Life-cycle structural reliability of concrete bridges considering spatial variability of corrosion and model updating

This paper presents a computational approach to life-cycle structural reliability assessment of concrete bridges under chloride-induced corrosion considering spatial variability of damage and model updating based on the results of diagnostic activities to gather information on material properties and exposure scenario. The proposed approach implements random fields to account for the effects of spatial variability of corrosion and Bayesian inference for model updating. The main steps of the reliability assessment procedure are presented and discussed with emphasis on the application to an existing prestressed concrete box-girder railway bridge

Efficient sampling techniques for simulation-based life-cycle structural reliability and seismic fragility assessment

Life-cycle structural reliability assessment and risk analysis of deteriorating systems may involve the modeling of complex time-variant probabilistic processes. Although simulation methods are frequently the only viable tools to solve this kind of problems, they are time-consuming and might be computationally inefficient and unfeasible in practice if small probabilities of failure need to be estimated, particularly for large-scale reliability and risk analysis problems. To mitigate the computational effort of simulation methods in estimating the time-variant failure probability of deteriorating structures, a novel computational approach based on Importance Sampling and clustering-based data reduction techniques is proposed. The computational efficiency of the proposed methodology is demonstrated with practical applications to life-cycle reliability and seismic fragility of reinforced concrete structures exposed to corrosion

Cross-Entropy-based Stationary Proposal Importance Sampling for life-cycle structural reliability and seismic risk assessment

Life-cycle reliability assessment of deteriorating systems may involve the modeling of complex stochastic processes, further propagating uncertainties and exacerbating computational efforts. This paper discusses a novel simulation-based framework to estimate the time-variant failure probabilities based on Importance Sampling (IS) with Stationary Proposal (SP) distribution. IS methodologies allow to improve computational efficiency and estimate accuracy of simulation-based failure probabilities. The proposed methodology extends adaptive numerical approaches traditionally developed for time-invariant problems, in which the Kullback–Leibler Cross-Entropy is minimized to find a near-optimal simulation density from a chosen family of parametric distributions. The proposed framework is applied to typical reliability problems extended to account for a life-cycle perspective and time-variant seismic risk of deteriorating bridge networks

On the equivalence of different approaches for generating multisoliton solutions of the KPII equation

The unexpectedly rich structure of the multisoliton solutions of the KPII equation has been explored by using different approaches, running from dressing method to twisting transformations and to the tau-function formulation. All these approaches proved to be useful in order to display different properties of these solutions and their related Jost solutions. The aim of this paper is to establish the explicit formulae relating all these approaches. In addition some hidden invariance properties of these multisoliton solutions are discussed

Soliton solutions of the Kadomtsev-Petviashvili II equation

We study a general class of line-soliton solutions of the Kadomtsev-Petviashvili II (KPII) equation by investigating the Wronskian form of its tau-function. We show that, in addition to previously known line-soliton solutions, this class also contains a large variety of new multi-soliton solutions, many of which exhibit nontrivial spatial interaction patterns. We also show that, in general, such solutions consist of unequal numbers of incoming and outgoing line solitons. From the asymptotic analysis of the tau-function, we explicitly characterize the incoming and outgoing line-solitons of this class of solutions. We illustrate these results by discussing several examples.Comment: 28 pages, 4 figure

Young diagrams and N-soliton solutions of the KP equation

We consider $N$-soliton solutions of the KP equation, (-4u_t+u_{xxx}+6uu_x)_x+3u_{yy}=0 . An $N$-soliton solution is a solution $u(x,y,t)$ which has the same set of $N$ line soliton solutions in both asymptotics $y\to\infty$ and $y\to -\infty$. The $N$-soliton solutions include all possible resonant interactions among those line solitons. We then classify those $N$-soliton solutions by defining a pair of $N$-numbers $({\bf n}^+,{\bf n}^-)$ with ${\bf n}^{\pm}=(n_1^{\pm},...,n_N^{\pm}), n_j^{\pm}\in\{1,...,2N\}$, which labels $N$ line solitons in the solution. The classification is related to the Schubert decomposition of the Grassmann manifolds Gr$(N,2N)$, where the solution of the KP equation is defined as a torus orbit. Then the interaction pattern of $N$-soliton solution can be described by the pair of Young diagrams associated with $({\bf n}^+,{\bf n}^-)$. We also show that $N$-soliton solutions of the KdV equation obtained by the constraint $\partial u/\partial y=0$ cannot have resonant interaction.Comment: 22 pages, 5 figures, some minor corrections and added one section on the KdV N-soliton solution

Large-Scale Experimental Static Testing on 50-Year-Old Prestressed Concrete Bridge Girders

