From b8581ead3e7f186a04eb6fbd3fa95d5e7f264bd3 Mon Sep 17 00:00:00 2001
From: Amira Abdel-Rahman <amira-rahman@aucegypt.edu>
Date: Mon, 1 Jun 2020 09:43:35 -0400
Subject: [PATCH] hca
---
README.md | 2 +-
hca.html | 19 +++++++++----------
hca.md | 7 +++----
3 files changed, 13 insertions(+), 15 deletions(-)
diff --git a/README.md b/README.md
index 4ac02e5..295ed18 100644
--- a/README.md
+++ b/README.md
@@ -19,7 +19,7 @@ Search methods used: nelder mead, gradient descent, EM and CMAES.
- [ ] Arep
- [ ] lsystems
- No representation
- - [hybrid cellular automata with local update rules](./hca.html)
+ - [hybrid cellular automata with local update rules](https://amiraa.pages.cba.mit.edu/cpp_frep/hca.html)
---
diff --git a/hca.html b/hca.html
index 91fb20b..db1853b 100644
--- a/hca.html
+++ b/hca.html
@@ -24,13 +24,12 @@
</head>
<body class="vscode-light">
- <script type="text/javascript"
- src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.0/MathJax.js?config=TeX-AMS_CHTML"></script>
+ <script type="text/javascript" src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.0MathJax.js?config=TeX-AMS_CHTML"></script>
<h1 id="local-opimization-hybrid-cellular-automata">Local Opimization: Hybrid Cellular Automata</h1>
-<p><img src="file:///c:\Users\amira\Documents\cpp_frep\img\hca\hca_strut.gif" alt=""></p>
+<p><img src=".\img\hca\hca_strut.gif" alt=""></p>
<h2 id="approach">Approach:</h2>
<h3 id="a-cellular-automaton-generating-topological-structures-1994"><a href="https://www.spiedigitallibrary.org/conference-proceedings-of-spie/2361/0000/Cellular-automaton-generating-topological-structures/10.1117/12.184866.short?SSO=1">A Cellular Automaton Generating Topological Structures (1994)</a></h3>
-<p><img src="file:///c:\Users\amira\Documents\cpp_frep\img\hca\connection.png" width="300" /><br></br></p>
+<p><img src=".\img\hca\connection.png" width="300" /><br></br></p>
<h4 id="algorithm">Algorithm:</h4>
<ol>
<li>Define cells, load, fixed conditions</li>
@@ -43,7 +42,7 @@
<li>Chang cell state ("death", "birth" or "division")</li>
<li>return to step 2</li>
</ol>
-<p><img src="file:///c:\Users\amira\Documents\cpp_frep\img\hca\res_1.png" width="300" /><br></br></p>
+<p><img src=".\img\hca\res_1.png" width="300" /><br></br></p>
<hr>
<h3 id="topology-optimization-using-a-hybrid-cellular-automaton-method-with-local-control-rules"><a href="https://asmedigitalcollection.asme.org/mechanicaldesign/article-abstract/128/6/1205/477095/Topology-Optimization-Using-a-Hybrid-Cellular?redirectedFrom=fulltext">Topology Optimization Using a Hybrid Cellular Automaton Method With Local Control Rules</a></h3>
<p><strong>State</strong> <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>α</mi><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">\alpha_i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.0037em;">α</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:-0.0037em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span> of each cell is defined by <strong>design variables</strong> <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>x</mi><mi>i</mi></msub><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">x_i(t)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord mathdefault">t</span><span class="mclose">)</span></span></span></span> (density,geometry,elastic modulus), and <strong>field variables</strong> <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>S</mi><mi>i</mi></msub><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">S_i(t)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em;">S</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:-0.05764em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord mathdefault">t</span><span class="mclose">)</span></span></span></span> (stress, stain, strain energy density) (the relation between the amount of energy employed to deform a volume unit of a solid and imposed strain)).</p>
@@ -55,7 +54,7 @@
<p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>U</mi><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">U_i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.10903em;">U</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:-0.10903em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>
Strain energy density, <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>v</mi><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">v_i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em;">v</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span> volume</p>
<p>The local minimization problem defined as:</p>
-<p><img src="file:///c:\Users\amira\Documents\cpp_frep\img\hca\opt.png" width="200" /><br></br>
+<p><img src=".\img\hca\opt.png" width="200" /><br></br>
The error signal <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>e</mi><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">e_i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathdefault">e</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>:</p>
<p><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>e</mi><mi>i</mi></msub><mo>=</mo><msub><mover accent="true"><mi>U</mi><mo>ˉ</mo></mover><mi>i</mi></msub><mo>−</mo><msubsup><mi>U</mi><mi>i</mi><mo>∗</mo></msubsup></mrow><annotation encoding="application/x-tex">e_i= \bar{U}_i-U^*_i
