Structural evaluation of materials by artificial neural networks

It is shown that due to the complexity of interaction of the excitation field with a material in determining its physical characteristics, as well as sophisticated correlation relationships between the physical characteristics and structure of a real material, in many cases, relization of the structural evaluation of materials on the basis of idealized mathematical models of the underlying physical processes is of limited use. As an alternative, it is proposed to use an artificial neural network for the extraction of quantitative information of interest from measurements of the physical characteristics. A general overview of artificial neural networks is given. A methodology of the use of a multilayer perceptron for determining various structural parameters from the dielectric spectra is described. As an example, determination of the moisture content and density of sawdust from the dielectric modulusis considered by the neural-network technique. The noise performance of the neural network is analyzed by applying an additive and multiplicative noise to the input data.Institute of Polymer Mechanics, University of Latvia, Riga, LV-1006 Latvia. Published in Mekhanika Kompozitnykh Materialov, Vol. 35, No. 1, pp. 109–124, January–February, 1999.     

Structure of quasi-Newton minimization methods

A scheme for the design of quasi-Newton methods for unconstrained optimization problems is examined. A criterion for the positive definiteness of the quasi-Newton modification of the Hessian matrix is given. Quasi-Newton methods are described that cannot be placed within the classical scheme specified by the family of Broyden methods.     

Modeling in the theory of differential electrical prospecting methods

Translated from Pryamye i Obratnye Zadachi Matematicheskoi Fiziki, pp. 132–139, 1991.     

Multirate methods for the transient analysis of electrical circuits

Multirate integration is an important tool to increase the speed of the transient analysis of circuits. This paper shows an approach for the “Compound-Fast” multirate algorithm how to control the errors at the coarse and the refined time-grid by means of the independent stepsizes of these grids. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Testing methods for predicting the life of polymeric materials

On the assumption that the performance of polymeric materials can be predicted only on the basis of long-time tests under conditions similar to those that obtain in practice, the authors consider creep, stress relaxation, and dynamic measurements at various temperatures and frequencies. Theoretical methods of estimating the life of polymeric materials are investigated with allowance for changes in the physical and chemical structure of the polymer and the nonconstancy of the activation energy of the relaxation processes over a broad temperature interval.Lenin Moscow State Pedagogical Institute, Laboratory of Problems Polymer Physics. Translated from Mekhanika Polimerov, No. 2, pp. 212–220, March–April, 1971.     

Finite element methods for micropolar models of granular materials

We present a thermodynamically based finite element scheme for rate-independent materials and demonstrate its application in modelling the rheological behaviour of granular materials. Starting from the laws of thermodynamics, we have recently developed a new class of micropolar-type constitutive relations for two-dimensional densely packed granular media. This class of constitutive laws is expressed in terms of particle-scale properties, thus providing a direct link between observed macroscopic behaviour and the underlying particle–particle interactions. Here, we demonstrate how the connection to the underlying physics can be maintained and carried through to the finite element implementation phase of the modelling process via the same thermodynamical principles used to construct the constitutive laws. Notably, the study indicates that while the traditional Galerkin-FEM method admits a range of weighting functions, the proposed formulation provides an additional constraint that narrows the choice of admissible weighting functions via the second law of thermodynamics. Additionally, this paper presents insights into the finite element implementation of micropolar models deemed to be appropriate for modelling several classes of heterogeneous media (e.g. granular materials, cellular composites and biological materials). As the kinematics and kinetics of micropolar continua are enriched by the addition of rotational degrees of freedom to each material point, the equations governing boundary value problems for such materials differ from those of other continuum models both from the viewpoint of the constitutive law and the governing conservation laws. Analysis of elastoplastic deformation of micropolar continua is presented.     

Structure and properties of magnetic fibrous polymeric materials

Characteristic features of the filtration of liquids by magnetic fibrous polymeric materials (MFPM) are addressed; these materials are a set of fibers of a polymeric material containing a ferritic filler; they are adhesively bound at points of their intersection. It is demonstrated that variations in structural parameters (fiber thickness, distribution of fiber throughout the material, and its concentration), as well as the degree and direction of magnetization of the MFPM exert an influence on the efficiency of the liquid filtration. Optimum parameters for MFPM designed to purify liquids of ferromagnetic and nonmagnetic contaminants are given.A paper to be presented at the Ninth International Conference on the Mechanics of Composite Materials, Riga, October, 1995.Translated from Mekhanika Kompozitnykh Materialov, Vol. 31, No. 3, pp. 291–297, May–June, 1995.     

