Detecting structural changes with ARMA processes

ABSTRACT

In this paper, we discuss the application of autoregressive moving average (ARMA) processes in structural health monitoring. For this aim, we consider a linear system of differential equations driven by white noise, which could be seen as a continuous time model of an engineering structure under ambient excitation. A single component of the solution of such a system reflects the position or velocity of a fixed point of the observed structure. We first show that every such component behaves like an ARMA process. These considerations are illustrated by an example, where we show how the natural frequencies can be calculated from the process coefficients. However, the main focus of the paper lies in the detection of structural changes with ARMA processes. For this purpose, we propose a new distance measure that relies on the one-step prediction errors and some sampling strategies. Two case studies are included, which serve to demonstrate the performance of the proposed method. The first one is an off-duty steel truss railway bridge, followed by an in-depth study of an aluminium shear frame construction. In the latter case scenario, we show that the distance measure increases with increasing damage extent.     

Critical levels of oriented defects in brittle fracture

Conclusions For an orthotropic system of defects we derived a brittle failure criterion whose coefficients are determined by the parameters of the structure. The discussed examples show that the proposed relationships can be used more efficiently to determine the behavior of the structure on the basis of the macroproperties of the material. The effects of variations in the dimensions of the defects, merging of the defects and the appearance of new defects are described quantitatively. After compiling a sufficient amount of information, the relations can be used to solve the main problem of determining the ultimate strength on the basis of the behavior of the structure of defects.Translated from Mekhanika Kompozitnykh Materialov, No. 4, pp. 623–630, July–August, 1989.     

Exponential decay for elastic systems with structural damping and infinite delay

ABSTRACT

In this paper, we consider nonlinear evolution equations of second order in Banach spaces involving unbounded delay, which can model an elastic system with structural damping involving infinite delays. By using fixed point for condensing maps, we prove the existence and exponential decay of mild solutions. The obtained results can be applied to the nonlinear vibration equation of elastic beams with structural damping and infinite delay.     

NHPP models for categorized software defects

We develop NHPP models to characterize categorized event data, with application to modelling the discovery process for categorized software defects. Conditioning on the total number of defects, multivariate models are proposed for modelling the defects by type. A latent vector autoregressive structure is used to characterize dependencies among the different types. We show how Bayesian inference can be achieved via MCMC procedures, with a posterior prediction‐based L‐measure used for model selection. The results are illustrated for defects of different types found during the System Test phase of a large operating system software development project. Copyright © 2005 John Wiley & Sons, Ltd.     

Thermo-mechanical modeling of turbine blades taking into account structural defects

In turbine blades of aero-engines typical defects are cracks due to high mechanical and thermal loads. The extended finite element method (XFEM) is used for simulations of fracture mechanics problems with cracks. Discontinuities in the displacement and temperature field are allowed and the crack opening displacement and crack tip stress field are reproduced accurately. Since crack closure and non-physical penetration of the crack surfaces may occur under certain load conditions, it becomes necessary to enforce the non-penetration condition for crack surfaces. This contact formulation is assumed to be frictionless. The node-to-segment approach proposed in [3] is extended to ten-node tetrahedral elements with quadratic shape functions. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Simulation of Lamb wave interaction with defects in laminated plates by SEM

For the simulation of the interaction of elastic waves in CFRP Plates with inhomogeneities and defects the spectral finite element method (SEM) is under investigation. The SEM uses high-order shape functions which are composed of Lagrange polynomials with nodes at the Gauss-Lobatto quadrature (GLq) points. In this way we obtain a diagonal mass matrix which makes an explicit time scheme more efficient. In a numerical example based on the first order shear deformation theory (FSDT) a computation by FEAP of an interaction with an inhomogeneity is presented. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Terminal defects in crystalline polyethylene

Conclusions 1. Possible modes of transverse movement of terminal defects in crystalline polyethylene have been investigated for the three-dimensional case. It has been found that the probability of aggregation of two columns of monovacancies by means of their transverse movement decreases rapidly with increase in the initial distance between defects.2. The process of decrease in volume of a column of vacancies during compression has been investigated. A dependence of the degree of compression of a vacancy on the angle between the external force and the plane of zigzag of the chain has been found.3. Three positions of stable equilibrium of doubling of the three-dimensional model of polyethylene containing a series of vacancies have been observed during loading of the simple shear type.For Communication 1, see [1].Institute for Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 4, pp. 588–595, July–August, 1978.     

