Analysis and retrofitting design of a single-span R.C. bridge

This paper deals with the case history of a damaged one-span prestressed concrete bridge on a crucial artery near the city of Cagliari (Sardinia), along the sea-side. After being involved in a disastrous flood, attention has arisen on the worrying safety state of the deck, submitted to an intense daily traffic load. Evident signs of this severe condition were the deterioration of the beams concrete and the corrosion, the lack of tension and even the rupture of the prestressing cables. After performing a limited in situ test campaign, consisting of sclerometer, pull out and carbonation depth tests, a first evaluation of the safety of the structure was performed. After collecting the data of dynamic and static load tests as well, a comprehensive analysis have been carried out, also by means of a properly calibrated F.E. model. Finally the retrofitting design is presented, consisting of the reparation and thickening of the concrete cover, providing flexural and shear FRP external reinforcements and an external prestressing system, capable of restoring a satisfactory bearing capacity, according to the current national codes. The intervention has been calibrated by the former F.E. model with respect to transversal effects and influence of local and overall deformation of reinforced elements. © 2012 Taylor & Francis Group.

Fixed-rank matrix factorizations and Riemannian low-rank optimization

Motivated by the problem of learning a linear regression model whose parameter is a large fixed-rank non-symmetric matrix, we consider the optimization of a smooth cost function defined on the set of fixed-rank matrices. We adopt the geometric framework of optimization on Riemannian quotient manifolds. We study the underlying geometries of several well-known fixed-rank matrix factorizations and then exploit the Riemannian quotient geometry of the search space in the design of a class of gradient descent and trust-region algorithms. The proposed algorithms generalize our previous results on fixed-rank symmetric positive semidefinite matrices, apply to a broad range of applications, scale to high-dimensional problems, and confer a geometric basis to recent contributions on the learning of fixed-rank non-symmetric matrices. We make connections with existing algorithms in the context of low-rank matrix completion and discuss the usefulness of the proposed framework. Numerical experiments suggest that the proposed algorithms compete with state-of-the-art algorithms and that manifold optimization offers an effective and versatile framework for the design of machine learning algorithms that learn a fixed-rank matrix. © 2013 Springer-Verlag Berlin Heidelberg.