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Publication# Updated braking forces for the assessment of road bridges

Abstract

Safety assessments of road bridges to braking events combine the braking force, acting along the longitudinal axis of the deck, with a vertical load that accounts for the vertical component of the traffic action. In modern design standards the vertical load models result from probabilistic calibration procedures targeting predefined return periods. On the contrary, the braking force was derived from a deterministic characterization of the vehicle configurations and of the braking process. Therefore, the return period of the braking force is unclear and may not be consistent with that of the vertical load model. Significant deviations from the target return period might lead to either uneconomical decisions, e.g. uncalled-for retrofitting interventions, or to inaccurate structural safety verifications. This thesis presents an original stochastic model to compute site-specific values of the braking force as a function of the return period. The developed stochastic model takes into account the length of the bridge deck and its dynamic properties for vibrations in the longitudinal direction, as well as different sources of randomness related to braking events, all of which comply with real-world measurements, including: - vehicle configurations, resorting to a time-history of crossing vehicles; - driver response times, randomly generated from probability distributions defined in the scope of this project; - deceleration profiles of the vehicles, resampled from catalogues of realistic deceleration profiles. The stochastic model uses Monte Carlo simulation of braking events and computes the maximum of the dynamic response of the bridge to each event. The computed maxima are collected in an empirical distribution function of the braking force. In the end, the model returns the quantile of this distribution that is suitable for safety assessments. This value of braking force is specific to the bridge given properties, to the traffic characteristics, and to the target return period. An additional novelty of this research work is the estimation of a rate of occurrence on motorways of braking events per vehicle-distance travelled. This parameter enables the estimation of the period of time covered by the simulations of braking events as a function of traffic flow and of the total number of braking events simulated. This step is fundamental to determine the value of the braking force that has a given return period. The braking forces returned by the stochastic model show significant dependence on the bridge length, the natural vibration period of the deck in the longitudinal direction, and the number of directions of traffic on the deck. On the contrary, damping ratio, traffic on the fast-lane or on weekends, and an augmentation of traffic in 20% show no substantial influence on the braking force. Moreover, the two motorway locations considered as sources of traffic data, Denges and Monte Ceneri, both in Switzerland, yielded braking forces with similar magnitudes, despite the significant differences in traffic characteristics. Finally, the results compiled served to calibrate an updated braking force that depends explicitly on the parameters found relevant, as well as on the return period so that it can be adopted by different standards even if they enforce different safety targets. This updated expression evidences that the braking forces of current codes tend to be conservative and, hence, can be improved based on the findings of this project.

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Magnetoencephalography (MEG) is an imaging technique used to measure the magnetic field outside the human head produced by the electrical activity inside the brain. The MEG inverse problem, identifying the location of the electrical sources from the magnetic signal measurements, is ill-posed, that is, there are an infinite number of mathematically correct solutions. Common source localization methods assume the source does not vary with time and do not provide estimates of the variability of the fitted model. Here, we reformulate the MEG inverse problem by considering time-varying locations for the sources and their electrical moments and we model their time evolution using a state space model. Based on our predictive model, we investigate the inverse problem by finding the posterior source distribution given the multiple channels of observations at each time rather than fitting fixed source parameters. Our new model is more realistic than common models and allows us to estimate the variation of the strength, orientation and position. We propose two new Monte Carlo methods based on sequential importance sampling. Unlike the usual MCMC sampling scheme, our new methods work in this situation without needing to tune a high-dimensional transition kernel which has a very high cost. The dimensionality of the unknown parameters is extremely large and the size of the data is even larger. We use Parallel Virtual Machine (PVM) to speed up the computation.