Bracketing brackets with bras and kets

Highlights

• Bracket standardization for efficient aircraft manufacture is considered

• Hierarchical clustering is used to reduce a set of historical bracket data

• Many test brackets can be described sufficiently accurately with the reduced set

• The number of clusters can be varied to balance performance and standardization

Abstract

Brackets are an essential component in aircraft manufacture and design, joining parts together, supporting weight, holding wires, and strengthening joints. Hundreds or thousands of unique brackets are used in every aircraft, but manufacturing a large number of distinct brackets is inefficient and expensive. Fortunately, many so-called “different” brackets are in fact very similar or even identical to each other. In this manuscript, we present a data-driven framework for constructing a comparatively small group of representative brackets from a large catalog of current brackets, based on hierarchical clustering of bracket data. We find that for a modern commercial aircraft, the full set of brackets can be reduced by 30% while still describing half of the test set sufficiently accurately. This approach is based on designing an inner product that quantifies a multi-objective similarity between two brackets, which are the “bra” and the “ket” of the inner product. Although we demonstrate this algorithm to reduce the number of brackets in aerospace manufacturing, it may be generally applied to other large-scale component standardization efforts.

Introduction

Component part standardization has been shown to be highly beneficial in manufacturing processes, leading to higher efficiency and reduced costs [11], [12], [5], [30], [32], [33]. In the aircraft manufacturing industry, Boeing already employs a platform approach for the overall design of many aircraft, in which new models may be rapidly designed to fit specific marketplace niches by rescaling existing parts or groups of parts [28]. However, some component parts in the manufacturing process have yet to be standardized, including brackets, which join parts, strengthen joints, and hold wires. Currently, a new bracket is designed for nearly every new purpose. Reducing the number of unique brackets would result in improved efficiency. However, standardizing the set of brackets is a complex problem and must account for the dimensions of the joint or intersection, the type of interface, the frequency of use, and cost of materials and manufacturing, where these variables can be more or less important on a case by case basis. In this work, we present an optimization strategy for reducing a large set of brackets down to a comparatively small set of standardized brackets, based on hierarchical clustering of the bracket data. We find that by using our machine learning strategy, the number of unique brackets can be reduced by approximately 30% with little reduction in performance.

Industry standardization is often achieved by building a family of standardized component parts, where the parts can be combined to design new products. It is highly inefficient to custom design each component part for every new product, so having a predetermined set of possible parts to draw from can lead to significant savings in both time and money, as well as guaranteeing that components will be compatible with one another. A prominent example of product family design is in the automotive industry [29], where many companies utilize platforms, a standardized group of parts such as the floor, suspension, engine, and fuel tank, which serves as the base for multiple products. Unique features such as the car body and steering can be added to the platform, yielding an entirely new product far more efficiently in terms of engineering and manufacturing than if it were custom designed.

The parts that make up the platform and the unique parts that are added to it are often specifically engineered for that purpose. However, what about the case where there is a large library of parts from past products that have similar functionalities? It may be beneficial to standardize the library into a reduced set. In fact, Perera et al. [30] performed an analysis of the savings accrued through component part standardization and found that costs are reduced throughout the entire life cycle of a product. These savings occur during product development, where engineering efforts are reduced; manufacturing, as materials can be purchased more cheaply in bulk, and machine setup and labor costs are reduced; distribution, since taking inventory is simpler, and facilities are more robust to damaged components; usage, where the customer has better access to spare parts and maintenance support; and disposal, with recycling being easier with fewer unique parts. The one major disadvantage sited is that if parts are too standardized, they may not be able to meet customers’ satisfaction completely.

Despite the clear benefits of component part standardization, the literature on how to standardize a large library of past parts is surprisingly sparse, with most sources on standardization focusing on its benefits, as in Perera et al. [30]; Vakharia et al. [33] or quantification of standardization, e.g., Collier [11]; Wacker and Treleven [34]. Jun-min et al. [21] describe a standardization method based on calculating the topological similarity of parts’ form features (geometrical shapes that make up the part), but this method is very general, as opposed to the bracket standardization problem, where we can leverage the fact that every bracket of the same type has the same underlying structure.

However, in recent years big data and machine learning techniques have proven highly effective for predictive manufacturing, which improves efficiency, quality, and cost savings; see, e.g., Harding et al. [17]; Wang [35]; Lee et al. [24]; Lechevalier et al. [23]; Esmaeilian et al. [14]. Moreover, dimensionality reduction methods have been applied to manufacturing in many contexts: Guo and Banerjee [15] use topological data analysis (TDA) for prediction and fault detection and Guo et al [16] extend TDA through sparse sampling. Principal component analysis (PCA) has been widely used to predict assembly variation, for example, Manohar et al. [26]; Camelio and Hu [7]; Camelio and Yim [8]; Lindau et al. [25]. And Zhang et al. [37] adopt PCA for surface characterization and outlier rejection. These methods prove that machine learning and dimensionality reduction techniques can improve prediction, control, and decision making for manufacturing, and now we employ a common unsupervised learning algorithm for the reduction of a large set of bracket data.

Our approach to standardization is to consider past bracket data and perform clustering in parameter space to identify a relatively small number of brackets to approximately represent the entire set (a similar framework to that of coresets [3]). The part standardization problem can be viewed in several possible ways, but we identify two main questions:

• Given a set number of standardized brackets to be designed from the training set, how accurately are the brackets in the test set represented?

• How many standardized brackets are required for a given accuracy in representing the test set?

There are also multiple ways to quantify accuracy. Accuracy could be taken as the mean error of the test set, where the error is the distance between a test bracket and the nearest representative bracket, for some distance metric. Or one could set a distance threshold and count the number of test set brackets that fall below it, i.e., are said to be correctly described by a standardized bracket. Thus, there are two mathematically rigorous ways to formulate questions 1 and 2, as described in Section 2.1.

The goal of bracket standardization is to identify a standardized bracket that most closely matches the specification of a gap or joint along with the required tolerances. While the number of standardized brackets is predetermined, since accuracy is of primary importance in aircraft manufacture, if the closest standardized bracket is not within tolerance, the system will be allowed to return a new bracket that fits the gap or joint perfectly.

To this end, we use hierarchical clustering [36], an unsupervised machine learning algorithm offering flexibility in both within- and between-cluster distance metrics, to group the brackets in the training set by similarity, and choose one bracket from each cluster as a representative. We leverage the manufacturing process to achieve higher accuracy: to manufacture a bracket, it is extruded or cut and bent into shape, and then the hole pattern is stamped into it. Therefore, we cluster on geometrical and hole pattern variables separately. We then apply the set of standardized brackets to the test set and calculate the accuracy both in terms of error and number correctly categorized. By varying the number of clusters, we balance accuracy and a reduction in the number of unique brackets. We leave room for user-specified tolerances when calculating the number of brackets correctly categorized. As a result, our method is highly intuitive and interpretable, but also tailored specifically to the bracket data set. However, because of this method's interpretability and the ease of implementation of hierarchical clustering, we expect it would be simple to apply a similar technique for the standardization of other data sets of a similar format, with only small modifications necessary.

An outline of our procedure is given in Fig. 1. In Section 2, we state the optimization problems, present the bracket data set, and provide some background on hierarchical clustering. In Section 3, we show the results of our bracket clustering algorithm, and we present conclusions in Section 4.