LENS-type Additive Manufacturing Process-Structure LinkagesThis website is showcasing the research exploring the process-structure relationships of strained polyethylene. Sets of XRD image data along with stress and strain data are analyzed to model structure evolution with respect to strain. Big data methods are applied to derive this relationship in part to satisfy the Materials Informatics Course ME8883 at Georgia Tech.
http://Materials-Informatics-Class-Fall2015.github.io/MIC-LENS/
Sun, 13 Dec 2015 01:37:26 +0000Sun, 13 Dec 2015 01:37:26 +0000Jekyll v2.4.0Summarizing our Work<p>Due to the dynamic nature of this research project we’d like to summarize the many directions of this project and give closure to the work that did not end up in the <a href="http://materials-informatics-class-fall2015.github.io/MIC-LENS/2015/12/01/Final_Test/">Executive Summary Post</a>.</p>
<h2 id="defining-structure-relevant-statistics">Defining Structure-Relevant Statistics</h2>
<p>To define spacial correlations both 2pt statistics and Chord Length Distribution were collected for both structures. The 2pt statistics were collected using non-periodic conditions, and truncated to capture maximum 100-pixel autocorrelations. With this truncation the number of statistics for each structure was 7,880,599 compared to the maximum 900 for CLDs. Our original workflow is shown below:</p>
<p><img src="/MIC-LENS/img/Final_Post/Latest_Workflow.png" alt="Workflow" />
<strong>Fig.1.</strong> Original workflow</p>
<p>The CLD statistics presented no problem to analyze and we used them to to PCA and build Process-Structure Linkages using Linear Polynomial Regression. However the 2pt statistics became too unwieldy to analyze due to their size. The microstructure ensemble represented by 2pt statistics was about 90GB memory and over 260GB for PCA algorithm to run. Our access to high RAM computing nodes was limited and the set computation could not be run. The PCA of small subsets of our dataset showed promising separation in PC space and future work will include 2pt statistics analysis given the necessary tools. This may lend us improved linkages in certain PC dimensions.</p>
<h2 id="reconsidering-truncation-of-the-dataset">Reconsidering Truncation of the Dataset</h2>
<p>The 2pt statistics PCA could also give us access to the ‘low-confidence’ structures because the statistic is well defined within the simulation space for all structures. This would enable us to extend the model prediction range rather than truncating the dataset to exclude these structures.</p>
Fri, 11 Dec 2015 16:26:00 +0000
http://Materials-Informatics-Class-Fall2015.github.io/MIC-LENS/2015/12/11/summary/
http://Materials-Informatics-Class-Fall2015.github.io/MIC-LENS/2015/12/11/summary/Refinement on Linear Polynomial Regression Model<p>This post will show you our trials on building an effective model to fit the first three PC scores using as many process parameters as possible.</p>
<h2 id="increasing-order-of-polynomial-fit">Increasing Order of Polynomial Fit</h2>
<p>Thanks to Ahmet, we can effectively create multi-variance polynomial fit with linear regression using his matlab <a href="https://github.com/ahmetcecen/MultiPolyRegress-MatlabCentral">function</a> as a very powerful tool.</p>
<p>To get a fit with reasonable mean average error(MAE) and R square, we decided to use all of our process variables. The following figures show goodness of fit for models using different number of terms and orders.</p>
<p>Due to the discrete nature of our process variables, meaning for each variable we have 3 or 4 different values, we got rank deficiency in our model if we try to fit with up to 3rd power for every process variable. To refine the model, we will have to selectively add 3rd order terms to original 2nd order model. So by exhausting all the combinations for a 3rd order fit, a more modified model was created totally with 74 terms.</p>
<h2 id="about-principle-components">About Principle Components</h2>
<p>Although as mentioned previously, the first three PCs capture over 95% variance, the choice of PCs to fit also depends on their importance in structure-property linkage - the other part of the problem. But for now, fitting the first three PCs satisfies our need to correlation process to structure information.</p>
Fri, 11 Dec 2015 12:00:00 +0000
