The prediction of foundation pit based on genetic back propagation neural network

Abstract

Predicting the deformation of the foundation pit is one of the key issues for the construction safety of the foundation pit. In the traditional construction process often neglects the deformation prediction. It will cause the best time of repairing the pit is often missed. BP neural network has the characteristic of markova chain which is exactly match temporal-series data collected from displacement monitoring. So the BP neural network can understand the data better than SVM and RF. Further, the GA-BP neural network improved the training process based on BP neural network. We proposed a GA-BP neural network to predict the deformation of the foundation pit. To enforce the validation of the performance, we collected the real data from the Zhoushan foundation pit project. Compared with support vector regression and random forest regression, the results showed that GA-BP method has the error basically within $-$ 0.05–0.05 mm, the maximum relative error 0.36% and the predicted fitting value IA above 0.9, which are obviously better than other two methods.

Keywords

Foundation pit monitoring genetic algorithm BP neural network time series and spatial features

1. Introduction

With the rapid development of the infrastructure industries in modern cities, the construction market has continued to expand. The construction of office buildings, shopping malls, and schools has also increased the number of foundation pit projects. The safety issues caused by the foundation pit projects have also received attention. The monitoring of the foundation pit problem has become one of the hot spots in the current research. In recent years, the monitoring methods in the construction process of the foundation pit have also been continuously improved. The BP neural network shows a good ability of self-adaptation and real-time learning in solving some engineering applications [1]. The nonlinear problem has a wide range of applications, it has also become one of the important artificial intelligence technologies for monitoring the deformation of the foundation pit. In the process of excavation, the foundation pit will bring about problems of its own slope, surrounding buildings and groundwater level settlement [2]. In order to ensure the safety of foundation pits and avoid personal safety accidents and property losses, we generally need to predict the level and settlement displacement deformation of the foundation pit project. X. Wang and J. Wang proposed an optimized support vector machine-chaotic BP neural network model to predict the deformation of foundation pit. According to case study results, the de-noising effect of the wavelet functions are relatively superior and the mean relative error of the prediction results are less than 2% [3]. Wang et al. proposed a Bayesian method for predicting the settlement of foundation pits by using discrete test data to update semi-empirical models. The results show that the accuracy of the maximum settlement prediction can be improved and the model uncertainty can be reduced by the Bayesian method [4]. Zheng et al. used the BP neural network to predict the deformation of a certain foundation pit. The results show that the BP neural network can effectively predict the deformation and stability of the deep foundation pit [5]. However, it is found that the initial network weight has a great influence on the network weight. Each training algorithm has different initial weights, and the result converges to the local minimum.

The genetic algorithm is a parallel random search method that simulates the natural genetic mechanism. In the search process, unlike the BP neural network, it is not easy to converge to a local minimum, which can help BP neural network to determine the initial value quickly and accurately and then quickly find the optimal solution [6]. Therefore, this paper combines the genetic algorithm with the BP neural network and applies the improved algorithm to the Zhoushan pit project deformation prediction. In the past, scholars used BP neural networks to predict only from single-factor (such as time series) pits. This paper not only considers the time series as an influencing factor, but also considers the impact of adjacent pits on Zhoushan pit monitoring. We use these factors as the training samples of the algorithm respectively and use the BP neural network optimized by the genetic algorithm to run on MATLAB to verify the feasibility of the combination of the genetic algorithm and the BP neural network.

2. Method

2.1 Framework for multidimensional error compensation

BP neural network is also known as backpropagation neural network. It was proposed by Rumelhart et al. in 1986 [7]. In order to reduce the global error coefficient to the minimum, the algorithm propagates backwards through each layer of the neural network and adopts the rapid descent method to constantly adjust the weights and thresholds of the network [8]. The BP neural network is mainly composed of one input layer $L_{A}$ , one or more hidden layers $L_{B}$ , and one output layer $L_{C}$ . The connection weights of the input layer to the hidden layer are set $v$ , and the connection weights of the hidden layer to the output layer are set $w$ . The threshold of the hidden layer is $\theta$ and the threshold of the output layer is $\gamma$ . During the training process, the model repeats to generalize the error among each unit, correction right $w$ and the threshold value $\gamma$ to adjust the connection weight $v$ and gate threshold $\theta$ , until the network convergence is obtained.

