# Battery Life Prediction for Ensuring Robust Operation of IoT Devices in Remote Metering
## 3 Remote Metering Life Prediction Method
### C-SDFormer Model for Predicting the Discharge Capacity of MSD Primary Battery
They then pass through the input embedding layer, which consists of a CNN and facilitates the feature extraction process within the encoder layer, mapping them to a 128-dimensional vector. The C-SDFormer model lacks a recursive architecture, necessitating the inclusion of position tokens to indicate the position of each element in the sequence. This aids the model in comprehending the sequence's item order and retaining this order. Various techniques exist for incorporating positional information into sequences, but in this study, we employ sine and cosine functions, as defined in Equations (6) and (7). \[PE_{(pos,2i)} =sin(\frac{pos}{10,000^{(2i/d_{model})}}), \tag{6}\] \[PE_{(pos,2i+1)} =cos(\frac{pos}{10,000^{(2i/d_{model})}}), \tag{7}\]  
where \(pos\) is the position of the embedding vector in the sequence and \(i\) is the index for each dimension of the embedding vector. If the index is even, we use the sine function. If the index is odd, we use the cosine function. Subsequently, the input, now encompassing positional information, proceeds to the encoder block. This encoder block comprises multiple layers, including a multi-head self-attention layer, a series decomposition layer, a feed-forward network (FFN), residual connections (Add), and layer normalization (LayerNorm). Residual connections serve to mitigate the risk of gradient vanishing, while layer normalization aids in convergence learning and enhances the model's resilience to data variations. The self-attention mechanism, a potent tool for learning dependencies within sequence components, enables the model to focus on the most pertinent information in the sequence. It operates by generating three matrices: Query (\(Q\)), Key (\(K\)), and Value (\(V\)) for the input sequence. These matrices are computed using distinct weight matrices, \(W^{q}\), \(W^{k}\), and \(W^{v}\), learned during training. The \(Q\) and \(K\) matrices are multiplied and scaled by \(\sqrt{d_{k}}\), and then converted into a probability distribution using the softmax function. Subsequently, the \(V\) matrix is multiplied by this probability distribution to yield the attention value, which provides the model with more detailed insights into the elements deserving of focus. The calculation of the attention value can be summarized by Equation (8). \[Attention(Q,K,V)=softmax(\frac{QK^{T}}{\sqrt{d_{k}}})V, \tag{8}\]  
where \(d_{k}\) is the dimension of the \(K\) vector. Our model also incorporates multi-head self-attention, an enhancement of the self-attention mechanism. Multi-head self-attention simultaneously applies multiple self-attention mechanisms to model the relationships among input data from various perspectives and extracts comprehensive information. This approach empowers the model to distinguish between distinct features within the input sequence, thereby enhancing its learning capacity. After passing through Add&LayerNorm, the model employs a series decomposition layer to segregate the data into seasonal and trend components. This separation streamlines the identification of seasonal and trend information in isolation, with only the seasonal features undergoing processing through the FFN. This step allows for more detailed information extraction and pattern learning from the seasonal features. Ultimately, following transit through the series of \(N\) encoder blocks, the discharge capacity is predicted utilizing \(M\) convolution layers and a dense layer. For specific model hyperparameters, please refer to Section 4 for detailed information. Figure 7: Structure of the proposed C-SDFormer model.