Indirect measurement of the impulsive load to a nonlinear system from dynamic responses: Inverse problem formulation

A novel procedure to identify an impact load is proposed, that acts on a nonlinear system; an inverse identification problem is formulated from the dynamic responses of the system. Whereas the original dynamic system we consider is nonlinear, we succeed to establish a linear relation concerning the impact load through a formalism. Although the problem is shown to have a unique solution, the formalism results in a Volterra-type of integral equation of the first kind. Thus, the new problem at hand is ill-posed and inevitable small errors during the measurement can make the prediction of the applied (impact) force useless. This leads to numerical instability in the solution. This difficulty is overcome by applying a stabilization technique (known as regularization). The practicality of the proposed procedure is examined through a numerical experiment.