Overview of Foundation Soil

The high plateau airport studied is located in Kangding area of Sichuan Province. This area belongs to the eastern margin of the Qinghai-Tibet Plateau. Influenced by the uplifting of the continental plate and the down-cutting of the river, the complex land-forms such as high mountains and deep valleys have been formed.

Indoor tests can obtain the mineral composition characteristics of the foundation soil and the basic physical and mechanical properties of the foundation soil when applied to practical engineering, and these characteristics often reflect the post-construction settlement properties of the foundation soil. Therefore, when the prediction of foundation soil settlement is carried out in this paper, the relevant indoor test results are analyzed first.

The foundation soil in the airport area is mainly quaternary alluvial silty clay (Fig. 1). The variation of mineral components (montmorillonite and illite) of foundation soil at different depths was obtained by the laboratory XRD tests, which were shown in Fig. 2. In airport engineering, the deformation of foundation soil usually changes obviously only when it reaches a certain load condition. In order to clearly analyze the deformation of foundation soil at different depths, soil with a certain load gap should be selected for research. A large number of practical projects show that the change of foundation soil is more obvious when the depth spacing is 5m. Therefore, the depth of the soil samples selected in this paper is 5 m, 10 m, 15 m, 20 m and 25 m respectively. The basic physical properties of foundation soil with different depths are obtained, which were shown in Table 1.

Fig. 2.

Variation law of mineral components of foundation soil with foundation depth of high plateau airport. a) The content of Montmorillonite, b) The content of illite.

Training Data Samples

Two test sections (Section A and Section B) were selected in the airport yard area, and each section was buried with stratified settlement meters to measure the settlement of foundation soil. By taking 60 days’ site monitored values as training samples, the modified LSTM model and BP model are constructed respectively, and the 90-day, 120-day and 240-day of foundation settlement are analyzed by using the established models. In the prediction process of the two models, when the sample data training is carried out, the learning rate of the training process is 0.01, and the sample convergence error is 10-5.

According to the actual engineering situation of foundation soil, settlement should be observed every two days. The monitoring data of foundation settlement in the first 60d is shown in Fig. 4.

Fig. 1.

Field pictures of the foundation soil of High-Plateau Airport in sampling box

Fig. 3.

Test sections of high plateau airport.

LSTM Model

Artificial neural network is a large-scale nonlinear dynamic system composed of many neurons. It has strong nonlinear dynamic processing ability and functions such as large-scale parallel computing, partition storage, self-organization, self-adaptation and self-learning. It can train and learn knowledge from accumulated engineering examples without knowing the distribution form of data and the relationship between variables. The establishment of highly nonlinear mapping relationship among various influencing factors, especially the strong fault-tolerant ability for incomplete or fuzzy random uncertain information, determines that the neural network method has a good application basis in the prediction and analysis of foundation settlement. LSTM model is an improvement on the Recursive Neural Network (RNN) model. Special units of memory cells are used to replace the traditional neurons in the hidden layer to remember the required information and forget the unwanted information. In addition, three gating structures including input gate, output gate and forgetting gate are combined to solve the problem of gradient explosion and gradient disappearance in the process of RNN training. In this paper, a prediction model of foundation settlement based on LSTM neural network is proposed by using the good nonlinear mapping ability and strong learning ability of artificial neural network. It overcomes the disadvantages of the existing linear regression prediction model, and predicts and analyzes the actual foundation settlement.

Fig. 4.

Foundation settlement monitoring rules of two observation sections for 60 days (training samples).

The input gate of each memory cell in the LSTM model determines the probability of new information input at the current stage, that is, the intensity of new input is controlled. The activation function sigmoid layer and tanh layer jointly control the input of new information. The output gate controls the amount of information visible from the current state to the next state, hides the internal hidden state information, and thus generates a new hidden layer. The output of the hidden layer of the previous stage and the input of the current stage in the forgetting gate are times the weight and the state of the memory cells of the previous stage are activated to obtain the memory amount that the memory cells of the previous stage should leave behind, that is, to make a choice of historical information. If the forgetting gate is completely closed, that is, the output of the forgetting gate ft = 0, the history has no influence on the current state. The calculation formula of each gate function is as follows:

In Formula (1)-(3), σ represents generally a nonlinear activation function, such as a sigmoid or tanh function; b_i, b_f and b₀, represents the offset terms of each layer node; Xt is the sample data input at time t; W_i, Wo and W_f are the weight parameters of sigmoid layer, output gate and forgetting gate at time t. Represent the bias vector of sigmoid layer, output gate and forgetting gate, respectively.

Candidate memory cells Ĉ_t at time t are determined by the implied state of the previous time, while memory cells at time t are determined by input gate and forgetting gate [23], i.e

In Equations (4)-(5), bc is the offset term of tanh layer; Wc is the bias parameter of the tanh layer, ⊙ represents matrix multiplication.

The hidden state at time t is determined by the output gate and memory cells passing through the tanh layer. Namely is shown in Fig. 5.

Modified LSTM Model

Genetic algorithm is a random global search and optimization method developed by imitating the biological evolution mechanism in nature. It draws lessons from Darwin’s evolution theory and Mendel’s genetic theory. It is an efficient, parallel and global search method, which can automatically acquire and accumulate knowledge about search space during the search process and control the search process adaptively to obtain the best solution.

The genetic algorithm takes the population as the solution of the problem and generates a new population through the operation of selection, crossover and mutation. Its judgment criterion is fitness function. In the process of searching cycle, it gradually tends to the population with the best fitness value to obtain the solution of the problem.

