained by the chip geometry and thermomechanical cutting. Then the heat generation term is estimated by the conjugated gradient method (CGM) with adjoint problem for parameter estimation. The experimental trials were organized to perform six different conditions to provide heat sources of different intensities. This method was compared with others in the literature and advantages are discussed. (C) 2012 Elsevier Ltd. All rights reserved.

Factorization method and inclusions of mixed type in an inverse elliptic boundary value problem

In various imaging problems the task is to use the Cauchy data of the solutions to an elliptic boundary value problem to reconstruct the coefficients of the corresponding partial differential equation. Often the examined object has known background properties but is contaminated by inhomogeneities that cause perturbations of the coefficient functions. The factorization method of Kirsch provides a tool for locating such inclusions. In this paper, the factorization technique is studied in the framework of coercive elliptic partial differential equations of the divergence type: Earlier it has been demonstrated that the factorization algorithm can reconstruct the support of a strictly positive (or negative) definite perturbation of the leading order coefficient, or if that remains unperturbed, the support of a strictly positive (or negative) perturbation of the zeroth order coefficient. In this work we show that these two types of inhomogeneities can, in fact, be located simultaneously. Unlike in the earlier articles on the factorization method, our inclusions may have disconnected complements and we also weaken some other a priori assumptions of the method. Our theoretical findings are complemented by two-dimensional numerical experiments that are presented in the framework of the diffusion approximation of optical tomography.

Numerical solutions of elliptic inverse problems via the equation error method

To estimate a parameter in an elliptic boundary value problem, the method of equation error chooses the value that minimizes the error in the PDE and boundary condition (the solution of the BVP having been replaced by a measurement). The estimated parameter converges to the exact value as the measured data converge to the exact value, provided Tikhonov regularization is used to control the instability inherent in the problem. The error in the estimated solution can be bounded in an appropriate quotient norm; estimates can be derived for both the underlying (infinite-dimensional) problem and a finite-element discretization that can be implemented in a practical algorithm. Numerical experiments demonstrate the efficacy and limitations of the method.

An image-based method to automatically propagate bony landmarks: application to computational spine biomechanics.

In attempts to elucidate the underlying mechanisms of spinal injuries and spinal deformities, several experimental and numerical studies have been conducted to understand the biomechanical behavior of the spine. However, numerical biomechanical studies suffer from uncertainties associated with hard- and soft-tissue anatomies. Currently, these parameters are identified manually on each mesh model prior to simulations. The determination of soft connective tissues on finite element meshes can be a tedious procedure, which limits the number of models used in the numerical studies to a few instances. In order to address these limitations, an image-based method for automatic morphing of soft connective tissues has been proposed. Results showed that the proposed method is capable to accurately determine the spatial locations of predetermined bony landmarks. The present method can be used to automatically generate patient-specific models, which may be helpful in designing studies involving a large number of instances and to understand the mechanical behavior of biomechanical structures across a given population.

A stochastic model updating method for parameter variability quantification based on response surface models and Monte Carlo simulation

Stochastic model updating must be considered for quantifying uncertainties inherently existing in real-world engineering structures. By this means the statistical properties,instead of deterministic values, of structural parameters can be sought indicating the parameter variability. However, the implementation of stochastic model updating is much more complicated than that of deterministic methods particularly in the aspects of theoretical complexity and low computational efficiency. This study attempts to propose a simple and cost-efficient method by decomposing a stochastic updating process into a series of deterministic ones with the aid of response surface models and Monte Carlo simulation. The response surface models are used as surrogates for original FE models in the interest of programming simplification, fast response computation and easy inverse optimization. Monte Carlo simulation is adopted for generating samples from the assumed or measured probability distributions of responses. Each sample corresponds to an individual deterministic inverse process predicting the deterministic values of parameters. Then the parameter means and variances can be statistically estimated based on all the parameter predictions by running all the samples. Meanwhile, the analysis of variance approach is employed for the evaluation of parameter variability significance. The proposed method has been demonstrated firstly on a numerical beam and then a set of nominally identical steel plates tested in the laboratory. It is found that compared with the existing stochastic model updating methods, the proposed method presents similar accuracy while its primary merits consist in its simple implementation and cost efficiency in response computation and inverse optimization.

