Browsing by Author "Tsavachidis, Spiridon"

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    Deterministic and stochastic analysis of nonlinear systems with Biot hysteretic damping
    (2001) Tsavachidis, Spiridon
    Time domain analysis of nonlinear systems with hysteretic damping is conducted. Specifically, the viscoelastic model proposed by Biot is examined. This hysteretic element represents an integral transform in the time domain. Thus, it yields integro-differential equations when it is incorporated into the system dynamics models. Two numerical methods are proposed to solve these equations. The first method approximates the kernel of this integral transform by a sum of exponentials making the computational cost minimal. The second method uses digital filters designed to match the transfer function, real and imaginary parts, of the Biot hysteretic element. These techniques are employed in calculating the response of a single-degree-of-freedom (SDOF) system with hysteretic damping and nonlinear stiffness subjected to deterministic, seismic, and random excitation. The method of statistical linearization is used to estimate the variance of the response of the SDOF system subjected to white noise. The accuracy of the results is verified by pertinent Monte Carlo studies. The presented approaches can be extended to treat multi-degree-of-freedom (MDOF) systems with hysteretic behavior.
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    Eliminating incoherence from subjective estimates of chance
    (2003) Tsavachidis, Spiridon; Vardi, Moshe Y.
    Human expertise is a significant source of information about environments with inherent uncertainty. However, it is well documented that subjective estimates of chance tend to violate the mathematical axioms of probability, that is, they are incoherent. This fact makes the use of such estimates problematic for statistical inference, decision analysis, economic modelling or aggregation of expert opinions. In order for the subjective probability estimates to be used in a correct and meaningful way, they must be reconstructed so that they are coherent. The proposed algorithms for coherent reconstruction are based on heuristic search methods, namely, Genetic Algorithms and Simulated Annealing. These algorithms are combined with efficient data structures that compactly represent probability distributions. The reconstructed estimates are coherent and close to the initial judgments with respect to some distance measure, maintaining the insight of the expert. Empirical studies shown that the coherent approximations are more stochastically accurate than the original subjective estimates.