http://Materials-Informatics-Class-Fall2015.github.io/MIC-LENS/2015/12/11/Refinement_on_Linear_Polynomial_Regression_Model/
http://Materials-Informatics-Class-Fall2015.github.io/MIC-LENS/2015/12/11/Refinement_on_Linear_Polynomial_Regression_Model/Executive Summary<h1 id="process-structure-linkages-in-simulated-lens-type-additive-manufacturing-microstructures">Process-Structure Linkages in Simulated LENS-type Additive Manufacturing Microstructures</h1>
<h1 id="introduction">Introduction</h1>
<p>The LENS additive manufacturing process creates fully-dense alloy components with process-dependent microstructure. In this project we investigate the morphology of the microstructure crystal grains and it’s dependence on process parameters using a data science approach. A simulated dataset shared with us through Harvard’s Dataverse was subjected to a data science approach. The dataset’s creator Theron Rogers of Sandia National Labs has been our collaborator and domain expert, guiding the direction of the project. More detail can be found <a href="http://materials-informatics-class-fall2015.github.io/MIC-LENS/2015/09/24/Intro_LENS/">here</a>.</p>
<h1 id="motivation">Motivation</h1>
<p>The LENS deposit physical properties are governed by the microstructure which is a function of the process parameters. We would like to be able to design the function and physical properties of the LENS-made components by using Process-Structure-Property Linkages. The focus of this project is to create Process-Structure Linkages.</p>
<h1 id="objective">Objective</h1>
<p>The objective of this project was to extract Process-Structure Linkages from the simulated dataset. The grain size- and shape-distribution was specified as an important structure metric. The general direction of the project became extraction of grain patterns with respect to simulation process parameters. The linkages map a parameter combination to a unique microstructure in PC-space.</p>
<h1 id="approach-and-workflow">Approach and Workflow</h1>
<p>The dataset represents 1799 unique 3D digital microstructures created by SPPARKS monte carlo simulations. Each structure occupies a 300x300x200 unit volume and is associated with a unique set of processing parameters listed below:</p>
<ol>
<li>(X/XY)Scan Pattern Linear and layer-by-layer cross-hatch</li>
<li>(W)Melt spot width</li>
<li>(V)Velocity</li>
<li>(D)Melt spot depth</li>
<li>(L)Melt spot tail length</li>
<li>(HAZ)Heat-affected-zone width</li>
<li>(T)Heat-affected-zone tail length</li>
</ol>
<p>The 1799 unique microstructures have a variety of grain size and shape distributions, and example of which is shown below. The pseudo-periodic nature present in all these structures owes itself to the linear-serpentine scan pattern of the heat source in the simulation which mimics the movement of the LENS deposition nozzle and deposit formation.</p>
<p><img src="/MIC-LENS/img/GB_post/Full_structure.png" alt="SPPARKS simulated structure" />
<strong>Fig.1.</strong> Example microstructure with parameter combination: T=20, X, V=2.5, W=60, D=100, L=50, HAZ=5</p>
<p>As received, the data in the dataset was organized in a folder tree, each branch of which defined a microstructure with a unique parameter combination. A code was written to navigate these branches, access the microstructure, and collect metadata (the process parameter combinations). A detailed explanation <a href="http://materials-informatics-class-fall2015.github.io/MIC-LENS/2015/10/11/Data_org_folder_crawl/">here</a>.</p>
<p>The journey to extract the Process-Structure linkage is summarized in the worklfow diagram below:</p>
<p><img src="/MIC-LENS/img/Final_Post/new_workflow.png" alt="Workflow" />
<strong>Fig.2.</strong> Workflow</p>
<p>In the Digital Representation step the data is processed and transformed into a computationally-convenient form, after which the microstructure is subjected to grain-boundary segmentation. The Spatial Correlations within the microstructure can be interpreted in different ways but we selected 2-point statistics and Chord-Length-Distributions (CLD) in this step. Details <a href="http://materials-informatics-class-fall2015.github.io/MIC-LENS/2015/09/29/Data_Process_GB_2Pt/">here</a> and <a href="http://materials-informatics-class-fall2015.github.io/MIC-LENS/2015/10/25/One_Kind_of_Statistics_Describing_the_Structures/">here</a> and <a href="http://materials-informatics-class-fall2015.github.io/MIC-LENS/2015/10/26/The_Weighted_Chord_Length_Distribution/">here</a>. Both 2pt-statistics and CLDs are different statistical descriptions of microstructure. The 1799 microstructures are interpreted with a set of 1799 2-pt statistics and a set of 1799 CLDs. Before a linkage is built, the variance in each set is quantified and reduced in dimensionality using Principal Component Analysis (PCA). The PC space is truncated to a handful of PCs immensely reducing complexity yet capturing most of the variance.</p>
