Optimal design of strain sensor placement for distributed static load determination

Abstract

In many applications it is desirable to inverse-calculate the distributed loading on a structure using a limited number of sensors. Yet, the calculated loads can be extremely sensitive to the placement of these sensors. In the case of predicting point loading applied at a known location, best results are typically achieved when one sensor is collocated with the force. However, the extension of this rule to distributed loading remains uncertain, and even simple sensor system design scenarios often require the designer to directly optimize the sensor placements using a numerical model. In an effort to provide designers with guidance, we identify optimal sensor configurations for predicting static distributed loads on beams with classical boundary conditions. An influence coefficient method, wherein the strain is related linearly to the static load, is used to estimate the applied forces. The loading distribution on the structure is assumed to be either a piece-wise linearly-distributed load or a uniformly-distributed load, allowing for distributed loads to be estimated using the magnitudes of a small number of control points. Given the simplicity of the beam structure, the equations of the influence coefficient method are derived analytically, which allows for the sensor placement to be specified using continuous optimization methods. The condition number of the influence coefficient matrix is used as a surrogate for error during optimization. ‘Rules of thumb’ for sensor placement are presented based on the optimization results. Results show that the optimal and rule-of-thumb sensor configurations are more resistant to input noise than naïve configurations, with the rule-of-thumb configurations yielding similar force predictions relative to the optimal configurations. We expect the rules of thumb to be useful guidelines for engineers designing tests on beam-like structures such as aircraft wings or marine propellers where the inverse calculation of distributed loads is of interest.