Algorithm process of BPNN.
In the forward propagation process, the input object is divided into n input vectors. The weight coefficient is denoted as “In Eq (The domains of the mentioned functions are sets of real numbers, and their range is [0, 1]. After obtaining the outputs from all the hidden layers, the cross-entropy loss function is used to measure the discrepancy between the predicted values and the observed values, thus evaluating the predictive capability of the model. The loss function can be represented by Eq (In Eq (During the error backpropagation process, the gradient of the loss function is propagated backward from the output layer to the hidden layer, and the loss value is distributed to each layer of neurons. Through continuous iteration, the parameters between layers are updated to minimize the error between the actual output and the expected output values. This procedure enhances the robustness of the BPNN by adjusting the weights and thresholds associated with the smallest error [In Eqs (The selection of the number of nodes in the hidden layer is a challenging aspect of feature layer fusion based on BPNN. Currently, there is no standardized method for determining the number of nodes in the hidden layer, which directly affects the overall performance of the network. Therefore, careful consideration must be given to the selection of hidden layer nodes [In Eq (For this work, a dataset was collected by inviting twenty male football players who had different heights and weights to perform kicking actions. Among the players, one player stood out as being taller than the rest, and his kicking action data was used as the standard action. High-speed cameras were utilized to capture the kicking action data, with a frame rate of 25fps and a resolution of 1024×1280. The BPNN algorithm was employed to analyze the similarity between the kicking actions of young players and the standard action, providing valuable insights for their football training.