PSI - Issue 75

Jörg Baumgartner et al. / Procedia Structural Integrity 75 (2025) 120–128 Jo¨rg Baumgartner / Structural Integrity Procedia 00 (2025) 000–000

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2. Algorithms for data processing

When a weld scan is conducted using FLP, the result is a 3D point cloud with a point spacing of 25 µ m. The initial task is to identify the weld within the scan. Typically, this process is performed manually, requiring the user to define the weld area and its direction. With this information, cutting planes can be established that are perpendicular to the weld line. However, this method can be cumbersome when multiple weld lines require evaluation and may lead to incorrect results if the weld line follows a curved path in 3D space. Therefore, an algorithm is needed to automatically identify both the weld and its direction in the 3D scan. This information can then be used to create cutting planes and derive 2D profiles. Following this initial step – or if 2D profiles are derived directly from LLS – these profiles must be evaluated. The challenge lies in accurately identifying the weld. What may appear to be a straightforward task for the human eye becomes significantly more complex when developing and implementing a reliable algorithm. Only if the correct locations of the weld toes are identified, the relevant parameters weld toe radii r and the weld toe angle α or any other quality related dimensions defined in [5] can be evaluated. The following sections present approaches and algorithms to e ff ectively address these two tasks. A commonly used algorithm for 3D data processing is Random Sample Consensus (RANSAC) [9]. RANSAC is an iterative algorithm designed to estimate the parameters of a mathematical model, such as a line or plane, from a dataset that may contain outliers, see Figure 2 (a). The process involves randomly selecting a minimal subset of data points to fit the model, identifying the consensus set of inliers, and iterating until the best-fitting model is found. RANSAC is especially e ff ective in fields such as computer vision and robotics for tasks like line fitting and object recognition in noisy environments. It is already applied for determining geometrical features in 3D scans of welded joints [10, 21]. Combining a linear and a quadratic RANSAC function provides a straightforward way to determine the weld toe on weld cross-sections, as illustrated in Figure 2 (b). A relatively simple way to identify the weld toe location in a 2D or even 3D data point space is the so-called curvature method [18, 15]. An additional advantage is that this approach can also determine the weld toe radius rr, as illustrated in Figure 2(c). The curvature of an arc or circle is expressed as where κ represents the curvature and r denotes the radius of the arc or circle. For a plane curve, curvature is defined as the rate of change of the tangent vector: κ = ∂ T ∂ c (2) with T being the tangent vector and c representing the arc length parameter along the curve. A normal unit vector N can be defined on the weld surface, which consistently points away from the material. By slightly modifying the definition of κ , it is possible to incorporate information about the direction of the plane curve ( κ ∗ = N · ∂ T ∂ c ). In this context, curvature in concave regions of the weld surface is associated with a positive connotation, whereas convex regions are associated with a negative connotation. 2.1. Rule-based algorithms κ = 1 r (1) In academic literature, there are relatively few ANN models specifically designed for 3D point data processing. The pioneering deep learning model PointNet by [14] uniquely handles unordered point clouds for classification. In such ANNs, points traverse the network layers independently, with multi-layer perceptrons (MLPs) extracting high-dimensional features. The PointNet includes a T-network that predicts transformations to align the input and intermediate features, thus minimizing rotation variability. An advancement of PointNet is PointNet ++ [13], which utilizes neighboring points for local feature extraction. With three successive set abstraction layers, the PointNet ++ classification mimics conventional CNNs through feature 2.2. Machine learning approach