Weigh-in-motion of train loads based on measurements of rail strains

This paper deals with the identification of the weight of a train in motion, based on the measurement of the time-history of strains at the foot of the rail. The direct problem is initially considered, modelling the rail as a one-dimensional infinite Euler-Bernoulli beam, resting on a viscoelastic soil and subjected to a Dirac delta load travelling at constant speed. A closed-form solution is used to investigate the sensitivity of the response to the main mechanical parameters. Then, the inverse problem consisting of the identification of the loads for a given time-history of measured strains is addressed as a minimization problem whose objective function is based on the difference between experimental and model time-histories of strains. First, an updating of the interpretative model using the time-history of a train of known weight is pursued. Then, the actual load identification is performed. The procedure proposed is initially applied to numerical data, also contaminated by noise. Within the context of a Bayesian approach, identifiability of model parameters and minimum number of measurements are examined; moreover, the sensitivity of parameter estimation to errors in the known load, and the sensitivity of load identification to errors in the model parameters are investigated, as well as the effect of noise. A validation is finally performed, using rail strains measured on a stretch of line run by a locomotor.