DeepVIVONet: Using deep neural operators to optimize sensor locations with application to vortex-induced vibrations

TL;DR

DeepVIVONet uses the DeepONet framework to build a data-driven surrogate for vortex-induced vibrations (VIV) of a marine riser, reconstructing and forecasting full-field dynamics from sparse observer signals. The method couples a dual-network DeepONet architecture with a dynamic data structure to map time-series observations to space-time outputs, and applies a linear beam-string model to guide the physics-informed setup. A key contribution is an outer-loop optimization that learns optimal observer sensor locations, outperforming traditional POD-based placement in reconstruction accuracy and cost efficiency, and a transfer-learning experiment demonstrates extrapolation to unseen flow conditions. Overall, the approach provides fast, accurate VIV predictions and a practical, data-driven path to sensor deployment in offshore engineering settings.

Abstract

We introduce DeepVIVONet, a new framework for optimal dynamic reconstruction and forecasting of the vortex-induced vibrations (VIV) of a marine riser, using field data. We demonstrate the effectiveness of DeepVIVONet in accurately reconstructing the motion of an off--shore marine riser by using sparse spatio-temporal measurements. We also show the generalization of our model in extrapolating to other flow conditions via transfer learning, underscoring its potential to streamline operational efficiency and enhance predictive accuracy. The trained DeepVIVONet serves as a fast and accurate surrogate model for the marine riser, which we use in an outer--loop optimization algorithm to obtain the optimal locations for placing the sensors. Furthermore, we employ an existing sensor placement method based on proper orthogonal decomposition (POD) to compare with our data-driven approach. We find that that while POD offers a good approach for initial sensor placement, DeepVIVONet's adaptive capabilities yield more precise and cost-effective configurations.

Figures (15)

• Figure 1: DeepONet architecture. This unique architecture is comprised of two primary networks, namely, Trunk Network (TN) and Branch Network (BN). It forms a mapping from the input $u$ to the BN to the output evaluated at input $z^\star$ to the TN.
• Figure 2: DeepVIVONet in VIV problem: DeepVIVONet is based on DeepONet for the VIV problem. This framework reconstructs the dynamics of a marine riser by using only a few measurements from "observer" sensors. It essentially builds a mapping from observer data to the entire domain.
• Figure 3: Detailed structure of input and output data for the DeepVIVONet framework. Left: the background shows the actual space--time data. We assume that we have $m$ observers shown with blue diamonds and we have $p$ sensors for training/testing data.
• Figure 4: NDP data set: CF strain for shear flow case "test2430". The vertical axis z is the distance from the bottom of the riser in meter. The horizontal axis is the time step at which the data has been collected with the frequency of 1200 Hz.
• Figure 5: DeepVIVONet: Prediction of CF strain for shear flow case "test2430". Left panel: the location of all sensors (dashed line), observers (green lines), and test sensor (arrow). Top panel: data (black), DeepONet training (blue) in the training window, and DeepONet prediction (red) in the prediction window. Middle panel: the FFT of data and DeepONet. Bottom panel: the zoomed-in plot of the prediction window.