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Robust optimal sensor placement for operational modal analysis based on maximum expected utility

机译：基于最大期望效用的用于运行模式分析的可靠的最佳传感器放置

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摘要

Optimal sensor placement is essentially a decision problem under uncertainty. The maximum expected utility theory and a Bayesian linear model are used in this paper for robust sensor placement aimed at operational modal identification. To avoid nonlinear relations between modal parameters and measured responses, we choose to optimize the sensor locations relative to identifying modal responses. Since the modal responses contain all the information necessary to identify the modal parameters, the optimal sensor locations for modal response estimation provide at least a suboptimal solution for identification of modal parameters. First, a probabilistic model for sensor placement considering model uncertainty, load uncertainty and measurement error is proposed. The maximum expected utility theory is then applied with this model by considering utility functions based on three principles: quadratic loss, Shannon information, and K-L divergence. In addition, the prior covariance of modal responses under band-limited white-noise excitation is derived and the nearest Kronecker product approximation is employed to accelerate evaluation of the utility function. As demonstration and validation examples, sensor placements in a 16-degrees-of-freedom shear-type building and in Guangzhou TV Tower under ground motion and wind load are considered. Placements of individual displacement meter, velocimeter, accelerometer and placement of mixed sensors are illustrated.
机译：最佳传感器放置本质上是不确定性下的决策问题。本文将最大期望效用理论和贝叶斯线性模型用于针对操作模式识别的鲁棒传感器放置。为避免模态参数与测量响应之间存在非线性关系，我们选择相对于识别模态响应来优化传感器位置。由于模态响应包含识别模态参数所需的所有信息，因此用于模态响应估计的最佳传感器位置至少为模态参数的识别提供了次优解决方案。首先，提出了一种考虑模型不确定性，负载不确定性和测量误差的传感器放置概率模型。然后，根据以下三个原理考虑效用函数，将最大期望效用理论应用于该模型：二次损失，香农信息和K-L散度。此外，推导了带有限白噪声激发下模态响应的先验协方差，并采用了最接近的克罗内克乘积近似来加速效用函数的评估。作为演示和验证示例，考虑了在地面运动和风荷载下，传感器在16自由度剪切型建筑物和广州电视塔中的传感器布置。说明了单个位移计，速度计，加速度计的位置以及混合传感器的位置。

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