⚡ electrical engineering

Longitudinal Segmentation and Terminal Classification of WAAM Single Beads from 3D Point Clouds

This study introduces an expert-informed, geometry-driven workflow utilizing a quadratic–linear–quadratic (Q–L–Q) algorithm to automatically segment and classify the START, MID, and END regions of WAAM single beads from 3D point clouds, successfully preserving transient geometric behaviors obscured by traditional longitudinal averaging.

Original authors: Janez Gotlih, Kristijan Šket, Rok Belšak, Timi Karner

Published 2026-10-16

📖 6 min read🧠 Deep dive

CC BY 4.0

Original authors: Janez Gotlih, Kristijan Šket, Rok Belšak, Timi Karner

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine a factory floor where giant robotic arms are building massive metal parts, layer by layer, using a process that looks a bit like a very precise, high-temperature welding torch. This method, known as wire arc additive manufacturing, is becoming a favorite for creating large, complex metal structures because it is fast and relatively cheap. However, for the robots to build these parts perfectly, the metal they lay down needs to be consistent. If the metal bead is too wide, too tall, or has the wrong shape, the layers won't stack correctly, and the final part could be weak or misshapen. For a long time, engineers have looked at these metal beads as if they were uniform strips, measuring the average width and height of the entire length to see if the process is working. But this approach has a blind spot. Just as a runner might start slowly, sprint in the middle, and slow down to stop, a metal bead does not form the same way from beginning to end. The start and the finish of the metal path are often chaotic and unstable, while the middle section is steady. If you average the whole thing together, you lose the details of those critical moments, hiding the very variations that could cause a part to fail.

A team of researchers at the University of Maribor in Slovenia decided to look closer at these metal beads to see if they could separate the chaotic start and finish from the steady middle. They worked with fifty single metal beads, each about 40 millimeters long, which had been laid down on steel plates by a robotic arm. To see the shape of these beads in incredible detail, they used a laser scanner to create a three-dimensional map of the surface, capturing thousands of tiny points that describe the bead's height and width at every single spot along its length. Instead of treating each bead as one long, uniform object, the researchers wanted to split it into three distinct zones: the start, the middle, and the end. Their goal was to prove that these zones behave differently and to create a computer method that could automatically find where one zone ends and the next begins, without needing a human to look at every single scan.

Before teaching the computer how to do this, the researchers first asked a human expert to look at the data and mark the boundaries by hand. This expert, guided by the visual shape of the metal, identified where the bead seemed to stabilize and where it was still settling in or winding down. When the team analyzed these human-marked sections, a clear pattern emerged. The middle section of the beads was remarkably stable, with very little change in width or height as the robot moved along. It was almost a straight, flat line. The start and end sections, however, were anything but flat. They curved and changed shape significantly, showing a rapid evolution in geometry that a simple straight line could not describe. This observation was crucial. It told the researchers that the middle part could be described with a simple, straight-line model, while the start and end parts needed a more complex, curved model to capture their changing shape.

Armed with this insight, the team built a new computer algorithm based on a "curved-straight-curved" idea. They taught the software to look at the laser scan data and find the two points where the bead's shape switched from the wild curve of the start, to the calm straight line of the middle, and back to the curve of the end. The computer didn't just guess; it tested millions of possible split points, looking for the combination that made the math fit the actual metal shape the best. It paid special attention to the cross-sectional area, which is essentially how much metal is in a slice of the bead, as this turned out to be the most important clue for finding the boundaries. The result was a system that could automatically slice the bead into its three functional parts with high precision.

When the researchers compared the computer's work to the human expert's original markings, they found the two agreed very well, though not perfectly. On average, the computer's boundaries were off by about 3.5 millimeters. This small difference isn't necessarily a mistake; it reflects that the computer and the human were using slightly different rules to define exactly where the "start" stops being the "start." More importantly, the computer successfully identified the middle section as the most stable part in every single one of the fifty beads. In fact, the variation in the middle section was so much lower than in the start or end sections that the computer could distinguish them with near-perfect certainty. The start and end sections were so geometrically different from each other that the computer could even tell which end of the bead was the beginning and which was the end, just by looking at the shape, even if it didn't know which way the robot was moving.

The study confirms that treating a metal bead as a single, uniform object is a simplification that hides important physical realities. By separating the bead into a stable middle and two changing ends, engineers can now analyze the process more accurately. They can focus on the steady middle to understand how the machine performs under normal conditions, while studying the start and end separately to understand the tricky moments of initiation and termination. This approach doesn't just describe the metal better; it offers a new way to control the manufacturing process. If a robot can be taught to recognize these specific zones in real-time, it might be able to adjust its speed or heat exactly when the bead is starting or stopping, ensuring that every part of the metal structure is built with the same high quality. The researchers note that while their method works well for the specific steel beads they tested, the true test will come when they try it on different materials and machines, but the fundamental idea—that the start, middle, and end of a metal bead are distinct worlds—now has a solid, data-driven foundation.

