By Dr. Jorge E. Hurtado (auth.)
This monograph provides an unique method of Structural Reliability from the point of view of Statistical studying idea. It proposes new tools for fixing the reliability challenge using the new advancements in Computational studying conception, corresponding to Neural Networks and aid Vector machines. It additionally demonstrates very important matters at the administration of samples in Monte Carlo simulation for structural reliability research reasons and examines the therapy of the structural reliability challenge as a trend attractiveness or class job. This rigorously written monograph is aiming at researchers and scholars in civil and mechanical engineering, specifically in reliability engineering, structural research, or statistical learning.
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Additional resources for Structural Reliability: Statistical Learning Perspectives
8 FORM and SORM Approximations with Statistical Learning Devices 41 to be in the direction of overcoming the problems of the RSM by adopting a classification paradigm. Some remarks made in this paper are considered in subsequent chapters. 8 FORM and SORM Approximations with Statistical Learning Devices As shown in the preceding, the FORM and SORM approximations to the limit-state function require information on the derivatives of the performance function at the design point. This information, and especially that required by SORM, is difficult to obtain in case of implicit limit-state functions.
This implies for instance the calculation of the derivatives of the stiffness matrices with respect to the basic variables or transformations thereof. This task, however, is also affected by the increase of the dimensionality, because the derivative of a N x N matrix with respect to a d x 1 vector i8 aNd x N d matrix. Of course, the situation is more severe for using SORM with such low-level derivatives. Similar dimensionality explosions also occur in using other analytical approaches such as those based on polynomial chaoses [55, 162].
The number of solver calls and the way of finding the coefficients depend on the experimental plan adopted (see Fig. 2). 49) where fJi, Ui are respectively the mean and standard deviation of the i-th variable and k is a coefficient for the point type. Obviously, k = 0 for the central points and typically k = 1 for edge points and k = 2 to 3 for axial points. After a first trial function, the design point in the standard space can be easily found and successive improvements of the response surface are obtained by locating the center of the experimental plan on the current design point (Fig.