The genetic algorithm was proposed by professor Holland from the University of Michigan in 1962. Genetic algorithm is a parallel random search method that simulates the natural genetic mechanism. It extends the coverage of the problem solution and the diversity of search direction [9]. It is a nonlinear global optimization algorithm inspired by biological evolution mechanisms (survival, crossover, mutation, etc.). The algorithm starts from any initial population and it effectively achieves a stable breeding and selection process through individual genetics and mutations. Genetic algorithm can process different individuals in the population simultaneously and guide the search direction of the algorithm according to the principle of uncertainty. It can effectively prevent convergence to the local optimal solution in the search process [10, 11], thus overcoming the disadvantage of BP neural network easily falling into the local optimal solution. The main implementation flow chart of genetic algorithm optimization BP neural network is as follows:

Figure 1.

The flow chart of GA-BP neural network model.

According to the flow chart algorithm, the main implementation process is as follows:

The algorithm combines the threshold with the weight of the neural network, and the neural network weights and thresholds are binary real coded [12, 13]. Let the total group population be N, each individual in the population consists of a real string containing the weights and thresholds of the neural network. We use genetic algorithms to optimize the initial weights of BP neural networks and obtain the best BP neural network parameters.

The fitness function is a function to evaluate the individual quality. We take the sum E of the absolute value of the predicted output value of the BP neural network and the expected output value as the individual fitness value F [14]. The calculation formula of F is:

$\displaystyle F={\rm k}\left(\sum\nolimits_{i=1}^{n}{\textit{abs}}(y_{i}-{\rm o% }_{i})\right)$ (1)

In Eq. (1), $n$ is the number of output nodes, $y_{i}$ is the output of the $i$ -th node of the BP neural network, $o_{i}$ is the expected output value of the node, and $k$ is the coefficient.

Selective operation is also known as “recombination” operation. Individuals with higher fitness values in the population are more likely to produce one or more offspring, so individuals with the best fitness values in the current population are replicated to the next generation. Genetic algorithm selection operation is generally used in the roulette selection method (based on the selection strategy of the fitness value in the proportion of the total fitness) [15], so that the probability of selection for the individual is, and the calculation formula is as follows:

$\displaystyle fi=\frac{k}{F_{i}}$ (2) $\displaystyle p_{i}=\frac{f_{i}}{\sum\nolimits_{j=1}^{N}{f_{j}}}$ (3)

In the formula, $F_{i}$ is the fitness value of the individual $i$ , where the reciprocal value of coefficient $k$ is $f i$ , $N$ is the individual number of the population.

The crossover operation also uses the real number method to cross and exchanges points on the chromosomes of the two individuals to generate new individuals, which helps to improve the convergence speed in the algorithm optimization process [16, 17] Let the value at $j$ th position of $k$ th chromosome $a_{kj}$ intersect with the value at $j$ th position of and the $l$ th chromosome $a_{lj}$ as follows:

$\displaystyle a_{kj}=a_{kj}(1-b)+a_{lj}b$ (4) $\displaystyle a_{lj}=a_{lj}(1-b)+a_{kj}b$ (5)

where $b$ is a random number between [0,1].

The mutation operation sets a certain probability in the population evolution process to select individuals in the population, and then mutates the chromosomes to prevent the algorithm from falling into a local optimal solution [18]. Let $a_{ij}$ be the $j$ -th gene on the individual $i$ . It uses the following formula for mutation:

$\displaystyle a_{ij}=\begin{cases}a_{ij}+(a_{ij}-a_{\max})\times f(g),&r>0.5\\ a_{ij}+(a_{\min}-a_{ij})\times f(g),&r\leqslant 0.5\\ \end{cases}$ (6) $\displaystyle f(g)=r\left(1-\frac{g}{G_{\max}}\right)^{2}r$ (7)

In the formula, $a_{\max}$ is the upper bound of gene $a_{ij}$ , $a_{\min}$ is the lower bound of gene $a_{ij}$ , let $f(g)$ is a random number, $G_{\max}$ is the maximum number of evolutions, $g$ is the number of iterations, and $r$ is between [0,1] random number.

Finally, the evolution of the algorithm continues until the fitness value is less than the termination criterion or converges to a value, or the generated quantity reaches a fixed generation time. We use the optimal weight threshold as the initial weight threshold of the BP neural network to train the network until the error reaches the set value output, otherwise, the program will restart.

