# Bayesian Optimal Experimental Design for Race Tracking in Resin Transfer Moulding
## 1 Introduction  
Resin Transfer Moulding (RTM) is a common advanced processing method for producing near-net-shaped composite parts. It consists of five key stages:  
1. Preform Manufacturing: The reinforcing fabric is manufactured, typically by stacking layers of fabric upon one another. 2. Lay-up and Draping: The fabric preform is layed up or draped in the mould. 3. Mould Closure: The fabric layers are compressed to the final thickness of the part. 4. Resin Injection: Resin is injected into the mould through the injection gate(s) until the preform is fully saturated and the resin exits through a vent. 5. Cure and Demouliding: A part is removed from the mould after the resin cures. RTM is often used within the industry because of the relatively short production times and simple experimental setup to construct near-net-shaped parts. However, these advantages come with caveats. An important stage in RTM is resin injection, where the flow of the resin must be carefully controlled to avoid incomplete fillings, in which air can be trapped inside the mould, forming macroscopic dry spots. Even very small regions without resin can cause catastrophic failure of the composite part [1; 2; 3; 4]. Accurate predictions of resin flow allow for strategic design of gates, vents, and injection schemes to optimally fill the composite part, with minimal chance of dry spot formation [1]. The flow of the resin through the fabric preform depends on the permeability. Deviations in the permeability from what is expected often come from the lay-up and drapingstage of manufacturing, when the preform is placed into the mould. Occasionally, there can be areas of very high permeability at the boundaries of the preform where the fabric density is lower. These are 'race tracks' for the resin as it fills the mould. The strength and existence of race tracking are influenced by a variety of factors, including fabric type, the preform manufacturing method, and the placement of the preform into the mould. It can vary from one part to the next in the same production run and is usually not repeatable [5]. The unpredictable nature of race tracks, in terms of their strength, can lead to significant variations in resin propagation, significantly changing the flow front movement pattern [6; 7; 8]. This can lead to dry spots in the composite parts, as the flow moves in an unpredictable way, trapping air. It is of great interest to be able to predict the effects of race tracking and mitigate the chance of dry spot formation, even in cases of high race tracking. When race tracking is predicted, one can use it as a method for advantageous resin distribution, rather than race tracking being an unpredictable problem. Research around the effects of race tracking is not mainly focused on the prevention of race tracking, which is inevitable to some extent, but on understanding and predicting the race-tracking effect. Techniques from areas of statistics and machine learning have been incorporated into prediction, as well as methods that incorporate existing physical models of RTM [8; 9; 10; 11; 12]. One significant example, [5], addresses the problem of predicting race tracking online, as the resin is injected. This is an important problem as it allows manufacturers to accurately predict the flow of the resin, taking into account the specific race-tracking scenario for each part. Online automation tools could then be used to change the resin flow to ensure that there are no dry spots by introducing control actions during filling, such as introducing new injection locations, opening and closing exit vents, and changing injection pressures [13]. The method is based on discretising potential race-tracking effects for each susceptible region and creating a database of resin flow for each permutation of potential effects for each region. As a part is filled, sensors collect data that are then compared to the closest scenario in the database. This method is efficient because all the extensive computation can be completed offline.