In this paper the conjugate gradient (CG) method is employed for identifying the parameters of crack in a functionally graded beam from natural frequency measurement. The crack is modeled as a massless rotational spring with sectional flexibility. By using the Euler-Bernoulli beam theory on two separate beams respectively and applying the compatibility requirements of the crack, the characteris...

The conjugate gradient optimization algorithm is combined with the modified back propagation algorithm to yield a computationally efficient algorithm for training multilayer perceptron (MLP) networks (CGFR/AG). The computational efficiency is enhanced by adaptively modifying initial search direction as described in the following steps: (1) Modification on standard back propagation algorithm by ...

Bordered almost block diagonal systems arise from discretizing a linearized rst-order system of n ordinary diierential equations in a two-point boundary value problem with non-separated boundary conditions. The discretization may use spline collocation, nite diierences, or multiple shooting. After internal condensation, if necessary, the bordered almost block diagonal system reduces to a standa...