Elsevier

Computers in Industry

Volume 64, Issue 3, April 2013, Pages 299-309
Computers in Industry

Cost estimation of custom hoses from STL files and CAD drawings

https://doi.org/10.1016/j.compind.2012.11.009Get rights and content

Abstract

We present a method for the cost estimation of custom hoses from CAD models. They can come in two formats, which are easy to generate: a STL file or the image of a CAD drawing showing several orthogonal projections. The challenges in either cases are, first, to obtain from them a high level 3D description of the shape, and second, to learn a regression function for the prediction of the manufacturing time, based on geometric features of the reconstructed shape. The chosen description is the 3D line along the medial axis of the tube and the diameter of the circular sections along it. In order to extract it from STL files, we have adapted RANSAC, a robust parametric fitting algorithm. As for CAD drawing images, we propose a new technique for 3D reconstruction from data entered on any number of orthogonal projections. The regression function is a Gaussian process, which does not constrain the function to adopt any specific form and is governed by just two parameters. We assess the accuracy of the manufacturing time estimation by k-fold cross validation on 171 STL file models for which the time is provided by an expert. The results show the feasibility of the method, whereby the relative error for 80% of the testing samples is below 15%.

Highlights

► We present a method for the quotation of custom hoses from STL files and images of CAD drawings. ► The method is able to reconstruct the 3D medial axis. ► Gaussian process has shown to accurately estimate the manufacturing time from size and geometry features.

Introduction

Price estimation of parts from digital models like CAD files or blueprints before their actual manufacture is a key task for many companies. In today's global competitive market, timely delivering accurate quotations to potential clients may make the difference of a company with respect to its competitors. This is even more necessary for small and medium-size enterprises for which a large share of their production consists in short series of custom parts. This means that price has to be estimated accurately, fast and frequently from part models provided by potential customers, being parts always different in size, shape and materials.

The quotation process includes as its main component the estimation of the unitary manufacturing cost, to which the profit margin is added in order to get the final price. Cost estimation in those companies is often performed by an expert on the basis of his/her experience over the years. This has some drawbacks: companies come to strongly depend on such qualified personnel, experts spend a large amount of time generating quotations rather than working on other important tasks [1], and their estimations may have a subjective component. Finally, in the event of peaks in the demand of bids, they act as involuntary bottlenecks of the production process because customers can not directly obtain their quotations by other means.

This article deals with the problem of cost estimation for a specific type of parts, namely custom hoses. They are used to transport liquids and gases often at high temperature and pressure, in a variety of sectors like automotive, nautical, chemical and medical industries. Their changing shape and production in short series explain why they are manually manufactured: a steel forming tool is first made that is used for molding the hose into shape by hand, wrapping a narrow band of some kind of textile material like rubber or silicone, to be later melted in an oven.

The cost depends on the amount of material employed and also on the manufacturing time. One may wonder whether the labor time cost is significant with respect to the materials cost. According to consultations we made to a leading company of this sector, in developed countries it may account for more than 60% of the total unitary cost, pushing this kind of industries into offshoring. While the materials cost can be readily computed from the part surface, labor time cost is much more difficult to determine because it is related in an unknown way to the part size and shape. Specifically, we only know from the expert that the larger the part, the longer it takes to manufacture. Likewise, the more bends and the higher their curvature, the longer it takes because it is harder to uniformly wrap the covering material into the mold.

Thus, the objective is to derive a procedure for the automatic estimation of the surface and the manufacturing time from a CAD model of a hose. The models may come in two formats, the easiest to generate and send electronically by a customer: stereolithography files (STL) or an image of the CAD drawing showing orthogonal projections. STL is a file format to describe the surface geometry of an object and it is supported by most CAD software packages. CAD designs can be printed and scanned, or simply saved in some image format like TIFF, JPEG, etc. Fig. 1 shows a gallery of tubes rendered from their STL models and Fig. 6a shows an image of a scanned blueprint.

Furthermore, this procedure must be implemented as a platform independent web application so that manufacturing companies representatives and customers alike may get quotations on-line from their web browsers without the hassle of software installation, version updating and hardware dependency problems.

