传感器布置中Fisher信息矩阵的协方差修正

Covariance Modification of the Fisher Information Matrix in Sensor Placement

  • 摘要: 针对传感器优化布置中对Fisher信息矩阵进行距离系数加权修正方法的不足,提出一种用模态贡献—距离系数修正模型误差协方差矩阵的方法,从而达到合理修正Fisher信息矩阵的目的.首先,阐述了Fisher信息矩阵和信息熵之间的关系;其次,考虑到预测误差对Fisher信息矩阵的影响,使用欧氏距离和模态贡献修正模型误差协方差矩阵;最后,以修正后的Fisher信息矩阵行列式最大化为目标,采用逐步累加法得到传感器优化布置方案.以一桁架模型为例,依据3种评价准则对比评定布置方案.结果表明,所提方法能够在得到更优评价值的同时避免测点聚集.

     

    Abstract: Considering that the drawbacks of the distance coefficient and the Fisher information matrix for optimal sensor placement, a mode contribution and distance coefficient are used to modify the model error covariance in the Fisher information matrix. Firstly, the relationship between the Fisher information matrix and the information entropy is illustrated. Secondly, considering the impacts of the prediction error on the Fisher information matrix, the Euclidean distance and the mode contribution coefficient are employed to modify the model error covariance matrix. Finally, the sensor placements are obtained by maximizing the determinant of the so-modified Fisher information matrix by using the sequential forward algorithm. According to three evaluation criteria, the efficiency of the different modification methods is compared using a truss model. The results showed that the proposed method could obtain better evaluation values and effectively avoids the aggregation of the sensor placements at the same time.

     

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