Firstly, it is necessary to combine the traditional method of expert knowledge judgment to summarize the qualitative methods for identification of sticking, which is one of the important basic work of artificial intelligence risk prediction. According to the different causes, the sticking can be divided into differential pressure, collapse, sand bridge, shrinkage, keyway, balling-up, and junk sticking [12]. The different types of sticking are correspond to different judgment methods. According to the field drilling practice and expert knowledge judgment [13,14], the judgment methods of sticking are summarized, as shown in Table 1.

According to the expert knowledge judgment of sticking failure, the comprehensive logging parameters that can characterize the sticking are hook load (WHO), standpipe pressure (SPP), torque (TOR), rate of penetration (ROP), rotary speed (RPM), and weight on bit (WOB). Although the types of sticking are different, the change rules of logging data before and after sticking are consistent. After the drill sticking fault occurs, the rotary table torque and the standpipe pressure increases, the rotary speed decreases. When sticking occurs during tripping out, the hook load and torque increases. When sticking occurs during tripping in, the hook load decreases, the torque increases, and the rotary speed increases.

The back propagation (BP) neural network is a typical multi-layer and feed-forward network. The main advantage of the BP neural network is its strong nonlinear mapping ability. It is a three-layer forward artificial neural network composed of input layer, hidden layer, and output layer. According to the calculation formula of neuron output signal, the output of each neuron in the hidden layer can be obtained as follows:

(1) Ij=∑i=1nνijxi−θj j=1,2,…lOj=f(Ij) j=1,2,…l

In the formula, v_ij—connection weight of input layer neuron i and hidden layer neuron j. θ_j—threshold value of hidden layer neuron j. f(I_j)—activation function of neurons.

Similarly, the output signal of the output layer of BP neural network is obtained as follows:

(2) Ik=∑j=1lμjkOj−βk k=1,2,…myk=f(Ik) k=1,2,…m

In the formula, μ_jk—connection weight of output layer neuron k and hidden layer neuron j.

β_k—threshold value of output layer neuron k. f(I_k)—activation function of neurons.

This paper systematically analyzed the learning steps of BP neural network.

a) Initialize parameters of neural network

The connection weights v_ij and μ_jk of each layer of neurons are given a random number between [−1, 1]. The learning rate η is set to a decimal within 0~1. The error E is set to 0. The error threshold E_min is set to a positive decimal. The number of hidden layer nodes m is obtained by an empirical formula. The sample mode calculator p and training times q are reset to 1. The default number of workouts is M.

b) Input training samples and calculate output of each layer

A pair of training samples (X^P, Q^P) are selected to assign values of the input parameters, and the output O, Y are calculated.

c) Calculating the output error of neural network

Suppose the total number of training samples is P. The error of each training is Ep=∑k=1l(qkp−ykp)2 . The total output error is ERME=1p∑p=1P(Ep)2 .

d) Calculate error signal of each layer

The error calculation formula of output layer and hidden layer is as follows:

(3) δky=(qk−yk)yk(1−yk)

The error calculation formula of hidden layer and input layer is as follows:

(4) δjO=(∑1lδkyμjk)Oj(1−Oj)

e) Adjust connection weight and threshold of each layer

The calculation formula of connection weight and threshold of output layer and hidden layer are as follows:

(5) Δμjk=η(qk−yk)yk(1−yk)Oj

(6) Δβk=η(qk−yk)yk(1−yk)

The calculation formula of connection weight and threshold value of hidden layer and input layer are as follows:

(7) Δvij=η(∑1lδkyμjk)Oj(1−Oj)xi

(8) Δθj=η(∑1lδkyμjk)Oj(1−Oj)

f) Determine whether to complete one training for all samples

If p < P, p, q increased by 1, return to Step b. Otherwise, go to Step g.

g) Check whether the total error of neural network meets the error threshold

E_RME < E_min or q > M, end. Otherwise, E is reset to 0, p is reset to 1, return to Step b.

The BP neural network has its own defects. It is difficult to get the optimal value of the connection weight and threshold value, which eventually results in a large error between the prediction result and the actual value of BP neural network. Therefore, it is necessary to combine another optimal solution algorithm with the BP neural network to improve the accuracy of prediction. In this paper, the ability of PSO to search the optimal solution globally is used together with BP network to improve the prediction accuracy. The principle and model of PSO [15] are as follows: The M particles are initialized to form a “bird swarm” T = {Z1,Z2,…,ZM},i=1,2,…,M. zi=(zi1,zi2,…,ziD),i=1,2,…,M , which represents the position vector of the i-th particle in D-dimensional space. si=(si1,si2,…,siD),i=1,2,…,M represents the velocity vector of the i-th particle in D-dimensional space. The flight motion experience of the particle itself is Pbesti=(Pbesti1,Pbesti2,…,PbestiD) . The global optimal position is Gbest=(Gbest1,Gbest2,…,GbestD) . The recurrence formula of particle algorithm is:

(9) si,dk+1=si,dk+c1r1(Pbesti,d−zi,dk)+c2r2(Gbestd−zi,dk)zi,dk+1=zi,dk+si,dk+1

In the formula, c1r1(Pbesti,d−zi,dk) —the memory ability of particles to their optimal position. At the same time, c2r2(Gbestd−zi,dk) —reflect the information sharing among particles.