The heritage of existing road infrastructures and in particular of bridges consists of structures that are approaching or exceeding their designed service life. Detrimental causes such as aging, fatigue and deterioration processes other than variation in loading conditions introduce uncertainties that make structural assessment a challenging task. Experimental data on their performances are crucial for a proper calibration of numerical models able to predict their behavior and life-cycle structural performance. In this scenario, an experimental research program was established with the aim of investigating a set of 50-year-old prestressed concrete bridge girders that were recovered from a decommissioned bridge. The activities included initial non-destructive tests, and then full-scale load tests followed by a destructive test on the material samples. This paper reports the experimental results of the full-scale tests conducted on the first group of four I-beams assumed to be in good condition from visual inspection at the time of testing. Loading tests were performed using a specifically designed steel reaction frame and a test setup equipment, as detailed in the present work. Due to the structural response of this first group of girders, a uniform behavior was found at both service and ultimate conditions. The failure mechanism was characterized by the crushing of the cast-in-situ top slab corresponding to a limited deflection, highlighting a non-ductile behavior. The outcomes of the experimental research are expected to provide new data for the life-cycle safety assessment of existing bridges through an extended database of validated experimental tests and models

The dispersion-managed Ginzburg-Landau equation and its application to femtosecond lasers

The complex Ginzburg-Landau equation has been used extensively to describe various non-equilibrium phenomena. In the context of lasers, it models the dynamics of a pulse by averaging over the effects that take place inside the cavity. Ti:sapphire femtosecond lasers, however, produce pulses that undergo significant changes in different parts of the cavity during each round-trip. The dynamics of such pulses is therefore not adequately described by an average model that does not take such changes into account. The purpose of this work is severalfold. First we introduce the dispersion-managed Ginzburg-Landau equation (DMGLE) as an average model that describes the long-term dynamics of systems characterized by rapid variations of dispersion, nonlinearity and gain in a general setting, and we study the properties of the equation. We then explain how in particular the DMGLE arises for Ti:sapphire femtosecond lasers and we characterize its solutions. In particular, we show that, for moderate values of the gain/loss parameters, the solutions of the DMGLE are well approximated by those of the dispersion-managed nonlinear Schrodinger equation (DMNLSE), and the main effect of gain and loss dynamics is simply to select one among the one-parameter family of solutions of the DMNLSE.Comment: 22 pages, 4 figures, to appear in Nonlinearit

Hypospadias: clinical approach, surgical technique and long-term outcome

Background: Hypospadias is one of the most common congenital abnormalities in male newborn. There is no universal approach to hypospadias surgical repair, with more than 300 corrective procedures described in current literature. The reoperation rate within 6–12 months of the initial surgery is most frequently used as an outcome measure. These short-term outcomes may not reflect those encountered in adolescence and adult life. This study aims to identify the long-term cosmetic, functional and psychosexual outcomes. Methods: Medical records of boys who had undergone surgical repair of hypospadias by a single surgical team led by the same surgeon at a single centre between August 2001 and December 2017 were reviewed. Families were contacted by telephone and invited to participate. Surgical outcome was assessed by combination of clinical examination, a life-related interview and 3 validated questionnaires (the Penile Perception Score-PPS, the Hypospadias Objective Score Evaluation-HOSE, the International Index of Erectile Function-5-IIEF5). Outcomes were compared according to age, severity of hypospadias, and respondent (child, parent and surgeon). Results: 187 children and their families agreed to participate in the study. 46 patients (24.6%) presented at least one complication after the repair, with a median elapsed time of 11.5 months (6.5–22.5). Longitudinal differences in surgical corrective procedures (p < 0.01), clinical approach (p < 0.01), hospitalisation after surgery (p < 0.01) were found. Cosmetic data from the PPS were similar among children and parents, with no significant differences in child’s age or the type of hypospadias: 83% of children and 87% of parents were satisfied with the cosmetic result. A significant difference in functional outcome related to the type of hypospadias was reflected responses to HOSE amongst all groups of respondents: children (p < 0.001), parents (p=0.02) and surgeon (p < 0.01). The child’s HOSE total score was consistently lower than the surgeon (p < 0.01). The HOSE satisfaction rate on functional outcome was 89% for child and 92% for parent respondents. Conclusion: Surgeons and clinicians should be cognizant of the long-term outcomes following hypospadias surgical repair and this should be reflected in a demand for a standardised approach to repair and follow-up

On a family of solutions of the KP equation which also satisfy the Toda lattice hierarchy

We describe the interaction pattern in the $x$-$y$ plane for a family of soliton solutions of the Kadomtsev-Petviashvili (KP) equation, $(-4u_{t}+u_{xxx}+6uu_x)_{x}+3u_{yy}=0$. Those solutions also satisfy the finite Toda lattice hierarchy. We determine completely their asymptotic patterns for $y\to \pm\infty$, and we show that all the solutions (except the one-soliton solution) are of {\it resonant} type, consisting of arbitrary numbers of line solitons in both aymptotics; that is, arbitrary $N_-$ incoming solitons for $y\to -\infty$ interact to form arbitrary $N_+$ outgoing solitons for $y\to\infty$. We also discuss the interaction process of those solitons, and show that the resonant interaction creates a {\it web-like} structure having $(N_--1)(N_+-1)$ holes.Comment: 18 pages, 16 figures, submitted to JPA; Math. Ge