Deep Learning-Based Characterization of Detonation-Cell Size Distributions in Soot-Foil Records

Technical Summary: Deep Learning–Based Characterization of Detonation-Cell Size Distributions in Soot-Foil Records

Problem Statement
The geometric size and regularity of detonation cells are fundamental parameters for characterizing the chemical kinetic sensitivity and hydrodynamic instability of detonation waves. Traditionally, these parameters are extracted from soot-foil records using manual measurement, a process that is time-consuming, subjective, and prone to error. While existing computer vision and semantic segmentation techniques offer automation, they often struggle with generalization when applied to real experimental images. These images frequently exhibit high noise levels, blurred boundaries due to uneven soot deposition, and severe cell overlapping, leading to misidentification of connected components and inaccurate statistical distributions.

Methodology
To address these limitations, the authors propose a novel automated recognition and feature extraction framework based on deep learning instance segmentation, specifically utilizing the Mask R-CNN (Mask Region-based Convolutional Neural Network) architecture.

• Network Architecture: The model employs a ResNet-50 backbone initialized with ImageNet pre-trained weights to extract multi-scale features. It utilizes a Path Aggregation Feature Pyramid Network (PAFPN) as the neck to fuse low-level spatial and high-level semantic information. The detection head includes a Region Proposal Network (RPN) with multiscale anchors and a Region of Interest (RoI) head featuring RoIAlign for precise pixel-level mask generation.
• Training Strategy: To overcome the scarcity of annotated data and prevent overfitting, the study employs a two-stage transfer learning strategy. The model is first pre-trained on general natural images and subsequently fine-tuned on a custom heterogeneous dataset. This dataset combines high-fidelity numerical simulations and physical experimental soot-foil records, organized in the standard COCO format.
• Data Preprocessing and Augmentation: Input images are resized to 1024×1024 pixels. To enhance robustness, the training pipeline includes random flipping and PhotoMetric Distortion to simulate variations in illumination and soot thickness.
• Patching Strategy: Recognizing that direct inference on large, high-density images leads to feature scale mismatch and missed detections, the authors establish a standardized preprocessing paradigm where elongated soot-foil images are partitioned into a 2×3 grid of sub-patches for independent inference before aggregation.

Key Contributions

1. Instance Segmentation for Detonation Cells: Unlike semantic segmentation which classifies pixels, this approach isolates individual cell instances, enabling the statistical analysis of geometric features (length, width, area) for every single cell, even in densely packed and overlapping regions.
2. Standardized Preprocessing Paradigm: The paper identifies "prior distribution shift" and "feature scale mismatch" as causes for missed detections in high-density images. It proposes and validates a specific image patching strategy (2×3 grid) as a necessary condition for maintaining model performance on large-format experimental data.
3. High-Order Feature Extraction: Moving beyond simple average cell size ($\lambda$), the model automatically extracts advanced morphological metrics, including the Irregularity Index (RI) and the standard deviation of cell deflection angles ($\sigma_\theta$), which quantify the stability and chaos of the detonation wave.
4. Spatial Evolution Tracking: The method enables the automated tracking of cell size evolution along the propagation direction, allowing for the distinction between transient initiation states and stable Chapman-Jouguet (CJ) propagation.

Results

• Benchmark Validation: On numerically simulated data (both regular and irregular), the model achieved near-perfect pixel-level agreement with ground truth. For irregular simulated cells, the predicted average cell size differed from the ground truth by a negligible margin (37.61px vs. 37.64px).
• Experimental Validation:
  • Irregular Conditions: On noisy, real-world experimental soot foils, the model achieved a relative error of 3.5% in the average cell size compared to manual measurements. While the total cell count was slightly lower due to the exclusion of truncated cells at patch boundaries, the probability density distribution showed high overlap with manual references.
  • Regular Conditions: For regular experimental cells, the relative error in average cell size was less than 2%.
• Robustness and Sensitivity:
  • Resolution: The model demonstrated strong scale invariance, maintaining a relative error of approximately 5% even when input resolution was downsampled to 30%.
  • Object Density: Direct inference on full images (containing ~1,500 cells) resulted in severe missed detections and a biased mean size. The 2×3 patching strategy successfully mitigated this, restoring detection counts and statistical accuracy.
• Feature Extraction: The extracted high-order metrics (RI and $\sigma_\theta$) for both regular and irregular cases aligned with theoretical expectations, correctly distinguishing between stable fish-scale arrangements and chaotic, unstable wave fronts.

Significance
The paper claims that this method provides a robust, objective, and efficient tool for the quantitative analysis of detonation combustion. By automating the extraction of both global averages and local spatial evolutions, the model overcomes the subjectivity and limitations of traditional manual analysis. It transforms complex, noisy physical morphologies into structured data, facilitating deeper investigations into the correlations between chemical kinetic sensitivity and macroscopic hydrodynamic instabilities. The study establishes a standardized workflow for processing large-scale detonation data, serving as a foundation for future research into the intrinsic mechanisms of detonation propagation.