BP Network for Predicting the TBM utilization

: This paper proposed the idea of combining genetic algorithm (GA) with BP (back propagation) neural network, and establishes the TBM tunneling utilization prediction model based on BPNN-GA. Based on the analysis of rock parameters affecting TBM utilization, the rock mass grade, uniaxial compressive strength UCS and joint spacing DPW are selected as the input parameters for TBM utilization prediction. The TBM utilization prediction model based on BPNN-GA is established. The node number and super parameters of hidden layer are determined by empirical formula. The prediction results of bpnn-ga model are combined with the traditional BPNN model The results show that, compared with the traditional BPNN model, BPNN has been improved under the optimization of genetic algorithm, the prediction accuracy on the test set is increased by about 8.95%, and the mean square error is reduced by about 60%. BPNN-GA model does not rely on specific data sets in prediction, showing good portability and generalization.


Introduction
As urban construction develops， TBM has become very important. As the TBM technology improves and tunnel projects tend to be deeper and longer in distance, TBM is more widely applied in tunnel construction through time.
TBM utilization is the ratio of TBM net excavation time to total working time, which is an important performance index. The utilization is about 5% under difficult and complex geological environment or accident in field occurs. In perfect working condition the utilization can rise to 55%. And most common utilization ranges from 20% to 30%. This indicates that the net excavation time of TBM is only 6 to 8 hours per day. Most of the working time is spent on the maintenance and repair of TBM. Meanwhile, staff transfer, initial payment and material transportation also take up part of the time. The total downtime usually accounts for 70-80% of the total time. TBM utilization rate can evaluate the construction progress and construction period, and indirectly provide scientific basis for the construction party to adjust the construction scheme in time. Researchers have established different prediction models for TBM utilization rate prediction.
Based on the data collected from Karaj tunnel, O. Frough [1] established the relationship between rock mass classification system and TBM utilization rate based on regression analysis. The study shows that the maximum downtime related to rock quality occurs in broken rock and fault zone (at this time, RMR is the lowest). In the region where RMR is about 60, the downtime is the shortest. global optimal solution through efficient parallel heuristic search. Therefore, we adopt GA to BPNN optimization to effectively avoid the algorithm falling into local optimum and improve the prediction accuracy.

A brief introduction of BPGA-NN
Neural network is a mathematical model that imitates human brain or biological information processing mechanism in different degrees and levels. It integrates algorithm and structure, and is used to solve nonlinear and uncertain problems [8]. As shown in Fig. 1, BP neural network is a typical multilayer feedforward neural network. Its main characteristics are: the process of forward propagation of input data and the process of error back propagation constitute a learning process of BP neural network. Forward propagation makes the input information transmit to the output layer under the corresponding weight threshold and activation function.
If the error between the output and the actual value exceeds the set value, the weight and deviation are modified by gradient descent for retraining using back propagation. The above process is repeated until the output value meets the sufficient accuracy [9]. The calculation process of hidden layer output and output layer output is shown in formula 1.1 [10] and equation where , stand for the output of jth hidden layer and output layer respectively. ℎ , stand for the activation function of hidden layer and output layer respectively.
stands for the j-th weight parameter of i-th layer. is the threshold value of network layer.
x is the input of the network.

