Abstract 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.

中文翻译：

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一种在测量噪声和建模误差下可靠扩展模态形状的最佳传感器放置策略

摘要 模态扩展技术通常用于将传感器位置处的实验模态位移扩展到所有未测量的自由度。由于在大多数情况下，传感器只能安装在结构中的有限位置，因此扩展对于确定整个结构的振型、应变、应力等至关重要，可用于结构健康监测。传统的传感器放置算法大多旨在使不同模式的传感器位置处的模态位移尽可能线性无关。然而，在存在建模误差和测量噪声的情况下，不能保证基于该准则的最佳位置提供接近于实模态振型的扩展模态振型。在这项工作中，实际振型和扩展振型之间的法向距离的期望值用作两个实体之间接近度的度量。可以通过最小化该距离来确定最佳传感器位置。这一新标准适用于简单的悬臂梁和工业磨粉塔。在这两种情况下，通过对所有可能的传感器配置进行详尽搜索，可以找到传感器位置，与传统的最佳传感器放置策略相比，这导致距离显着减少。还建议使用足够准确的次优顺序传感器放置算法作为详尽搜索的替代方案，然后将其与基于遗传算法的搜索进行比较。