Prediction of surface subsidence in Changchun City based on LSTM network

WANG He and WU Qiong

College of Geo-Exploration Science and Technology,Jilin University,Changchun 130026,China

Abstract:Monitoring and predicting of urban surface subsidence are important for urban disaster prevention and mitigation.In this paper,the Long Short-Term Memory (LSTM) network was used to predict the surface subsidence process of Changchun City from 2018 to 2020 based on PS-InSAR monitoring data.The results show that the prediction error of 57.89% of PS points in the LSTM network was less than 1mm with the average error of 1.8 mm and the standard deviation of 2.8 mm.The accuracy and reliability of the prediction were better than regression analysis,time series analysis and grey model.

Keywords:LSTM neural network;surface subsidence;PS-InSAR

Introduction

Urban surface subsidence is characterized by slow formation,long duration,and irreversibility (Zhanget al.,2009).The causes of subsidence include instability of the urban geological structure,urban construction and over-exploitation of groundwater (Zhouet al.,2020).Large-scale urban surface subsidence may lead to foundation collapse,underground pipeline damage and road damage (Khanet al.,2021).Therefore,monitoring and predicting of urban surface subsidence are of great significance to urban maintenance.Conventional land subsidence observation methods such as leveling and Global Navigation Satellite System (GNSS) measurement have high operating costs and long operation time.These methods can only obtain the settlement value of point and line areas with low spatial resolution (Wuet al.,2019).Synthetic aperture radar interferometry (InSAR) has the characteristics of large monitoring range,low cost,high spatial resolution and it is not affected by climate conditions.It has been widely used in regional and urban deformation monitoring of important ground objects (Guoet al.,2017).Synthetic aperture radar differential interferometry (D-InSAR) is susceptible to spatial incoherence,temporal incoherence and atmospheric delayed phase,which leads to certain limitations in application (Qiuet al.,2016).Permanent scatterers InSAR (PS-InSAR) identifies permanent scatter based on a time series of SAR images covering the same area and the amplitude deviation index threshold method.It not only maintains the scattering characteristics on the long time series and not be affected by temporal and spatial decorrelation,but also overcomes the deficiency of differential synthetic aperture radar and can monitor the regional settlement process of the long time series with millimeter accuracy (Zhu &Li,2021;Linet al.,2017).

The main models used in deformation monitoring simulation and prediction include regression analysis,time series analysis,gray model,etc.,which usually have good accuracy in single point settlement prediction (Sun &Shi,2016;Zhaoet al.,2017;Wang&Tang,2008).An artifciial neural network is a braintype intelligent information processing system that imitates the structure and function of the human brain.It can be used for information analysis and prediction by abstracting the human brain neuron network to establish a simple model,forming different networks according to different connections (Denget al.,2018).Commonly used settlement prediction networks include Back Propagation (BP) neural network and Elman neural network.(Fenget al.,2019) These methods may fall into local minimization,resulting in training failure and their slow convergence affects settlement prediction efficiency (Zhonget al.,2019).LSTM neural network takes the nonlinearity and time dependence of data into account and avoids local minimization and other problems,which can be used for the simulation and prediction of PS-InSAR regional settlement monitoring data with long time and high frequency (Dinget al.,2021).In this paper,we calculated surface subsidence based on PS-InSAR technology,used LSTM neural network model to predict the surface subsidence in Changchun City from 2018 to 2020,compared the accuracy and reliability differences of this method with regression analysis,time series analysis and gray model,and analyzed the applicability of LSTM neural network in urban surface subsidence prediction.