The genetic algorithm was used to optimize the parameters of LSTM layer, fully connected layer and the number of neurons in each layer of the LSTM model. The root-mean-square error of the test data was used as fitness function to obtain the optimal solution in the search space, and then the modified LSTM prediction model was obtained,which is shown in Fig. 6.

Fig. 5.

Structure diagram of LSTM unit.

Fig. 6.

The flow chart of genetic algorithm.

In conclusion, LSTM optimized by GA has the characteristics of accurate data feature extraction, long-term time series prediction, and highly nonlinear function fitting. Therefore, it is of research value to apply it to airport foundation settlement prediction is shown in Fig. 7.

Evaluation Index of Modified LSTM Model

This paper takes the historical data of foundation settlement as input. The data are divided into training set and test set in a scale of 1:3. The first 25% of the data is used for training, while the remaining 75% of the data is used to evaluate the model. Three evaluation indexes, goodness of fit R², mean absolute error EMA and mean square error ERMS, were used to evaluate the model performance comprehensively. Goodness of fit calculation formula:where, the determination coefficient is represented by R², y is the label value, ŷ is the predicted value, y is the average value, and the value range of R² is [0, 1]. The larger R² is, the stronger the ability of X to explain Y of this chromosome is, and the more likely it is to be passed on to the next generation.

Average absolute error calculation formula:

Root mean square error calculation formula:

Where, y_i represents monitoring data and predicted value, and N represents data sample size.

Fig. 7.

The flow chart of GA-LSTM prediction model.

Parameters Optimization

In the Genetic Algorithm, the size of the attention weight population, the size of the selected subset population ,and the number of the epochs also influence on the convergence and efficiency of the optimization process.In order to obtain more accurate results when determining the number of layers and neurons in the LSTM network using the GA algorithm, we first set the hidden layer number of the model to three and use the Relu function as the activation function. Then, we use SGD, Adam, RMSprop, and Adagrad as the optimization functions respectively, repeat the iteration for 1000 times, and set the learning rate to 0.01 for debugging and optimizing.The optimal parameters are shown in Table 2 and Table 3.

Prediction Steps

BP network is short for Error Back Propagation Network. It consists of input layer, hidden layer and output layer. BP neural network is trained in the way that teachers learn. When a pair of learning modes are provided to the network, the activation value of its neurons will propagate from the input layer to the output layer through each hidden layer, and each neuron in the output layer will output the network response corresponding to the input mode. Then, according to the principle of reducing the error between the desired output and the actual output, from the output layer through the hidden layer, finally, go back to the input layer to correct each connection weight layer by layer. The learning process can be summarized into four processes: pattern forward propagation, error back propagation, cyclic memory training and learning result discrimination. The steps are as follows:

(a) Initialize, give each connection weight, and threshold, give random value between (0,1).

(b) Randomly select a mode pair to provide to the network.

(c) The input (activation value) of each neuron in the intermediate layer is calculated with the input mode, connection weight and threshold, and then the through activation function is used:

Calculate the output of each unit in the middle layer:

Where, Sj=∑i=1nWijai−θj

(d) Calculate the input (activation value) of each element in the output layer with the output, connection weight and threshold of the hidden layer, and then calculate the response of each element in the output layer with the activation function:

Where, lt=∑j=1pVjt·bj−γt(t=1,2,...,q)

(e) Correction error of each unit of the actual output layer of the network with the desired output mode:

(f) Calculate the correction error of the intermediate layer with,

(g) Calculate the next new connection weight between the intermediate layer and the output layer with, and:

Where N is the number of learning times.

(h) Calculate the next new connection weight between the input layer and the intermediate layer with, and:

(i) Randomly select the next learning mode pair to provide to the network and return to step (3) until all m mode pairs are trained.

(j) Randomly select a mode pair from the m learning mode pairs again and return to step (c) until the global error function E of the network is less than the preset value (network convergence) or the number of learning cycles is greater than the preset value (network convergence failure).

(k) End of learning: In the above learning steps, (c)~(f) represents the “forward propagation process” of the input learning mode, (g)~(i) represents the “reverse propagation process” of network error, and (j) and (k) complete the training and convergence process is shown in Fig. 8.

BP Model for Settlement Prediction

When using the BP neural network model for ground subsidence prediction, it is necessary to first establish the nonlinear relationship between the subsidence influencing factor parameters (such as treatment method, thickness of soft soil layer and hard crust layer, embankment height, compression modulus, etc.) and subsidence, and then input the measured subsidence influencing factor parameters of the test point into the trained network to obtain the predicted subsidence. According to engineering experience, factors affecting subsidence mainly include time, ground parameters, fill parameters, ground treatment methods, construction period, etc. After considering the above factors comprehensively and the characteristics of the actual project, three parameters can be selected as inputs to the model. The output data is the subsidence of the foundation.

Settlement prediction according to BP model includes the following four steps,

(a) Establish an appropriate network structure according to the specific problem, that is, determine the number of neurons in the input layer, hidden layer and output layer.

(b) Establish the learning sample set and expected output.

(c) Determine the sample convergence error and train the network until it converges.

(d) Prediction with convergent networks.

It uses the training function “trainglm” and the Levenberg-Marquardt algorithm to train the network. The number of training iterations is set to 1000, and the learning rate is set to 0.01. In this network, the transfer function of the neurons in the hidden layer is set as the sigmoid function “tansig”, and the transfer function of the neurons in the output layer is set as the logarithmic sigmoid function “logsig”.