<p>The Process-Structure linkages are formulated to answer either of two questions:</p>
<ol>
<li>Given the process parameters what microstructure do they create? (Forward linkage)</li>
<li>Given a microstructure, what Process parameters are needed to create it? (Inverse linkage)</li>
</ol>
<p>The linkages are extracted by using linear polynomial regression.</p>
<h1 id="results">Results</h1>
<p>The CLD statistics were more appropriate to the structure information we wished to quantify. The results of PCA on CLD sets of the entire dataset are presented below.</p>
<h2 id="data-visualization-in-pc-space">Data Visualization in PC Space</h2>
<p>The 1799 structures are plotted below in PC space, along with an accumulated variance plot.</p>
<p><img src="/MIC-LENS/img/Final_Post/CLD_PCA_and_Var.png" alt="CLD PCA" />
<strong>Fig.3.</strong> The CLD variance in PC space and corresponding accumulated variance plot</p>
<p>The separation of structures with respect to process parameters is immediately evident by visual inspection. The plot is color coded for different parameter values of V and W below.</p>
<p><img src="/MIC-LENS/img/Final_Post/CLD_PCA_Vprm.png" alt="CLD PCA" />
<strong>Fig.4.</strong> Color coded structures show visual separation in PC space (2 views shown) as a function of V</p>
<p><img src="/MIC-LENS/img/Final_Post/CLD_PCA_Wprm.png" alt="CLD PCA" />
<strong>Fig.5.</strong> Color coded structures show visual separation in PC space (2 views shown) as a function of W</p>
<p>The V and W parameter-microstructure correlation is displayed as an example but other parameters also display correlation.</p>
<h2 id="modeling-with-polynomial-regression">Modeling with Polynomial Regression</h2>
<p>Modeling the linkages for the entire dataset:
Forward method was used to create a model of microstructures a function of the process parameters. Low order polynomial models were used.</p>
<p><img src="/MIC-LENS/img/Final_Post/Forward_PC1_model_full.png" alt="CLD PCA" />
<strong>Fig.6.</strong> Forward model for PC1 with 4 process parameters and degree 2</p>
<h2 id="model-improvement">Model Improvement</h2>
<p>Modeling the entire dataset for CLD structure interpretation should be done with some amount of truncation. The nature of a small subset of the structures makes them ‘low-confidence’ structures as explained <a href="http://materials-informatics-class-fall2015.github.io/MIC-LENS/2015/10/25/CLD_probs/">here</a>. The models were vastly improved after a truncation of the dataset to structured containing no more than 10% edge chords in the distribution.</p>
<p><img src="/MIC-LENS/img/Final_Post/10_percent.png" alt="CLD PCA Outliers" />
<strong>Fig.7.</strong> The histogram of the number of structures vs. the edge chord fraction with 10% threshold shown.</p>
<p>The Removed structures are shown below in red and PCA redone on the ‘high-confidence’ dataset.</p>
<p>[discuss the CLD2 thresholding scheme and need for thresholding]
<img src="/MIC-LENS/img/Final_Post/Outliers.png" alt="CLD PCA Outliers" />
<strong>Fig.8.</strong> Outliers in the CLD PCA space</p>
<p>The improved model for PC1 is shown below, displaying good fit, low standard deviation and low mean average error.
[discuss the CLD2 thresholding scheme and need for thresholding]
<img src="/MIC-LENS/img/Final_Post/PC1_best.png" alt="CLD PCA Outliers" />
<strong>Fig.9.</strong> Outliers in the CLD PCA space</p>
<p>The model selection was a comprehensive assessment of R^2 goodnes of fit, Standard deviation, mean average error, and leave one out cross validation CVR^2. Three model classes were defined described by their highest order terms, shown below with the best class shown in red. This class is the modified 3rd order polynomial models.
