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Appl. Sci. 2020, 10, 4999 8 of 21 Layers Input size Input layer Layer 1 Layer 2 Layer 3 Layer 4 Layer 5 Layer 6 Output layer Output size Stage 1: Field Reconstruction Model Basic Block Shortcut Batch Size × 5 (number of design variables) Linear (in = 5, out = 8192) Stage 2: Performance Prediction Model Basic Block Shortcut Stator blade: Batch Size (64) × grid size (36 × 104) Rotor blade: Batch Size (64) × grid size (51 × 232) Interpolation (Batch Size × 256 × 64 × 4) Conv2d (k = 3, s = 1, c = 32) Table 1. Architecture of two-stage deep convolutional neural network. Deconv2d (k = 3, s = 2, c = 512 Deconv2d (k = 3, s = 1, c = 512) Deconv2d (k = 3, s = 2, c = 256) Deconv2d (k = 3, s = 1, c = 256) Deconv2d (k = 3, s = 2, c = 128) Deconv2d (k = 3, s = 1, c = 128) Deconv2d (k = 3, s = 1, c = 128) Deconv2d (k = 3, s = 1, c = 128) Deconv2d Deconv2d (k = 3, s = 2, c = 512) Deconv2d (k = 3, s = 2, c = 256) Deconv2d (k = 3, s = 2, c = 128) / Deconv2d (k = 3, s = 2, c = 64) / Deconv2d (k = 3, s = 2, c = 32) Deconv2d (k = 3, s = 1, c = 16) Conv2d (k = 3, s = 1, c = 64) Conv2d (k = 3, s = 1, c = 64) Conv2d (k=3,s=2,c=128) Conv2d (k=3,s=1,c=128) Conv2d (k=3,s=2,c=256) Conv2d (k=3,s=1,c=256) Conv2d (k=3,s=1,c=256) Conv2d (k=3,s=1,c=256) Conv2d (k = 3, s = 2, c = 512) Conv2d (k = 3, s = 1, c = 512) Conv2d (k = 3, s = 2, c = 1024) Conv2d (k = 3, s = 1, c = 1024) Conv2d (k = 3, s = 2, c = 64) Conv2d (k = 3, s = 2, c = 128) Conv2d (k = 3, s = 2, c = 256) / Conv2d (k = 3, s = 2, c = 512) Conv2d (k = 3, s = 2, c = 1024) (k = (k = (k = (k = (k = (k = (k = (k = Stator blade: Batch Size (64) × grid size (36 × 104) Rotor blade: Batch Size (64) × grid size (51 × 232) 3,s=2,c=64) Deconv2d 3, s = 1, c = 64) Deconv2d 3, s = 1, c = 64) Deconv2d 3, s = 1, c = 64) Deconv2d 3,s=2,c=32) Deconv2d 3,s=1,c=32) Deconv2d 3,s=1,c=16) Deconv2d 3, s = 1, c = 16) Conv2d (k AvgPool2d (k = 3, s = 3) Linear (in = 5120, out = 256) Linear (in = 256, out = 2) Batch Size × 2 (number of performance) = 3, s = 1, c = 4) Interpolation (256 × 64) The Adaptive Moment Estimation (Adam) [40] optimizer was adopted in the optimization process. In essence, it is Root Mean Square Prop (RMSProp) [41] with a momentum factor. By combining the advantages of RMSProp and Adaptive Gradient (AdaGrad) [42], the Adam has lower calculation cost. In addition, it has good performance for high-dimensional space, large data sets, and most nonconvex optimization. Mathematically, the definitions of Adam are as follows: t←t−1 (14) gt ← ∇θlt(θt−1) (15) mt ← β1·mt−1 + (1 − β1)·gt (16) vt ← β2·vt−1 + (1 − β2)·gt ⊙ gt (17) mˆ t ← m t / ( 1 − β t1 ) (18) vˆ t ← v t / ( 1 − β t2 ) (19)PDF Image | Performance Prediction of a S-CO2 Turbine
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