An optimal sensor placement strategy for reliable expansion of mode shapes under measurement noise and modelling error

Modal expansion techniques are typically used to expand the experimental modal displacements at sensor positions to all unmeasured degrees of freedom. Since in most cases, sensors can be attached only at limited locations in a structure, an expansion is essential to determine mode shapes, strains, stresses, etc. throughout the structure which can be used for structural health monitoring. Conventional sensor placement algorithms are mostly aimed to make the modal displacements at sensor positions of different modes as linearly independent as possible. However, under the presence of modelling errors and measurement noise, an optimal location based on this criterion is not guaranteed to provide an expanded mode shape which is close to the real mode shape. In this work, the expected value of normal distance between the real mode shape and the expanded mode shape is used as a measure of closeness between the two entities. Optimal sensor locations can be determined by minimizing this distance. This new criterion is applied on a simple cantilever beam and an industrial milling tower. In both cases, by using an exhaustive search of all possible sensor configurations it was possible to find sensor locations which resulted in a significant reduction in the distance when compared to a conventional optimal sensor placement strategy. Sufficiently accurate sub-optimal sequential sensor placement algorithm is also suggested as an alternative to the exhaustive search which is then compared with a genetic algorithm-based search. The efficiency of this new sensor placement criterion is further verified using Monte Carlo simulations for some realistic modelling error conditions.