Inverse estimation of the elastic and anelastic properties of the porous frame of anisotropic open-cell foams

This paper presents a method for simultaneously identifying both the elastic and anelastic properties of the porous frame of anisotropic open-cell foams. The approach is based on an inverse estimation procedure of the complex stiffness matrix of the frame by performing a model fit of a set of transfer functions of a sample of material subjected to compression excitation in vacuo. The material elastic properties are assumed to have orthotropic symmetry and the anelastic properties are described using a fractional-derivative model within the framework of an augmented Hooke's law. The inverse estimation problem is formulated as a numerical optimization procedure and solved using the globally convergent method of moving asymptotes. To show the feasibility of the approach a numerically generated target material is used here as a benchmark. It is shown that the method provides the full frequency-dependent orthotropic complex stiffness matrix within a reasonable degree of accuracy.     

Reconstruction of the shape of echo-sounded objects

The paper considers the problem of reconstructing the shape of echo-sounded objects under conditions when the well-known methods, e.g., the Boyarskii method, are inapplicable or inefficient. A variant of the method is proposed for reconstructing the shape of an object using the function from the Gaussian curvature of the surface. As well, it is shown that the main information on this function is carried by the initial region of the echo signal and that the results of reconstructing the shape depend on the correlation duration of probing signals. When ultra-wideband probing signals are applied, this method is fundamentally suitable for reconstructing the shape of silt-covered objects. Formally, the method is applicable only for convex surfaces, but it can be expanded to more complex surfaces under certain conditions.     

Identification of stiffness and damping properties of plates by using the local equation of motion

This paper deals with the identification of stiffness and damping properties of vibrating structures by an inverse method inspired from the Force Analysis Technique (FAT). The proposed approach uses a local equation of motion assumed a priori, which provides a relative straightforward relationship between the displacement field and material properties. The spatial derivatives of the displacement in the equation are calculated using finite differences. As this operation amplifies measurement noise, a regularization step is applied before solving the inverse problem. A procedure is proposed to automatically adjust the level of regularization. The method also allows one to identify local stiffness and damping on a heterogeneous structure. Illustrations for both homogeneous and heterogeneous cases are shown using simulated and measured displacement fields.     

Identification of the type and parameters of fastening from the natural frequencies of a fastened rod

A rod can be fastened in a number of ways. If the rod ends are inaccessible to visual observation, the question arises of whether it is possible to determine the type and parameters of their fastening from sound vibrations induced by an impact on the rod. In this connection, a possible statement of the problem is as follows: to identify the type and parameters of fastening on both ends of a homogeneous rod from its natural frequencies. In other words, it is necessary to determine the type of fastening of each of the ends of a homogeneous rod (clamping, free support, elastic support, elastic fixing, floating fixing, or free end) and its parameters (the stiffness coefficients of springs for elastic fixing). The duality and stability of the solution to this problem is demonstrated. A method of solving this problem with the use of 9 natural frequencies is proposed. The results of numerical experiments on reconstructing various types of fastening from 9 natural frequencies are presented.     

Acoustic tomography of the nonlinear parameter by a small number of transducers

A wave approach to solving the problem of reconstructing the acoustic nonlinear parameter distribution by a simple transmitting-receiving system with broadband modulation of primary waves is proposed. The approach uses the effect of sound scattering by sound, which makes it possible to employ a complicated time processing of signals instead of spatial processing and, consequently, to reduce the number of transmitting and receiving transducers. The possibility of practical implementation of a two-dimensional tomographic scheme based on coherent correlation processing of broadband quasi-random signals at combination frequencies is analyzed. Results of model numerical experiments on reconstructing complicated spatial distributions of the nonlinear parameter are presented.     

On optimal reconstruction of constitutive relations

In this investigation we develop and validate a computational method for reconstructing constitutive relations based on measurement data, applicable to problems arising in nonequilibrium thermodynamics and continuum mechanics. This parameter estimation problem is solved as PDE-constrained optimization using a gradient-based technique in the optimize-then-discretize framework. The principal challenge is that the control variable (i.e., the relation characterizing the constitutive property) is not a function of the independent variables in the problem, but of the state (dependent) variable. The proposed method allows one to reconstruct a smooth constitutive relation defined over a broad range of the dependent variable. It relies on three main ingredients: a computationally friendly expression for the cost functional gradient, Sobolev gradients used in lieu of discontinuous L₂ gradients, and a systematic technique for shifting the identifiability region. The performance of this approach is illustrated by the reconstruction of the temperature dependence of the thermal conductivity in a one-dimensional model problem.     

