## 2 Methods
### Fusion of Safety Performance Parameters and BP Neural Network
#### 2.1.2 Basic Principle of BP Neural Network  
An artificial neural network has the advantages of self-adaptation, self-organization, strong robustness, and high efficiency, which can deal with linear programming, nonlinear programming, geometric programming, dynamic programming, and stochastic programming [25; 26]. At present, the most widely used artificial neural network has more than 10 types, the most representative being the BP neural network. This algorithm has the ability to preliminarily analyze the original data and to repeatedly adjust the process parameters to achieve the adaptive processing consistent with the desired purpose. It is widely used in engineering, finance, chemical industry, energy, communication, and other fields, and has been continuously studied, optimized, and improved [27; 28].  
In practical application engineering, neural networks are often used in combination with some learning algorithms because different learning algorithms represent different thinking processes in human brain activities. A BP neural network is an intelligent data processing model used by a BP algorithm and neural network [29]. From the perspective of perceptron, a neural network can be divided into the input layer, hidden layer, and output layer [30]. The network topology in the neural network simulates the connection between human brain neurons. The activation function is a tool for analysis instead of human brain neurons, as shown in Figure 1.  
From the perspective of function approximation, Equation (2) can be used to approximate any complex function. The nonlinear function represented by it can be realized by the BP network with a hidden layer without a bias value and linear transfer function of the output layer neurons:  
\[y_{k}=\sum_{j=1}^{N_{2}}\omega_{kj}^{2}f\left(\sum_{i=1}^{N_{1}}\omega_{ji}^{ 1}x_{i}+b_{j}\right). \tag{2}\]  
In the Equation, \(y_{k}\) is the \(k\)th output. \(\omega_{kj}^{2}\) is the weight of \(j\)--the neuron in the second layer (hidden layer), to \(k\)--the neuron in the output layer. \(f(\cdot)\) is the transfer function of the hidden layer neurons. \(\omega_{ji}^{1}\) is the weight of \(i\)--the neuron in the first layer (input layer), to \(j\)--the neuron in the hidden layer. \(b_{j}\) is the bias value of \(j\)--the neuron in the hidden layer. \(N_{1}\) is the number of neurons in the input layer. \(N_{2}\) is the number of hidden neurons. As long as the number of hidden layer neurons is sufficient, the BP network with a hidden layer can approximate any complex nonlinear function with an arbitrary accuracy.  
The nonlinear transfer function of BP neural network is usually taken as the Sigmoid function and expressed as Equation (3):  
\[f(x)=\frac{1}{1+e^{-\beta x}}. \tag{3}\]  
The BP neural network is a multi-input and multi-output network. The network realizes the mapping from n-dimensional input to m-dimensional output. This mapping can be linear or nonlinear. This mainly depends on the type of transfer function used  
Figure 1: Neural network structure diagram.  
by neurons. The BP neural network realizes the pattern recognition function in the form of mapping.