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2018/12/06 高橋 佑亮,鈴木良郎(東工大)
東京工業大学
構造最適化問題に対する
ディープラーニングの適用
1
高橋 佑亮
鈴木 良郎
2018/12/06 高橋 佑亮,鈴木良郎(東工大)
研究背景
 ディープラーニング (DL) の躍進
以降「DLを用いたCNN」を単に「CNN」と表記
※1 A. Esteva, Dermatologist-level classification of skin cancer with deep neural networks, Nature Letter, Vol. 542, 2017.
DLを用いた畳み込みニューラルネットワーク
(Convolutional Neural Network: CNN)
2017年 スタンフォード大学
皮膚画像から皮膚癌を検出するCNNを開発※1
高い画像認識能力
皮膚科医と同精度
2
2018/12/06 高橋 佑亮,鈴木良郎(東工大)
研究背景
犬
ク
ラ
ス
分
類
層
中
間
層
中
間
層
剛
性
推
定
層
剛性
CNN
材料密度分布を
画像として入力
 研究目的
1.CNNの画像認識能力を利用し,材料密度分布を画像と
して認識し,剛性を推定するCNNの構築
2.構築したCNNを用いて剛性を最大化する材料密度分布
の探索と評価
本研究における構造
→材料密度分布で表現
剛体 設計領域
集中荷重
3
2018/12/06 高橋 佑亮,鈴木良郎(東工大)
剛性推定時
CNNの構築手法
1.設計領域を分割し
ランダムな材料密度
分布を作成
2.荷重を加えFEMで
剛性を取得
3.剛性を推定する
CNNを構築
集中荷重
A
B
C
剛
性
推
定
層
剛体 設計領域
A B C
剛
性
中
間
層
4
2018/12/06 高橋 佑亮,鈴木良郎(東工大)
CNNを用いた構造最適化手法
1.剛性を推定する
CNNを構築
2.最適性基準法
による剛性最大化
更新回数 0 回 剛
性
推
定
層
剛性最大化時
剛
性
最大化
12
中
間
層
最適性基準法
:最適性の条件を満たす
更新を実施する.
5
2018/12/06 高橋 佑亮,鈴木良郎(東工大) 6
低
密
度
高
 境界条件  訓練サンプルの例
剛体 設計領域
集中荷重
解析モデル
16×32
2018/12/06 高橋 佑亮,鈴木良郎(東工大)
最適化における諸設定
目的関数
平均コンプライアンス𝑐の
最小化
⇒ min
𝛒
𝑐 𝛒 = min
𝛒
𝐮 𝑻
𝐟
制約条件
総面積比 50%
集中荷重𝑓
変位𝑢
7
2018/12/06 高橋 佑亮,鈴木良郎(東工大)
CNNの構成
 down-convolution, flat-convolution, up-convolutionを使用
 材料密度分布を入力,節点変位分布を出力
構築したCNNの構成
8
down-convolution up-convolution
flat-convolution
材料密度分布
節点変位分布
2018/12/06 高橋 佑亮,鈴木良郎(東工大) 9
提案手法による最適化結果
低
密
度
高
SIMP法(従来手法) CNN(提案手法)
提案手法の最適解は,連続性が低い
 CNNによる最適解をSIMP法の初期解として用いることで,
・構造の実現性を高めること
・優れた解を得ること を期待
2018/12/06 高橋 佑亮,鈴木良郎(東工大)
 提案手法
 条件
作成した材料分布の個数:400個
10
提案手法の解析手順
CNNで初期解を獲得
初期解にノイズ加算
SIMP法の実施
最適解を獲得
・・・
2018/12/06 高橋 佑亮,鈴木良郎(東工大) 11
提案手法による最適化結果
従来手法と比較し,
平均コンプライアンスの小さい,
優れた材料密度分布を獲得
2018/12/06 高橋 佑亮,鈴木良郎(東工大)
初期解 SIMP法後
SIMP法
(従来手法)
提案手法
最適化結果の比較
低
密
度
高
12
2018/12/06 高橋 佑亮,鈴木良郎(東工大)
最適化結果の定量的評価
低
密
度
高
 材料密度分布  平均コンプライアンス𝒄
従来手法より優れた
材料密度分布を獲得
𝒄
SIMP法
(従来手法)
1340
提案手法 1324
13
SIMP法(従来手法)
提案手法
2018/12/06 高橋 佑亮,鈴木良郎(東工大) 14
 DLの一技術であるCNNを用いた構造最適化手法を
提案した
 剛性最大化問題に対して,CNNを用いた構造最適化
手法の有効性を示唆した
 今後の課題
 高精度なCNNを構築し,より高剛性な材料密度分布
を得る
結言

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