Stochastic inverse method to identify parameter random fields in a structure

The parameters in a structure such as geometric and material properties are generally uncertain due to manufacturing tolerance, wear, fatigue and material irregularity. Such parameters are random fields because the uncertain properties vary along the spatial domain of a structure. Since the parameter uncertainties in a structure result in the uncertainty of the structural dynamic behavior, they need to be identified accurately for structural analysis or design. In order to identify the random fields of geometric parameters, the parameters can be measured directly using a 3-dimensional coordinate measuring machine. However, it is often very expensive to measure them directly. It is even impossible to directly measure some parameters such as density and Young’s modulus. For that case, the parameter random fields should be identified from measurable response data samples. In this paper, a stochastic inverse method to identify parameter random fields in a structure using modal data is proposed. The proposed method consists of the following three steps: (i) obtaining realizations of the parameter random field from modal data samples by solving an optimization problem, (ii) obtaining the deterministic terms in the Karhunen-Loève expansion by solving an eigenvalue problem and (iii) estimating the distributions of random variables in the Karhunen-Loève expansion using a maximum likelihood estimation method with kernel density.