Cost evaluation of airline maintenance investigation-triggering methods

A reliable investigation-triggering mechanism is critical for airlines in managing aircraft fleet reliability. This study developed a simulation model to evaluate the performance of various investigation-triggering mechanisms in various scenarios of aircraft fleet reliability. Factors that affect performance include flight delay costs, investigation costs, the costs of corrective actions, the accuracy of investigations, the effectiveness of corrective actions, and the monthly improvement rate. Nine investigation-triggering mechanisms were evaluated. The simulation results show that the monthly improvement rate significantly influences performance. The subject airline’s original investigation-triggering mechanism is not outstanding in most scenarios. This study recommends two of the nine investigation-triggering mechanisms for airlines when they select investigation-triggering mechanisms in various scenarios. Thus, useful guidance for adjusting airlines’ investigation-triggering mechanisms can be effectively provided.     

Item selection by latent class-based methods: an application to nursing home evaluation

The evaluation of nursing homes is usually based on the administration of questionnaires made of a large number of polytomous items to their patients. In such a context, the latent class model represents a useful tool for clustering subjects in homogenous groups corresponding to different degrees of impairment of the health conditions. It is known that the performance of model-based clustering and the accuracy of the choice of the number of latent classes may be affected by the presence of irrelevant or noise variables. In this paper, we show the application of an item selection algorithm to a dataset collected within a project, named ULISSE, on the quality-of-life of elderly patients hosted in Italian nursing homes. This algorithm, which is closely related to that proposed by Dean and Raftery in 2010, is aimed at finding the subset of items which provides the best clustering according to the Bayesian Information Criterion. At the same time, it allows us to select the optimal number of latent classes. Given the complexity of the ULISSE study, we perform a validation of the results by means of a sensitivity analysis, with respect to different specifications of the initial subset of items, and of a resampling procedure.     

Numerical evaluation of approximation methods in stochastic programming

We study an approach for the evaluation of approximation and solution methods for multistage linear stochastic programmes by measuring the performance of the obtained solutions on a set of out-of-sample scenarios. The main point of the approach is to restore the feasibility of solutions to an approximate problem along the out-of-sample scenarios. For this purpose, we consider and compare different feasibility and optimality based projection methods. With this at hand, we study the quality of solutions to different test models based on classical as well as recombining scenario trees.     

Nondestructive methods of determining the dielectric constants of anisotropic polymeric materials

Procedures for determining the principal constants of the dielectric constant tensor of anisotropic polymeric materials are described. It is shown that the simplest solution of the problem corresponds to the use of external measuring capacitors. Two variants of measuring apparatus for determining the principal constants of the ε tensor and the anisotropy coefficient of polymeric materials are described with reference to block diagrams. The results of testing laboratory models are presented.     

Sparsity reconstruction in electrical impedance tomography: An experimental evaluation

We investigate the potential of sparsity constraints in the electrical impedance tomography (EIT) inverse problem of inferring the distributed conductivity based on boundary potential measurements. In sparsity reconstruction, inhomogeneities of the conductivity are a priori assumed to be sparse with respect to a certain basis. This prior information is incorporated into a Tikhonov-type functional by including a sparsity-promoting ?¹-penalty term. The functional is minimized with an iterative soft shrinkage-type algorithm. In this paper, the feasibility of the sparsity reconstruction approach is evaluated by experimental data from water tank measurements. The reconstructions are computed both with sparsity constraints and with a more conventional smoothness regularization approach. The results verify that the adoption of ?¹-type constraints can enhance the quality of EIT reconstructions: in most of the test cases the reconstructions with sparsity constraints are both qualitatively and quantitatively more feasible than that with the smoothness constraint.     

Two displacement methods for in-plane deformations of orthotropic linear elastic materials

Two displacement formulation methods are presented for the plane strain and plane stress problems of orthotropic linear elastic materials having the three planes of symmetry at x₁ = 0, x₂ = 0 and x₃ = 0. The first method starts with solving the two governing partial differential equations simultaneously, while the second method begins with solving one equation and ends with enforcing the other. The former follows the approach of Eshelby, Read and Shockley, whereas the latter is based on an extended version of Green's theorem and thus has similarities with Airy's stress function method. The two displacement methods lead to the same characteristic equation that is identical to the one obtained by Lekhnitskii using a stress formulation method. The general solutions resulting from the two displacement methods can be used to solve plane elasticity problems of orthotropic materials with displacement or mixed boundary conditions.     

Analysis of methods of determining the interlaminar shear strength of composite materials

Conclusions The range of geometrical dimensions of a sample in which the values of the interlaminar shear strength determined by four of the five methods discussed are practically constant has been established. Good agreement is shown in the values of the characteristic being determined which are obtained by each of the four methods. It has been established that the experimental data obtained by the method of three-point deflection of short beams does not characterize their interlaminar shear strength. It is shown that the interlaminar shear strength of glass-plastic and the shear strength of the adhesive with which it is prepared are very similar in value.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 4, pp. 640–648, July–August, 1976.