</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathdefault">e</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.9701099999999999em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8201099999999999em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.10903em;">U</span></span></span><span style="top:-3.25233em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.22222em;"><span class="mord">ˉ</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.9856959999999999em;vertical-align:-0.247em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.10903em;">U</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.7386959999999999em;"><span style="top:-2.4530000000000003em;margin-left:-0.10903em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mbin mtight">∗</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.247em;"><span></span></span></span></span></span></span></span></span></span></span></p>
@@ -63,7 +62,7 @@ The error signal <span class="katex"><span class="katex-mathml"><math xmlns="ht
<p><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mover accent="true"><mi>U</mi><mo>ˉ</mo></mover><mi>i</mi></msub><mo>=</mo><mfrac><mrow><msub><mi>U</mi><mn>1</mn></msub><mo>+</mo><munderover><mo>∑</mo><mrow><mi>j</mi><mo>=</mo><mn>1</mn></mrow><mi>N</mi></munderover><msub><mi>U</mi><mi>j</mi></msub></mrow><mrow><mi>N</mi><mo>+</mo><mn>1</mn></mrow></mfrac></mrow><annotation encoding="application/x-tex">\bar{U}_i=\frac{U_1+ \sum_{j=1}^{N}U_j }{N+1}
</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.9701099999999999em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8201099999999999em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.10903em;">U</span></span></span><span style="top:-3.25233em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.22222em;"><span class="mord">ˉ</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:2.576379em;vertical-align:-0.7693300000000001em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.8070490000000001em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.10903em;">N</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord">1</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.825818em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.10903em;">U</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.10903em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mop"><span class="mop op-symbol small-op" style="position:relative;top:-0.0000050000000000050004em;">∑</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.981231em;"><span style="top:-2.40029em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.05724em;">j</span><span class="mrel mtight">=</span><span class="mord mtight">1</span></span></span></span><span style="top:-3.2029em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.10903em;">N</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.43581800000000004em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.10903em;">U</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.311664em;"><span style="top:-2.5500000000000003em;margin-left:-0.10903em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.05724em;">j</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em;"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.7693300000000001em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></p>
<p><em>Neighborhood</em>:</p>
-<p><img src="file:///c:\Users\amira\Documents\cpp_frep\img\hca\neigh.png" alt=""></p>
+<p><img src=".\img\hca\neigh.png" alt=""></p>
<p><em>Local Control Rules</em>:</p>
<ol>
<li>Two position control<p><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">Δ</mi><msub><mi>x</mi><mi>i</mi></msub><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mo>=</mo><msub><mi>c</mi><mi>T</mi></msub><mo>∗</mo><mi>s</mi><mi>g</mi><mi>n</mi><mo stretchy="false">[</mo><msub><mi>e</mi><mi>i</mi></msub><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">]</mo></mrow><annotation encoding="application/x-tex">\Delta x_i(t)=c_T * sgn[e_i(t)]
@@ -87,10 +86,10 @@ The error signal <span class="katex"><span class="katex-mathml"><math xmlns="ht
<li>Apply local rules and update the design variables</li>
<li>check for convergence if not return to step 2</li>
</ol>
-<p><img src="file:///c:\Users\amira\Documents\cpp_frep\img\hca\algo.png" width="300" /><br></br></p>
+<p><img src=".\img\hca\algo.png" width="300" /><br></br></p>
<h2 id="implementation-of-hca">Implementation of HCA</h2>
-<p><a href="./HCA_notebook.html">Jupyter Notebook</a></p>
-<p><img src="file:///c:\Users\amira\Documents\cpp_frep\img\hca\hca_strut.gif" alt=""></p>
+<p><a href="https://amiraa.pages.cba.mit.edu/cpp_frep/HCA_notebook.html">Jupyter Notebook</a></p>
+<p><img src=".\img\hca\hca_strut.gif" alt=""></p>
<h2 id="next-steps">Next Steps</h2>
<ul class="contains-task-list">
<li class="task-list-item"><input class="task-list-item-checkbox" disabled="" type="checkbox"> change to triangular lattice</li>
diff --git a/hca.md b/hca.md
index 14d65e3..9217b51 100644
--- a/hca.md
+++ b/hca.md
@@ -1,5 +1,4 @@
-<script type="text/javascript"
- src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.0/MathJax.js?config=TeX-AMS_CHTML"></script>
+<script type="text/javascript" src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.0MathJax.js?config=TeX-AMS_CHTML"></script>
# Local Opimization: Hybrid Cellular Automata
@@ -76,9 +75,9 @@ $$\bar{U}_i=\frac{U_1+ \sum_{j=1}^{N}U_j }{N+1} $$
## Implementation of HCA
-[Jupyter Notebook](./HCA_notebook.html)
+[Jupyter Notebook](https://amiraa.pages.cba.mit.edu/cpp_frep/HCA_notebook.html)
-
+
## Next Steps
--
GitLab