Preliminary results of the relation between ice viscosity and water content using an inverse method

One of the outstanding problems of the modelling of temperate ice dynamics is the limited knowledge on the rheology of temperate ice and, in particular, on how the rate factor depends on the liquid water content. Though it is well known that the rate factor depends strongly on the water content, in practice the only available experimentally-based relationship is that by Duval (1977), which is only valid for water contents up to 1%. However, actual water contents found in temperate and polythermal glaciers are sometimes substantially larger.

Use of an Inverse Method for Time Series to Estimate the Dynamics of and Management Strategies for the Box Jellyfish Carybdea marsupialis

Frequently, population ecology of marine organisms uses a descriptive approach in which their sizes and densities are plotted over time. This approach has limited usefulness for design strategies in management or modelling different scenarios. Population projection matrix models are among the most widely used tools in ecology. Unfortunately, for the majority of pelagic marine organisms, it is difficult to mark individuals and follow them over time to determine their vital rates and built a population projection matrix model. Nevertheless, it is possible to get time-series data to calculate size structure and densities of each size, in order to determine the matrix parameters. This approach is known as a “demographic inverse problem” and it is based on quadratic programming methods, but it has rarely been used on aquatic organisms. We used unpublished field data of a population of cubomedusae Carybdea marsupialis to construct a population projection matrix model and compare two different management strategies to lower population to values before year 2008 when there was no significant interaction with bathers. Those strategies were by direct removal of medusae and by reducing prey. Our results showed that removal of jellyfish from all size classes was more effective than removing only juveniles or adults. When reducing prey, the highest efficiency to lower the C. marsupialis population occurred when prey depletion affected prey of all medusae sizes. Our model fit well with the field data and may serve to design an efficient management strategy or build hypothetical scenarios such as removal of individuals or reducing prey. TThis This sdfsdshis method is applicable to other marine or terrestrial species, for which density and population structure over time are available.

An inverse method for designing loaded RF coils in MRI

Radio-frequency ( RF) coils are designed such that they induce homogeneous magnetic fields within some region of interest within a magnetic resonance imaging ( MRI) scanner. Loading the scanner with a patient disrupts the homogeneity of these fields and can lead to a considerable degradation of the quality of the acquired image. In this paper, an inverse method is presented for designing RF coils, in which the presence of a load ( patient) within the MRI scanner is accounted for in the model. To approximate the finite length of the coil, a Fourier series expansion is considered for the coil current density and for the induced fields. Regularization is used to solve this ill-conditioned inverse problem for the unknown Fourier coefficients. That is, the error between the induced and homogeneous target fields is minimized along with an additional constraint, chosen in this paper to represent the curvature of the coil windings. Smooth winding patterns are obtained for both unloaded and loaded coils. RF fields with a high level of homogeneity are obtained in the unloaded case and a limit to the level of homogeneity attainable is observed in the loaded case.

Bayesian analysis of the scatterometer wind retrieval inverse problem:Some new approaches

The retrieval of wind vectors from satellite scatterometer observations is a non-linear inverse problem. A common approach to solving inverse problems is to adopt a Bayesian framework and to infer the posterior distribution of the parameters of interest given the observations by using a likelihood model relating the observations to the parameters, and a prior distribution over the parameters. We show how Gaussian process priors can be used efficiently with a variety of likelihood models, using local forward (observation) models and direct inverse models for the scatterometer. We present an enhanced Markov chain Monte Carlo method to sample from the resulting multimodal posterior distribution. We go on to show how the computational complexity of the inference can be controlled by using a sparse, sequential Bayes algorithm for estimation with Gaussian processes. This helps to overcome the most serious barrier to the use of probabilistic, Gaussian process methods in remote sensing inverse problems, which is the prohibitively large size of the data sets. We contrast the sampling results with the approximations that are found by using the sparse, sequential Bayes algorithm.

A meshless method for an inverse two-phase one-dimensional nonlinear Stefan problem

We extend a meshless method of fundamental solutions recently proposed by the authors for the one-dimensional two-phase inverse linear Stefan problem, to the nonlinear case. In this latter situation the free surface is also considered unknown which is more realistic from the practical point of view. Building on the earlier work, the solution is approximated in each phase by a linear combination of fundamental solutions to the heat equation. The implementation and analysis are more complicated in the present situation since one needs to deal with a nonlinear minimization problem to identify the free surface. Furthermore, the inverse problem is ill-posed since small errors in the input measured data can cause large deviations in the desired solution. Therefore, regularization needs to be incorporated in the objective function which is minimized in order to obtain a stable solution. Numerical results are presented and discussed. © 2014 IMACS.