Uncertainty Quantification of a Machine Learning Model for Identification of Isolated Nonlinearities With Conformal Prediction

Structural nonlinearities are often spatially localized, such joints and interfaces, localized damage, or isolated connections, in an otherwise linearly behaving system. Quinn and Brink (2021, “Global System Reduction Order Modeling for Localized Feature Inclusion,” ASME J. Vib. Acoust., 143(4), p. 041006.) modeled this localized nonlinearity as a deviatoric force component. In other previous work (Najera-Flores, D. A., Quinn, D. D., Garland, A., Vlachas, K., Chatzi, E., and Todd, M. D., 2023, “A Structure-Preserving Machine Learning Framework for Accurate Prediction of Structural Dynamics for Systems With Isolated Nonlinearities,”), the authors proposed a physics-informed machine learning framework to determine the deviatoric force from measurements obtained only at the boundary of the nonlinear region, assuming a noise-free environment. However, in real experimental applications, the data are expected to contain noise from a variety of sources. In this work, we explore the sensitivity of the trained network by comparing the network responses when trained on deterministic (“noise-free”) model data and model data with additive noise (“noisy”). As the neural network does not yield a closed-form transformation from the input distribution to the response distribution, we leverage the use of conformal sets to build an illustration of sensitivity. Through the conformal set assumption of exchangeability, we may build a distribution-free prediction interval for both network responses of the clean and noisy training sets. This work will explore the application of conformal sets for uncertainty quantification of a deterministic structure-preserving neural network and its deployment in a structural health monitoring framework to detect deviations from a baseline state based on noisy measurements.