Page 69 - 《爆炸与冲击》2026年第11期

第 46 卷 王帅帅，等： 数据驱动的箍筋加密钢筋混凝土柱爆炸损伤预测与评估模型 第 11 期

Database

Root node Layer 1
M 1 samples M 2 samples ... M n samples
True False N 1 features N 2 features N n features
Internal Leaf Layer 2
node node ...
True False
Tree-1 Tree-2 Tree-n
Leaf Leaf
node node Layer 3 Output 1 Output 2 Output n
Averaging
Mean Mean Mean Final output
(a) DT [40] (b) RF [46]
Data set X T T
{x; Y} n×1 ={(x 1 , x 2 , ···, x p ) ; (Y 1 , Y 2 , ···, Y e ) } n×1
Tree 1 Tree 2 Tree k
{X, θ 1 } {X, θ 2 } {X, θ k } DT 1 DT k1 DT 1 DT ke
Node splitting by
objective function ... Residual

… … … Iteration … T 1,1 (x) ... T 1,k1 (x) T e,1 (x) ... T e,ke (x)
Residual Residual Residual Leaf-wise
f 1 (X, θ 1 ) f 2 (X, θ 2 ) … f k−1 (X, θ k−1 ) f k (X, θ k ) Y 1 =∑ T 1,k (x) tree growth Y e =∑ T e,ke (x)
ke
k1
k=1
k=1
∑ f k (X, θ k ) Y=F(x)
(c) XGBoost [15] (d) LightGBM [15]
Hidden layer 1 Hidden layer 2
Input
layer

Output layer

...
... ...

Bias Bias
(e) MLP [15, 47]
2D TabPFN layer (12×)
Input dataset
x 1 x 2 y 1D feature attention 1D sample attention MLP Predictions: y ˆ test
1.2 6.1 3.0
Test training rows 8.9 9.1 3.1 Density

6.7
2.9
1.0
2.2
33.3
?
Predicted y distribution
Predicted entry
Each node represents one entry in the table
(f) TabPFN [45]
图 9 算法模型示意图 [15, 40, 45-47]
Fig. 9 Schematic diagrams of the algorithm models [15, 40, 45-47]

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