Data driven forecasting of dynamic cable loads for tunnel immersion operations

The immersion of the tunnel elements is a critical operation in the construction of an immersed tunnel. During this operation, the tunnel element is lowered to the seabed, guided by vertical cables, whose loads vary continuously as a result of the interaction with environmental and operational inputs, such as water density changes and cable pay out events. Predicting these loads accurately would allow the operation to be optimized, enhancing both the safety and the efficiency of the lowering process.

In current practice, cable loads are estimated using methods of increasing fidelity. Engineering hand calculations (low-fidelity) are quick to compute but rely on simplifying assumptions that neglect hydrodynamic forces, limiting their accuracy. Mid-fidelity models such as OrcaFlex estimate these hydrodynamic forces using potential flow theory and Morison-type force equations, which improves accuracy but introduces calibration coefficients that must be estimated. High-fidelity methods such as Computational Fluid Dynamics (CFD) resolve the Navier--Stokes equations and can capture the fluid structure interaction, but at a high computational cost, which makes them impractical for operational use. Furthermore, none of these methods can adapt to cable loads measured during previous immersion operations. This research investigates to what extent machine learning models, trained on operational monitoring data, can improve the accuracy and generalizability of cable load estimation compared to these traditional engineering methods.

The machine learning models are benchmarked against the engineering estimates: the DEME immersion sheet for the static loads and a two-degree-of-freedom (2DOF) analytical model for the dynamic loads. The monitoring data used in this study comes from the Oosterweel tunnel in Antwerp, from which six immersion sequences were retrieved, each containing operational and environmental variables. Quality control was applied to remove sensor faults, after which a data analysis was performed to characterise the stationarity of the data and the signal was filtered to retain the structural behaviour of the system. The target data were then split into static and dynamic cable loads. For the static loads, a multivariate regression (MVR) and a multilayer perceptron (MLP) were selected: the MVR captures the linear correlation between the input forces, while the MLP additionally captures the non-linear behaviour. For the dynamic loads, a long short-term memory (LSTM) and Fourier neural operator (FNO) were developed because these models both account for sequential inductive bias and the FNO also works with spectral inductive bias. For the MVR, MLP, and LSTM, a weighted mean squared error (MSE) loss function was used, and for the FNO, a Sobolev loss function. The models were evaluated by their coefficient of determination (R²) and root mean squared error (RMSE) against the evaluation set, and for the dynamic models, the period distribution was additionally compared. 

The data analysis revealed a two-regime structure in the monitoring data. The boundary between these regimes is the moment the element passes through the waterline. Besides this, the analysis indicated that the oscillation period decreases as the element descends and increases again near the seabed. This contradicts the available literature on immersed tunnels in wave environments. This effect is most likely caused by the depth-dependent added mass.

The machine learning models outperformed the engineering estimates in both regimes. For the static loads, the MLP reached an average of R²  = 0.92 and RMSE = 5.7t, against R² = 0.33 and RMSE = 16.1t, for the immersion sheet. For the dynamic loads, the FNO and LSTM achieved positive R² values (0.44 and 0.42 respectively), where the 2DOF estimate scored negative. Both models reproduced the non-constant oscillation period. However, the peak amplitudes remained underestimated. A convergence study showed the number of training sequences required to outperform the engineering estimates (static n = 2, dynamic n = 5).

This study indicates that operational monitoring data can be used to train machine learning models that estimate cable loads more accurately than the engineering methods currently in use. Although the dynamic models still underestimate peak amplitudes, limiting their direct use for optimizing the cable payout rate, the modelling can be transferred to future immersion projects.