2.2 Foundation pit data summary and network design

The first phase project of Zhoushan Cultural and Creative Industrial Park is located on the west side of Suzhou Taihu National Tourism Resort Administrative Committee, south of Sunwu Road, east of Yaoshe Road and south of Houtang Road. Suzhou has a subtropical monsoon climate with heavy rainfall and mild humidity. The groundwater in the depth of the proposed site is the pore-type diving, micro-confined water and fissure water in the soil. The total construction area of the project covers an area of 11,8306.9 m ${}^{2}$ , of which the basement building area accounts for 35,097.65 m ${}^{2}$ .

Except the surface layer filling, the remaining soil layers of the foundation pit project are all lacustrine sedimentary layers and alluvial-diluvial layers, mainly composed of cohesive soil and silty soil. The site belongs to different micro-geological units and can be divided into normal deposition areas and lime-soil deposition areas. In order to accurately reflect the deformation of the top of the retaining structure, we monitor the buried monitoring points on the top of the retaining foundation pit structure, using the studs or the steel bar with a length of about 10 cm to guide the crosshairs, and the points are concrete reinforced [19]. Prior to this, we did a lot of pre-research work and used a multi-dimensional error compensation method to locate the monitoring center of Zhoushan pit engineering. The results showed that the centers determined after compensation were closer to the actual target than the original centers [20].

In the monitoring project of Zhoushan, Y1–Y103 points are monitoring points for horizontal displacement and vertical displacement at the top of the slope, G1–G24 points are monitoring points for pipeline settlement, S1–S5 points are monitoring points for groundwater level, and points D1–D40 are settlements for surrounding roads. The horizontal displacement monitoring point Y20 at the top of the slope is selected as the research object and cumulative monitoring data from November 5, 2015 to July 30, 2016 are used. The reason of choosing Y20 as the key point is based on three point. Firstly, Y20 point is in the corner of the pit, and the movement from neighbor monitoring points will directly influence on the Y20 displacement. Section 20 has a better viewing for monitor the displacement than the others. Lastly, in the actual dataset, the monitoring data of Y20 and its neighbors’ is intact, while others monitoring points have missing data. After three days of continuous measurement, we take the average value as the initial value (the subsequent measurement variables are based on the initial value). At the same time, a prediction model of the foundation pit deformation based on BP neural network and genetic algorithm is established.

We select the monitoring point for the top displacement of the Zhoushan pit project and its 10 adjacent monitoring points, which based on the deformation monitoring data from November 5, 2015 to July 30, 2016. We use the input time series features for the last 5 days of the Y20 point in the sample data, and the displacement of the day after the neighboring point Y15–Y19, Y21–Y25 as input spatial features to predict the displacement of the Y20 point in the next day.

The network training sequentially takes five samples of the time series feature as sliding windows and maps them into one-day values, November 5, 2015 (the first day), November 6 (the second day), and November 7th (the third day), November 8th (the fourth day), and November 9th (the fifth day) of the month, the Y20 displacement changes 5 data, and the spatial feature 10 samples use Y15–Y19 on November 10. The displacements of Y21–Y25 points are used to predict the deformation value on November 10 (day 6) and the combination of time series features and spatial features with 15 samples as network input samples, and so on. A total of 186 sets of data were constructed. 85% of the sample data is the training sample, and the last 15% of the data is the prediction sample. Deformation of the first five time points of the monitoring point Y20 and the displacement of each of the five monitoring points before and after the adjacent pit have become the input features. When both the time series and the adjacent points are used as input factor influencing factors, the number of input layer units is 15, the number of output layer units is 1, the number of hidden neurons is 8, the learning rate is 0.05, the training target is 0.001. Table 1 shows the input and output layer design of the space-time series feature combined with the network:

Table 1
Network input and output layer design

No	Input layer	Out put layer
1	$Y20_{(1)(2)(3)(4)(5)}Y15-19,21-25_{(6)}$	$Y20_{(6)}$
2	$Y20_{(2)(3)(4)(5)(6)}Y15-19,21-25_{(7)}$	$Y20_{(7)}$
…	…	…
$n$	$Y20_{(n)(n+1)(n+2)(n+3)(n+4)}Y15-19,21-25_{(n+5)}$	$Y20_{(n+5)}$
…	…	…
186	$Y20_{(186)(187)(188)(189)(190)}Y15-19,21-25_{(191)}$	$Y20_{(191)}$

Figure 2.