Technical Summary: Longitudinal Segmentation and Terminal Classification of WAAM Single Beads from 3D Point Clouds

Problem Statement
Wire Arc Additive Manufacturing (WAAM) relies on controlling deposited geometry, as bead width, height, and cross-sectional area dictate layer height, overlap, and dimensional accuracy. However, existing process–geometry studies typically summarize beads using global descriptors or sparse cross-sections, which suppresses the longitudinal structure of individual deposition paths. This approach obscures transient geometric behaviors occurring during the initiation (START) and termination (END) of deposition, where conditions differ from the quasi-steady operating regime. Consequently, averaging the entire bead can mask systematic nonlinear evolution at the terminals and reduce the physical interpretability of geometry-based process models. There is a need for a reproducible, operational definition to separate and characterize the START, MID, and END regions directly from dense post-process 3D point cloud data.

Methodology
The study utilized a dataset of 50 single beads deposited on three S355 structural-steel plates using a robotic WAAM cell. The beads were measured using a laser-profile scanner to generate six partially overlapping 3D point clouds. The methodology proceeded in three sequential stages:

Expert-Informed Reference Establishment: Before developing an automatic algorithm, a domain expert visually assessed the 50 beads to establish a reference START–MID–END segmentation. This process involved defining spatial regions of interest (ROI) and an initial MID interval, which were then refined using standardized rules for regional length and sampling.
Empirical Basis and Q–L–Q Formulation: Statistical analysis of the expert-informed regions revealed that the MID region exhibited approximately linear, low-variation behavior, while the START and END regions showed systematic nonlinear evolution. This observation motivated a Quadratic–Linear–Quadratic (Q–L–Q) model formulation.
Automatic Segmentation Algorithm: A geometry-driven algorithm was developed to automatically determine the transition coordinates ( $u_1$ $u_{1}$ and $u_2$ $u_{2}$ ) between START, MID, and END. The algorithm minimizes an objective function combining:
- Regional Model Fit: Least-squares fitting of quadratic polynomials to width, height, and cross-sectional area in START/END and a linear polynomial in MID.
- Continuity: Penalizing discontinuities in fitted values at the transition points.
- Length Penalty: Discouraging excessively short MID regions.
  The algorithm exhaustively searches admissible transition pairs to minimize the combined objective function.
Validation and Classification: The automatic segmentation was validated against the expert-informed reference using Mean Absolute Boundary Difference (MABD). Furthermore, a position-independent classification model (logistic regression with L2 regularization) was trained to distinguish START from END based solely on geometric descriptors (mean, median, standard deviation, and coefficient of variation of width, height, and area), excluding positional information. Validation included nested leave-one-bead-out (LOBO) and leave-one-plate-out schemes.

Key Results

Geometric Characterization: The expert-informed analysis confirmed that the MID region has significantly lower longitudinal variation (mean coefficient of variation for cross-sectional area $CV_A = 0.040$ ) compared to START ($0.319$) and END ($0.369$). Quadratic models significantly outperformed linear models in representing the terminal regions, particularly for height and cross-sectional area.
Automatic Segmentation Performance: The automatic Q–L–Q algorithm successfully segmented all 50 beads. The resulting MID regions consistently exhibited the lowest $CV_A$ (mean $0.054$) compared to START ($0.346$) and END ($0.437$).
Boundary Correspondence: The automatic transition coordinates showed a combined MABD of 3.49 mm relative to the expert-informed reference. The automatic method tended to define a slightly longer MID region, shifting the START–MID boundary toward lower coordinates and the MID–END boundary toward higher coordinates.
Descriptor Contribution: Leave-one-descriptor-out ablation revealed that cross-sectional area was the strongest contributor to transition-coordinate estimation (55.4% of total contribution), followed by height (24.0%) and width (20.6%).
Terminal Classification: The classification model achieved perfect accuracy (1.00) in distinguishing START from END using original, unequal-length terminal regions. Crucially, even after extracting matched-length physical spans to remove length bias, the model maintained high accuracy (0.94 under LOBO and 0.96 under leave-one-plate-out validation). This indicates that START and END possess distinct geometric distributions independent of their physical length or position.

Significance and Claims
The paper claims to provide a reproducible, geometry-driven workflow that preserves longitudinal geometric information often lost in whole-bead averaging. By establishing a Q–L–Q formulation based on empirical evidence, the study offers a method to separate quasi-stationary (MID) and transient (START/END) deposition regimes.

The authors emphasize that this approach enables:

Region-Specific Modeling: Characterizing stable deposition behavior in the MID region separately from the transient responses at the start and end.
Process Strategy Comparison: Facilitating the analysis of start and stop strategies by isolating terminal transients.
Toolpath Compensation: Supporting the development of location-dependent compensation strategies.

The study explicitly notes that its results represent internal validation within a specific experimental campaign (S355 steel, specific robotic cell, and process window). The authors state that broader generalizability across different materials, deposition systems, and process windows requires further validation with independent datasets. The work does not claim to replace real-time control but rather provides a post-process framework for identifying regions that may require different modeling or monitoring strategies.

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