Inverse Sensitivity Analysis of Singular Solutions of FRF matrix in Structural System Identification

The problem of structural damage detection based on measured frequency response functions of the structure in its damaged and undamaged states is considered. A novel procedure that is based on inverse sensitivity of the singular solutions of the system FRF matrix is proposed. The treatment of possibly ill-conditioned set of equations via regularization scheme and questions on spatial incompleteness of measurements are considered. The application of the method in dealing with systems with repeated natural frequencies and (or) packets of closely spaced modes is demonstrated. The relationship between the proposed method and the methods based on inverse sensitivity of eigensolutions and frequency response functions is noted. The numerical examples on a 5-degree of freedom system, a one span free-free beam and a spatially periodic multi-span beam demonstrate the efficacy of the proposed method and its superior performance vis-a-vis methods based on inverse eigensensitivity.

A pseudo-dynamical systems approach to a class of inverse problems in engineering

A pseudo-dynamical approach for a class of inverse problems involving static measurements is proposed and explored. Following linearization of the minimizing functional associated with the underlying optimization problem, the new strategy results in a system of linearized ordinary differential equations (ODEs) whose steady-state solutions yield the desired reconstruction. We consider some explicit and implicit schemes for integrating the ODEs and thus establish a deterministic reconstruction strategy without an explicit use of regularization. A stochastic reconstruction strategy is then developed making use of an ensemble Kalman filter wherein these ODEs serve as the measurement model. Finally, we assess the numerical efficacy of the developed tools against a few linear and nonlinear inverse problems of engineering interest.

Inverse Correlation between Vitamin D and C-Reactive Protein in Newborns

Some studies suggested that adequate vitamin D might reduce inflammation in adults. However, little is known about this association in early life. We aimed to determine the relationship between cord blood 25-hydroxyvitamin D (25(OH)D) and C-reactive protein (CRP) in neonates. Cord blood levels of 25(OH)D and CRP were measured in 1491 neonates in Hefei, China. Potential confounders including maternal sociodemographic characteristics, perinatal health status, lifestyle, and birth outcomes were prospectively collected. The average values of cord blood 25(OH)D and CRP were 39.43 nmol/L (SD = 20.35) and 6.71 mg/L (SD = 3.07), respectively. Stratified by 25(OH)D levels, per 10 nmol/L increase in 25(OH)D, CRP decreased by 1.42 mg/L (95% CI: 0.90, 1.95) among neonates with 25(OH)D <25.0 nmol/L, and decreased by 0.49 mg/L (95% CI: 0.17, 0.80) among neonates with 25(OH)D between 25.0 nmol/L and 49.9 nmol/L, after adjusting for potential confounders. However, no significant association between 25(OH)D and CRP was observed among neonates with 25(OH)D ≥50 nmol/L. Cord blood 25(OH)D and CRP levels showed a significant seasonal trend with lower 25(OH)D and higher CRP during winter-spring than summer-autumn. Stratified by season, a significant linear association of 25(OH)D with CRP was observed in neonates born in winter-spring (adjusted β = −0.11, 95% CI: −0.13, −0.10), but not summer-autumn. Among neonates born in winter-spring, neonates with 25(OH)D <25 nmol/L had higher risk of CRP ≥10 mg/L (adjusted OR = 3.06, 95% CI: 2.00, 4.69), compared to neonates with 25(OH)D ≥25 nmol/L. Neonates with vitamin D deficiency had higher risk of exposure to elevated inflammation at birth.

Identification of dynamical systems with fractional derivative damping models using inverse sensitivity analysis

The problem of identifying parameters of time invariant linear dynamical systems with fractional derivative damping models, based on a spatially incomplete set of measured frequency response functions and experimentally determined eigensolutions, is considered. Methods based on inverse sensitivity analysis of damped eigensolutions and frequency response functions are developed. It is shown that the eigensensitivity method requires the development of derivatives of solutions of an asymmetric generalized eigenvalue problem. Both the first and second order inverse sensitivity analyses are considered. The study demonstrates the successful performance of the identification algorithms developed based on synthetic data on one, two and a 33 degrees of freedom vibrating systems with fractional dampers. Limited studies have also been conducted by combining finite element modeling with experimental data on accelerances measured in laboratory conditions on a system consisting of two steel beams rigidly joined together by a rubber hose. The method based on sensitivity of frequency response functions is shown to be more efficient than the eigensensitivity based method in identifying system parameters, especially for large scale systems.

Estimation in a multiplicative mixed model involving a genetic relationship matrix.