Network training structure topology model.

Among them, $Y20_{(n)}$ is the horizontal displacement deformation value of the $Y20$ point of the $n$ -th day, $Y15-19,Y21-25_{(n)}$ is the horizontal displacement deformation of the $Y15$ point to the $Y19$ point and the $Y21$ point to the $Y25$ point of the $n$ -th day. When both the time series and the adjacent points are used as input factor influencing factors, the number of input layer units is 15, the number of output layer units is 1, the number of hidden neurons is 8, the learning rate is 0.05, the training target is 0.001. At the same time, the training parameters such as the minimum root mean square error are set, and then BP neural network training is performed. The structure topology is described in the Fig. 2.

2.3 Foundation pit prediction method based on genetic BP neural network

Taking the horizontal displacement monitoring point Y20 of the Zhoushan pit as the research object, using the accumulated monitoring data of the Y point from November 5, 2015 to July 30, 2016, the prediction model of the foundation pit deformation based on the GA-BP neural network was established and applied. We used MATLAB to write the program according to the above Fig. 1.

The main steps are as follows:

(1) (1)
For sample data preprocessing. Since the value range of the S-type transfer function (tansig or logsig function) is between ( $-$ 1, 1), we use 0.8 and 0.1 to normalize the value to (0.0, 0.9].

$\displaystyle X^{\prime}=0.8\times\frac{X-X_{\min}}{X_{\max}-X_{\min}}+0.1$ (8)

In the formula, $X$ is the normalized value of the sample, $X_{\max}$ is the maximum value in the sample data, and $X_{\min}$ is the minimum value in the sample data.
(2)
Create a new BP neural network using the newff function in the neural network toolbox [21]. The calling form of the newff function is:

$\displaystyle\textit{net}=\textit{newff}[PF,\left[{\textit{S1S2\ldots Si}}% \right],\left\{{\textit{TF1 TF2\ldots TFi}}\right\},\textit{BTF},\textit{BLF},% \textit{PF}]$ (9)

Among them, $P F$ is set to the mean square error “mse”, which are $R\times 2$ dimensional matrix composed of the maximum and minimum values of each group of input ( $F$ groups in total), and the number of cells in the $i$ layer is 2; the transfer function of the second layer is TFi; The training function is BTF, set to “trainlm”; the learning algorithm is BLF, set to “learngdm”.
(3)
The parameters of the genetic algorithm are initialized and the population is initialized. The number of iterations of the genetic algorithm is 10, the crossover probability is 0.7, and the mutation probability is 0.25.
(4)
Through the selection, crossover, and mutation operations in the genetic algorithm, the best chromosome in the previous iteration is replaced, the optimal weight threshold is obtained, and the best fitness and average fitness in each iteration are recorded [22]. Terminated at the maximum number of iterations.
(5)
The BP neural network is assigned the optimal initial weight threshold obtained in the above steps, and the displacement deformation of the Y20 point of the foundation pit is predicted.

The BP model optimized by the genetic algorithm were respectively run in MATLAB and the results of the network denormalization were output. The experiments also respectively performed the combination of different features as only the time features only the spatial features, and the combination of time and spatial features. Simulations have verified that it is better to use neighboring points as input feature prediction results. In order to strengthen the verification experimental results, this paper compared genetic algorithm neural network with Support Vector Regression (SVR), Random Forest (RF) and BP neural network. In addition, the Root Mean Squared Error (RMSE) and Index of Agreement (IA) are used as evaluation metrics [23]:

$\displaystyle\textit{RMSE}=\sqrt{\frac{\sum\nolimits_{i=1}^{n}{(X_{\textit{obs% , i}}-X_{\textit{pred, i}})^{2}}}{n}}$ (10)

Where $n$ is the total number of samples, $X_{obs,i}$ is the actual value of the $i$ -th sample, and $X_{\textit{pred, i}}$ is the predicted value of the $i$ -th sample.

