2.2.3. GM(1,1)-BP Neural Network Model

Grey system models are suitable for single exponential growth, but these models cannot be self-fed and exhibit low prediction accuracy for short-term data with a large variation trend of drug resistance. BP neural network models can easily fall into local minima, but have the advantages of a fast learning speed, nonlinear mapping, and a high fitting accuracy. In this study, an improved model was proposed that combined these two models. An ashing layer was added in front of the neural network for data ashing treatment to weaken randomness, and an albino layer was added later for information reduction. These changes were designed to utilize the advantages of the two models and improve the accuracy of the model for the drug resistance [44,45]. The modeling process is as follows:

According to the GM(1,N) equation, the differential equation with parameters can be expressed as:

The time response equation of Equation (5) is embedded into the BP neural network with the structure shown in Figure 2, and can be written as:

Neural network topology.

In Figure 2, t is the sequence number of the input sequence,x2(1)(t),…,xn(1)(t) is each input parameter,w21,w22,…w2n,w31,w21,w32,…w3n are weights, LA, LB, LC, and LD represent the four-layer structure of the grey neural network and are the output values.

(1) The input parameter sequence is b1,b2,…,bn. The initial network weight can be expressed as:

(2) This next step is forward transfer, calculating each layer of output for each input sequence as:

LA output:

LB output:

LC output:

LD output:

The threshold value of the LD layer output node can be expressed as:

According to the equation:

(3) Back propagation is then used to calculate the error between the output value and the expected value, and then the weight and threshold can be adjusted according to the error from LD to LB layer.

LD layer error:

LC layer error:

LB layer error:

The forward weight can then be adjusted according to the output value.

The LB to LC weight is changed to:

The LA to LB weight is changed to:

The threshold is modified to:

(4) Next, whether or not the predicted value meets the requirements is assessed. If not, return to Step 2. If so, stop the training of the model.