Localization of Simulated Damage on a Steel Beam from Random Vibrations

The performance of a few localization schemes using measured mode shapes was tested in an experimental case study with respect to the Ultimate Limit State (ULS). The first question to be posed was: Is it possible to indicate and locate damage under laboratory conditions before the ULS is reached? Relatively simple localization criteria were chosen, which do not require extensive FE analysis. A new combination of them, designated here as Combined Localization Criterion (CLI), was proposed that performed well in the presented case. A simple supported beam with the damage progressing in three consecutive stages was used for the experiments. Mode shapes in the range of up to 100 Hz were extracted from the response of the structure to the air stream.

LOCAL SUPREMA OF DIRICHLET POLYNOMIALS AND ZEROFREE REGIONS OF THE RIEMANN ZETA-FUNCTION

A new family of zerofree region of the Riemann Zeta-function ζ is identified by using Turán's (P. Turán, Eine neue Methode inter Analysis und deren Anwendungen (Akadémiai Kiadó, Budapest, Hungary, 1953); Analytic number theory, Proc. Symp. Pure Math., vol. XXIV (Amer. Math. Soc. Providence, RI, 1972)) localization criterion linking zeros of ζ with uniform local suprema of sets of Dirichlet polynomials expanded over the primes. The proof is based on a randomization argument. An estimate for local extrema for some finite families of shifted Dirichlet polynomials is established by preliminary considering their local increment properties by means of Montgomery-Vaughan's variant of Hilbert's inequality. A covering argument combined with Turán's localization criterion allows to conclude.

Edge Detector Design Based on LS-SVR

For locating inaccurate problem of the discrete localization criterion proposed by Demigny, a new criterion expression of “good localization” is proposed. Firstly, a discrete expression of good detection and good localization criterion of two dimension edge detection operator is employed, and then an experiment to measure optimal parameters of two dimension Canny's edge detection operator is introduced after. Moreover, a detailed performance comparison and analysis of two dimension optimal filter obtained via utilizing tensor product for one dimension optimal filter are provided which can prove that least square support vector regression (LS-SVR) is a smoothness filter and give the construct method of the derivate operator. This paper uses LS-SVR as the object function constructor and then realizes the approximation of two dimension optimal edge detection operator. This paper proposes the utility method of using singleness operator to realize multiscale edge detection by referencing the multiscale analysis technology of the wavelets theory. Experiment shows that the method has utility and efficiency.