$\displaystyle IA=1-\frac{\sum\nolimits_{i=1}^{n}{(X_{\textit{obs, i}}-X_{% \textit{pred, i}})^{2}}}{\sum\nolimits_{i=1}^{n}{(|X_{\textit{{pred, i}}}-% \overline{X_{\textit{obs}}}|+|X_{\textit{obs, i}}-\overline{X_{\textit{obs}}})% ^{2}}}$ (11)

where $\overline{X_{\textit{obs}}}$ is the average of all actual values in the samples.
3. Experiments and discussions

3.1 Comparison of time series and spatial feature prediction

The program predicts the horizontal displacement of Y20 point from the time series features, the spatial features and the combination of time series features and spatial features. The normalized output is shown in Fig. 3a. The BP neural network model predicts the simulation values and actual monitoring values of the horizontal displacement of Y20 points in the time features, spatial features and combination of time series features and spatial features. Figure 3b shows the simulated and actual monitored values of the GA-BP neural network model optimized by genetic algorithm for predicting the horizontal displacement of the Y20 point in the same three cases. Table 2 shows the predicted mean square error and the fit index between BP model and GA-BP model under three conditions.

Table 2
Comparison of prediction accuracy between BP model and GA-BP model

BP model/GA-BP model	RMSE (BP/GA-BP)	IA (BP/GA-BP)
Time features	0.0959/0.0649	0.8907/0.9027
Spatial features	0.1311/0.0811	0.8691/0.9152
Combination	0.0357/0.0153	0.9131/0.9835

Table 2 indicates that the GA-BP model with combination of the time features and spatial features is more consistent than BP model and does not affect the training duration. In this paper, a total of 30 experimental predictions were made. The average of 30 results was used as the result.

3.2 Comparison between BP model and GA-BP model

The comparison of the output values of the two models with the measured values and the relative error RE (%) is shown in Table 3 (the results retain two decimal places).

Table 3
Comparison of displacement and RE between BP and GA-BP model

No	Actual value (mm)	BP (mm)	RE (%)	GA-BP (mm)	RE (%)
1	26.68	26.82	0.5382	26.75	0.2464
2	26.75	26.91	0.6075	26.78	0.1174
3	26.77	26.98	0.7856	26.87	0.3624
4	26.96	27.06	0.3694	26.92	$-$ 0.1304
5	27.03	27.11	0.3049	27.04	0.0191
6	27.10	27.22	0.4403	27.09	$-$ 0.0328
7	27.13	27.32	0.6866	27.14	0.0321
8	27.19	27.36	0.6019	27.24	0.1533
9	27.39	27.38	$-$ 0.0347	27.34	$-$ 0.1927
10	27.45	27.39	$-$ 0.2310	27.45	$-$ 0.0189
11	27.57	27.52	$-$ 0.2071	27.53	$-$ 0.1445
12	27.66	27.64	$-$ 0.0680	27.63	$-$ 0.0912
13	27.70	27.73	0.0895	27.70	$-$ 0.0014
14	27.79	27.77	$-$ 0.0936	27.79	$-$ 0.0091
15	27.91	27.89	$-$ 0.0885	27.86	$-$ 0.1984
16	28.01	27.94	$-$ 0.2506	27.97	$-$ 0.1678
17	28.09	28.01	$-$ 0.3062	28.05	$-$ 0.1510
18	28.15	28.13	$-$ 0.0878	28.13	$-$ 0.0946
19	28.25	28.20	$-$ 0.2028	28.19	$-$ 0.2423
20	28.29	28.26	$-$ 0.1184	28.25	$-$ 0.1678
21	28.31	28.32	0.0211	28.28	$-$ 0.1239
22	28.34	28.38	0.1182	28.31	$-$ 0.1239
23	28.35	28.41	0.1975	28.32	$-$ 0.1010
24	28.35	28.42	0.2423	28.35	$-$ 0.0131
25	28.35	28.45	0.3477	28.36	0.0396
26	28.40	28.45	0.1781	28.39	$-$ 0.0575
27	28.44	28.44	0.0021	28.42	$-$ 0.0926
28	28.49	28.57	0.2548	28.45	$-$ 0.1630

Among them, the underlined mark represents that the prediction effect of the GA-BP model is better than that of the BP model. The relative error is the ratio of the absolute error of the predicted value to the expected output value and the expected output value. From Table 3, the GA-BP model predicts the value of most prediction results are closer to the measured value (expected output value) than the BP model. The relative error of the BP neural network prediction model is 0.79% at the maximum, while the maximum relative error of the BP model after optimization by the genetic algorithm is 0.36%. The BP model prediction is absolute. The maximum error is 0.21 mm. The maximum absolute error of the BP model optimized by the genetic algorithm is 0.1 mm, and the GA-BP model prediction error basically floats within $-$ 0.05–0.05 mm. The GA-BP model and the BP model predict the mean square error.