[fit]
<img src="/MIC-LENS/img/Final_Post/fit.png" alt="CLD PCA Outliers" />
<strong>Fig.10.</strong> Error analysis among 3 classes of models</p>
<h2 id="conclusions">Conclusions:</h2>
<p>Using data science tools a data-driven model was developed for a LENS-type additive manufacturing system</p>
<p>Process-Structure Linkages were extracted between process parameters and final grain size distributions</p>
<h2 id="future-work">Future Work:</h2>
<ol>
<li>Optimize the data-driven models by exploring other model types and regression types.</li>
<li>Study the relationship of the truncation threshold on model integrity</li>
<li>Future work may include the 2pt statistics PCA. The 2-point statistics showed promising results during preliminary tests.</li>
</ol>
<h2 id="acknowledgementsreferences">Acknowledgements/References:</h2>
<ul>
<li>Dr. Surya Kalidindi Ahmet Cecen, Yuksel Yabansu, David Brough, David, Montes, Fred Hohman, Evdokia Popova, Theron Rogers</li>
</ul>
<h2 id="presnetation-slides">Presnetation Slides</h2>
<p><a href="https://www.slideshare.net/secret/wHAe73S6zv5UoQ">Process-Structure Linkages in a LENS-type Additive Manufacturing System</a></p>
Tue, 01 Dec 2015 18:30:00 +0000
http://Materials-Informatics-Class-Fall2015.github.io/MIC-LENS/2015/12/01/Final_Test/
http://Materials-Informatics-Class-Fall2015.github.io/MIC-LENS/2015/12/01/Final_Test/PCA of Entire Microstructure Ensemble<h2 id="work-in-progress">Work in Progress</h2>
<p>We are eagerly awaiting the PCA results of the entire 1799 microstructure ensemble. The job requires over 64GB of memory to run with a rough estimate of ~90GB. Currently the job is pending in the PACE queue waiting for the resources to become available.</p>
<p>Meanwhile work is continued on CLD algorithm. The idea is to supplement the CLD PCA with 2pt statistics PCA where one fails. The Class 2 data can only be meaningfully modeled using 2pt statistics PCA while both can be used for Class 1 data.</p>
Thu, 29 Oct 2015 01:00:00 +0000
http://Materials-Informatics-Class-Fall2015.github.io/MIC-LENS/2015/10/29/The_1799_PACE/
http://Materials-Informatics-Class-Fall2015.github.io/MIC-LENS/2015/10/29/The_1799_PACE/Tentative Polynomial Model between PC and process parameters<p>Judging from the preliminary result of 2-pt statistics PCA, we decided to fit our structure with polynomial model. This post should show you how this model works on our 72 structure so far with reasonable visualization.</p>
Wed, 28 Oct 2015 12:00:00 +0000
http://Materials-Informatics-Class-Fall2015.github.io/MIC-LENS/2015/10/28/Tentative_Polynomial_Model_between_PC_and_process_parameters/
http://Materials-Informatics-Class-Fall2015.github.io/MIC-LENS/2015/10/28/Tentative_Polynomial_Model_between_PC_and_process_parameters/Principle Component Analysis(PCA) on 2-point Statistics for Partial Structures<p>Some preliminary results of PCA on 2-pt statistics of partial (72) structures are generated. We will discuss the variance, cluttering and possible trends from those results.</p>
Wed, 28 Oct 2015 12:00:00 +0000
http://Materials-Informatics-Class-Fall2015.github.io/MIC-LENS/2015/10/28/PCA_on_2-point_Statistics_for_Partial_Structures/
http://Materials-Informatics-Class-Fall2015.github.io/MIC-LENS/2015/10/28/PCA_on_2-point_Statistics_for_Partial_Structures/Meeting with Sandia National Labs Domain Expert<p>We were lucky to have a teleconference with the domain expert and the creator of the SPPARKS LENS data set Theron Rogers of Sandia National Labs. We discussed the details of the data set and the state of our project.</p>
<p>The number of extracted files (1799) was confirmed to be accurate. The missing parameter combinations are a result of upload issues and not all 2160 combinations were uploaded. Some anomalies in the folder trees were addressed as well. The mystery files of unknown origin and extension were added automatically by the Harvard’s Dataverse repository where the data set was uploaded for public use. These files were safely discarded, however the implication is the necessity of data filtering and cleanup considerations for anyone using Dataverse.</p>
<p>Theron also discussed the physical coupling between process parameters that is empirically observed. The scan velocity V is directly linked to melt spot tail length L and inversely to melt spot width W and melt spot depth D. The data set does not express this coupling because for a variety of V values the ranges of L,W,D are the same. This leads to the conclusion that some of these microstructures are not physically achievable. An improvement to the project will be limiting the microstructure space to only the physically achievable parameter combinations. The current data set describes a LENS-like process but without considerations of physical parameter coupling the final process-structure linkages will be describing a ‘generalized LENS’ system.</p>
