## 4 Analysis and Discussion  
### Experimental Methods  
The BP neural network, or error feedback neural network algorithm, is a multilayer feed-forward neural network that has been trained according to the error back propagation algorithm (as shown in Figure 4). The structure of the network is straightforward and comprises three principal layers: the input layer, the hidden layer, and the output layer. The input layer is the initial layer of the neural network that receives external information. It contains multiple nodes, each representing an input feature or variable. The hidden layer constitutes the central component of the neural network, situated between the input and output layers. The nodes in the hidden layer are not directly connected to the external environment, yet their state can influence the relationship between the input and output. The output layer is the final layer of the neural network and is responsible for generating the output of the neural network, which may deviate from the desired result of the actual problem. The BP neural network adjusts the network parameters to minimize this error through the error back propagation algorithm. This experiment is based on the dataset established in Section 3.4 (Table 1), which extracts the product's affective design parameters and sustainable design parameters as inputs for training the model. The various satisfaction levels of the product serve as the model's outputs. The corresponding user satisfaction is used as output values. In order to eliminate the effect of the difference in dimension between the input and output values on the accuracy of the model, data normalization is employed in scikit-learn. This involves the normalization of all the input and output data. The design parameters derived from affective design and sustainable design are inputted into two fully connected layers. The number of neurons in the first layer is 256, while the second layer contains 512 neurons. The number of neurons in the output layer is equivalent to the number of labels, specifically 10 neurons for the design parameter and 10 neurons for the user satisfaction parameter. The data in Table 1, which combine the design parameters extracted from different products based on emotional design and sustainable design with user satisfaction, were selected for the model dataset. Subsequently, 80% of the data were randomly selected as the training set of the model, which was put into the BP neural network prediction model for training. The remaining 20% of the data were not involved in the training and served as the validation set, which was used for validating the results of the model. The BP neural network comprises a hidden layer, which contains a neuron structure. The neurons in each layer are connected to each other by weights. The weights are adjusted continuously during the neural network training process in order to optimize the network's performance. The activation function is employed to introduce nonlinearities in the neurons, thereby enabling the neural network to address complex nonlinear problems. The training process of the BP neural network comprises two phases: forward propagation and back propagation. In the forward propagation phase, the input signal acts on the output node via the hidden layer, undergoing a nonlinear transformation to produce an output signal. In the event that the actual output does not correspond to the desired output, the back propagation stage is initiated. This involves the back propagation of the output error layer by layer through the implicit layer to the input layer. The network parameters (e.g., weights and biases) are then updated in order to reduce the error. \(\mathrm{X_{n}}\) represents the nth design parameter, and \(\mathrm{W_{n}}\) (weight) is the corresponding weight of \(\mathrm{X_{n}}\), which represents the magnitude of the effect of \(\mathrm{X_{n}}\) on the next neuron. For a single neuron, the positive feedback signal it obtains is the sum of the previous values of each node and its weight.