Robust state-space realizations of digital filters against finite word length errors

This article deals with two important issues in digital filter implementation： roundoff noise and limit cycles. A novel class of robust state-space realizations, called normal realizations, is derived and characterized. It is seen that these realizations are free of limit cycles. Another interesting property of the normal realizations is that they yield a minimal error propagation gain. The optimal realization problem, defined as to find those normal realizations that minimize roundoff noise gain, is formulated and solved analytically. A design example is presented to demonstrate the behavior of the optimal normal realizations and to compare them with several well-known digital filter realizations in terms of minimizing the roundoff noise and the error propagation.

Deformation tests and failure process analysis of an anchorage structure

In order to study the failure process of an anchorage structure and the evolution law of the body＇s defor- mation field, anchor push-out tests were carried out based on digital speckle correlation methods （DSCM）. The stress distribution of the anchorage interface was investigated using the particle flow numerical simulation method. The results indicate that there are three stages in the deformation and fail- ure process of an anchorage structure： elastic bonding stage, a de-bonding stage and a failure stage. The stress distribution in the interface controls the stability of the structure. In the elastic bonding stage, the shear stress peak point of the interface is close to the loading end, and the displacement field gradually develops into a ＂V＂ shape, in the de-bonding stage, there is a shear stress plateau in the center of the anchorage section, and shear strain localization begins to form in the deformation field. In the failure stage, the bonding of the interface fails rapidly and the shear stress peak point moves to the anchorage free end. The anchorage structure moves integrally along the macro-cracl~ The de-bonding stage is a research focus in the deformation and failure process of an anchorage structure, and plays an important guiding role in roadway support design and prediction of the stability of the surrounding rock.