Slope Deformation Prediction Based on MT-InSAR and Fbprophet for Deep Excavation Section of South–North Water Transfer Project

Abstract

In the operation and maintenance of the South–North Water Transfer Project, monitoring and predicting the canal slope deformation quickly and efficiently is one of the urgent problems to be solved. To predict the slope deformation of the deep excavated canal section at the head of the canal. We propose a new idea of adopting the joint prediction of MT-InSAR and Fbprophet. Firstly, MT-InSAR monitoring technology was used to invert channel deformation using 88 Sentinel-1A orbit-raising image data with a time baseline from 2017 to 2019. The time-series deformation of nine monitoring points was also extracted, and it was found that the time-series curves of the cumulative deformation of the channel slope showed fluctuations. The Fbprophet algorithm was then used to train the prediction model in Python to predict the channel slope deformation over the next 365 days. Finally, the prediction results were compared with the MT-InSAR monitoring values to analyze the prediction accuracy and applicability of the Fbprophet algorithm for the slope deformation monitoring of the South–North Water Transfer Project. The results show that: the deformation rate of the slope of the deep excavation section is in the range of 10 mm/a to 25 mm/a, the maximum accumulated deformation is about 60 mm, and the slope of the excavation canal shows a lifting phenomenon; among the nine monitoring points, the minimum and maximum predicted values of deformation using the machine learning prediction model trained in this paper were 56 mm and 73 mm, respectively; comparing the predicted and monitored values, their correlation coefficients were 0.998 at the highest and 0.988 at the lowest, and the minimum and maximum values of RMSE (RootMean Square Error) were 0.72 mm and 2.87 mm, respectively. It shows that the prediction model trained by the Fbprophet algorithm in this paper applies to the prediction of slope deformation in the deep excavation section, and our prediction results can provide a data reference for disaster prevention and the sustainable development of the South–North Water Transfer Project.

1. Introduction

As a major infrastructure project for the optimal allocation of water resources in China, the South–North Water Transfer Project can not only alleviate the water shortage in the North China Plain, but can also improve the problems of groundwater overdraft and the ecological environment along its route [1]. The total length of the trunk canal is 1432 km, of which the length of the deep excavated section at the head of the canal is about 14 km, and it crosses the swelling soil. Swelling soil is a typical cohesive soil with rising and shrinking properties that can cause slope deformation during construction and later operation and maintenance [2]. It is manifested by water loss and shrinkage, producing fissures; it expands when water intrudes and will form a low-stress zone near the fissure surface, along with primary fissures and closed micro-fissures [3]. Therefore, the slope of the deep excavation section of the South–North Water Transfer Project may produce slope instability and damage to the building (structure) when it crosses the swelling soil distribution area [4]. Drainage slope deformation is manifested by a variety of factors, and if some algorithm can be used to predict the drainage slope deformation in a certain period in the future, the management can make a risk management response, and it can take measures to reduce the disaster at the source.

From a review of the relevant literature, we found that regression analysis [5], exponential smoothing [6], grey theory [7], neural networks [8], and support vector machines [9] have been proposed for slope deformation prediction. However, linear regression is more difficult in building nonlinear models [10]; grey theory has low accuracy and high data requirements in predicting fluctuating data [11], and neural networks make it difficult to solve convergence and local extrema problems in the prediction [12,13]; with SVM, it is difficult to solve the parameter search problem in the prediction process [14]. Although the above prediction algorithms are widely used in the slope prediction, they have high data requirements and usage thresholds, and there are challenges in predicting the nonlinear deformation of deep excavation sections of the South–North Water Transfer Project. In 2017, Facebook proposed the Fbprophet algorithm [15] for the volatility problem of time-series forecasting, which showed superiority in commercial volatility-based time-series forecasting [16]. Subsequently, scholars promoted the algorithm with their research directions, and LIM used the algorithm for electricity demand forecasting and obtained better results [17]. Li et al. programmatically implemented the integrated energy scheduling aspect and verified that the algorithm is also applicable to energy supply forecasting [18]. Chikkakrishna et al. applied the algorithm to short-time traffic flow forecasting and verified that the algorithm is also applicable to passenger flow forecasting [19]. In their study, Darapaneni et al. applied the Fbprophet algorithm to the medical field to predict the trend of the epidemic in the three states most affected by COVID-19 in India [20]. With the increase in global warming throughout the 21st century, Zar et al. used the Fbprophet algorithm to predict the annual temperature of Myitkyina, Myanmar, thus applying the algorithm to the field of meteorology [21]. With the successive reports in the related literature, the Fbprophet algorithm has been gradually applied to time-series predictions in several fields [22,23,24]. Given this, for the difficult problem of predicting the slope deformation of the deep excavation at the head of the South–North Water Transfer Project, we have tried to implement the Fbprophet deformation prediction model using Python based on MT-InSAR (Multi-temporal InSAR, MT-InSAR) monitoring data and have used it to predict the deformation of the slopes in the coming year. It provides a new idea for the prediction of slope deformation of the South–North Water Transfer Project and provides a data reference for its sustainable operation and maintenance.

In this paper, the deep excavated canal section at the head of the South–North Water Transfer Project is used as the study area. We use 88-view Sentinel-1A orbit-raising images to invert the canal slope deformation field by the MT-InSAR technique. The time-series deformation of nine monitoring points is extracted and we try to predict it using the Fbprophet algorithm. The prediction and analysis of the canal slope deformation for the next 365 days verified the applicability of this new idea of slope prediction for the South–North Water Transfer Project.

