## 2 Proposed Method
### ATASML Algorithmic Procedure  
The ATASML framework is designed to enhance fault diagnosis through a systematic approach incorporating meta-learning and adversarial training, which improve model robustness and adaptability. Refer to Figure 3 for a visual representation of the ATASML algorithm's architecture, which illustrates the critical components and their interactions within the framework. 1. Parameter Initialization: Begin with a random initialization of model parameters \(\theta_{0}\), which helps in avoiding local minima and promotes better convergence towards optimal solutions. 2. Task Sampling: Sample a set of tasks \(\{T_{i}\}_{i=1}^{B}\) from the task distribution \(p(\mathcal{T})\). This step ensures that the model is trained across a diverse set of scenarios, enhancing its generalization capabilities. 3. Data Augmentation: Utilize the pre-augmented dataset \(\mathcal{X}_{aug}\) to select augmented tasks \(T_{i,aug}\). This dataset already includes transformations applied via Gaussian noise and temporal warping, thus directly enhancing the data's variability and complexity: \[T_{i,aug}=\text{SelectFrom}(\mathcal{X}_{aug},T_{i})\] (7)
4. Adversarial Task Generation: Generate adversarial tasks \(T_{i,adv}\) using the dataset \(\mathcal{X}_{adv}\), which has been specifically prepared to challenge the model's robustness under simulated adversarial conditions: \[T_{i,adv}=\text{GenerateAdversarial}(\mathcal{X}_{adv},T_{i})\] (8)
5. Task Combination and Difficulty Assessment: Combine the original tasks \(T_{i}\) from \(p(\mathcal{T})\), the augmented tasks \(T_{i,aug}\) and the adversarial tasks \(T_{i,adv}\) into composite tasks \(T_{i,comp}\). This step evaluates the complexity of integrating different types of tasks, which helps in assessing the model's robustness and adaptability across a diverse range of conditions: \[T_{i,comp}=\text{Combine}(T_{i},T_{i,aug},T_{i,adv})\] (9)Assess the difficulty of these composite tasks to ensure the model can handle varying levels of challenge and complexity. This assessment aids in tuning the model's sensitivity to subtle and extreme variations alike:  
\[D_{T_{i,comp}}=\text{AssessDifficulty}(T_{i,comp}) \tag{10}\]  
Wasserstein Distance Calculation: Compute the Wasserstein distance to measure how closely the composite tasks \(T_{i,comp}\) align with the original task distribution, aiding in maintaining the integrity of the model's training process:  
\[W_{T_{i,comp}}=\text{ComputeWassersteinDistance}(T_{i,comp},p(\mathcal{T})) \tag{11}\]  
7. Task Ranking: Rank the tasks based on assessed difficulty and Wasserstein distance, which helps in prioritizing the tasks that will most effectively enhance the model's learning:  
\[\{T_{j}\}=\text{RankTasks}(\{T_{i,comp}\},D_{T_{i,comp}},W_{T_{i,comp}}) \tag{12}\]  
8. Support and Query Set Sampling: From each ranked task \(T_{j}\), extract support and query sets \(S_{j}\) and \(Q_{j}\), respectively. These sets are crucial for tuning the model parameters specifically to each task:  
\[S_{j},Q_{j}=\text{SampleSets}(T_{j}) \tag{13}\]  
Figure 3: Architecture of the ATASML framework showing the interaction between the datasets and task processes. Model Optimization: Update the model parameters \(\theta_{i}\) using the support set \(S_{j}\) and evaluate the performance on the query set \(Q_{j}\). This step is vital for iterative learning and adaptation of the model:  
\[\theta_{i}^{\prime}=\theta_{i}-\alpha\
abla_{\theta_{i}}\mathcal{L}_{S_{j}}(f_{ \theta_{i}}) \tag{14}\]  
\[\mathcal{L}_{Q_{j}}(f_{\theta_{i}^{\prime}})=\text{EvaluateLoss}(Q_{j},f_{ \theta_{i}^{\prime}}) \tag{15}\]  
10. Global Parameter Update: Perform a global update of the model parameters \(\theta\) using the aggregated losses from the query sets across all tasks.