Statistical moving load identification including uncertainty

Most existing approaches of moving load identification treat the structure–load interaction problem as deterministic in which the identified results do not have any statistical prediction on their quality. In fact, uncertainties exist in both the interaction forces and structural responses, and the existence of the uncertainty erodes the accuracy of the identified moving loads. A new stochastic moving load identification technique is presented in this paper in which statistics of the moving force time histories are identified from samples of the structural responses. The Karhunen–Loève Expansion is adopted to represent both the structural responses and the interaction forces which are assumed as Gaussian random processes. Numerical simulations with two forces moving over a simply supported Bernoulli–Euler beam show that the accuracy of the identified force time histories can be significantly improved with only a small number of measured response samples compared with that obtained from an existing deterministic method. The variance of the moving forces can also be accurately estimated from a group of response samples when the statistics of the whole population can be well represented by these samples. The mean value of the identified forces is found independent of the effect from the different environmental effects and measurement errors in the simulation studies.

► Statistics of the moving forces are identified from samples of the structural responses.
► Karhunen–Loève Expansion is used to represent the Gaussian responses and interaction forces.
► Variance of the identified force is accurate when statistics of the whole population are well represented by the input.
► Mean value of the identified force is independent of environmental effects and measurement errors.