Exploring simple structural configurations for optimal network mutualism

There is a great interest in understanding how ecosystems organize into structural patterns they exhibit. The acquisition and utilization of energy has long been identified as one of the key issues of life; as the famous physicist Ludwig von Boltzmann once stated “life is the struggle for free energy”. Adopting the premise that energy flow is a primary organizing principle in ecological systems, here we explore an ecological goal function based on the net energy flow between system compartments. This approach, called network utility analysis, proposes that the integral utility (direct plus indirect) in well-developed systems tends to contain more positive relations than negative ones. In this research we use utility analysis to determine specific relationship types between compartments for several basic network structures. Simple networks exhibit relations that are fixed for that particular structure, whereas for more complex cases the system may be classified into utility regimes depending on the energy flow values in the system. Lastly, we present candidate structural configurations having the least and greatest utility values. This research contributes to the overall discipline of ecological network analysis.     

The effect of precipitates on the evolution of a martensitic phase boundary

In this article, we study the role of defects in the quasistatic evolution of a martensitic phase boundary. The formulation of the model gives rise to a nonlocal free boundary problem, for which we present an implicit finite-time discretization. For an approximate model, assuming a nearly flat interface, we show that the phase boundary exhibits a sick-slip behavior in the presence of a heterogeneous environment, thus leading to a transition from viscous kinetics to rate-independent behavior. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Sparse null basis computations in structural optimization

Summary We study the computation of sparse null bases of equilibrium matrices in the context of the force method in structural optimization. Two classes of structural problems are considered. For the class of rigid jointed skeletal structures, we use a partitioning method suggested by Henderson and Maunder to partition the problem into a set of independent null basis computations. For the class of structures represented by a continuum, we compute a sizable fraction of the null vectors in a basis from a consideration of the finite element formulation and the bipartite graph of the equilibrium matrix. The remaining null vectors are computed by the triangular algorithm in [6]. The new algorithms find sparser bases than the triangular algorithm and are also faster.This research was partially supported by NSF grant CCR-8701723 and AFOSR grant 88-0161     

Induced good gradings of structural matrix rings

Our approach to structural matrix rings defines them over preordered directed graphs. A grading of a structural matrix ring is called a good grading if its standard unit matrices are homogeneous. For a group G, a G-grading set is a set of arrows with the property that any assignment of these arrows to elements of G uniquely determines an induced good grading. One of our main results is that a G-grading set exists for any transitive directed graph if G is a group of prime order. This extends a result of Kelarev. However, an example of Molli Jones shows there are directed graphs which do not have G-grading sets for any cyclic group G of even order greater than 2. Finally, we count the number of nonequivalent elementary gradings by a finite group of a full matrix ring over an arbitrary field.     

Single dopant diffusion in semiconductor technology

The paper deals with the analysis of pair diffusion models in semiconductor technology. The underlying model contains reaction‐drift‐diffusion equations for the mobile point defects and dopant‐defect pairs as well as reaction equations for immobile dopants which are coupled with a non‐linear Poisson equation for the chemical potential of the electrons. For homogeneous structures we present an existence and uniqueness result for strong solutions. Starting with energy estimates we derive further a priori estimates such that fixed point arguments due to Leray–Schauder guarantee the solvability of the model equations. Copyright © 2004 John Wiley & Sons, Ltd.     

Uniqueness for the determination of sound-soft defects in an inhomogeneous planar medium by acoustic boundary measurements

We consider the inverse problem of determining shape and location of sound-soft defects inside a known planar inhomogeneous and anisotropic medium through acoustic imaging at low frequency. In order to determine the defects, we perform acoustic boundary measurements, with prescribed boundary conditions of different types. We prove that at most two, suitably chosen, measurements allow us to uniquely determine multiple defects under minimal regularity assumptions on the defects and the medium containing them. Finally, we treat applications of these results to the case of inverse scattering.

