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Online Gate-Driven Flow Control in Resin Transfer Moulding Using a Neural-Network Surrogate
Nicholas Wright, Oliver Maclaren, Piaras Kelly, Suresh Advani, Ruanui Nicholson
TL;DR
Resin transfer moulding requires complete preform saturation before vent arrival, but race tracking distorts the flow front and can create dry spots. The paper combines online race-tracking estimation with auxiliary-gate control using neural-network surrogates, achieving higher filling success in a forked-geometry study while showing sensitivity to control-gate configuration.
Problem
Race tracking creates preferential flow channels that distort filling, while computationally expensive forward simulations hinder real-time estimation and control.
Method
The framework estimates race-tracking strengths from pressure data with an iterated extended Kalman filter and optimises auxiliary gate pressures using neural-network surrogates with Bayesian approximation-error correction.
Results
Under the 2% dry-area criterion, success rose from 18/100 without control to 42/100 with controlled actions evaluated by the FECV model.
Takeaways & Limitations
Flow-front geometry depends only on time-averaged injection pressures, enabling real-time-capable surrogate training and combined estimation-control in the studied forked geometry.
Takeaways & Limitations
Online use of the original FECV solver is computationally prohibitive because inference and control require repeated forward-model and Jacobian evaluations.
Abstract
from arXiv · showhide
In resin transfer moulding, complete saturation of the fibre preform is necessary before the resin front reaches the outlet vent(s), to prevent dry-spot formation. In practice, the flow front rarely advances uniformly due to race-tracking effects. We propose a combined estimation and control strategy to address this issue. We use pressure-sensor data collected during filling to estimate the unknown race-tracking strengths via an iterated extended Kalman filter, and to simultaneously optimise auxiliary gate pressures to prevent the resin from arriving at the vent before complete saturation occurs. To make this approach feasible in real time, we replace the expensive finite element-control volume model with neural network surrogate models. The Bayesian approximation error framework is used to account for the discrepancy between the surrogates and the original model. To make the training of the surrogates feasible with time-dependent control actions, we prove that the flow-front geometry depends only on the time-averaged gate pressures. We demonstrate the methodology on a representative forked geometry, showing that the combined estimation-and-control framework can substantially reduce the number of unfilled nodes at the end of filling compared with an uncontrolled baseline. However, the level of improvement depends strongly on the location and number of auxiliary gates.
1 Introduction
RTM requires complete preform saturation before resin reaches the vents, but race tracking can distort the flow front and create dry spots. The paper combines online race-tracking estimation, gate-pressure control, and neural-network surrogates to address this in real time.
- RTM injects thermoset resin through gates into a closed mould, where it impregnates a dry fibre preform before curing.
- Premature arrival at all outlet vents traps air, producing dry spots that become voids and degrade the cured part’s structural and mechanical performance.
- Race tracking creates preferential high-permeability channels that make the flow front advance non-uniformly and complicate reliable filling control.
- Neural-network surrogates replace expensive FECV simulations, enabling online estimation and control while addressing the computational demands of real-time operation.
- The framework estimates unknown race-tracking strengths from pressure sensors with an IEKF while optimising auxiliary gate pressures to steer the front away from premature vent arrival.
2 Mathematical Modelling in RTM
The RTM model represents resin filling as a time-evolving free-boundary problem governed by Darcy flow, pressure conditions, and front motion. Race-tracking strengths modify local permeability, while sensor observations provide noisy information for parameter estimation.
- The preform is partitioned into a resin-filled region and a dry region, with the evolving flow front forming their free boundary.
- Darcy’s law and mass conservation determine resin flux and the elliptic pressure field within the evolving resin domain.
- Gate pressures impose time-varying Dirichlet conditions, while mould walls use zero-flow Neumann conditions and the flow front has zero pressure.
- The Stefan condition governs front advancement through the pressure gradient normal to the flow boundary.
- Race-tracking parameters are log-permeability ratios that scale permeability in designated preferential-flow regions relative to the bulk preform.
- The FECV method tracks control-volume saturation, while pressure sensors observe noisy measurements at discrete mould locations.
3 Online Estimation and Control
The framework combines sequential Bayesian estimation of race-tracking strengths with surrogate-based gate-pressure control. An average-pressure theorem makes time-dependent control tractable, while the online algorithm uses IEKF updates and surrogate optimisation to select actions.
- Online estimation: The Bayesian formulation approximates the posterior with a Gaussian centred at the MAP estimate, with covariance obtained by linearising the forward model.For the original FECV model, the required Jacobian must be approximated by finite differences, which are expensive and can be inaccurate because of model non-smoothness.
- Online estimation: The IEKF sequentially updates race-tracking estimates from successive in-mould pressure measurements, using each posterior as the next prior.The nonlinear MAP problem is solved with multiple Gauss–Newton iterations, making the method an iterated rather than standard EKF.
- Surrogate models: Fast differentiable surrogates g and h replace the FECV forward and control models, while Bayesian approximation error correction accounts for their systematic discrepancy.The surrogates evaluate in milliseconds and provide exact Jacobians through automatic differentiation for estimation and control optimisation.