Improvement in image resolution based on dispersive representation of data

A method for reconstructing the resolution of images, based on selection and optimization of significant local features and sparse representation of processed-image blocks (using optimized low- and high-resolution dictionaries), has been substantiated for the first time. This method, making it possible to improve significantly the resolution of images of various nature, is interpreted physically. A block diagram of the processing system corresponding to the new approach to image reconstruction has been developed. A simulation of the new method for reconstructing images of different physical natures and known algorithms showed an advantage of the new scheme for reconstructing resolution in terms of universally recognized criteria (peak signal-to-noise ratio, mean absolute error, and structural similarity index measure) and in visual comparison of the processed images.     

Identification of the structure parameters using short-time non-stationary stochastic excitation

In this paper, we propose an approach to the flexural stiffness or eigenvalue frequency identification of a linear structure using a non-stationary stochastic excitation process. The idea of the proposed approach lies within time domain input-output methods. The proposed method is based on transforming the dynamical problem into a static one by integrating the input and the output signals. The output signal is the structure reaction, i.e. structure displacements due to the short-time, irregular load of random type. The systems with single and multiple degrees of freedom, as well as continuous systems are considered.     

Trimmed autocalibrating k-space estimation based on structured matrix completion

PurposeParallel imaging allows the reconstruction of undersampled data from multiple coils. This provides a means to reject and regenerate corrupt data (e.g. from motion artefact). The purpose of this work is to approach this problem using the SAKE parallel imaging method.Theory and methodsParallel imaging methods typically require calibration by fully sampling the center of k-space. This is a challenge in the presence of corrupted data, since the calibration data may be corrupted which leads to an errors-in-variables problem that cannot be solved by least squares or even iteratively reweighted least squares. The SAKE method, based on matrix completion and structured low rank approximation, was modified to detect and trim these errors from the data.ResultsSimulated and actual corrupted datasets were reconstructed with SAKE, the proposed approach and a more standard reconstruction method (based on solving a linear equation) with a data rejection criterion. The proposed approach was found to reduce artefacts considerably in comparison to the other two methods.ConclusionSAKE with data trimming improves on previous methods for reconstructing images from grossly corrupted data.     

Wavelet frame based scene reconstruction from range data

How to reconstruct the scene (a visible surface) from a set of scattered, noisy and possibly sparse range data is a challenging problem in robotic navigation and computer graphics. As most real scenes can be modeled by piecewise smooth surfaces, traditional surface fitting techniques (e.g. smoothing spline) generally can not preserve sharp discontinuities of surfaces. Based on sparse approximation of piecewise smooth functions in frame domain, we propose a new tight frame based formulation for reconstructing a piecewise smooth surface from a sparse range data set, which is robust to both additive noise and outliers. Furthermore, the resulting minimization problem from our formulation can be efficiently solved by the split Bregman method [1], [2]. The numerical experiments show that the proposed approach is capable of reconstructing a piecewise smooth surface with sharp edges from sparse range data corrupted with noise and outliers.     

Method of Bayesian estimates in the problem of laser gas analysis

The problem of reconstructing gas concentrations is considered for laser multicomponent gas analysis. For the differential absorption method, the procedures of signal processing are described based on the method of Bayesian estimates. It is demonstrated that the use of the method of Bayesian estimates the problem of reconstructing gas concentration both for few-and multicomponent gas mixtures allows to be solved effectively even for gases whose absorption spectrum has no noticeable maxima. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 29–35, September, 2008.     

X-ray diffraction scattering and determination of the structural parameters of a film with a variable strain gradient

Characteristics of the x-ray diffraction field in structures with a variable strain gradient are analyzed using a model with an exponential profile. It is shown that the problem of reconstructing the structural parameters of the strained layer from the angular positions of the principal maximum and the oscillations is generally multivalued even when the strain varies monotonically over depth. Conditions are determined for which this problem can be solved. An analogy is identified with the results of an approach to determine the parameters of the strained layer based on using the integral characteristics of the diffraction reflection curve. Zh. Tekh. Fiz. 69, 67–70 (June 1999)     

Vibrations and buckling of a beam on a variable winkler elastic foundation

Two methods for solving the eigenvalue problems of vibrations and stability of a beam on a variable Winkler elastic foundation are presented and compared. The first is based on using the exact stiffness, consistent mass, and geometric stiffness matrices for a beam on a variable Winkler elastic foundation. The second method is based on adding an element foundation stiffness matrix to the regular beam stiffness matrix, for vibrations and stability analysis. With these matrices, it is possible to find the natural frequencies and mode shapes of vibrations, and buckling load and mode shape, by using a small number of segments. It is concluded that the use of the element foundation stiffness approach yields better convergence at lower computation costs.     

