Machine Learning to predict location of ice recrystallization May - July 2022 UGA and IGE internship M1 Statistics and Data Sciences (SSD) Renan MANCEAUX Supervisor : Thomas CHAUVE

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Abstract

    Ice is a polycrystalline material composed of grains with an hexagonal crystallographic structure. The main deformation mecanism in laboratory condition is dislocation creep. Dynamic recrystallization occurs during deformation, leading to a modification of the microstructure by nucleating new grains with a new orientation. The location of these new grains is not constrained and lead with other recrystalization mechanism such as grain boundary migration to strong change in mechanical behavior through texture (crytal prefered orientation) development. Estimate the location of recrystallization area can be helpfull to construct full field recrystalisation model. We applied machine learning classification methods to predict the location of the recrystallized grains using experimental data (crystalographic orientation mapping, AITA) and full field numerical modelling (CraFT). Indeed, the goal was to indentify pixels in the initial microstructure which will be recrystallized after deformation. The amont of recrystalized area is low (\(4\) to \(5 \%\)), therefore we worked with unbalanced data. By comparing prediction results of several distinct models applied with several strategies and by varying parameters, hyperparameters and selected variables, the classification problem seems to be harder than we thought because of the nature and structure of data. Actually, the similarity of the two classes to identify seems to be too high to allow to build a model giving a satisfying classification. In other term, grain germination seems to be too much unpredicatible beyond the distance to grain boundary or triple junction.

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Acknowledgments

    I would like to thank Thomas Chauve, at the origin of the intership topic, for his support and his accompaniment all along this 3 months. Thank you for your patience in explaining to me as a nonphysicist a specific scientific context.

Also, thank you to Maurine Montagnat for her expertise and her comments, leading us to a better evaluation of the range of our results and the impact to the objectives.

Thanks also to team Cryodyn and to IGE for giving me the opportunity to live this professional experience immersed into another scientific domain.

I want to also thank Jean-François Cœurjolly and Adeline Leclerc-Sanson, in charge of Master SSD, for their follow-up and their implication into the internship research of their students, without forgetting to thank Pierre Maé for his course of statistical learning which I used as basis all along the internship.

Thank you to all !