<p>Further discussion revealed model limitaitons and current and future work including efforts to model oddly shaped parts, unrestricted melt spot trajectory, CFD-based meltpool shape and evolution, and porosity considerations in the deposit.</p>
Tue, 27 Oct 2015 00:09:00 +0000
http://Materials-Informatics-Class-Fall2015.github.io/MIC-LENS/2015/10/27/Domain_post/
http://Materials-Informatics-Class-Fall2015.github.io/MIC-LENS/2015/10/27/Domain_post/The Weighted Chord Length Distribution<p>I had two major moves in the chord length distribution: 1. We made a modification on how we acquire the length of our chords. 2. Weighted chord length distribution is also created with a clearer physical meaning. We will show more details on those in this post.</p>
Mon, 26 Oct 2015 12:00:00 +0000
http://Materials-Informatics-Class-Fall2015.github.io/MIC-LENS/2015/10/26/The_Weighted_Chord_Length_Distribution/
http://Materials-Informatics-Class-Fall2015.github.io/MIC-LENS/2015/10/26/The_Weighted_Chord_Length_Distribution/Problems with Chord Length Distribution<p>It became apparent that the latest revision of Chord Length Distribution (CLD) algorithm is only accurate for a subset of microstructures. The definition of chord length is the length of the line joining points lying on two boundaries. However in order for the chord length to be meaningful we need to make an important distinction between the grain boundaries and the boundaries of the simulation volume. This logic demands that the chords that span the distance between simulation boundary and the first grain boundary be dismissed. This method is detailed in the CLD2 post.</p>
<p>Of course throwing out various numbers of chords from our microstructures introduces inaccuracy in itself, but this is mitigated if the percent of total lengths dismissed is small relative to the total. We were operating under the assumption that this criterion holds true for all microstructures only to realize that there are many structures where it is completely invalid. The figure below shows an example of a possible algorithm failure mode.</p>
<p><img src="/MIC-LENS/img/CLD_prob_post/slice_100_GB.jpg" alt="enter image description here" />
<strong>Fig.1.</strong> The grain boundary section of a large-grained class of microstructures.</p>
<p><img src="/MIC-LENS/img/CLD_prob_post/slice_100_GB_affected.png" alt="enter image description here" />
<strong>Fig.2.</strong> Diagram of omitted chords.</p>
<p>Yet many other microstructures have small grains throughout the volume, as shown below:</p>
<p><img src="/MIC-LENS/img/CLD_prob_post/structure_92.png" alt="enter image description here" />
<strong>Fig.3.</strong> The grain boundary section of a small-grained class of microstructures.</p>
<p><img src="/MIC-LENS/img/CLD_prob_post/str_92_slice_100_affected.png" alt="enter image description here" />
<strong>Fig.4.</strong> Diagram of omitted chords.</p>
<p>One possible solution is to calculate the total omitted chord length and check the validity of the criterion for every microstructure. A threshold can be set to separate the dataset into 2 classes.</p>
<ol>
<li>Class 1: Total omitted chord length is below threshold and CLD accurately captures grain geometry distribution.</li>
<li>Class 2: Total omitted chord length is above threshold and CLD accurately captures grain geometry distribution.</li>
</ol>
<p>This modification is a work in progress.</p>
Sun, 25 Oct 2015 22:33:00 +0000
http://Materials-Informatics-Class-Fall2015.github.io/MIC-LENS/2015/10/25/CLD_probs/
http://Materials-Informatics-Class-Fall2015.github.io/MIC-LENS/2015/10/25/CLD_probs/One Kind of Statistics Describing the Structures<p>Inspired by Dr. Kalidindi’s comments on our second presentation, we decided to introduce another kind of statistics - chord length distribution to describe our structures. In this post we will talk about the reason and expect of using chord length distribution. Some preliminary results are also included in this post.</p>
Sun, 25 Oct 2015 12:00:00 +0000
http://Materials-Informatics-Class-Fall2015.github.io/MIC-LENS/2015/10/25/One_Kind_of_Statistics_Describing_the_Structures/
http://Materials-Informatics-Class-Fall2015.github.io/MIC-LENS/2015/10/25/One_Kind_of_Statistics_Describing_the_Structures/