S₁ Ds S₂ S3 D₁ Ꭲ, | Encoder Output (shifted right) Output 0.0 00 Input Embedding Muti-Head Add & Attention Norm Feed Forward Add & Norm Encoder #N| Muti-Head Add & Attention Norm Muti-Head Attention Add & Norm Forward Feed Add & Norm Decoder #N Linear 00 T₁ S₁ T₁ S₁ S₂ S3 Linear Кт VT Qs Vs Ks Cross Adaptive Layer Sigmoid Muti-Head Cross Attention Add & Norm Muti-Head Attention Add & Norm ypred T₁ S₁ S₁ LMMD LMSE Feed Forward Add & Norm Feed Forward Add & Norm Ldistillation Y label T1 S₁ Cross Adaptive Layer | Ltotal = arg min (waLdistillation+ WMLMMD + W,Lregression) Fig. 6. Architecture of the proposed MSCATN. 7

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1. Teacher Model Architecture (T)

 

Dataset C: Clean data with complete inputs and labels

 

Architecture

 

Input Embedding Layer

Converts multivariate sensor inputs into dense vectors.

 

Positional Encoding

Adds time-step order information to each embedding.

 

Transformer Encoder Stack (repeated N times)

 

Multi-Head Self-Attention: Captures temporal dependencies across time steps.

 

Add & Norm: Applies residual connections and layer normalization.

 

Feedforward Network: Applies MLP with non-linearity (e.g., ReLU or GELU).

 

Feature Representation Layer (F_T)

Intermediate latent feature vector used for feature distillation.

 

Regression Head

Linear layer that outputs the final RUL prediction y_T.

 

Learning Objective

 

Supervised loss with ground truth RUL.

 

Provide F_T and y_T as guidance to student models.

 

2. Student A Architecture – Handling Missing Inputs

 

Dataset A: Incomplete inputs, complete RUL labels

 

Architecture

 

Masked Input Embedding Layer

 

Maps inputs with missing values into dense vectors.

 

Missing values are masked or replaced with a learned token.

 

Positional Encoding

Adds time-step information to each embedding.

 

Transformer Encoder Stack (N layers)

 

Multi-Head Self-Attention

Learns dependencies among available channels and ignores masked ones.

 

Add & Norm

 

Feedforward Layer

 

Feature Representation Layer (F_A)

Used for feature distillation against F_T.

 

Regression Head

Predicts RUL → y_A.

 

Knowledge Distillation

 

Feature Distillation

 

Mean Squared Error between F_A and F_T.

 

Prediction Distillation

 

MSE or KL divergence between y_A and y_T.

 

Supervised Loss

 

Ground truth RUL is available.

 

Total Loss

 

Ltotal_A=Lsup(yA,ytrue)+λ1⋅Lfeature(FA,FT)+λ2⋅Lpred(yA,yT)L_{\text{total\_A}} = L_{\text{sup}}(y_A, y_{\text{true}}) + \lambda_1 \cdot L_{\text{feature}}(F_A, F_T) + \lambda_2 \cdot L_{\text{pred}}(y_A, y_T)

 

3. Student B Architecture – Handling Missing Labels

 

Dataset B: Complete inputs, partial RUL labels

 

Architecture

 

Input Embedding Layer

Dense transformation of sensor values.

 

Positional Encoding

Adds sequential time-step information.

 

Transformer Encoder Stack (N layers)

 

Multi-Head Self-Attention

 

Add & Norm

 

Feedforward Layer

 

Regression Head

Predicts RUL → y_B

 

Knowledge Distillation

 

Prediction Distillation Only

 

For unlabeled samples: use y_T as pseudo-labels

 

For labeled samples: use supervised loss

 

Total Loss

 

Ltotal_B=Lsup(yB,ytrue)+λ3⋅Lpred(yB,yT)L_{\text{total\_B}} = L_{\text{sup}}(y_B, y_{\text{true}}) + \lambda_3 \cdot L_{\text{pred}}(y_B, y_T)