Genetic models partitioning additive and non-additive genetic effects for populations tested in replicated multi-environment trials (METs) in a plant breeding program have recently been presented in the literature. For these data, the variance model involves the direct product of a large numerator relationship matrix A, and a complex structure for the genotype by environment interaction effects, generally of a factor analytic (FA) form. With MET data, we expect a high correlation in genotype rankings between environments, leading to non-positive definite covariance matrices. Estimation methods for reduced rank models have been derived for the FA formulation with independent genotypes, and we employ these estimation methods for the more complex case involving the numerator relationship matrix. We examine the performance of differing genetic models for MET data with an embedded pedigree structure, and consider the magnitude of the non-additive variance. The capacity of existing software packages to fit these complex models is largely due to the use of the sparse matrix methodology and the average information algorithm. Here, we present an extension to the standard formulation necessary for estimation with a factor analytic structure across multiple environments.

Synthesis and Characterization of Carbon-Coated LiNi1/3Co1/3Mn1/3O2 in a Single Step by an Inverse Microemulsion Route

Layered LiNi1/3Co1/3Mn1/3O2, which is isostructural to LiCoO2, is considered as a potential cathode material. A layer of carbon coated on the particles improves the electrode performance, Which is attributed to an increase of the grain connectivity and also to protection of metal oxide from chemical reaction. The present work involves in situ synthesis of carbon-coated submicrometer-sized particles of LiNi1/3Co1/3Mn1/3O2 in an inverse microemulsion medium in the presence of glucose. The precursor obtained from the reaction is heated in air at 900 degrees C for 6 h to get crystalline LiNi1/3Co1/3Mn1/3O2. The carbon coating is found to impart porosity as well as higher surface area in relation to bare samples of the compound. The electrochemical characterization studies provide that carbon-coated LiNi1/3Co1/3Mn1/3O2 samples exhibit improved rate capability and cycling performance. The carbon coatings are shown to suppress the capacity fade, which is normally observed for the bare compound. Impedance spectroscopy data provide additional evidence for the beneficial effect of a carbon coating on LiNi1/3Co1/3Mn1/3O2 particles.

Application of inverse filtering technique in power system studies

This paper demonstrates the application of inverse filtering technique for power systems. In order to implement this method, the control objective should be based on a system variable that needs to be set on a specific value for each sampling time. A control input is calculated to generate the desired output of the plant and the relationship between the two is used design an auto-regressive model. The auto-regressive model is converted to a moving average model to calculate the control input based on the future values of the desired output. Therefore, required future values to construct the output are predicted to generate the appropriate control input for the next sampling time.

A Newton-Euler formulation for the inverse dynamics of the Stewart platform manipulator

This paper presents an inverse dynamic formulation by the Newton–Euler approach for the Stewart platform manipulator of the most general architecture and models all the dynamic and gravity effects as well as the viscous friction at the joints. It is shown that a proper elimination procedure results in a remarkably economical and fast algorithm for the solution of actuator forces, which makes the method quite suitable for on-line control purposes. In addition, the parallelism inherent in the manipulator and in the modelling makes the algorithm quite efficient in a parallel computing environment, where it can be made as fast as the corresponding formulation for the 6-dof serial manipulator. The formulation has been implemented in a program and has been used for a few trajectories planned for a test manipulator. Results of simulation presented in the paper reveal the nature of the variation of actuator forces in the Stewart platform and justify the dynamic modelling for control.

Inverse Problem for Fractional Brownian Motion with Discrete Data

The problem of recovering information from measurement data has already been studied for a long time. In the beginning, the methods were mostly empirical, but already towards the end of the sixties Backus and Gilbert started the development of mathematical methods for the interpretation of geophysical data. The problem of recovering information about a physical phenomenon from measurement data is an inverse problem. Throughout this work, the statistical inversion method is used to obtain a solution. Assuming that the measurement vector is a realization of fractional Brownian motion, the goal is to retrieve the amplitude and the Hurst parameter. We prove that under some conditions, the solution of the discretized problem coincides with the solution of the corresponding continuous problem as the number of observations tends to infinity. The measurement data is usually noisy, and we assume the data to be the sum of two vectors: the trend and the noise. Both vectors are supposed to be realizations of fractional Brownian motions, and the goal is to retrieve their parameters using the statistical inversion method. We prove a partial uniqueness of the solution. Moreover, with the support of numerical simulations, we show that in certain cases the solution is reliable and the reconstruction of the trend vector is quite accurate.

