This article presents an optimal sensor placement algorithm for modifying the Fisher information matrix and effective information. The modified Fisher information matrix and effective information are expressed using a dynamic equation constrained by the condensed relationship of the incomplete mode shape matrix. The mode shape matrix row corresponding to the master degree of freedom of the lowest-contribution Fisher information matrix and effective information indices is moved to the slave degree of freedom during each iteration to obtain an updated shape matrix, which is then used in subsequent calculations. The iteration is repeated until the target sensors attain the targeted number of modes. The numerical simulations are then applied to compare the optimal sensor placement results obtained using the number of installed sensors, and the contribution matrices using the Fisher information matrix and effective information approaches are compared based on the proposed parameter matrix. The mode-shape-based optimal sensor placement approach selects the optimal sensor layout at the positions to uniformly allocate the entire degree of freedom. The numerical results reveal that the proposed F-based and effective information–based approaches lead to slightly different results, depending on the number of parameter matrix modes; however, the resulting final optimal sensor placement is included in a group of common candidate sensor locations. However, the resulting final optimal sensor placement is included in a group of common candidate sensor locations.

本文提出了一种用于修改 Fisher 信息矩阵和有效信息的最佳传感器放置算法。修改后的 Fisher 信息矩阵和有效信息使用一个动态方程来表示，该方程受不完全振型矩阵的压缩关系约束。每次迭代时，将贡献最小的Fisher信息矩阵的主自由度和有效信息指标对应的振型矩阵行移动到从自由度，得到更新后的形状矩阵，用于后续计算。重复迭代直到目标传感器达到目标模式数。然后应用数值模拟来比较使用安装的传感器数量获得的最佳传感器放置结果，并基于提出的参数矩阵比较使用Fisher信息矩阵和有效信息方法的贡献矩阵。基于模态形状的最佳传感器放置方法在位置选择最佳传感器布局以均匀分配整个自由度。数值结果表明，所提出的基于 F 的方法和基于有效信息的方法导致结果略有不同，这取决于参数矩阵模式的数量；然而，最终的最佳传感器放置包含在一组常见的候选传感器位置中。然而，最终的最佳传感器放置包含在一组常见的候选传感器位置中。