Optimal sensor placement methodology for parametric identification of structural systems.

*(English)*Zbl 1236.74208Summary: Theoretical and computational issues arising in the selection of the optimal sensor configuration for parameter estimation in structural dynamics are addressed. The information entropy, measuring the uncertainty in the system parameters, is used as the performance measure of a sensor configuration. A useful asymptotic approximation for the information entropy, valid for a large number of measured data, is derived. The asymptotic estimate is then used to rigorously justify that selections of the optimal sensor configuration can be based solely on a nominal structural model, ignoring the time history details of the measured data which are not available in the experimental design stage. It is further shown that the lower and upper bounds of the information entropy are decreasing functions of the number of sensors. Based on this result, two algorithms are proposed for constructing effective sensor configurations that are superior, in terms of computational efficiency and accuracy, to the sensor configurations provided by genetic algorithms. The theoretical developments and the effectiveness of the proposed algorithms are illustrated by designing the optimal configuration for a 10-degree-of-freedom (d.o.f.) chain-like spring-mass model and a 240-d.o.f. three-dimensional truss structure.

##### MSC:

74M05 | Control, switches and devices (“smart materials”) in solid mechanics |

74K99 | Thin bodies, structures |

74P99 | Optimization problems in solid mechanics |

93B30 | System identification |