An inverse method for optimizing elastic properties considering multiple loading conditions and displacement criteria

Significant research effort has been devoted to topology optimization (TO) of two- and three-dimensional structural elements subject to various design and loading criteria. While the field of TO has been tremendously successful over the years, literature focusing on the optimization of spatially varying elastic material properties in structures subject to multiple loading states is scarce. In this article, we contribute to the state of the art in material optimization by proposing a numerical regime for optimizing the distribution of the elastic modulus in structural elements subject to multiple loading conditions and design displacement criteria. Such displacement criteria (target displacement fields prescribed by the designer) may result from factors related to structural codes, occupant comfort, proximity of adjacent structures, etc. In this work, we utilize an inverse problem based framework for optimizing the elastic modulus distribution considering N target displacements and imposed forces. This approach is formulated in a straight-forward manner such that it may be applied in a broad suite of design problems with unique geometries, loading conditions, and displacement criteria. To test the approach, a suite of optimization problems are solved to demonstrate solutions considering N = 2 for different geometries and boundary conditions

Damage tomography as a state estimation problem : crack detection using conductive area sensors

Typically, structural damage tomography (SDT) approaches aim to reconstruct a parameter field containing damage information from distributed data by solving an iterative inverse problem. Often, there are two shortcomings in adopting such an approach: (a) the high computational expense and (b) temporal information is inadequately used. In principle, both issues may be alleviated by approaching SDT as a state-estimation problem – i.e. treating the reconstruction problem as a temporally-evolving stochastic process. In this letter, we study the feasibility of state estimates in SDT. For this, we use an extended Kalman filter (EKF) for electrical resistance tomography (ERT) imaging of progressive cracking on an experimentally-tested reinforced concrete beam with an applied surface area sensing skin. In the investigation, we quantitatively analyze the effect of including multiple temporal data sets and corroborate EKF-ERT reconstructions with standard and advanced ERT approaches. It is shown that increasing the amount of temporal data significantly improves the quality of EKF-ERT reconstructions, which compare favorably with the standard and advanced ERT approaches. In addition, for the data sets used herein, the EKF-ERT regime computed seven reconstructions approximately 50-100 times faster than the standard and stacked approaches required to reconstruct one image, respectively

Nonstationary shape estimation in electrical impedance tomography using a parametric level set-based extended Kalman filter approach

This paper presents a parametric level set based reconstruction method for non-stationary applications using electrical impedance tomography (EIT). Owing to relatively low signal to noise ratios in EIT measurement systems and the diffusive nature of EIT, reconstructed images often suffer from low spatial resolution. In addressing these challenges, we propose a computationally efficient shape-estimation approach where the conductivity distribution to be reconstructed is assumed to be piecewise constant, and the region boundaries are assumed to be non-stationary in the sense that the characteristics of region boundaries change during measurement time. The EIT inverse problem is formulated as a state estimation problem in which the system is modeled with a state equation and an observation equation. Given the temporal evolution model of the boundaries and observation model, the objective is to estimate a sequence of states for the nonstationary region boundaries. The implementation of the approach is based on the finite element method and a parametric representation of the region boundaries using level set functions. The performance of the proposed approach is evaluated with simulated examples of thorax imaging, using noisy synthetic data and experimental data from a laboratory setting. In addition, robustness studies of the approach w.r.t the modeling errors caused by inaccurately known boundary shape, non-homogeneous background and varying conductivity values of the targets are carried out and it is found that the proposed approach tolerates such kind of modeling errors, leading to good reconstructions in non-stationary situations

Electrical tomography for characterizing transport properties in cement-based materials: A review

The ability to spatially and temporally quantify the state and distribution of moisture and ions is of central importance to understanding the durability of cement-based materials and structures. Owing to the heterogeneous nature of concrete and challenges associated with using point-based measurements in accomplishing such a task, the use of two- and three-dimensional tomography for quantifying transport properties has become the source of much research interest. Distinct from electromagnetic radiation-based modalities – Electrical Tomography (ET), including Electrical Resistance Tomography, Electrical Impedance Tomography, and Electrical Capacitance Tomography, has emerged as a viable means for characterizing transport in cement-based materials. In this work, we provide a technical overview of ET and the nature of ET inverse problems. We also review historical challenges and successes of ET for imaging transport properties in cement-based materials. Based on realizations from the review, challenges and opportunities afforded by ET for characterizing transport properties are provided and discussed

B-spline based sharp feature preserving shape reconstruction approach for electrical impedance tomography

This paper presents a B-spline based shape reconstruction approach for electrical impedance tomography (EIT). In the proposed approach, the conductivity distribution to be reconstructed is assumed to be piecewise constant. The geometry of the inclusions is parameterized using B-spline curves, and the EIT forward solver is modified as a set of control points representing the inclusions’ boundary to the data on the domain boundary. The low order representation decreases the computational demand and reduces the ill-posedness of the EIT reconstruction problem. The performance of the proposed B-spline based approach is tested with simulations which demonstrate the most popular biomedical application of EIT: lung imaging. The approach is experimentally validated using water tank data. In addition, robustness studies of the proposed approach considering varying initial guesses, inaccurately known contact impedances, differing numbers of control points, and degree of B-spline are performed. The simulation and experimental results show that the B-spline based approach offers improvements in image quality in comparison to the traditional Fourier series based reconstruction approach, as measured by quantitative metrics such as relative size coverage ratio and relative contrast. Inasmuch, the proposed approach is demonstrated to offer clear improvement in the ability to preserve the sharp properties of the inclusions to be imaged

Optimizing electrode positions in 2D electrical impedance tomography using deep learning

