# Penetration Overload Prediction Method Based on a Deep Neural Network with Multiple Inputs
## 3 Method
### Model Introduction
#### 3.2.2 The Improved PF-Informer Model
In the original Informer, an open-source library called \"pandas\" is directly used to extract and normalize the characteristic values (year-month-day-hour). This approach makes the average characteristic value 0, the maximum characteristic value 0.5 and the minimum characteristic value \(-0.5\). The two data sets contain the data of multilayer targets and thick targets. The numbers of sampling points acquired for the two types of targets are different. For multilayer targets, the first objective is to distinguish the target layers in the time sequence, and the priority is the slope of the overload change. Furthermore, the magnitude of the amplitude loss has little influence on distinguishing the target layers. According to different data sizes, two coding methods can be chosen: when the test set possesses a certain size, 1 to the end of corresponding sequence can be used for the time coding; in the absence of data set support, time coding can produce a sequence-length cycle consisting of 1 to a single-layer target. For thick targets, axial overload changes are very important. During the process of penetrating a thick target, the axial overload drops sharply due to the change in attitude, so the time coding process needs to cycle from 1 to the whole long sequence. The time sequence of the penetration process cannot be directly time coded using dates. Here, the time sequence is divided, and the time corresponding to each data point in the experimental process is coded as (starting position, starting position plus total time sequence length). The normalization logic is as follows:  
\[Output=\left(\frac{Input}{\text{Length of corresponding sequence}}-0.5\right) \tag{7}\]  
In this way, the characteristic value of the input time code is 0, the maximum value is 0.5, the minimum value is \(-0.5\), and the variance is 1. The regularization operation is performed at the input, which can effectively improve the training progress. Modification of the Non-Variable Physical Quantity Inputs of the PF-Informer Model  
The PF-Informer model optimizes a large number of repeated and immutable physical input parameters, significantly reducing the MSE of the prediction model and making the model more robust. The multivariate inputs used by PF-Informer for the time series prediction process include time, speed, angle of attack, bullet weight, bullet length and other parameters. The PF-Informer model can easily adjust the speed-related weight according to the speed change trend. Parameters such as the attack angle, bullet weight and bullet length are input into the model in advance, and the corresponding parameters in the time series do not change. Through a large number of training analyses, it can be concluded that adding too many immutable parameters causes serious model overfitting, making the universality of the model seriously worse. As shown in Figure 5, the change in the MSE of the prediction model is modified by adding categories that introduce constant input parameters. It is obvious from the Figure 5 that the introduction of more immutable input parameters significantly increases the MSE and decreases the prediction ability of the model. Since the model based on the transformer architecture inputs too many identical parameters, the self-attention weights corresponding to these invariable parameters are greatly increased, which results in the self-attention weights corresponding to other variable input parameters being reduced or even ignored during the model training process. Finally, the model deteriorates. To prevent model weight disorder, the input parameters should be preprocessed. For a time series prediction task with a long sequence input, the model with the transformer architecture sends the characteristic values of each time series to the activation function. When multiple identical constant parameters appear, the value obtained by multiplying the query value corresponding to each key value is higher, which makes the corresponding weight obtained after being sent to the activation function abnormal.