Damage identification in a concrete dam by fitting measured modal parameters

We propose a method, based on an inverse problem, to obtain numerically the material parameters that characterize the elasticity tensor of a body with linear elastic behavior, using accurate measurements of the first modal parameters, namely the natural frequencies and the modes of vibration (the eigenfrequencies and the eigenvectors). Appropriate functionals are defined, whose minimum points correspond to the unknown material parameters. To obtain these minimum points a highly nonlinear parametric optimization problem is solved. Its resolution involves specific mathematical tools like the derivative of the eigenvalues and eigenvectors with respect to the material parameters, the adjoint method, and gradient methods for the minimization of the functional. An application is presented, which considers a cracked dam in which is assumed the presence of transversely isotropic material in the cracked zone. The material parameters of the transversely isotropic material are obtained by minimizing the distance between the modal parameters (eigenfrequencies and eigenvectors) of a numerical model of the dam and the observed modal parameters physically measured in the dam. The algorithm is implemented in a C++ home made code with the aid of open-source libraries for scientific computation.     

Fast integral wavelet transform on a dense set of the time-scale domain

Summary. The objective of this paper is to introduce a fast algorithm for computing the integral wavelet transform (IWT) on a dense set of points in the time-scale domain. By applying the duality principle and using a compactly supported spline-wavelet as the analyzing wavelet, this fast integral wavelet transform (FIWT) is realized by applying only FIR (moving average) operations, and can be implemented in parallel. Since this computational procedure is based on a local optimal-order spline interpolation scheme and the FIR filters are exact, the IWT values so obtained are guaranteed to have zero moments up to the order of the cardinal spline functions. The semi-orthogonal (s.o.) spline-wavelets used here cannot be replaced by any other biorthogonal wavelet (spline or otherwise) which is not s.o., since the duality principle must be applied to some subspace of the multiresolution analysis under consideration. In contrast with the existing procedures based on direct numerical integration or an FFT-based multi-voice per octave scheme, the computational complexity of our FIWT algorithm does not increase with the increasing number of values of the scale parameter. Received March 3, 1994     

Global existence of analytic solutions to the Cauchy problem in a complex domain

We present results on the global existence of analytic solutions to the Cauchy problem in starshaped or convex complex domains. No growth conditions are imposed. Our results rely on a notion of solution-tube that we introduce. à la mémoire de Jean Leray     

A criterion of solvability of the elliptic Cauchy problem in a multi-dimensional cylindrical domain

In this paper, we consider the Cauchy problem for multidimensional elliptic equations in a cylindrical domain. The method of spectral expansion in eigenfunctions of the Cauchy problem for equations with deviating argument establishes a criterion of the strong solvability of the considered elliptic Cauchy problem. It is shown that the ill-posedness of the elliptic Cauchy problem is equivalent to the existence of an isolated point of the continuous spectrum for a self-adjoint operator with deviating argument.     

Identification of crack in a rotor system based on wavelet finite element method

The dynamics and diagnosis of cracked rotor have been gaining importance in recent years. In the present study a model-based crack identification method is proposed for estimating crack location and size in shafts. The rotor system has been modeled using finite element method of B-spline wavelet on the interval (FEM BSWI), while the crack is considered through local stiffness change. Based on Rayleigh beam theory, the influences of rotatory inertia on the flexural vibrations of the rotor system are examined to construct BSWI Rayleigh beam element. The slender shaft and stiffness disc are modeled by BSWI Rayleigh–Euler beam element and BSWI Rayleigh–Timoshenko beam element, respectively. Then the crack identification forward and inverse problems are solved by using surface-fitting technique and contour-plotting method. The experimental examples are given to verify the validity of the BSWI beam element for crack identification in a rotor system. From experimental results, the new method can be applied to prognosis and quantitative diagnosis of crack in a rotor system.     

Numerical evaluation of a 2-D Cauchy principal value integral based on quasi-interpolating splines

In this paper the author presents a method for the numerical solution of a 2-D Cauchy principal value of the form where S is a domain with a continuous boundary. By using polar coordinates, the integral is reduced to the form where the finite-part of the integral. We construct the relative product rule based on quasi-inter polating splines. Convergence results are proved and numerical examples are given.     

Locating Pairs of Vertices on a Hamiltonian Cycle in Bigraphs

Let G be a simple \(m\times m\) bipartite graph with minimum degree \(\delta (G)\ge m/2+1\). We prove that for every pair of vertices x, y, there is a Hamiltonian cycle in G such that the distance between x and y along that cycle equals k, where \(2\le k<m/6\) is an integer having appropriate parity. We conjecture that this is also true up to \(k\le m\).     

Hierarchical forecasting based on AR-GARCH model in a coherent structure

This paper compares the accuracy of the aggregate forecasting with the bottom-up forecasting based on AR-GARCH model for the return rate of simulated Dow Jones Industrial Average. Most of the existing stock price index studies did not consider the hierarchical structure and often missed the coherent relationships between individual components. In this experiment, we simulated 30 coherent components based on AR(2)-GARCH(1, 1) model. Then we evaluated the performance of both forecasting methods ignoring the coherent structure. The results of our experiment indicated that the accuracy of forecasting method varied depending on the correlation degree of 30 coherent components, however the data noise did not significantly influenced the performance of hierarchical forecasting method.     

Asymptotically sharp error bounds for a quadrature rule for Cauchy principal value integrals based on piecewise linear interpolation

For the numerical evaluation of Cauchy principal value integrals of the form f(x)(x - λ) -1dx withλ ∈ (-1,1)and f ∈ C1[-1,1], we investigate the quadrature formula Q(n+1)Spl1[·;λ] obtained by replacing the integrand function f by its piecewise linear interpolant at an equidistant set of nodes as proposed by Rabinoivitz (Math. Comp. , 51:741 - 747,1988). We give upper bounds for the Peano - type error constantsfor s∈ {1,2}. These are the best possible constants in inequalities of the typeFurthermore, we prove that our upper bounds are asymptotically sharp.     

Estimate of the modulus of continuity of a cauchy-type integral in a domain and on its boundary

We estimate the modulus of continuity of a Cauchy-type integral in a closed domain and its limit values on the boundary in the case where the boundary of the domain is an arbitrary closed rectifiable Jordan curve.     

Instability in a geometric parabolic equation on convex domain instability on convex domain

We prove that any non-constant smooth static solution to a geometric parabolic system is unstable, provided that the domain is convex. As the important applications, we shall consider the Landau-Lifshitz equation and the heat flow for harmonic map.