# Bayesian Optimal Experimental Design for Race Tracking in Resin Transfer Moulding
## 7 Discussion and Conclusions
### Conclusions  
By representing the permeability throughout a preform as a homogeneous but anisotropic property, except for regions of race tracking, we are able to predict the race-tracking effect as well as the bulk permeability to a high level of certainty. A Bayesian inversion algorithm was used to achieve this and was demonstrated with two example scenarios that showed that the precision of the estimates increased with fewer race-tracking regions and when more sensors were used. Although these models are simple and only two-dimensional, the approach could be extended to three-dimensional, with many race-tracking regions.  
In this paper, we only estimated the permeability once the mould had been filled and measurements had been collected throughout the filling process. However, in the future, this methodology could be applied through different stages of mould filling. This would allow researchers to estimate race tracking and then predict the flow front propagation pattern for the remainder of the filling. It would then be possible to take some control actions if we predict that the resin will propagate in an unfavourable way.  
The uncertainty in the computed posterior distributions developed here considers only measurement error from sensors, where the measurement from the sensor is made noisy by the addition of randomly and independently sampled error. However, there are approaches that deal with another significant type of error--the approximation errors that arise due to the use of an approximate model, which differs from the true RTM process. There are  
Figure 11: The true posteriors visualised for a one-parameter formulation.  
approaches to deal with this so-called Bayesian approximation error [41; 42; 43] that could be investigated and integrated into the current framework in the future. In particular, this paper made several simplifying assumptions to the model, such as a piecewise homogeneous permeability and fixed porosity, which add to this Bayesian approximation error.  
We have also used the Bayesian formulation to develop a methodology for optimising sensor placement within a mould to extract maximum insight. This investigation also revealed the decaying value of adding more sensors. The optimal sensor configuration showed significant decreases in uncertainty compared to random locations. In the future, this framework could be combined with an online permeability estimation tool for increased predictive power. The results show that using a large number of sensors with a tedious, disruptive, and potentially expensive setup is not necessary--very similar accuracy can be achieved with between five and seven sensors, provided that they are in optimal locations. The investigation has also shown that even two sensors can provide reasonably accurate estimates for race tracking for simple scenarios.  
Conceptualization, N.W. and S.A.; methodology, N.W., P.K., O.M. and R.N.; software, N.W.; validation, N.W.; formal analysis, N.W.; resources, P.K.; writing--original draft preparation, N.W.; writing--review and editing, N.W., R.N., P.K. and S.A.; visualization, N.W.; supervision, P.K., O.M., R.N. and S.A. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
The authors declare no conflict of interest.