An On-line Search for Optimum Operating Conditions of Noisy Systems

Optimum process operating conditions are often achieved by on-line computer programming. A general method has been developed which is capable of optimizing processes whose responses are corrupted by random error. The method is particularly useful for application to processes whose response functions contain sharp ridges. Application to ridge and non-ridge systems gives the same results in each case showing that the rate of convergence of the search is totally unaffected by the presence of a ridge. An accelarated gradient method is used which obtains its derivatives from a quadratic interpolation. The inability of the gradient method to move along a ridge is overcome by projecting a straight line through points on the ridge to obtain new starting points for a gradient search. Points on the ridge are located by finding the stationary point of the polynomial which is constructed by regression through points found by the gradient search. The method is applied to several test functions known to the literature—a fast convergence rate is obtained for a wide range of noise levels.     

The Fourier theorem

It has been tacitly understood that Fourier's representation theorem applies only to a very restricted class of functions. On the contrary, by adopting an appropriate algebraic viewpoint, it is explained in this article how the theorem can be readily extended to include all (non-pathological) functions.     

Perforation of Nonlocal Visco- Plastic Plates by a Cylindrical Projectile

This paper is concerned with the analysis of the problem of dynamic perforation of visco-plastic plates by a cylindrical projectile, leading to a failure of the plate by a plug formation. Assuming the behavior of the plate material is nonlocal visco-plastic, the classical theory of visco-plasticity for Bingham solids is generalized to take the non-local effects into consideration. The target plate being thin, it is assumed that only the contributions of vertical shearing stress need be taken into account. The effect of the impact is represented by a uniform velocity distribution over a circular region of the plate surface. The expressions of velocity, strain rate and shear stress are obtained and some particular cases are discussed. Some numerical results concerning stress distributions are also included.