Direct and Inverse Scattering for Beltrami Fields

We consider an obstacle scattering problem for linear Beltrami fields. A vector field is a linear Beltrami field if the curl of the field is a constant times itself. We study the obstacles that are of Neumann type, that is, the normal component of the total field vanishes on the boundary of the obstacle. We prove the unique solvability for the corresponding exterior boundary value problem, in other words, the direct obstacle scattering model. For the inverse obstacle scattering problem, we deduce the formulas that are needed to apply the singular sources method. The numerical examples are computed for the direct scattering problem and for the inverse scattering problem.

A Reactive Inverse PN Algorithm for Collision Avoidance among Multiple Unmanned Aerial Vehicles

While performing a mission, multiple Unmanned Aerial Vehicles (UAVs) need to avoid each other to prevent collisions among them. In this paper, we design a collision avoidance algorithm to resolve the conflict among UAVs that are on a collision course while flying to heir respective destinations. The collision avoidance algorithm consist of each UAV that is on a collision course reactively executing a maneuver that will, as in `inverse' Proportional Navigation (PN), increase Line of Sight (LOS) rate between them, resulting in a `pulling out' of collision course. The algorithm is tested for high density traffic scenarios as well as for robustness in the presence of noise.

Optimal iterative schemes for computing the Moore-Penrose matrix inverse

Among the iterative schemes for computing the Moore — Penrose inverse of a woll-conditioned matrix, only those which have an order of convergence three or two are computationally efficient. A Fortran programme for these schemes is provided.

Bending the Rules of Cell Protrusions : Molecular Mechanisms and Biological Roles of Inverse-BAR Proteins in Cell Morphogenesis

Plasma membrane adopts myriad of different shapes to carry out essential cellular processes such as nutrient uptake, immunological defence mechanisms and cell migration. Therefore, the details how different plasma membrane structures are made and remodelled are of the upmost importance. Bending of plasma membrane into different shapes requires substantial amount of force, which can be provided by the actin cytoskeleton, however, the molecules that regulate the interplay between the actin cytoskeleton and plasma membrane have remained elusive. Recent findings have placed new types of effectors at sites of plasma membrane remodelling, including BAR proteins, which can directly bind and deform plasma membrane into different shapes. In addition to their membrane-bending abilities, BAR proteins also harbor protein domains that intimately link them to the actin cytoskeleton. The ancient BAR domain fold has evolved into at least three structurally and functionally different sub-groups: the BAR, F-BAR and I-BAR domains. This thesis work describes the discovery and functional characterization of the Inverse-BAR domains (I-BARs). Using synthetic model membranes, we have shown that I-BAR domains bind and deform membranes into tubular structures through a binding-surface composed of positively charged amino acids. Importantly, the membrane-binding surface of I-BAR domains displays an inverse geometry to that of the BAR and F-BAR domains, and these structural differences explain why I-BAR domains induce cell protrusions whereas BAR and most F-BAR domains induce cell invaginations. In addition, our results indicate that the binding of I-BAR domains to membranes can alter the spatial organization of phosphoinositides within membranes. Intriguingly, we also found that some I-BAR domains can insert helical motifs into the membrane bilayer, which has important consequences for their membrane binding/bending functions. In mammals there are five I-BAR domain containing proteins. Cell biological studies on ABBA revealed that it is highly expressed in radial glial cells during the development of the central nervous system and plays an important role in the extension process of radial glia-like C6R cells by regulating lamellipodial dynamics through its I-BAR domain. To reveal the role of these proteins in the context of animals, we analyzed MIM knockout mice and found that MIM is required for proper renal functions in adult mice. MIM deficient mice displayed a severe urine concentration defect due to defective intercellular junctions of the kidney epithelia. Consistently, MIM localized to adherens junctions in cultured kidney epithelial cells, where it promoted actin assembly through its I-BAR andWH2 domains. In summary, this thesis describes the mechanism how I-BAR proteins deform membranes and provides information about the biological role of these proteins, which to our knowledge are the first proteins that have been shown to directly deform plasma membrane to make cell protrusions.

Pseudo-time marching schemes for inverse problems in structural health assessment and medical imaging

We propose a self-regularized pseudo-time marching strategy for ill-posed, nonlinear inverse problems involving recovery of system parameters given partial and noisy measurements of system response. While various regularized Newton methods are popularly employed to solve these problems, resulting solutions are known to sensitively depend upon the noise intensity in the data and on regularization parameters, an optimal choice for which remains a tricky issue. Through limited numerical experiments on a couple of parameter re-construction problems, one involving the identification of a truss bridge and the other related to imaging soft-tissue organs for early detection of cancer, we demonstrate the superior features of the pseudo-time marching schemes.