Improving the accuracy of cosmic ray mass composition estimation using the scale factor of the electron lateral distribution in air showers

The prospects for using the scale factor of the lateral distribution of electrons in air showers as an indicator of the type of cosmic ray primary particle is studied. The developed approach allows to improve the accuracy of reconstructing the mass composition of high-energy cosmic radiation on both an average and event-by-event basis, along with the reanalysis and verification of the congruence between data from different experiments and their cross-calibration and validation. The problem of estimating the scale factor of the electron lateral distribution using data from existing EAS arrays in light of their prospective upgrading is discussed.     

Ocean acoustic tomography with a nonstandard representation of refractive inhomogeneities

The two-dimensional tomography problem of reconstructing a refractive inhomogeneity in the ocean is considered. A distinction of this paper is the expansion of the inhomogeneity under investigation in a nonstandard (nonorthogonal and overfull) basis. This basis makes it possible to overcome some problems inherent in the conventional schemes dividing the ocean into squares, triangles, and other figures with corners. In addition, the perturbation matrix can be easily constructed in such a basis. The proposed approach can be used in its present form for reconstructing flows and solving combined refractive-kinetic problems. The solution of the tomography problem with the use of the proposed basis is carried out in both ray and wave representations.     

Inverse problem of the event reconstruction in the LORD experiment using the signal speсtrum information

Using the modified random search method, the solution of the inverse problem of reconstructing events in the LORDlunar experiment is considered using the signal spectral analysis, where the total frequency band of 200–400 MHz is divided into four equal frequency bands. Additional information about the signal will allows one to achieve a higher accuracy in the solution of the inverse problem.     

Dynamic behaviour of structures in large frequency range by continuous element methods

The continuous element method is presented in the context of the harmonic response of beam assemblies. A general formulation is described from the displacement solution of the elementary problem. A direct computation of elementary dynamic stiffness matrices is presented. In the present formulation, distributed loadings are taken into account. In the case of more complex geometries for which many coupling phenomena occur, an explicit formulation is no more conceivable. In this case, a numerical approach is presented. This approach allows an algorithmic computation of exact dynamic stiffness matrices. This method, called “Numerical Continuous Element”, allows one to consider the coupled vibrations of curved beams and those of helical beams. The validation of this numerical method is achieved by comparisons with the harmonic response of various beams obtained by a finite element approach. Finally, a comparison between eigenfrequencies obtained experimentally and numerically for a straight beam and a helical beam has been made to evaluate the performances of the method.     

Choosing the ranges for measuring the reflectivity of a prism coupler in the waveguide spectroscopy of thin films

A criterion for selecting the best ranges for measuring the reflectivity of a prism coupler, based on minimizing the error in reconstructing the parameters of thin films using the least-square method, is proposed. The effectiveness of the criterion is demonstrated by solving the inverse optical problem for a SiO_x film deposited on a silicon substrate as an example.     

The use of asymptotic modelling in vibration and stability analysis of structures

The use of springs with very large stiffness to model constraints in vibratory systems has been a popular approach to overcome the limitations on the choice of admissible functions in the Rayleigh-Ritz method. The maximum possible error resulting from this asymptotic modelling can be determined by using positive and negative stiffness values, or in general terms using positive and negative penalty functions. This paper illustrates how this method could be used to determine the critical loads of structures.     

Stochastic collocation method for secondary bifurcation of a nonlinear aeroelastic system

A stochastic collocation method is proposed to investigate the secondary bifurcation of a two-dimensional aeroelastic system with structural nonlinearity represented by cubic restoring forces, and uncertainties expressed by random parameters in the cubic stiffness coefficient and in the initial pitch angle. The accuracy of the stochastic collocation method is improved by incorporating higher order schemes, such as piecewise cubic interpolation and piecewise cubic spline interpolation, instead of a piecewise linear interpolation formula. For an aeroelastic problem with the uncertainty expressed by a time dependent combination of five random variables, an efficient collocation method is developed using a sparse grid approach with a dimension adaptive strategy. Numerical simulations are carried out to demonstrate the effectiveness of the proposed method for long term computation and discontinuous problems.