Path-resolved melt-track width enables relative spatial-stability characterization and velocity–orientation mapping in laser powder bed fusion

Technical Summary: Path-Resolved Melt-Track Width for Relative Spatial-Stability Characterization in LPBF

Problem Statement
In Laser Powder Bed Fusion (LPBF), melt-track width is traditionally analyzed using condition-level statistics, such as the arithmetic mean (Mean Width). While intuitive, this approach compresses the full spatial trajectory of the melt track into a single value, thereby losing critical local information. Specifically, mean aggregation obscures local narrowing, sustained drift, clustered fluctuations, and the spatial persistence of variations along the scan path. Furthermore, existing process-window studies often treat scan orientation merely as a secondary parameter, failing to explicitly map its interaction with scan speed. The study addresses the need to retain the spatial order of width profiles to characterize relative stability without relying on posterior defect labels (e.g., porosity or fatigue data), which are often unavailable in single-track datasets.

Methodology
The study utilized a public dataset of single-track melt-track widths for Ti-6Al-4V alloy on an EOS M290 system. The experimental design fixed the laser power at 370 W while varying scan speeds (1300–1700 mm/s) and scan orientations (0°–315° in 45° increments), resulting in 72 unique velocity–orientation conditions.

1. Path-Resolved Signal Extraction: Instead of real-time liquid melt-pool monitoring, the study analyzed processed melt-track width as a function of path position, denoted as $Width(x)$.
2. Spatial Signature Construction: Seven spatial signatures were extracted from each $Width(x)$ trajectory to capture different dimensions of instability:
   • Amplitude/Fluctuation: Width Coefficient of Variation (CV), Leading-segment CV (first 10% of path), and Remaining-path CV (remaining 90%).
   • Tail Behavior: Width P5 (the 5th percentile of the width distribution), representing the persistent low-width tail.
   • Spatial Memory: Autocorrelation Function (ACF) correlation length, indicating the distance over which width disturbances remain correlated.
   • Frequency Organization: Spectral entropy and High-Frequency Energy Fraction (EHF) derived from Fast Fourier Transform (FFT) analysis.
3. Composite Index ($S_{spatial}$): These seven signatures were direction-consistently normalized and weighted to form $S_{spatial}$, an empirical composite index for relative instability ranking. The weights (0.20 for CV, Remaining-path CV, and P5; 0.10 for others) were assigned based on empirical proximity to instability rather than fitted coefficients.
4. Validation and Modeling:
   • State Partitioning: Conditions were categorized into Stable, Transition, and Unstable groups based on $S_{spatial}$ tertiles.
   • Blocked Validation: The study employed Leave-One-Velocity-Out (LOVO) and Leave-One-Orientation-Out (LOOO) cross-validation to test the recoverability of stability rankings from process inputs (velocity, linear energy, orientation, and interactions).
   • Attribution: Random Forest models were used for prediction, with SHAP (SHapley Additive exPlanations) values employed to interpret feature contributions within the validated LOVO range.

Key Results

• Decoupling of Mean and Fluctuation: A moderate negative correlation ($r = -0.48$) was found between Mean Width and Width CV. This confirms that average geometry cannot replace local within-path fluctuation information; conditions with similar mean widths can exhibit vastly different stability profiles.
• Multidimensional Stability: The seven spatial signatures revealed that path stability is not determined by a single statistic. Unstable conditions exhibited not only higher fluctuation amplitudes but also distinct spatial memory (longer ACF correlation lengths) and shifted frequency organization (lower spectral entropy and high-frequency energy fraction).
• Predictive Performance:
  • LOVO (Speed Generalization): Models achieved strong performance in predicting stability rankings within the observed orientation set. The Random Forest model yielded a Spearman $\rho = 0.811$ and Mean Absolute Error (MAE) = 0.086.
  • LOOO (Orientation Extrapolation): Performance degraded significantly when predicting unobserved orientations. The Random Forest Spearman $\rho$ dropped to 0.554, and the precision for retrieving the top 20% of high-instability conditions fell to 0.143. This indicates a clear boundary for orientation extrapolation.
• Process Attribution: SHAP analysis revealed that velocity and linear energy (coupled under fixed power) contributed 57.5% to the model, defining the primary stability gradient. A transition region was identified near 1500–1550 mm/s. Orientation effects were primarily captured through interaction terms (28.3% contribution), indicating that orientation modulates the speed-energy response rather than acting as a uniform bias.

Significance and Claims
The paper claims to extend the utility of melt-track width from a condition-level mean to a path-resolved spatial response. The primary contribution is the establishment of $S_{spatial}$, a testable, relative-stability index that organizes process conditions based on their geometric signatures without requiring defect labels.

The authors explicitly define the scope and limitations of their work:

• Relative, Not Absolute: $S_{spatial}$ is an empirical index for relative ranking and review prioritization within the specific fixed-power (370 W) and observed-orientation set. It is not a physical ground truth, a defect-probability model, or a general process window.
• Bounded Applicability: The process map is valid only for the 72 observed conditions. The study demonstrates that while speed-related stability is predictable within the observed orientation set, extrapolating to unobserved orientations is unreliable without denser sampling or direct imaging.
• Practical Utility: The map serves as a tool for identifying high-instability candidates (e.g., the top 20%) for targeted review, repeat experiments, or denser orientation sampling, rather than as a final quality certification tool.

In summary, the work provides a methodological framework for characterizing relative spatial stability in LPBF by preserving the spatial order of melt-track width, offering a bounded, data-driven approach to process monitoring that acknowledges the specific limitations of orientation extrapolation.