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Brackets are an essential component in aircraft manufacture and design,joining parts together, supporting weight, holding wires, and strengtheningjoints. Hundreds or thousands of unique brackets are used in every aircraft,but manufacturing a large number of distinct brackets is inefficient andexpensive. Fortunately, many so-called "different" brackets are in fact verysimilar or even identical to each other. In this manuscript, we present adata-driven framework for constructing a comparatively small group ofrepresentative brackets from a large catalog of current brackets, based onhierarchical clustering of bracket data. We find that for a modern commercialaircraft, the full set of brackets can be reduced by 30\% while stilldescribing half of the test set sufficiently accurately. This approach is basedon designing an inner product that quantifies a multi-objective similaritybetween two brackets, which are the "bra" and the "ket" of the inner product.Although we demonstrate this algorithm to reduce the number of brackets inaerospace manufacturing, it may be generally applied to any large-scalecomponent standardization effort.

Bracketing brackets with bras and kets