As a final and minor goal, the system must be able to render realistic orthogonal views of the model like that of Fig. 6b. Generating them from the STL file is fairly easy. However, it is not from CAD drawing images because it requires the reconstruction of the 3D model from orthogonal views. Rendered model images are to be included in the quotation document, to show the customers that the part shape has been understood well and support the quotation result.

In order to deal with the issues derived of cost estimation from part models by an expert, several researchers have addressed its automation, notably in the domains of rapid prototyping and tooling, and machining manufacturing. Refs. [2], [1] are nice and through reviews of the works on these two fields, respectively. For this reason, and because we address a different type of production, we will only pay attention to the two aspects most related to our work: the classification of cost estimation methods and web-based quotation systems.

Automated cost estimation methods have been grouped into the three following categories [3], [1]:

  • Analogy. The values of part attributes related with, for example, shape, size and material characteristics, have been previously stored in a database along with their actual cost. When a new part description arrives, the most similar part in the database is retrieved and its registered cost is somehow adapted to produce the estimation for the new part. The success of this approach relies on the proper selection of the part attributes, the similarity measure, the database size and a balanced distribution of shapes within it. Two representative examples are [4], [5].

  • Analytic. The part and/or the manufacturing process is divided into components or simpler subtasks so that for each one it is possible to calculate the cost deterministically. Later, all costs are aggregated.

  • Parametric. Like in analogy, a set of part attributes is previously selected because they are considered to be highly related to the cost. For instance, volume, area, surface curvature or type of finishing. But instead of trying to retrieve the most similar part in a database, they are used to directly estimate the cost through regression analysis. This kind of methods draw from statistical regression and machine learning techniques [17].

With regard the adoption of the analogy approach for our problem, we have found impossible to define a good similarity measure, given the variety of shapes and sizes. Another reason is that fairly globally similar shapes may have associated quite different times because it seems to also depend on local shape characteristics like surface curvature. A third obstacle is that it is not clear at all how to adapt the time of the most similar part to the present object. Analytic methods are better suited to manufacturing processes which can be decomposed in distinct, cost-quantifiable tasks, which is not the case. The parametric approach, instead, has shown to fit well to our problem: we have been able to select both global and local features and learn a regression function from a training set of samples which accurately estimates the manufacturing time.

There are web applications for cost estimation from STL models. One is QuickParts, which can be found in [15] although no description on how it works is provided, beyond that it performs some kind of geometric analysis. Conversely, Lan et al. [16] detail a web-based automated quotation system which can provide instant price quotations. However, both works are specific of rapid prototyping and machining parts.

In the following sections we will describe the most important components of the cost estimation system we have built for customized hoses. Two of them have in common the goal of extracting one same 3D high-level and complete description of the part to quote: the 3D curve of the tube medial axis and the diameter of section at each point along it. They will allow to compute the surface — and thus the materials cost—, and also the value for attributes to be subsequently used for time regression analysis, namely, medial axis length, curvature and diameter mode. The first component obtains the medial axis from an STL file (Section 2), which contains an unsorted list of triangles covering the part surface, specified by their vertices and normal in 3D space. Therefore, it is far from trivial to get the central axis curve. The second component does the same but from an image of the CAD drawing showing three orthogonal views. We have devised a semi-automated algorithm for the 3D reconstruction of the model which works with one or more orthogonal projections in a CAD drawing image (Section 3).

The third main component is the time regression. We are given a large number of samples consisting of STL files plus their time as estimated by a human expert. From this training set, we extract the value of a few relevant features related to the part size and shape in order to learn a Gaussian process. We can then estimate the cost from the features for new parts (Section 4). In Section 5 we assess the accuracy of the cost regression by means of a well known testing methodology in machine learning, k-fold cross validation, and justify the choice of the only two Gaussian process hyperparameters, the scale and the data noise variance.

We apply these techniques to the specific problem of hose quotation. However, we believe they are useful in a broader sense. The algorithm for medial axis extraction is applicable to any tubular shape described by points on its circular sections, and the same can be said of the 3D reconstruction. Regression through a Gaussian process from geometric features can be applied to other shapes for cost estimation also, avoiding the need to study each subtask like in the analytic approach. It has the advantages of being an almost-free parameter regression method, not assuming any specific class for the regression function, and its few parameters (two, in the simplest setting) can be easily tuned to the available data.