- Average-pressure parameterisation: The average-pressure theorem shows that the resin domain at a fixed time depends only on the vector of time-averaged gate pressures, not the detailed injection history.This reduces the pressure-history input to a fixed-dimensional representation without losing information about the flow-front geometry.
- Average-pressure parameterisation: Restricting future actions to constant pressures preserves all potential filling outcomes, allowing the control surrogate to use the current average pressure and a constant future candidate.The resulting control model has fixed-dimensional inputs h(t, x, ā, af).
- Online control: Once two policies reach the same time-averaged gate pressures, their flow fronts and resin domains become indistinguishable, including under the illustrated permeability scenarios.The example reaches 100 kPa at each gate by the final time; stable control actions were observed after race-tracking estimates stabilised.
4 Numerical Example
The fork-geometry experiment combines online race-tracking estimation with auxiliary-gate control using neural-network surrogates trained from LIMS simulations. Across Monte Carlo trials, control improved filling outcomes over no control, but performance was limited by the available gate-pressure range and controllability of individual scenarios.
- Experimental setup: The study uses a fork geometry with six potential race-tracking regions, one controllable auxiliary gate, one fixed gate, and 12 pressure sensors.The fixed gate operates at 100 kPa, while the auxiliary gate is independently controlled.
- Surrogate models: The pressure surrogate g predicts sensor pressures, while the control surrogate h predicts terminal dry area from race-tracking, time, and gate-pressure inputs.Both networks are trained from FECV/LIMS-generated data and use the architecture summarized in Table 1.
- Surrogate models: The pressure surrogate achieved a final physical-unit RMSE of approximately 2.74 kPa per sensor after validation loss decreased to 7.5 × 10^-4 in scaled space.Training took 2100 seconds on a single RTX 5080 GPU.
- Surrogate models: The control surrogate h uses one output neuron for terminal dry area and reached a final validation loss of approximately 155 in squared node counts after about three epochs.Training took approximately 1900 seconds on a single RTX 5080 GPU.
- Computational performance: Replacing finite-difference IEKF updates based on LIMS reduced the estimated update cost from roughly 23 seconds to a real-time-capable surrogate loop compatible with one-second measurements.The high-fidelity update would require approximately 35 full-fill simulations, whereas measurements arrive every second.
- Results: Under the successful-fill criterion of fewer than 2% empty nodes, controlled actions achieved 42/100 successes versus 18/100 without control, while the surrogate predicted 58/100.The surrogate controller was optimistic relative to high-fidelity evaluation.
- Controllability: Only 51/100 sampled scenarios were controllable within the 0–200 kPa auxiliary-gate range, so perfect filling could not be guaranteed for every scenario.The constant-pressure scan provides a complete controllability test because time-varying policies have equivalent time-averaged pressures.
5 Conclusion
The framework combines online race-tracking estimation with surrogate-based gate-pressure control, improving filling success but remaining constrained by controllability, surrogate accuracy, and the simulation-to-reality gap.
- Under the 2% dry-area criterion, controlled filling succeeds in 42/100 scenarios versus 18/100 without control.
- Only 51/100 race-tracking scenarios were controllable with the study’s single auxiliary gate and vent design.The authors therefore identify gate and vent locations and numbers as important design choices.
- Surrogate-model accuracy limits performance because pressure-surrogate errors increase BAE uncertainty, while control-surrogate errors reduce control-action accuracy.
- Increasing the number of controllable gates makes the one-dimensional golden-section search unsuitable for scalable optimisation.The authors propose gradient-based optimisation over the differentiable control surrogate for larger gate sets.
- Physical deployment must address curing-induced viscosity and temperature changes absent from the isothermal Darcy-flow model.The authors identify validation against these transient effects as necessary before production deployment.
Declarations
The authors report no funding and state that supporting data are available from the corresponding author upon request.
- The authors declare no funding.
- Data supporting the findings are available from the corresponding author upon request.
A Proof of the average-pressure theorem
The proof shows that, under the quasi-static Darcy formulation, the filled region depends on cumulative gate pressures rather than the detailed pressure history, enabling constant-pressure continuation policies.
- The theorem defines the filled region from cumulative gate pressures up to sets of measure zero and does not require connected or smoothly parameterised fronts.
- The proof rewrites the moving-boundary problem as a fixed-domain obstacle problem using the time-integrated pressure.
- At fixed time, the filled region and moving front do not explicitly appear in the variational inequality; gate histories enter through cumulative gate pressures.
- The argument applies from any initial time and resin domain, supporting constant-pressure continuation and controllability tests during filling.
- Componentwise larger cumulative gate pressures produce larger resin domains under the comparison lemma.
- For convex admissible pressure sets, replacing any admissible time-varying continuation by its time average preserves admissibility, vent-arrival time, and terminal resin domain.
B Training history for surrogates
Training and validation losses are reported for the control surrogate h and pressure-related surrogate g, with g trained in two stages.
- Figure 8 reports training and validation loss over iterations for surrogates h and g.
- For g, adding a ReLU output layer marks the transition between two training stages, after which validation loss continues to improve.