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Table of contents

• 1. Introduction
  • 1.1. Pedagogic context
    • 1.1.1. IGE presentation
    • 1.1.2. CRYODYN research team
  • 1.2. Scientific context
    • 1.2.1. Ice
      • 1.2.1.1. Ice crystallographic structure
      • 1.2.1.2. Plastic deformation mechanisms
      • 1.2.1.3. Ice polycrystal
    • 1.2.2. Recrystallisation
    • 1.2.3. Experimental tools
      • 1.2.3.1. Uniaxial Compression
      • 1.2.3.2. Orientaions maps
      • 1.2.3.3. Simulation fields
    • 1.2.4. Machine learning tools
      • 1.2.4.1. Machine learning algorithms
        • 1.2.4.1.1. Unsupervised learning
        • 1.2.4.1.2. Supervised learning
      • 1.2.4.2. Classification evaluation
      • 1.2.4.3. Python tools
  • 1.3. Objectives
• 2. Data description
  • 2.1. Experimental Data
    • 2.1.1. AITA data : orientations and microstructure
    • 2.1.2. Data Computing : Geometric variables
      • 2.1.2.1. Distance to grain boundary and triple junction
      • 2.1.2.2. Schmid factor
      • 2.1.2.3. Schmid difference and misorientation angle
    • 2.1.3. CraFT data : Strain/Stress modelization
    • 2.1.4. RX map : variable to explain
  • 2.2. Additional data
    • 2.2.1. Data computing : Anisotropy factors of triple jonctions
    • 2.2.2. Triple jonctions dataset for tabular data learning
    • 2.2.3. Triple jonctions dataset for convolutional and mixture Artificial Neural Network learning
  • 2.3. Data exploration
    • 2.3.1. Data correlations
      • 2.3.1.1. Tabular dataset of pixels
      • 2.3.1.2. Tabular dataset of Triple Junctions
    • 2.3.2. Principal Components Analysis (PCA)
      • 2.3.2.1. PCA on pixels dataset
      • 2.3.2.2. PCA on TJ dataset
    • 2.3.3. T-Stochastic Neighbor Embleding (t-SNE)
    • 2.3.4. Pixel threshold
• 3. Pixel classification
  • 3.1. Tree Based Classifiers
    • 3.1.1. Random forest
    • 3.1.2. Extreme Gradient Boosting
    • 3.1.3. Balancing dataset : Oversampling and Undersampling
  • 3.2. Neighbourhood based classifiers
    • 3.2.1. K-Nearest Neighbours
    • 3.2.2. K-means
    • 3.2.3. Support Vector Machine
  • 3.3. Pixels classification conclusion
• 4. Triple junction classification
  • 4.1. Support Vector Machine for Triple Junction dataset
  • 4.2. Artificial Neural Network classifiers
    • 4.2.1. Convolutional Neural Network
    • 4.2.2. Mixture Neural Network
  • 4.3. Analysis
• 5. Discussion
• 6. Conclusion
• 7. Bibliography
• 8. Annexes
  • 8.1. Compute and save anisotropy factors
    • 8.1.1. Load data
    • 8.1.2. CI02
    • 8.1.3. CI04
    • 8.1.4. CI06
    • 8.1.5. CI09
    • 8.1.6. CI21
    • 8.1.7. Save new data
  • 8.2. Compute Triple Junction dataset
    • 8.2.1. Loading data
    • 8.2.2. Compute variables
      • 8.2.2.1. Compute map of TJ and distance
      • 8.2.2.2. Filter TJ to close to border
      • 8.2.2.3. Compute RX of each TJ (10%)
      • 8.2.2.4. Compute schmid factor of each 3 grains
      • 8.2.2.5. Compute schmid diff for each 3 GB
      • 8.2.2.6. Compute misorientation angle of each 3 GB
      • 8.2.2.7. Compute volume ratio anisotropy of each TJ
      • 8.2.2.8. Compute mean of craft variables for each TJ
      • 8.2.2.9. Compute Distance to other TJ
      • 8.2.2.10. Compute number of pixel of the 3 grains of each TJ
    • 8.2.3. Building dataset
      • 8.2.3.1. Save New Dataset
  • 8.3. Computation pipeline of Dataset for CNN and Mixuture NN
    • 8.3.1. Loadind data
    • 8.3.2. Compute TJ coordinates, grains and distance using xarrayaita
    • 8.3.3. Filter TJ too close to border
    • 8.3.4. Compute variables and maps
      • 8.3.4.1. Volume ratio anisotropy of TJ (single value)
      • 8.3.4.2. Distance to other TJ
      • 8.3.4.3. Number of pixel of TJ grains (sum)
      • 8.3.4.4. Mapped values (schmid, diff_schmid, misangle and CraFT data) with a \(10 \times 10\) px window around TJ
      • 8.3.4.5. RX value
    • 8.3.5. Building xarray dataset
      • 8.3.5.1. Save dataset
    • 8.3.6. Data view
  • 8.4. Principal Components Analysis (PCA) on pixel dataset (with anisotropy)
    • 8.4.1. Import packages
    • 8.4.2. Loading data
    • 8.4.3. PCA with anisotropy factors
      • 8.4.3.1. Variables selection
      • 8.4.3.2. Normalization
      • 8.4.3.3. Apply PCA
    • 8.4.4. Results
      • 8.4.4.1. Eigen values / Explained variance ratio
      • 8.4.4.2. First Principal plan of individuals
      • 8.4.4.3. Individuals on 1-4 components
      • 8.4.4.4. Density maps
      • 8.4.4.5. Correlation cirle on components 1-2, 3-4 and 5-6
  • 8.5. Principal Components Analysis (PCA) on TJ dataset
    • 8.5.1. Loading data
    • 8.5.2. PCA
      • 8.5.2.1. Variables selection
      • 8.5.2.2. Normalization and apply PCA
    • 8.5.3. Results
      • 8.5.3.1. Eigen values / Explained variance ratio
      • 8.5.3.2. First Principal plan of individuals
      • 8.5.3.3. Individuals on 1-4 components
      • 8.5.3.4. Density maps
      • 8.5.3.5. Correlation cirle on components 1-2 and 3-4
  • 8.6. t-distribued Stochastic Neighbor Embleding (t-SNE) on TJ dataset
    • 8.6.1. Loading data
    • 8.6.2. t-SNE on CI02 geom and craft data
      • 8.6.2.1. Variables selection
      • 8.6.2.2. Normalization
      • 8.6.2.3. Apply t-SNE for class
      • 8.6.2.4. Projection of individuals on 2 dimensional space with labeling for pixel status
  • 8.7. Tresholding data for class balance
    • 8.7.1. Loading data
    • 8.7.2. Description of variables
    • 8.7.3. Threshold on dist2GB
    • 8.7.4. Threshold on dist2TJ
    • 8.7.5. Subdatasets