A fractional-order accumulative regularization filter for force reconstruction

•A fractional order accumulative regularization filter for the force reconstruction is presented.•The formulation can refine the measured response with noise by a dynamic refresh strategy.•The method is validated numerically and experimentally.•The FARF method is superior to the traditional Tikhonov-like regularization method. The ill-posed inverse problem of the force reconstruction comes from the influence of noise to measured responses and results in an inaccurate or non-unique solution. To overcome this ill-posedness, in this paper, the transfer function of the reconstruction model is redefined by a Fractional order Accumulative Regularization Filter (FARF). First, the measured responses with noise are refined by a fractional-order accumulation filter based on a dynamic data refresh strategy. Second, a transfer function, generated by the filtering results of the measured responses, is manipulated by an iterative Tikhonov regularization with a serious of iterative Landweber filter factors. Third, the regularization parameter is optimized by the Generalized Cross-Validation (GCV) to improve the ill-posedness of the force reconstruction model. A Dynamic Force Measurement System (DFMS) for the force reconstruction is designed to illustrate the application advantages of our suggested FARF method. The experimental result shows that the FARF method with r=0.1 and α=20, has a PRE of 0.36% and an RE of 2.45%, is superior to other cases of the FARF method and the traditional regularization methods when it comes to the dynamic force reconstruction.