Probabilistic Approach to NASA Langley Research Center Multidisciplinary Uncertainty Quantification Challenge Problem

The role of the Bhattacharyya distance in stochastic model updating

“…As already proved in the previous example, only the input directly involved in the determination of the center of the mass of the samples, namely 𝜃 1 and 𝜃 4 herein, can be updated with the Euclidian distance metric. Similar histograms or PDFs, especially for the variances and correlation, are obtained in the works of Patelli et al [14] and Ghanem et al [15], implying the variance information is difficult to be updated by the classical Bayesian approaches with classic distance metrics.…”

“…Ref. [14][15][16], do not converge to a unique solution. Nevertheless, the proposed ABC approach with the Bhattacharyya distance metric demonstrates its ability on variance updating and capturing the complex non-linear relationship between inputs and outputs.…”

“…Both samples are corresponding to a set of prescribed (but unknown in the original introduction of the problem) values of 𝜃 1 -𝜃 8 . Three published works [14][15][16] on the NASA UQ challenge problem are referred here for a comparison to assess the feasibility and potential superiority of the Bhattacharyya distance metric in association with the ABC updating framework. Note that, in the original NASA UQ challenge problem, there were different tasks in Subproblem A, where the first 25 observations (x1) are supposed to be used for model updating in Task 1, and the remaining (x2) for model validation in Task 2.…”

“…The max-p values of 𝜃 2 and 𝜃 4 are omitted in Table 4, since their posterior distributions remain approximately uniform as shown in Fig. 11, mainly because the output is insensitive to 𝜃 2 and 𝜃 4 , which has been addressed by the previously published works [14][15][16] in other sub-tasks of the NASA UQ challenge problem [2].…”

“…Sub-problem A is closely related to model updating, and its results can be significantly influenced by different UQ metrics. Three of the works previously published on solving the NASA UQ challenge problem, namely the papers by Patelli et al [14], Ghanem et al [15], and Safta et al [16], are used as reference works to assess the updating results. All of these three works are also employing Bayesian updating methodologies.…”