Section snippets

Medial axis extraction from STL models

The STL file format describes the approximate shape of an object in a very simple way: an unsorted list of triangles whose mesh covers the surface, each specified by its three vertices and unitary normal vector. We aim at obtaining a high-level shape description, namely, the medial axis defined as an ordered list of circular section centers and their corresponding diameters (Fig. 2), from one of the tube ends to the other.

The medial axis line, also called curve-skeleton in the literature, is a

3D reconstruction from CAD drawings

The second source of hose descriptions are images of CAD drawings showing orthogonal views, like in Fig. 6a. Like STL files, they are easy to obtain, for instance by scanning a printed design, saving it to a file in some common image format (TIFF, JPEG, etc.) or printing the screen while running the CAD application. If the model is geometrically simple, it is even possible to draw by hand a sketch of several projections on a sheet of paper and scan it.

CAD drawings of hoses typically show

Time regression

Once we have obtained the medial axis representation of a tube we are ready to compute relevant shape and size features from it and then estimate the manufacturing time. But which features? And how to estimate that time? One has first to find good, relevant features on which the time depends. Then, learn a good prediction (regression) function from a training set, consisting of a number of tubes for which the STL files and the expert's estimated times are available.

As for the features, what

Results

The available sample set consists of 171 STL files of assorted sizes and shapes plus the corresponding expert's predicted time. The medial axis length and representative section diameter range from 13 cm to 1.2 m and from 8 mm to 20 cm, respectively. The number of bends, with or without torsion is 1–5. We partition this set into training and testing sets according to the k-fold cross-validation technique, commonly used to estimate the accuracy of a predictive model when the samples are scarce [17].

Conclusions

We have presented a method for the quotation of custom hoses from STL files and images of CAD drawings. In both cases, it is based on the extraction of the 3D medial axis and section diameters. Size and geometry features are then computed, and a regression function, learned from a training set, is able to estimate the manufacturing time with a low relative error, assessed by k-fold cross validation. The 3D reconstruction from either STL files or CAD drawing images allows to accurately estimate

Acknowledgements

This research was partially supported by projects TRA2011-29454-C03-01, TIN2011-29494-C03-02 and Consolider Ingenio 2010: MIPRCV (CSD2007-00018).

Joan Serrat received the Ph.D. degree in computer science from the Universitat Autònoma de Barcelona (UAB), Spain, in 1990. He is currently an Associate Professor with the Department of Computer Science, UAB, where he is also a member of the Computer Vision Center. He has been the head of several machine vision projects for local industries and served as board member of the Spanish Chapter of the International Association for Pattern Recognition. He has coauthored more than 40 papers. He is the

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    Joan Serrat received the Ph.D. degree in computer science from the Universitat Autònoma de Barcelona (UAB), Spain, in 1990. He is currently an Associate Professor with the Department of Computer Science, UAB, where he is also a member of the Computer Vision Center. He has been the head of several machine vision projects for local industries and served as board member of the Spanish Chapter of the International Association for Pattern Recognition. He has coauthored more than 40 papers. He is the holder of three patents. His current research interest is the application of probabilistic graphical models to computer vision problems such as feature matching, tracking, and video alignment.

    Felipe Lumbreras received the electromechanical B.Sc. degree in physics from the Universitat de Barcelona in 1991 and the Ph.D. degree in computer science from the Universitat Autònoma de Barcelona in 2001. He is currently an associated professor in the Computer Science Department and member of the Computer Vision Center. His research interest include wavelet and texture analysis, 3D reconstruction, and computer vision for automotive applications.

    Antonio M. López received the B.Sc. degree in computer science from the Universitat Politècnica de Catalunya, Barcelona, Spain, in 1992 and the M.Sc. degree in image processing and artificial intelligence and the Ph.D. degree from the Universitat Autònoma de Barcelona (UAB), Cerdanyola, Spain, in 1994 and 2000, respectively. Since 1992, he has been giving lectures with the Department of Computer Science, UAB, where he is currently an Associate Professor. In 1996, he participated in the foundation of the Computer Vision Center, UAB, where he has held different institutional responsibilities and is currently responsible for the research group on Advanced Driver Assistance Systems by computer vision. He has been responsible for public and private projects and is a coauthor of more than 50 papers, all in the field of computer vision.

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