Sparse Bayesian technique for load identification and full response reconstruction

Most load identification methods require that the load location is known in advance. A sparse Bayesian framework is proposed in this study to identify the force location and time history simultaneously and then reconstruct the responses with consideration of the uncertainties of the input force and response measurement. The prior distribution of the unknown forces is assumed to be the product of multiple independent Gaussian distributions of each individual potential force. Then, the most probable values of the unknown forces, measurement noise, and variances of the forces are derived and iteratively calculated by a self-adaptive posterior maximization strategy. In such a way, the estimated force vector is nonzero merely at the positions where loads are applied, and it thus possesses the sparsity in space. Consequently, the input forces are located and quantified simultaneously, and the full-field structural responses are sequentially reconstructed with suppressed uncertainties. The proposed approach is applied to numerical and experimental examples. The results demonstrate that the technique is able to identify the force and reconstruct the responses accurately.