Optimizing sizing schedules of aircrew helmets using machine learning techniques

Challenges in sizing

A sizing system classifies a specific population into homogeneous subgroups based on some key body dimensions of body shape characteristics, and they share the same garment size.^[1] Conventionally, designers have identified a set of key body dimensions and linearly divided them into sets varying from small to large. A linear division of a parameter only works if the relationships between the critical parameters required for sizing are linear. Joshi et al. in their study of a prototype aircrew helmet showed that for a helmet that utilized head length and head breadth as sizing parameters, the overall fitment was poor due to a linear sizing schedule.^[2] It would thus be understandable that standard statistical measures of percentile, which are graded from small to large, are inadequate to capture the diversity of the human body.

Data mining for group identification

In recent years, with the availability of large volumes of data, data mining has been employed in various industries using various machine learning techniques. This allows researchers to sift through huge amounts of data and classify them into groups which may make sense to the human observer. One important method of data mining is called cluster analysis, which classifies or partitions the data set into subsets (clusters) so that the data in each subset share some common traits.^[3-6] The use of data mining techniques in clothing industry has been reviewed in an article by Elawad et al.^[7]

Study population

This study was carried out on the data of fighter pilots, as they operate in high G environments, where snug fit of the helmet is considered essential. The present study does not include female fighter pilots due to the low numbers as on date. The long-term implications of this study in aircrew helmets are evident as the dimensions of the adult head do not change appreciably with age due to fat or muscle deposition as would be the case with other body dimensions. Therefore, the sizing schedule once made is unlikely to change over the career of an individual aircrew. The sizing schedules are also unlikely to show change in secular trends over the next four to five decades at the least.

Detecting outliers

There are very few equipment which may be designed with only one control anthropometric dimension. Most would use multiple anthropometric parameters, with the aircrew helmet being one of the simplest and the anti-G suit being an example of the more complex ones. Identification of outliers is useful, as accommodating unusual body sizes or proportions can be done by customization without affecting simpler sizing schedules for the majority of the population. The Mahalanobis distance is used to detect outliers in multivariate normal data. It measures how far away an observation is from the center of a sample while accounting for correlations in the data. It is better than looking at the univariate Z-scores of each coordinate because a multivariate outlier does not necessarily have extreme coordinate values.^[8,12,13] This is represented graphically in Figure 3.

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Figure 3:

Mahalanobis distance in multivariate space. Courtesy reference.^[13]

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In this study, the outliers’ detection was done in two steps. In the first step, outliers from the entire data were identified. In the second step, the outliers within each cluster were identified. After removing the outliers, 95.9% of the data was considered for the final sizing schedule. Considering the traditional practice of fitting 3^rd to 97^th percentile of a population, the fitment in this study may be considered adequate.

Cluster analysis

Clustering is the classification or partitioning of a data set into subsets (clusters) so that the data in each subset share some common trait. One of the commonly used methods is the K-means method. In this case, the initial clusters and the number of clusters are randomly chosen. The observations are reassigned by moving them to the cluster whose centroid is closest to that observation. Reassignment continues until every observation is appointed to the cluster with the closest centroid. This machine learning protocol uses iterative methods to improve the cluster formation in each step until there is no further improvement possible.^[3,6,7] In this study, the initial cluster numbers were randomly set between 2 and 10. The machine learning protocol prepared solutions with 2–10 clusters in the same data.

The optimal number of clusters was identified using silhouette coefficient analysis. Silhouette analysis is used to study the separation distance between the resulting clusters. The silhouette plot displays a measure of how close each point in one cluster is to points in the neighboring clusters and thus provides a way to assess parameters like number of clusters visually.^[11] This method of use of a combination of machine learning with human intervention can be considered as an example of semi-supervised machine learning. In this study, the solution with four clusters was found to be optimal from the silhouette scores. On visual assessment, such a classification has a high face validity in terms of the descriptors that can be applied to these four clusters, namely, Cluster-1: Long narrow, Cluster-2: Short broad, Cluster-3: Long broad, and Cluster-4: Short narrow.

ANOVA was done between the clusters for both the parameters of head length and head breadth. The statistically significant effect of clustering on the means (centroids) of the clusters demonstrates that these clusters that have been identified belong to different groups.

Cluster analysis from the designer perspective

The clusters identified by the machine learning techniques bring out naturally occurring groups within the population which have some commonality when all the control anthropometric parameters are considered together. These naturally occurring groups are not evident when individual parameters are considered in isolation. In this study, two parameters of head length and head breadth have been traditionally used to design aircrew helmets. However, using each of the parameters separately and using linear sizing techniques have resulted in poor fitment.^[2] The head types identified by the cluster analysis closely follow the proportional variation that exists in nature. Trying to design across these groups/head types would result in poor fitment. The designer can use these cluster boundaries to identify the sizing schedule for designing the equipment.^[1,3,4,7,14] Within the clusters, the intercluster variation would have to be addressed by provisions of adjustability. In this study, the use of liners within the helmet to ensure snug fit is advocated. The sizing of liner thickness has been discussed in an article by Joshi et al.^[2]

Cluster analysis from the user perspective

The user requires a proper sizing schedule for good fitment and proper stocking. The clusters which are taken from the actual population ensure that each person fits into one cluster or the other. The measurement of the head length and head breadth can be taken early in the career and the appropriate size advocated. It is unlikely that measurements of head length or head breadth would change for an individual during his lifetime. Individuals not included in the population for this particular study are likely to still fit into one of the four clusters as the sample size of 834 for two parameters is considered sufficiently large for representing the head sizes of the Indian fighter aircrew population.

The proportions of the population which fit into the various clusters are given in Table 1. Stocking of aircrew helmets in those proportions is likely to be helpful in providing the requisite sizes at any air base.