Modeling Uncertainty for a Vision System Applied to Vibration Measurements

In this paper, a new analytical model is proposed to describe the behavior of uncertainty for a generic vision-based measurement system applied to mechanical vibration measurement. In particular, this paper proposes a novel way to evaluate the effects of motion blur. The theoretical framework presented here takes into account the camera acquisition parameters, the dynamics of the measurand (in terms of instantaneous speed), and the image scaling factor to develop a physical model of uncertainty when measuring a mainly monomodal vibration. Uncertainty is evaluated starting from the normalized discrepancy between a measured position and the actual one. The analytical model proposed here has been validated extensively with the help of a test stand that can generate biaxial monomodal vibrations. The motion of a target mounted on the test stand has been simultaneously monitored by a stereo vision rig and a set of triangulation lasers. Model validation has been carried out using two measurement techniques: stereo vision blob analysis and digital image correlation. The experimental results show that the proposed model is able to represent the behavior of uncertainty for both the techniques. After the model has been validated, it is shown how it is possible to exploit it to estimate the uncertainty of a vision rig starting from the nominal characteristics of both the vision system and the target. This can be a tool to facilitate the design of vision-based measurement systems.