Reducing the Impact of Measurement Errors When Reconstructing Spatial Dynamic Forces

Inferring external spatially distributed dynamic forces from measured structural responses is necessary when direct measurement of these forces is not possible. The finite difference method and the modal method have been previously developed for reconstructing these forces. However, the accuracy of these methods is often hindered due to the amplification of measurement errors in the computation process. In order to analyze these error amplification effects by using the singular value decomposition approach, the mathematic expressions for these two force reconstruction methods are first transformed into a certain linear system of equations. Then, a regularization method, the Tikhonov method, is applied to increase computational stability. In order to achieve a good regularized result, the L-curve method is used in conjunction with the Tikhonov method. The effectiveness in reducing the influence of the measurement errors when applying the regularization method to the finite difference method and the modal method is investigated analytically and numerically. It is found that when the regularization method is appropriately applied, reliable computational results for the reconstructed force can be achieved.