Signal-based online acceleration and strain data fusion using B-splines and Kalman filter for full-field dynamic displacement estimation

Displacement plays a crucial role in structural health monitoring (SHM) and damage detection of structural systems subjected to dynamic loads. However, due to the inconvenience associated with the direct measurement of displacement during dynamic loading and the high cost of displacement sensors, the use of displacement measurements often gets restricted. In recent years, indirect estimation of displacement from acceleration and strain data has gained popularity. Several researchers have developed data fusion techniques to estimate displacement from acceleration and strain data. However, existing data fusion techniques mostly rely on system properties like mode shapes or finite element models and require accurate knowledge about the system for successful implementation. Hence, they have the inherent limitation of their applicability being restricted to relatively simple structures where such information is easily available. In this article, B-spline basis functions have been used to formulate a Kalman filter-based algorithm for acceleration and strain data fusion using only elementary information about the system, such as the geometry and boundary conditions, which is the major advantage of this method. Also, the proposed algorithm enables us to monitor the full-field displacement of the system online with only a limited number of sensors. The method has been validated on a numerically generated dataset from the finite element model of a tapered beam subjected to dynamic excitation. Later, the proposed data fusion technique was applied to an experimental benchmark test of a wind turbine blade under dynamic load to estimate the displacement time history. In both cases, the reconstructed displacement from strain and acceleration was found to match well with the response from the FE model.