Fig. 1 Neuron calculation diagram
BP neural network uses parallel distributed processing of information. It has good fault tolerance, self-learning, self-adaptive and generalization capabilities. However, BP neural network also has shortcomings such as low convergence efficiency, easy to fall into local minimums. The basic reason lead to different training results may be that BPNN is easy to fall into local minimums. Generally speaking, BPNN uses the gradient descent method to adjust the weighting parameters. This method optimizes the training errors along the direction where gradient decent. However, when the weighting parameters trap the network into a local minimums, the method cannot jump out of the local optimal solution for further search.
Therefore, the method is more dependent on the initial weights of the network, resulting in limited training accuracy.
Different from BP neural network, genetic algorithm can effectively avoid the situation that the optimization process falls into local minimums. Genetic algorithm is a heuristic global On the one hand, genetic algorithm initializes a group of weight parameters randomly, which is regarded as a population, which means that the genetic algorithm is operated from many random points, rather than limited to a certain region; on the other hand, the genetic algorithm can carry out efficient heuristic search in the solution space, and at the same time, the probability is not limited to a certain area. Hence the optimal global solution is obtained by deterministic state transition rules. In addition, genetic algorithm also has the advantages of parallel computing, and does not rely on gradient information. Therefore, genetic algorithm and neural network algorithm can be nested to effectively prevent the weight parameters from converging to local minimum in model training.
Based on the above analysis, the optimization of BP neural network algorithm has precision, but as a single-point search method, BP neural network algorithm is easy to fall into the local optimal solution, while the genetic algorithm can evaluate multiple solutions in the search space, and has strong global search ability. Therefore, the initial solution of the optimal weight parameter can be obtained by genetic algorithm, and its decoding can be brought into the model training of BP neural network to obtain a better training model.Applying this training model to the prediction of TBM utilization rate can not only ensure the accuracy of utilization rate prediction, but also avoid the problem that the BP neural network algorithm falls into local optimum [11] [12]. Fig. 2 is the flow chart of BPNN-GA algorithm.

Fig. 3.2 Genetic algorithm optimization neural network algorithm flow
Genetic algorithm searches the optimal solution of initial weight parameters of BP neural network through continuous iteration. Firstly, genetic algorithm needs to "code" the weight parameters in BP neural network, that is, the combination of weight parameters is transformed into a "chromosome". Selecting appropriate coding method can simplify the subsequent crossover and mutation operation of genetic algorithm. In this paper, according to the characteristics of parameters, the genetic algorithm is coded by real number coding to optimize the connection weights and thresholds of BP neural network. A coding string represents an individual, and several individuals constitute the initial population. The initial population performs the process of selection, crossover and mutation of genetic algorithm, and continuously generates a new generation of population. Real coded crossover is shown in Eq. 2.1 and Eq. 2.2: where C and D are the offspring of A and B, and t is a random number in the (0,1) interval.
(1 ) After coding the weight parameters, the genetic algorithm optimize the weight parameters in follow steps: 1. Initialize the population. It includes mutation probability Pm, crossover probability Pc and crossover size; real number is used in coding, and the size of the initial population is set as 50; 2. Individuals are ranked according to the evaluation function. The evaluation function is used to measure the probability that an individual can survive in the whole population, that is, the ratio of individual fitness to population fitness. As shown in Eq. 3.1 [13]. The higher the individual's fitness, the easier it is to retain the individual, otherwise it is easy to be eliminated 8. After the individual meets the relevant requirements, the final optimal individual is decoded. As a result, there may be landslides and falling blocks in the process of excavation, which will lead to the shutdown of TBM and the decrease of utilization rate. When the joint spacing increases, the rock breaking efficiency will gradually decrease, and the utilization rate will also decrease [23] [24]. To sum up, we select surrounding rock grade, uniaxial compressive strength and joint spacing as input parameters of utilization.

Factors affecting utilization
According to the change of surrounding rock grade, the whole tunnel is divided into 240 sections, and then the utilization rate of each section is calculated according to the daily construction records of each section. The information of surrounding rock grade, average rock mass parameters and average operation parameters corresponding to the section are obtained are used as the input parameter data in the utilization rate prediction.

