## 3 Methods
### KAN-BiLSTM Moisture Ratio Prediction Model
#### 3.4.2 KAN-BiLSTM  
In this study, an enhanced prediction model, KAN-BiLSTM, is proposed. The overall architecture of the model is illustrated in Figure 7. The input layer receives tangerine peel drying data and preprocesses it into a format compatible with the KAN layer. The KAN layer performs nonlinear transformations on the input features, thereby decoupling feature learning from temporal modeling. This enhances the model's ability to express complex input characteristics. The transformed features are then passed to the BiLSTM module for temporal sequence modeling. The BiLSTM unit employs a bidirectional gating mechanism--consisting of a forget gate, input gate, and output gate [27]--to simultaneously capture both forward and backward temporal dependencies present in the drying process. The first BiLSTM layer captures primary temporal features, and its output is passed through a fully connected layer before entering the second BiLSTM layer, which extracts higher-level temporal dependencies. Subsequently, the output from the BiLSTM is fed into an MHA module. This mechanism dynamically assigns weights to different time steps and features, enabling the model to focus on critical moments and subtle moisture variations, thereby improving prediction accuracy.  
As shown in Figure 7, the multi-head attention mechanism achieves this goal by mapping the input sequence to a query (\(Q\)), key (\(K\)), and value (\(V\)) vector, respectively. Subsequently, it employs an attention-scoring function to compute the attentional weights of each position relative to the others, effectively capturing long-range dependencies across the input sequence. The outputs of multiple attention heads are concatenated to form  
Figure 7: Structure of Kolmogorov–Arnold network bidirectional long short-term memory (KAN-BiLSTM) model.  
a comprehensive representation. Finally, the output layer produces the model's final prediction results. The MHA mechanism computes the attention output as follows:  
\[Attention(Q,K,V)=softmax\bigg{(}\frac{QK^{T}}{\sqrt{d_{k}}}\bigg{)}V \tag{14}\]  
where \(Q\), \(K\), and \(V\) represent the query, key, and value matrices, respectively, and \(d_{k}\) is the dimension of the key vectors. In the multi-head configuration, the attention mechanism is computed in parallel across multiple heads:  
\[MultiHead(Q,K,V)=Concat(head_{1},\dots,head_{h})W^{O} \tag{15}\]  
where each attention head is defined as:  
\[head_{i}=Attention(QW_{i}^{Q},KW_{i}^{K},VW_{i}^{V}) \tag{16}\]  
Here, \(W_{i}^{Q}\), \(W_{i}^{K}\),\(W_{i  
After optimization, the MHA layer is configured with 4 heads and embedding dimension (Dim) = 8, which not only satisfies dimensional consistency but also enhances prediction performance. As shown in Table 5, this configuration achieves RMSE = 0.027 and MAE = 0.0202, outperforming other combinations with no increase in parameter count (85 K). The key design consideration is that Dim = 8 matches the 32-dimensional output of the preceding BiLSTM layer (as 4 heads \(\times\) 8 dimensions = 32), ensuring compatibility, preventing redundancy, and preserving the integrity of feature representations in attention computation.  
Further ablation analysis validates the superiority of this setting. Compared to Heads = 2, Dim = 16 (RMSE = 0.0312, MAE = 0.0242), the proposed Heads = 4, Dim = 8 setting reduces RMSE by 12.8% and MAE by 16.5%, with an identical number of parameters. Although Heads = 4, Dim = 16 yields comparable performance, it incurs a 10.6% increase in parameter count. These findings indicate that the selected configuration achieves an optimal balance among representational capacity, computational efficiency, and dimensional alignment with the upstream features.