Dynamic Moving Load Identification Using Optimal Sensor Placement

A structure in service can be subjected to static, dynamic or moving loads. Several situations in practice involve estimation of moving loads which induce vibrations in the structure on which they are applied. An accurate estimation of these loads will ensure product quality and reliability of the final design, and mitigate the cost of structural health monitoring systems. The moving nature of dynamic loads increases the computational difficulty of the problem. One of the types of Inverse Problems involves estimation of the applied load from measured structural response such as strain or accelerations. Measuring response at a limited number of locations causes the unavailability of full set of structural response which can lead to inaccurate results. The unavailability of full structural response is mainly due to three reasons — (i) financial constraints limiting the number of sensors that can be used, (ii) inaccessibility of loading locations to place sensors, and (iii) sensor influence on structural response. The load recovered from such insufficient structural response data will be prone to errors. Ill-conditioning of the inverse problem can be eliminated by choosing optimum sensor locations on the structure, which leads to precise load estimate. No studies could be found which consider optimum sensor placement while recovering dynamic moving loads acting on a structure. In this paper, the recovery of the dynamic moving loads through measurement of structural response at a finite number of optimally selected locations is investigated. The developed algorithm is implemented using ANSYS APDL and MATLAB programming environment. Optimum sensor locations are identified using the D-optimal design algorithm and strain gages are placed at those locations. An algorithm is developed to utilize the strain data measured at optimum locations to estimate the moving load. The developed algorithm is applied to three example problems. The first example deals with the case where two orthogonal dynamic moving loads are applied at the same location. The second example involves a specific vehicle-bridge interaction problem. The vehicle is approximated as a half model consisting of two axles, where the dynamic loads from axles are modeled as point loads which move together. In both the cases, the estimated dynamic moving loads matched closely with the applied loads. In third example, the algorithm is also tested by adding 5% noise to the input response data. Even with random noise present in input strain data, the load estimates are obtained with a high degree of accuracy. Compared to conventional algorithms for estimating moving loads, the developed method makes the dynamic moving load recovery procedure accurate and relatively easy to implement.