1 Data and methods

1.1 Data

The PS-InSAR calculation data were obtained from 27 sentinel-1B Single Look Complex (SLC)data (interferometric wide mode,vertical transmit and vertical receive polarization mode) in the urban area of Changchun with a sampling interval of one month from October 2018 to December 2020.The 30 m resolution SRTM-1 DEM data and accurate orbit ephemeris data were used to correct the orbit information.The monitored settlement rate is shown in Fig.1.The main settlement areas are located in Jilin Overpass,Century Square,Guoxinmeiyi,and Ecological Square.The average settlement rate of Jilin Overpass is 4.2 mm/a,and the average cumulative settlement is 16.9 mm.The average settlement rate of Century Square is 7.3 mm/a,and the average cumulative settlement is 29.0 mm.The average settlement rate of the Guoxinmeiyi area is 9.4 mm/a,and the average cumulative settlement of 37.5 mm.The average settlement rate of Ecological Square is 4.7 mm/a,and the average cumulative settlement of 18.6 mm.The calculated results were compared with the monitoring data of 46 second-class levels in Changchun City in November 2019 and September 2020.The minimum difference was 0.1 mm/a,the maximum was 9.0 mm/a,the average error was 1.13 mm/a,and the standard deviation was 3.09 mm/a.It shows that the calculation results of PS-InSAR are high accuracy and reliability.

Fig.1 Urban deformation rate

1.2 LSTM network

LSTM is a specific form of the recurrent neural network model that can learn long-term laws and solve long-term dependence problems by reducing gradient disappearance.The model is composed of three basic units:forgetting gate,input gate,and output gate.Important information is retained and unimportant information is forgotten to improve the learning ability of the model through gate control (Liet al.,2018).The model structure is shown in Fig.2.

Fig.2 LSTM neural network structure

The input of the forgetting gate is the hidden stateht-1at the last moment and the input dataxtat the current moment.The value offtoutput ranges from 0 to 1.Ifftoutput is 0,the status information of the previous unit is forgotten and will not be input into the current unit.If theftoutput is 1,all the state information of the previous unit is retained by the current unit.The expression of forgetting gate is:

σis the Sigmoid function.Wfis the weight matrix;bfis the offset.

The input gate first updates all the values selected to be forgotten in the previous forgetting gate,and then uses the tanh layer to generate a new candidate valuethat can be added to the status.The two parts are then combined to update the stateCt-1toCt.The input gate update process is as follows:

The output gate determines whether to output the current state and what information can be output.The output valuehtof the hidden layer at the current moment is:

The surface settlement process is a long time series problem,and the value of an accumulated settlement in the first N period is used to predict the value of an accumulated settlement in the next period,then the mapping function can be expressed as:

The settlement monitoring data with the same time interval are used as training samples,x1-xNis extracted to form the first sample,where (x1,x2,…,xN-1) is the independent variable,xNis the objective function value;x2-xN+1was extracted to form the second sample,where (x2,x3,…,xN) is the independent variable,xN+1is the objective function value,and so on,finally forming the training matrix:

Among them,each column is a sample,and the last row is the expected output.

After sample construction,a neural network is created,which includes 15 neurons,with a learning rate of 0.001 and a loss function of mean square error.Adam optimizer is selected,and the maximum training period element is 60.After several training,the predicted value of the settlement is obtained.

1.3 Regression analysis,time series analysis,and grey model

1.3.1 Regression analysis

The establishment of the surface subsidence prediction model by regression analysis method is mainly based on the monitoring data of PS point and the establishment of a cumulative subsidence regression model.The best prediction model and data are obtained through the comparison of the following four common unitary regression models.Unitary regression models are as follows:

Linear regression model:

Logarithmic regression model:

Exponential regression model:

Power regression model:

1.3.2 Time series analysis

The establishment of the land subsidence model by the time series analysis method is mainly to establish the autoregressive AR(P) model,establish the model orderpsuitable for the model through the least square method and establish the prediction model according to the corresponding model parameter values.The model orderpis determined by theFtest:

where α is the given signifciance level (generally taken as 0.05).TheFtest is not signifciant whenF＜Fα,which means the model orderpis appropriate at this time.

1.3.3 Grey model

The grey model analysis method is mainly used to establish the prediction model of surface subsidence.GM(1,1) is used as the prediction model.First,the original observation data are accumulated,then the first-order differential equation is established for the new data,and the model parameters are calculated according to the least square principle.The frist-order differential equation is:

In the formula,ais the development coefficient;uis the gray action.