Electrical Impedance Tomography (EIT) is a powerful tool for non-destructive evaluation, state estimation, and process tomography – among numerous other use cases. For these applications, and in order to reliably reconstruct images of a given process using EIT, we must obtain high-quality voltage measurements from the target of interest. As such, it is obvious that the locations of electrodes used for measuring plays a key role in this task. Yet, to date, methods for optimally placing electrodes either require knowledge on the EIT target (which is, in practice, never fully known) or are computationally difficult to implement numerically. In this paper, we circumvent these challenges and present a straightforward deep learning based approach for optimizing electrodes positions. It is found that the optimized electrode positions outperformed “standard” uniformly-distributed electrode layouts in all test cases. Further, it is found that the use of optimized electrode positions computed using the approach derived herein can reduce errors in EIT reconstructions as well as improve the distinguishability of EIT measurements

Invisibility and indistinguishability in structural damage tomography

Structural damage tomography (SDT) uses full-field or distributed measurements collected from sensors or self-sensing materials to reconstruct quantitative images of potential damage in structures, such as civil structures, automobiles, aircraft, etc. In approximately the past ten years, SDT has increased in popularity due to significant gains in computing power, improvements in sensor quality, and increases in measurement device sensitivity. Nonetheless, from a mathematical standpoint, SDT remains challenging because the reconstruction problems are usually nonlinear and ill-posed. Inasmuch, the ability to reliably reconstruct or detect damage using SDT is seldom guaranteed due to factors such as noise, modeling errors, low sensor quality, and more. As such, damage processes may be rendered invisible due to data indistinguishability. In this paper we identify and address key physical, mathematical, and practical factors that may result in invisible structural damage. Demonstrations of damage invisibility and data indistinguishability in SDT are provided using experimental data generated from a damaged reinforced concrete beam

A parametric level set-based approach to difference imaging in electrical impedance tomography

This paper presents a novel difference imaging approach based on the recently developed parametric level set (PLS) method for estimating the change in a target conductivity from electrical impedance tomography measurements. As in conventional difference imaging, the reconstruction of conductivity change is based on data sets measured from the surface of a body before and after the change. The key feature of the proposed approach is that the conductivity change to be reconstructed is assumed to be piecewise constant, while the geometry of the anomaly is represented by a shape-based PLS function employing Gaussian radial basis functions (GRBFs). The representation of the PLS function by using GRBF provides flexibility in describing a large class of shapes with fewer unknowns. This feature is advantageous, as it may significantly reduce the overall number of unknowns, improve the condition number of the inverse problem, and enhance the computational efficiency of the technique. To evaluate the proposed PLS-based difference imaging approach, results obtained via simulation, phantom study, and in vivo pig data are studied. We find that the proposed approach tolerates more modeling errors and leads to a significant improvement in image quality compared with the conventional linear approach

Effect of different omega-6/omega-3 polyunsaturated fatty acid ratios on the formation of monohydroxylated fatty acids in THP-1 derived macrophages

Omega-6 and omega-3 polyunsaturated fatty acids (n-6 and n-3 PUFA) can modulate inflammatory processes. In western diets, the content of n-6 PUFA is much higher than that of n-3 PUFA, which has been suggested to promote a pro-inflammatory phenotype. The aim of this study was to analyze the effect of modulating the n-6/n-3 PUFA ratio on the formation of monohydroxylated fatty acid (HO-FAs) derived from the n-6 PUFA arachidonic acid (AA) and the n-3 PUFAs eicosapentaenoic acid (EPA) and docosahexaenoic acid (DHA) in THP-1 macrophages by means of LC-MS. Lipid metabolites were measured in THP-1 macrophage cell pellets. The concentration of AA-derived hydroxyeicosatetraenoic acids (HETEs) was not significantly changed when incubated THP-1 macrophages in a high AA/(EPA+DHA) ratio of 19/1 vs. a low ratio AA/(EPA+DHA) of 1/1 (950.6 +/- 110 ng/mg vs. 648.2 +/- 92.4 ng/mg, p = 0.103). Correspondingly, the concentration of EPA-derived hydroxyeicosapentaenoic acids (HEPEs) and DHA-derived hydroxydocosahexaenoic acids (HDHAs) were significantly increased (63.9 +/- 7.8 ng/mg vs. 434.4 +/- 84.3 ng/mg, p = 0.012 and 84.9 +/- 18.3 ng/mg vs. 439.4 +/- 82.7 ng/mg, p = 0.014, respectively). Most notable was the strong increase of 18-hydroxyeicosapentaenoic acid (18-HEPE) formation in THP-1 macrophages, with levels of 170.9 +/- 40.2 ng/mg protein in the high n-3 PUFA treated cells. Thus our data indicate that THP-1 macrophages prominently utilize EPA and DHA for monohydroxylated metabolite formation, in particular 18-HEPE, which has been shown to be released by macrophages to prevent pressure overload-induced maladaptive cardiac remodeling

Coupled digital image correlation and quasi-static elasticity imaging of inhomogeneous orthotropic composite structures

The ability to accurately determine elastic properties of orthotropic materials is important in the design and health assessment of composite structures. Direct methods using strain gauges and extensometers for estimating orthotropic properties have become popular in recent years. In cases where strains are highly localized, the material properties are inhomogeneous, or the material has localized damage, the use of these measurement schemes often provides insufficient information. To address this, we propose an inverse method, based on quasi-static elasticity imaging (QSEI) for determining inhomogeneous orthotropic elastic properties using distributed displacement measurements obtained from digital image correlation (DIC). The QSEI-based approach is first tested with simulated noisy displacement data considering in-plane deformations of plate geometries undergoing stretching and bending. Following this, experimental DIC measurements are applied to test the feasibility of the QSEI-based approach. Elastic properties of uni-directional CFRP beams with and without localized damage are estimated using the proposed approach. Results demonstrate the feasibility of the proposed inverse approach