Fig. 2 BP neural network structure
Funahashi [25] pointed out that if a three-layer neural network is used, the input layer and output layer use linear mapping function, and the hidden layer uses nonlinear incremental mapping function, then the network can be used to approximate any continuous function.
Hence in this study, a three-layer BP neural network is applied.
The loss function is usually used to measure the training quality of the model. In this paper, mean square error (MSE) is adopted. Assuming the number of data samples is N and the training data (actual value) is . The predicted output value of neural network is ^.
Then the mean square error loss function of BP neural network prediction is shown in Eq. 4 [26]. The lower MSE indicates better accuracy on training set. Generally speaking, the smaller the learning rate is, the smaller the step size is, the more epochs the model needs to trained; if the learning rate is too large, the iterative step size will reduce the training time, but it will affect the accuracy of the network structure and cause large training errors. It is necessary to adjust the model parameters continuously to find the model with the minimum test error.
In h = m n a (5) Where h is the number of hidden layer nodes; m is the number of input layer nodes; n is the number of output layer nodes; a is the adjustment constant between 1 and 10.
Firstly, set a small number of hidden layer neurons to train the network and record the prediction accuracy of the network; secondly, gradually increase the number of hidden layer neurons, and train with the same sample data, the number of hidden layer neurons that can make the output error of the network minimum is the optimal number of neurons; finally, through error comparison, it is concluded that the best effect is when the number of nodes is set to 10. The learning rate and the selection of activation function is tested through a large number of experiments, it turns out that when the learning rate is 0.01 and the activation function is Tansig function, the training effect of the network is the best. The specific parameter analysis is shown in Table 1.
In addition, for genetic algorithm, the size of the initial population, genetic generation, mutation rate, crossover rate has an impact on the prediction effect of the algorithm. In the process of parameter adjustment, population size is 10 ~ 50, step size is 10; iteration steps are 30 ~ 100, step size is 10; mutation rate is 0.01 ~ 0.05, step size is 0.01; crossover probability is 0.5 ~ 1, step size is 0.1, a total of 90 parameter groups are selected to test the combination of these parameters. The super parameters of the optimal model are shown in table 2.

Fitness and error analysis
According to the change of surrounding rock grade, the whole tunnel is divided into 240 sections. The utilization rate of the section and the corresponding surrounding rock grade, average rock mass parameters and average operation parameters are calculated according to the daily construction records of each section, and 240 groups of utilization data are obtained.
150 of them are randomly selected as the training set, 30 data point from the remaining 90 are randomly selected as the test set, and the last 60 groups of data are used as the validation set.
Both the test set and the validation set data do not participate in the network training process, but are used to reflect the network prediction effect after the network training. Table 3 shows the percentage distribution of utilization datasets.  But compared with BP neural network algorithm, due to the complex structure of BPNN-GA network, the data processing process involves encoding, decoding and other operations, which greatly increases the complexity of data processing, prone to a long time-consuming problem.

Comparison of prediction accuracy
In order to compare the two algorithms and evaluate the prediction results directly and accurately at the same time, the MSE and the mean absolute percentage error (MAPE) were used to evaluate the prediction results of the two models. The comparison chart of predicted data and actual data of the two models is shown in Fig. 6(a), the absolute percentage error of single point prediction data is shown in Figure 6 (b), and the comparison chart of MSE of single point prediction data is shown in Figure 6 (c).    From figure 6 (b), it can be seen that the percentage error of 17 sample points of the traditional BP neural network prediction value is more than 20%, the percentage error of 6 sample points is more than or close to 30%, and the maximum percentage error is 49.99%; while the percentage error of only 5 sample points is more than 20%, and the percentage error of 2 sample points is more than or close to 30%. The maximum percentage error is 44.05%. In addition, the percentage error of 22 samples predicted by BPNN-GA model is lower than that predicted by BP neural network. of BPNN-GA model is lower than that of BP neural network. In conclusion, for the test set, after the optimization of genetic algorithm, BPNN-GA has achieved better prediction effect, and BPNN-GA model has better stability and higher fitting degree.

Discussion and Conclusion
In view of the disadvantage of BPNN easily falling into local minimum value, this paper selects GA optimized BPNN algorithm to predict the utilization rate. It shows that the BPNN-GA model in this paper is not picky in the selection of data, and has good generalization. However, when BPNN-GA is applied to predict TBM utilization rate, some data points still have low prediction accuracy. Therefore, in further research, we will focus on strengthening the research on the factors affecting TBM utilization, and constantly improve the prediction accuracy.

Conclusion
The geological conditions, rock mass properties, and machine parameters h