A Reduced Order Model conditioned on monitoring features for estimation and uncertainty quantification in engineered systems

TL;DR

This paper tackles uncertainty-aware parametric nonlinear ROMs for engineered systems by conditioning local ROM bases on online monitoring features. It introduces VpROM, a cVAE-based ROM that, together with an auxiliary neural network for mapping monitoring features to system parameters, generates local bases and propagates dynamics with quantified confidence. The approach is validated on two synthetic nonlinear problems (arc with large deformations and a kingpin with plasticity), showing accurate response envelopes with tight uncertainty bounds and substantial online speedups. The work advances digital twin and SHM applications by enabling robust, real-time estimation under uncertainty using measurements derived from sensors.

Abstract

Reduced Order Models (ROMs) form essential tools across engineering domains by virtue of their function as surrogates for computationally intensive digital twinning simulators. Although purely data-driven methods are available for ROM construction, schemes that allow to retain a portion of the physics tend to enhance the interpretability and generalization of ROMs. However, physics-based techniques can adversely scale when dealing with nonlinear systems that feature parametric dependencies. This study introduces a generative physics-based ROM that is suited for nonlinear systems with parametric dependencies and is additionally able to quantify the confidence associated with the respective estimates. A main contribution of this work is the conditioning of these parametric ROMs to features that can be derived from monitoring measurements, feasibly in an online fashion. This is contrary to most existing ROM schemes, which remain restricted to the prescription of the physics-based, and usually a priori unknown, system parameters. Our work utilizes conditional Variational Autoencoders to continuously map the required reduction bases to a feature vector extracted from limited output measurements, while additionally allowing for a probabilistic assessment of the ROM-estimated Quantities of Interest. An auxiliary task using a neural network-based parametrization of suitable probability distributions is introduced to re-establish the link with physical model parameters. We verify the proposed scheme on a series of simulated case studies incorporating effects of geometric and material nonlinearity under parametric dependencies related to system properties and input load characteristics.

Figures (15)

• Figure 1: Architecture of a variational autoencoder (VAE).
• Figure 2: The architecture of a cVAE. The conditioning features $\hbox{\boldmath$w$}$ are injected via concatenation with the input vector $\hbox{\boldmath$X$}$ and the latent space $\hbox{\boldmath$Z$}$. The input refers to the ROM basis coefficients $\hbox{\boldmath$X$}$ in \ref{['eq:coeffs']}
• Figure 3: Architecture of the cVAE in basis generation mode: The prior distribution $\epsilon$ is sampled, and the latent vectors are taken after concatenating with the conditioning vector $\hbox{\boldmath$w$}$. Dimensionality serves only illustrative purposes.
• Figure 4: Graphical abstract depicting the training and prediction mode of the proposed framework.
• Figure 5: Arc structure: Two-dimensional FE model and example of the ECSW mesh. The monitored nodes are highlighted in red, whereas the ECSW elements are in orange for visualization purposes.