# Multi-Objective Optimization Study of Annular Fluid Flow Structure in Cordless Core Drilling Tools
## 2 Structural Design and Principles of Hydraulic Lifting Cordless Coring Drilling Tool
### Numerical Prediction Model of Spool Annular Flow Field Based on BP Neural Network  
Suitable spool back pressure and drilling fluid flow rate have a large impact on scoring quality and coring operation efficiency. Due to the complexity of the actual drilling conditions, it is difficult to accurately predict the flow field performance of the spool under different structural parameters only through experience or simple models. Therefore, it is important to establish an accurate prediction model. The prediction model can predict the spool back pressure and drilling fluid flow rate based on the existing design parameters and operation data, improve the coring quality and drilling fluid flow efficiency, and reduce energy consumption and cost. The effects of different structural parameters on spool back pressure and flow rate are analyzed by orthogonal experimental methods, which provide a training basis for the model based on the obtained data. The BP Neural Network is a common artificial neural network with good nonlinear mapping capability. It usually consists of an input layer, one or more hidden layers, and an output layer [36; 37; 38; 39; 40]. The neural network learns the patterns in the data by adjusting the weights. The specific process is as follows: First, forward propagation: the input data were passed through the input layer, layer by layer, to the hidden layer and the output layer to get the predicted output. Second, error calculation: the error between the predicted output and the actual output is calculated, in which the error calculation formula is shown in Equation (1);  
\[E=\frac{1}{2}\sum_{i=1}^{n}{(y_{i}-\hat{y}_{i})^{2}} \tag{1}\]  
where \(E\) is the total error, \(\hat{y}_{i}\) is the predicted output, \(y_{i}\) is the actual output, and \(n\) is the number of output nodes. Then, back-propagation: the error is passed backward from the output layer layer by layer, and the weights of each layer are adjusted by calculating the gradient. Finally, weight update: the weights are updated according to the gradient of the error to reduce the error, and the weight update formula is shown in Equation (2). The whole process is repeated until the error of the network is reduced to an acceptable range or reaches the preset number of training times. \[w_{ij}(t+1)=w_{ij}(t)-\eta\frac{\partial E}{\partial w_{ij}} \tag{2}\]  
where \(w_{ij}(t+1)\) is the value after weight update, \(w_{ij}(t)\) is the current weight value, \(\eta\) is the learning rate, \(\frac{\partial E}{\partial w_{ij}}\) is the partial derivative of the error with respect to the weight. During the training process using the BP neural network, 70% of them are used as training data for network training and 30% as test data for testing the fitting performance of the network. According to the nonlinear functional relationship between the structural parameters and the composition of the optimization objective, the structure of the BP neural network was set to be 5-10-2, with 5 nodes in the input layer, 10 nodes in the hidden layer, and 2 nodes in the output layer. The BP neural network was randomly initialized, and the relevant network parameter configurations were configured, in which the number of iterations was 1000, the error threshold was set to 1 \(\times\) 10\({}^{-6}\), and the learning rate was 0.01. Figure 3 shows the function of the correlation between the dependent variable, the ratio of the fluid back pressure and the spring force pressure, and the independent variables, the number of spearhead intakes, the diameter of spearhead intakes, the number of spool outlets, the diameter of outlets, and the distance between the two centers of the two circles of the outlet oblong hole. The fitting situation, recorded as model I, has a correlation coefficient of R = 0.94. R is the correlation coefficient. The larger the R, the higher the fitting accuracy.