3.3 Comparison between GA-BP models and other two models

In order to verify the performance of the experimental results better, the Support Vector Regression (SVR) prediction algorithm and the random forest regression (RF) prediction algorithm were used to input 15 time spatial features as input to the Y20 horizontal displacement deformation of the foundation pit. The SVR model has a penalty factor of 1 and the kernel function selects the ‘RBF’ model, which results the best. The prediction and comparison of the results with the genetic algorithm neural network show that the GA-BP algorithm has the best prediction result. Figure 4 shows the comparison of the GA-BP, RF and SVR models. Table 4 shows the simulation results of the three methods.

Table 4
Comparison between other two methods and GA-BP model

Model	RMSE	IA	Training time/s
SVR model	0.2457	0.6417	10
RF model	0.3215	0.5210	12
GA-BP model	0.0153	0.9835	7

Figure 3.

(a) Horizontal displacement of BP neural network; (b) Horizontal displacement of GA-BP neural network. Comparison of different features of BP model and GA-BP model.

Figure 4.

(a) Displacement comparison; (b) Error comparison. Comparison of GA-BP, RF and SVR models.

According to Fig. 4a and b and Table 4, the prediction effect of BP neural network optimized by using genetic algorithm far exceeds the other two methods. In Fig. 4a, the prediction result of GA-BP model is basically consistent with the expected output value and the SVR model. The error between the RF model prediction and the expected output value is relatively large. It is particularly obvious in Fig. 4b that the SVR model has a prediction error of 0.3 mm or more, and a small part exceeds 1 mm. The RF model prediction error is closer to half than 1 mm and the trend of error tends to trend. It is getting bigger and bigger, but the GA-BP model prediction error has been floating up and down. In Table 4, the root means square error and the fitting index of the two models are far behind the GA-BP model, and the training duration also exceeds that of GA-BP model. It can be seen that the BP neural network optimized by the genetic algorithm is very effective for predicting the deformation of the foundation pit and has reference significance for similar projects. The analysis process and method can also be similarly applied to other projects.

4. Conclusion

In this paper, the BP neural network is optimized by genetic algorithm to simulate the horizontal displacement deformation of Zhoushan foundation pit. The optimization of network weight and threshold in BP neural network makes the performance of the original algorithm greatly improved. The input features not only take into account the influence of time series but also the influence of spatial neighboring monitoring points. The experimental results show that the input characteristics predicted by the interaction are closer to the actual values. We applied genetic algorithm optimization BP neural network to predict pit displacement in actual engineering project. The displacement deformation data of the foundation pit support structure and the actual data deviation are within the range, which has a good practical effect on the foundation pit monitoring and support engineering. The effect also provides a new idea for the pit health monitoring program.

Footnotes

Acknowledgments

The work was supported in part by the Science and Technology Development Project of Suzhou under grant no. SNG201610, SYG201704, the Virtual Reality Key Laboratory of Intelligent Interaction and Application Technology of Suzhou, Suzhou Key Laboratory of Mobile Networking and Applied Technologies and Jiangsu Province Key Laboratory of Intelligent Building Energy Efficiency.

References

and Xu

, A short-term load forecasting model of natural gas based on optimized genetic algorithm and improved BP neural network, Applied Energy 134(134) (2014), 102–113.

Wang

Liu

et al., Field experiment and numerical simulation of coupling non-darcy flow caused by curtain and pumping well in foundation pit dewatering, Journal of Hydrology 549 (2017), 277–293.

Wang

and Wang

, Study of deformation prediction of foundation pit based on optimized support vector machine and chaotic BP neural network, Tunnel Construction 37(9) (2017), 1105–1113 (in Chinese).

Wang

Ravichandran

and Juang

C.H.

, Bayesian updating of kjhh model for prediction of maximum ground settlement in braced excavations using centrifuge data, Computers and Geotechnics 44(3) (2012), 1–8.

Zheng

Z.B.

Liu

J.Y.

et al., Research on prediction of foundation pit deformation and safety control based on neural networks, Journal of Railway Engineering Society 27(9) (2010), 64–68. (in Chinese).

Cao

Ding

W.Y.

Zhao

D.S.

et al., Time series forecast of foundation pit deformation based on BP neural network, Applied Mechanics and Materials (556–562) (2014), 5979–5983.

