Pareto Optimal Structural Models and Predictions Consistent With Data and Modal Residuals

Abstract

A multi-objective identification method for model updating based on modal residuals is proposed. The method results in multiple Pareto optimal structural models that are consistent with the measured modal data, the class of models used to represent the structure and the modal residuals used to judge the closeness between the measured and model predicted modal data. The conventional single-objective weighted modal residuals method for model updating is also used to obtain Pareto optimal structural models by varying the values of the weights. Theoretical and computational issues related to the solution of the multi-objective and single optimization problems are addressed. The model updating methods are compared and their effectiveness is demonstrated using experimental results obtained from a three-story laboratory structure tested at a reference and a mass modified configuration. The variability of the Pareto optimal models and their associated response prediction variability are explored using two structural model classes, a simple 3-DOF model class and a higher fidelity 546-DOF finite element model class. It is shown that the Pareto optimal structural models and the corresponding response predictions may vary considerably. The variability of Pareto optimal structural model is affected by the size of modelling and measurement errors. This variability reduces as the fidelity of the selected model classes increases.

A probabilistic approach for optimal sensor allocation in structural health monitoring

“…A heuristic sequential sensor placement algorithm is then used to predict the optimal sensor configuration. Work by Ntotsios et al [15], and earlier works by Udwadia [16] and Heredia-Zavoni et al [17], showed the importance of addressing the issue of uncertainty in handling the optimal sensor configuration. Other researchers [18,19] also reported the use of information entropy and information functions such as Fisher information to formulate the objective function for optimal sensor allocations.…”

“…Furthermore, Li et al [14] obtained a vector of sensor placement indices based on the weighted components of the mode shape matrix corresponding to the sensor position. Ntotsios et al [15] presented another approach that addresses the stochastic nature of the sensor measurements. The sensor allocation problem is handled within the context of uncertainty and information entropy.…”

“…Optimal locations (m) of15,16,17,18,19 and 20 sensors using the proposed probabilistic approach. of the sensors over the structure, we compare the POD for the five levels of damage using 17 and 20 sensors.…”