Identifying the Location of Dynamic Load Using a Region’s Asymptotic Approximation

Since it is difficult to obtain the positions of dynamic loads on structures, this paper suggests a new method to identify the locations of dynamic loads step-by-step based on the correlation coefficients of dynamic responses. First, a recognition model for dynamic load position based on a finite-element scheme is established, with the finite-element domain divided into several regions. Second, virtual loads are applied at the central points of these regions, and acceleration responses are calculated at the sensor measurement points. Third, the maximum correlation coefficient between the calculational and measured accelerations is obtained, and the dynamic load is located in the region with the virtual load corresponding to the maximum correlation coefficient. Finally, this region is continuously subdivided with the refined mesh until the dynamic load is pinpointed in a sufficiently small area. Different virtual load construction methods are proposed according to different types of loads. The frequency response function, unresolvable for the actual problem due to the unknown location of the real dynamic load, can be transformed into a solvable form, involving only known points. This transformation simplifies the analytical process, making it more efficient and applicable to analysis of the dynamic behavior of the system. The identification of the dynamic load position in the entire structure is then transformed into a sub-region approach, focusing on the area where the dynamic load acts. Simulations for case studies are conducted to demonstrate that the proposed method can effectively identify positions of single and multiple dynamic loads. The correctness of the theory and simulation model is verified with experiments. Compared to recent methods that use machine learning and neural networks to identify positions of dynamic loads, the approach proposed in this paper avoids the heavy computational cost and time required for data training.