Optimal sensor placement in timber structures by means of a multi-scale approach with material uncertainty

This paper investigates the optimal location of sensors in a timber structure when parametric uncertainty is considered in the microstructure of the material. In order to describe the proposed methodology, a timber beam is chosen for our numerical simulations. A classical sensor location methodology based on the Fisher information matrix is employed. Within a finite element framework, a homogenization-based multi-scale approach is adopted to model the constitutive response of timber, along with stochastic properties in the definition of the material. Nevertheless, by considering uncertainty in the micromechanical properties of wood, a significant computational cost is added to the solution of a large set of realizations represented by expensive multi-scale analyses. In order to tackle this high cost, we build a statistical approximation to the output of the computer model, known as a Bayesian emulator. Following this strategy, three micromechanical parameters are chosen to study their influence on the selection of different configurations of sensor placement. The optimal location of sensors is assessed with three different criteria: the Fisher matrix determinant, the modal assurance criterion error and the condition number. Furthermore, the robustness of this configuration is investigated in the presence of noise. Copyright (c) 2014 John Wiley & Sons, Ltd.