Algorithm 1 BPNN algorithm workflow

Input:        Training set: $D=\{({\mathbf{x}}_1,y_1),({\mathbf{x}}_2,y_2),...,({\mathbf{x}}_m,y_m)\}$, $y_i\in \mathbb{R}$;     Learning rate: $\eta$;     Initial neuron parameters: $\mathbf{w}$, $\mathbf{v}$, $\mathbf{\theta }$, $\mathbf{\gamma }$. Output:  Effective neuron parameters: $\mathbf{w}$, $\mathbf{v}$, $\mathbf{\theta }$, $\mathbf{\gamma }$. 1:The samples and network parameters are initialized according to Formula (13); 2:for all $({\mathbf{k}}_k,y_k)\in D$ do 3:      The input $\mathbf{\beta }$ of the output neuron is calculated according to Formula (14); 4:      The output ${\widehat{y}}_j^k$ of the current sample is calculated according to Formula (15); 5:      The gradient $g_j$ of the neuron in the output layer is calculated according to Formula (16); 6:      The gradient $e_h$ of neurons in the hidden layer is calculated according to Formula (17); 7:      The Neuron parameters are updated according to Formula (18); 8:      if The cumulative error calculated by Formula (19) is in accordance with the expectation then 9:          Break;       10:return The neuron parameters.