2 Results and analysis

2.1 LSTM settlement prediction

The monitoring data of PS points with a settlement rate greater than 10.0 mm/a in the subsidence area treated by PS-INSAR were used for modeling and prediction at an interval of 24 days and 21 periods.The data of the first 19 periods were taken as training samples,and the accuracy of the data of the last two periods was verified.A total of 95 PS points was selected for prediction in this experiment.The distribution of PS points is shown in Fig.3 including Jilin Overpass (13 points),Century Square (57 points),Guoxinmeiyi (19 points) and Ecological Square (6 points).The prediction results are shown in Fig.4.In the settlement prediction of the first phase,the predicted value was basically consistent with the actual cumulative settlement value and the trend was the same.The minimum difference,maximum difference and the mean error were 0.1 mm,9.6 mm and 1.8 mm respectively with the standard deviation of 2.8 mm,which showed that LSTM network prediction has very high accuracy and reliability.In the settlement prediction of the second phase,the accuracy and reliability of the predicted value are lower than that of the first phase,the minimum difference was 0.1 mm,the maximum difference was 28.3 mm,the average error was 5.0 mm and the standard deviation was 6.8 mm.

Fig.3 Distribution of PS points

Fig.4 Predicted values and actual accumulated sedimentation in the frist phase (a) and the second phase (b)

2.2 Regression analysis,time series analysis,and grey model

The accuracy of regression analysis,time seriesanalysis,and grey model in the two phases of prediction is shown in Table 1.In the first phase of settlement prediction,regression analysis had the highest prediction accuracy while the mean error of time series analysis was similar to that of the grey model.However,the standard deviation of time series analysis was larger than that of the grey model,indicating that time series analysis model is prone to maximum individual errors in prediction.The regression analysis had the highest reliability,followed by the grey model,and the reliability of time series analysis had average reliability.The average error and standard deviation of the LSTM network model were far less than those of the other three prediction models,indicating that the LSTM network model is better than the other three prediction models in terms of accuracy and reliability.

Table 1 Model prediction accuracy mm

In the second phase of subsidence prediction,the mean error and standard deviation of the regression analysis model were minimum and similar to that of the first phase,indicating that the regression analysis model has good ductility in long-term series prediction.The average error and standard deviation of time series analysis and gray model were similar,but the standard deviation of time series analysis was still larger than that of the gray model,and some prediction values have great errors.The regression analysis had the highest reliability,followed by the grey model,and time series analysis had average reliability.LSTM network model was second only to the regression model in predicting accuracy and reliability.

3 Conclusions

We obtained the surface subsidence data of Changchun City from 2018 to 2020 based on PSInSAR technology.The monitoring data of PS points with subsidence rate greater than 10.0 mm/a were selected and the LSTM network prediction model was used to predict surface subsidence.Comparing the accuracy and reliability of the LSTM network model with regression analysis,time series analysis and grey model,the main conclusions were drawn as follows:

(1) LSTM network has high accuracy and reliability in settlement prediction.The mean error was 1.8 mm in short-term prediction and 5.0 mm in longterm prediction.LSTM network has a good training effect on settlement data,and the extreme error of individual points was not found in the prediction process.It is suitable for long-time series prediction of high resolution settlement monitoring based on PSInSAR technology.

(2) In short-term prediction,regression analysis had the highest prediction accuracy,while time series analysis and grey model had similar prediction accuracy.The average prediction errors of the three models were 3.4 mm,4.9 mm and 4.9 mm,respectively.The regression analysis had the highest reliability,followed by the grey model,and time series analysis had the lowest reliability.In longterm prediction,the regression analysis model had good ductility in long-term series prediction and had the highest prediction accuracy.Time series analysis and gray model had similar prediction accuracy.The average prediction errors of the three models were 3.6 mm,6.1 mm,and 6.0 mm,respectively.The regression analysis had the highest reliability,followed by the grey model,and time series analysis had the lowest reliability.

(3) LSTM network was superior to the other three models in short-term prediction in terms of accuracy and reliability.In long-term prediction,the LSTM network was second only to regression analysis in accuracy and reliability.In terms of modeling complexity,regression analysis was the simplest,while the LSTM network was the most complex.In terms of computational complexity,regression analysis and time series analysis were more complicated.LSTM network and grey model can predict the settlement after modeling.