In this paper, the main steps of BP neural network based on PSO are as follows:

a) Initialization parameters.

Determine the topological structure of the BP neural network, initially set connect the weights and thresholds, and determine the particle swarm dimension D according to the number of weights and thresholds. Set the population size M and the number of iterations N. real code The weights and thresholds of the BP neural network are coded to obtain the initial population. In addition, the particle speed s_i,d and position z_i,d are set within the allowable range [s_min, s_max], [z_min, z_max], and set the learning factors c_1, c₂.

b) The mean square error of each iteration in neural network is taken as the fitness function of particles.

c) According to the steps of particle swarm optimization algorithm, the global optimal position of particles is solved.

d) Check whether the iteration termination condition is met, if satisfied, stop, output the optimal particle, and decode it to get the optimal weight and threshold.

e) Training and prediction according to BP neural network.

a) Input layer design

According to the expert knowledge, the six input neurons are set by selecting the characterization parameters with strong correlation with the sticking: hook load, standpipe pressure, torque, rate of penetration, rotary speed, and weight on bit.

b) Output layer design

This paper mainly deals with the identification of sticking. It only needs to judge whether it occurs and how likely it will happen. Therefore, there are two output neurons: expected output vector of sticking q₁ = (1, 0), expected output vector of no sticking q₂ = (0, 1).

c) Hidden layer design

In this paper, the number of hidden layers is set to 10 through research, and the result is most consistent with the actual situation.

Finally, the BP neural network structure is established, as shown in Fig. 1.

a) Particle coding

The structure of neural network is 6-10-2, as shown in Fig. 2. Therefore, there are 6 × 10 + 10 × 2 = 80 weight vectors and 10 + 2 = 12 threshold vectors. The number of particle swarm optimization parameters is 92, and the particle length is 92.

In this paper, the vector coding is used, and particle i is encoded as follows:

(10) particle(i)=[w10,1⋯w10,6⋯w19,1⋯w19,6,w20,10⋯w20,19⋯w21,10⋯w21,19,β10,1⋯β19,6,β20,1⋯β21,6]

b) Fitness function

The root mean square error of BP network training is taken as fitness function:

(11) MES=12M∑i=1M∑k=1l(yj,i−qj,i)2

c) Data processing

To avoid the increasing error of network prediction result caused by the large difference of input and output data, the data normalization is carried out. In this paper, the minimum-maximum method is used for normalization [16,17]:

(12) xk=(xk−xmeanxvar)

In formula, x_min, x_max—minimum and maximum values of logging data.

The elements of BP neural network and particle swarm optimization algorithm in the early warning model of sticking are set, as shown in Table 2.

Based on the logging and well history data of seven sticking wells in South Sichuan shale gas work area (XX-1, XX-2, XX-3, XX-4, XX-5, XX-6, and XX-8), the sixteen sets of working condition data are selected as samples, eight sets of data correspond to sticking and eight sets of data correspond to no sticking. The comprehensive logging parameters monitored in given time period before and after the occurrence of sticking are selected and normalized according to the minimum-maximum method. The results are shown in Table 3. The first twelve groups of samples are selected as training samples to train the model, and the other four groups of samples as verification samples to verify the accuracy of the model.

The training results of the sticking model are shown in Table 4. The conclusions are listed below: the simulation results are consistent with the actual downhole state, which shows that the training model can be applied to the early warning of sticking in the block.

To verify the accuracy of the developed early warning model, the being drilled WY-XX well in South Sichuan work area is selected for trial analysis. In the process of drilling in the fourth spud horizontal section, the sticking early warning model developed in this paper was used to conduct the real-time diagnosis of sticking. The probability of the sticking fault diagnosed at 4279 m was high (as shown in Table 5), and the drill sticking early warning information was timely sent to the driller operator. After drilling the column to 4280 m, the technicians took corresponding measures to avoid sticking. Thus, the possible sticking was effectively avoided. The field test application showed that the model developed in this paper can diagnose the sticking in real time, and the accuracy and efficiency of risk identification can meet the needs of field drilling operations and effectively ensure the safety of drilling operations.