     

Buckling stability of multilayer plates and shells with interfacial structural defects under axial compression

Based on the discrete-structural theory of thin plates and shells, a variant of the equations of buckling stability, containing a parameter of critical loading, is put forward for the thin-walled elements of a layered structure with a weakened interfacial contact. It is assumed that the transverse shear and compression stresses are equal on the interfaces. Elastic slippage is allowed over the interfaces between adjacent layers. The stability equations include the components of geometrically nonlinear moment subcritical buckling conditions for the compressed thin-walled elements. The buckling of two-layer transversely isotropic plates and cylinders under axial compression is investigated numerically and experimentally. It is found that variations in the kinematic and static contact conditions on the interfaces of layered thin-walled structural members greatly affect the magnitude of critical stresses. In solving test problems, a comparative analysis of the results of stability calculations for anisotropic plates and shells is performed with account of both perfect and weakened contacts between adjacent layers. It is found that the model variant suggested adequately reflects the behavior of layered thin-walled structural elements in calculating their buckling stability. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 43, No. 4, pp. 513–530, July–August, 2007.     

Numerical simulation of the rheological properties of granular composites by using a structural approach

Composites with an elastomeric matrix containing rigid particles of diameter 10–1000 μm are studied. One of possible mechanisms of the rheological behavior of such filled systems, related to the origination and growth of vacuoles near the rigid inclusions in a viscous matrix, is considered. For simulating the mechanism of formation of rheological properties of the filled elastomers, we use a structural cell in the form of an elastomeric cylinder, whose height and diameter are equal in magnitude, with a rigid spherical inclusion at its center. Deformation of the cells is examined with the observance of boundary conditions providing the preservation of their close packing. The inclusion is assumed to be rigid, and the matrix properties are described by equations of the linear hereditary viscoelasticity theory. The formation of vacuoles is described by using the approach suggesting that an initial debonding begins to propagate when the energy accumulated in the extended matrix reaches a value sufficient to create a new interface. The heterogeneity of the composite is simulated by taking into account the variability of the local filler concentration. Creep curves obtained for composite cells with different content of the solid phase are presented. Comparisons between the numerical and experimental results show a satisfactory agreement. Translated from Mekhanika Kompozitnykh Materialov, Vol. 44, No. 6, pp. 895–906, November–December, 2008.     

Existence of solutions for a mathematical model of structural phase transitions in shape memory alloys

In this paper a thermomechanical model for the dynamics of structural phase transitions in the so-called ‘shape memory alloys’ is developed. These materials exhibit rather spectacular hysteresis phenomena. The resulting mathematical model consists of a coupled and highly non-linear system of partial differential equations reflecting the balance laws of linear momentum and energy. For an appropriate weak formulation the local-in-time existence of weak solutions is shown.     

Stability analysis with respect to two measures of impulsive systems under structural perturbations

The asymptotic stability with respect to two measures of impulsive systems under structural perturbations is investigated. Conditions of asymptotic (ρ₀, ρ)-stability of the system in terms of the fixed signs of some special matrices are established. Published in Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 11, pp. 1476–1484, November, 1999.     

Mathematical modeling and numerical simulation of domain wall motion in magnetic nanostrips with crystallographic defects

We investigate field and current driven domain wall propagation in magnetic nanostrips in the framework of the modified Landau–Lifshitz–Gilbert equation including spin-torque effects. We focus our attention on a nonlinear “dry-friction” dissipation model useful for describing the effect of structural defects such as inclusions, impurities or dislocations. The analytical and numerical results herein obtained are compared and their physical implications are discussed.     

Non-metricity in the continuum limit of randomly-distributed point defects

We present a homogenization theorem for isotropically-distributed point defects, by considering a sequence of manifolds with increasingly dense point defects. The loci of the defects are chosen randomly according to a weighted Poisson point process, making it a continuous version of the first passage percolation model. We show that the sequence of manifolds converges to a smooth Riemannian manifold, while the Levi-Civita connections converge to a non-metric connection on the limit manifold. Thus, we obtain rigorously the emergence of a non-metricity tensor, which was postulated in the literature to represent continuous distribution of point defects.