Structural monitoring plays a central role in civil engineering; in particular, optimal sensor positioning is essential for correct monitoring both in terms of usable data and for optimizing the cost of the setup sensors. In this context, we focus our attention on the identification of the dynamic response of beam-like structures with uncertain damages. In particular, the non-localized damage is described using a Gaussian distributed random damage parameter. Furthermore, a procedure for selecting an optimal number of sensor placements has been presented based on the comparison among the probability of damage occurrence and the probability to detect the damage, where the former can be evaluated from the known distribution of the random parameter, whereas the latter is evaluated exploiting the closed-form asymptotic solution provided by a perturbation approach. The presented case study shows the capability and reliability of the proposed procedure for detecting the minimum number of sensors such that the monitoring accuracy (estimated by an error function measuring the differences among the two probabilities) is not greater than a control small value.

中文翻译：

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使用统计方法在梁的动态损伤检测中优化传感器放置

结构监测在土木工程中起着核心作用；特别是，最佳传感器定位对于正确监测可用数据和优化设置传感器的成本至关重要。在这种情况下，我们将注意力集中在识别具有不确定损伤的梁状结构的动态响应上。特别是，非局部损伤是使用高斯分布随机损伤参数来描述的。此外，基于损坏发生概率和检测损坏概率之间的比较，提出了选择最佳传感器放置数量的程序，其中前者可以从随机参数的已知分布中进行评估，而后者是利用微扰方法提供的封闭形式渐近解来评估的。所提出的案例研究显示了所提出的程序的能力和可靠性，用于检测最少数量的传感器，从而使监测精度（通过测量两个概率之间的差异的误差函数估计）不大于控制小值。