# Transfer Learning with Deep Recurrent Neural Networks for Remaining Useful Life Estimation
## 2 Methods
### Transfer Learning for RUL Prediction  
Based on the availability of sample labels, transfer learning can be divided into three categories: inductive transfer learning, transductive transfer learning, and unsupervised transfer learning [28]. Inductive transfer learning requires the availability of the target data labels. If the source data labels are available and the target data labels are unavailable, transductive learning should then be used. If both the target data labels and the source data labels are unavailable, then the unsupervised transfer learning should be used. According to the properties of C-MAPSS datasets in which both the target data labels and the source data labels are available, inductive transfer learning is the most suitable approach that we adopted.  
Based on what to transfer, transfer learning can be conducted at several levels: instance-transfer, feature-representation-transfer, parameter-transfer, and rational-knowledge-transfer [28]. Instance-transfer aims to re-weight some labeled data from the source domain and then use them in the target domain. Feature-representation-transfer tries to get the good feature representations that can reduce the difference between the source domain and the target domain. Parameter-transfer discovers shared parameters or prior knowledge between the source domain and the target domain. Relational-knowledge-transfer works by mapping the common relational knowledge or some similar patterns from the inputs to the outputs between both domains. According to the properties of the C-MAPSS datasets and experiment conditions, parameter-transfer is selected in our algorithm.  
In this research, we apply transfer learning to address one of the major challenges in data-driven prognostics by transferring model parameters learned from the different but approximately related domain with a large amount of source data to the target RUL prediction problem with a small amount of data. The parameter-transfer scheme can be defined as follows:  
Figure 1: Operational setting values in every sub-dataset.  
\[D_{s} =\{X_{s},T_{s}\} \tag{1}\] \[D_{t} =\{X_{t},T_{t}\} \tag{2}\]  
where \(D_{s}\), \(X_{s}\), \(T_{s}\), \(D_{t}\), \(X_{t}\), \(T_{t}\) respectively represent source domain, source samples, source task labels, target domain, target samples, target task labels. \(D_{s}\), \(D_{t}\) are related or similar domains.  
The relationship of the model weights of the source problem and of the target problem can be represented as follows:  
\[W_{s} =W_{0}+W_{1} \tag{3}\] \[W_{t} =W_{0}+W_{2}\] (4) \[Y_{s} =f_{s}(X_{s}+W_{s})\] (5) \[Y_{t} =f_{t}(X_{t}+W_{t}) \tag{6}\]  
Here, \(W_{s}\), \(W_{t}\) are parameters in the source and the target task, respectively. They have some common parts \(W_{0}\) and some different parts. \(Y_{s}\), \(Y_{t}\) are the real outputs. \(f_{s}\), \(f_{t}\) denote the learning models that map from the sample inputs to the task labels. The parameter-transfer scheme aims to transfer parameters from \(W_{s}\) to \(W_{t}\) by making use of the common parts \(W_{0}\) and fine-tuning the different parts by further training the models in the target task.