# Uncertainty Quantification of Mode Shape Variation Utilizing Multi-Level Multi-Response Gaussian Process

arXiv: https://arxiv.org/abs/2002.09287 · HTML: https://mlsanity.com/paper/2002.09287/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Feb 2020.

## Built on by (most cited first, 1 of 1)

- [Probabilistic Bearing Fault Diagnosis Using Gaussian Process with Tailored Feature Extraction](https://mlsanity.com/paper/2109.09189/) (2021)

## Abstract (arXiv)

Mode shape information play the essential role in deciding the spatial pattern of vibratory response of a structure. The uncertainty quantification of mode shape, i.e., predicting mode shape variation when the structure is subjected to uncertainty, can provide guidance for robust design and control. Nevertheless, computational efficiency is a challenging issue. Direct Monte Carlo simulation is unlikely to be feasible especially for a complex structure with large number of degrees of freedom. In this research, we develop a new probabilistic framework built upon Gaussian process meta-modeling architecture to analyze mode shape variation. To expedite the generation of input dataset for meta-model establishment, a multi-level strategy is adopted which can blend a large amount of low-fidelity data acquired from order-reduced analysis with a small amount of high-fidelity data produced by high-dimensional full finite element analysis. To take advantage of the intrinsic relation of spatial distribution of mode shape, a multi-response strategy is incorporated to predict mode shape variation at different locations simultaneously. These yield a multi-level, multi-response Gaussian process that can efficiently and accurately quantify the effect of structural uncertainty to mode shape variation. Comprehensive case studies are carried out for demonstration and validation.