Rumelhart

D.E.

Hinton

G.E.

et al., Learning representations by back-propagating errors, Nature 323(6088) (1986), 533–536.

Wan

Youhong

X.U.

Feng

et al., Application of genetic algorithms BP neural networks to predicting corrosion rate of carbon steel in co2/h2⁢s envitonment, Corrosion and Protection 38(9) (2017), 727–731. (in Chinese).

Wang

Wei

et al., Fitness-scaling adaptive genetic algorithm with local search for solving the multiple depot vehicle routing problem, Simulation 92(7) (2016), 601–616.

10.

Whitley

Rana

and Heckendorn

R.B.

, The island model genetic algorithm: on separability, population size and convergence, Journal of Computing and Information Technology 7(1) (2015), 33–47.

11.

Huang

S.C.

Jiau

M.K.

and Lin

C.H.

, A genetic-algorithm-based approach to solve carpool service problems in cloud computing, IEEE Transactions on Intelligent Transportation Systems 16(1) (2015), 352–364.

12.

Ganjehkaviri

Jaafar

M.N.M.

Hosseini

S.E.

et al., Genetic algorithm for optimization of energy systems: Solution uniqueness, accuracy, pareto convergence and dimension reduction, Energy 119 (2017), 167–177.

13.

Shahnewaz

Machial

Alam

M.S.

et al., Optimized shear design equation for slender concrete beams reinforced with frp bars and stirrups using genetic algorithm and reliability analysis, Engineering Structures 107 (2016), 151–165.

14.

Garcia

R.D.P.

et al., A rank-based constraint handling technique for engineering design optimization problems solved by genetic algorithms, Computers and Structures 187(C) (2017), 77–87.

15.

Deng

Jiang

Peng

et al., An intelligent outlier detection method with one class support tucker machine and genetic algorithm towards big sensor data in internet of things, IEEE Transactions on Industrial Electronics PP(99) (2018), 1–1.

16.

Beg

A.H.

and Islam

M.Z.

, Novel crossover and mutation operation in genetic algorithm for clustering, 2016 IEEE Congress on Evolutionary Computation (CEC), Vancouver, BC, Canada, 2016, pp. 2114–2121.

17.

Rashid

M.A.

Khatib

Hoque

M.T.

et al., An enhanced genetic algorithm for ab initio protein structure prediction, IEEE Transactions on Evolutionary Computation 20(4) (2016), 627–644.

18.

Guo

and Wang

, Interactive genetic algorithm containing crossover and mutation operation, Computer Engineering 41(3) (2015), 182–185 (in Chinese).

19.

Wang

Feng

et al., Numerical study of dewatering in a large deep foundation pit, Environmental Earth Sciences 69(3) (2013), 863–872.

20.

H.J.

Bian

K.H.

Q.M.

et al., A study on multi-dimension error compensation and application to the foundation pit monitoring, Journal of Computational Methods in Sciences and Engineering 18 (2018), 847–857.

21.

Fern

Akbarzadeh-Sharbaf

and Giannacopoulos

D.D.

, Solving finite-element time-domain problems with GaBP, IEEE Transactions on Magnetics 53(6) (2017), 1–4.

22.

Xin

Zhang

and Wang

, PSO and genetic algorithm optimization BP neural network contrast in collaboration innovation performance evaluation, IEEE Control and Decision Conference, 2016, pp. 4014–4018.

23.

Zhang

X.Y.

Zhang

Gong

Y.J.

et al., Kuhn-Munkres parallel genetic algorithm for the set cover problem and its application to large-scale wireless sensor networks, IEEE Transactions on Evolutionary Computation 20(5) (2016), 695–710.

The prediction of foundation pit based on genetic back propagation neural network

Abstract

Keywords

1. Introduction

2. Method

2.1 Framework for multidimensional error compensation

Table 1 Network input and output layer design

3.1 Comparison of time series and spatial feature prediction

Table 2 Comparison of prediction accuracy between BP model and GA-BP model

Table 3 Comparison of displacement and RE between BP and GA-BP model

Table 4 Comparison between other two methods and GA-BP model

Footnotes

Acknowledgments

References

Table 1
Network input and output layer design

Table 2
Comparison of prediction accuracy between BP model and GA-BP model

Table 3
Comparison of displacement and RE between BP and GA-BP model

Table 4
Comparison between other two methods and GA-BP model