2. Materials and Methods

2.1. Overview of the Study Area

In this paper, the deep excavation section of the South–North Water Transfer Project (pile number 0 + 300~14 + 465) is used as the study area, as shown in Figure 1. The maximum excavation depth of this section is 47 m, the minimum is 9.9 m, and the maximum width of the excavation cross-section is 400m, which is within the administrative area of Jiu Chong Town, Xichuan County, Henan Province, China. The area belongs to the edge of the east–west tectonic system of the Qinling Mountains and has a complex geological environment. The site investigation found that the stratigraphy along the South–North Water Diversion Project is river valley alluvium-type stratigraphy. The vertical spectrum of soil is yellowish-brown loam, brown loam, and dark brown loam, which is characterized by high capacitance, low porosity, water stagnation in the wet season and difficulty in moisture retention in the dry season, and belongs to the category of swelling soil. The stratigraphic sequence graph is shown in Figure 2. The study area has a north subtropical continental monsoon climate with four distinct seasons, concentrated rainfall and distinct rainfall time nodes, with June to October being the wet season, accounting for 60% of the annual rainfall, and December to February having the least rainfall.

2.2. Data Source

The paper employs MT-InSAR technology to monitor the deformation of the drainage slope in the study area, with data derived from 88 Sentinel-1A orbit-raising images. Precision satellite orbit data are stored in POD (Precise Orbit Ephemerides Data). DEM (Digital Elevation Model) is adapted from the open-source SRTM_DEM4 by NASA (National Aeronautics and Space Administration).

For data processing, the inversion method of the PS-InSAR and SBAS-InSAR methods is adopted. First, high coherence points are extracted as Ground Control Points (GCP) using PS-InSAR technology to obtain high-precision deformation information of ground permanent scatterers. Secondly, in the SBAS-InSAR process, high-quality Ground Control Points are screened as GCP parameters to avoid inadvertent mistakes produced by artificial spike points. PS-InSAR generated a total of 113,368 highly coherent points with correlation coefficients in the range of 0.72–0.95, and 281 points with correlation coefficients in the range of 0.86–0.95 were selected as GCPs. Finally, the deformation field in the line-of-sight (LOS) direction of the satellite is obtained through a series of processes such as interference, decoupling, inversion, and geocoding. The data processing flow is shown in Figure 3.

2.3. Fbprophet Algorithm

The Fbprophet prediction algorithm was proposed by Facebook Inc. (Menlo Park, CA, USA) in 2017, and it implements time-series prediction based on the periodicity of data, holidays, and other characteristics. Unlike other algorithms, it can handle abruptly changing outliers of time-series data. Usually, the Fbprophet algorithm can implement predictions through temporal decomposition and Scikit-learn machine learning API.

The Fbprophet algorithm decomposes the predicted data into 4 terms.

$$y(t)=g(t)+s(t)+h(t)+\epsilon (t)$$

(1)

where $g(t)$ represents the trend term, $s(t)$ represents the period term, $h(t)$ represents the time-series mutation outlier term, and $\epsilon (t)$ represents the residual term.

$g(t)$ employs logistic regression functions and linear segmentation functions that can cope with different types of time-series data. The logistic regression function of the Fbprophet algorithm is expressed in Equation (2).

$$g(t)=\frac{C(t)}{1+\exp (-(k+\alpha {(t)}^T\delta (t-(m+\alpha {(t)}^T\gamma ))))}$$

(2)

where $C(t)$ represents the parameter, $\alpha (t)$ represents the indicator function, $\delta$ represents the time growth, and $m$ and $\gamma$ represent the intermediate variables.

The segmentation function of the Fbprophet algorithm is expressed in Equation (3).

$$g(t)=(k+\alpha (t)\delta )\times t+(m+\alpha {(t)}^t\gamma )$$

(3)

where $k$ is the slope of the segmentation function.

The Fourier series is used to model the seasonality or periodicity in the time series by setting the number of days of variation to cope with different types of periods in the time series. The Fourier series expression of the Fbprophet method is expressed in Equation (4).

$$s(t)={\displaystyle \sum _{n=1}^N(a_n\cos (\frac{2\pi nt}{P})+(b_n\sin (\frac{2\pi nt}{P}))}$$

(4)

where $P$ represents the period, set $N$ is equal to 10 for annual time series ($P=365.25$) and $N$ is equal to 3 for weekly time series ($P=7$), and $a_n$ and $b_n$ represent the coefficients.

The holiday function is set to various window values throughout the algorithm since holidays’ levels of effect on the time series and their lengths are not constant. For example, the $ith$ holiday, $D_i$, represents the period of time before and after this holiday. The holiday term is as in Equation (5).

$$h(t)=Z(t)\tau ={\displaystyle \sum _{i=1}^L{\tau }_i\times 1\{t\in D_i\}}$$

(5)

where $Z(t)$ represents the indicator function of the holiday term, $Z(t)=(1\{t\in D_1\},\cdots ,1\{t\in D_L\}),\tau =({\tau }_1,\cdots ,{\tau }_L)$ and $\tau$ follows a normal distribution $\tau ~Normal(0,v^2)$.

2.4. Fbprophet Predicts Slope Deformation

The Fbprophet algorithm, proposed by Facebook, focuses on the prediction problem of volatile time series in the field of business data analysis. To facilitate the research of statistics and machine learning practitioners, both R and Python programming language interfaces are provided. In this paper, we try to apply the algorithm to the prediction of slope deformation in the deep excavation section of the South–North Water Transfer Project. To realize the prediction of slope deformation by Fbprophet algorithm, this paper uses the Python programming language to prepare the program and establish the prediction model through data training and parameter search. The programming process is based on method calls in third-party libraries such as PyStan, Pandas, and Scikit-learn. The training of the model is based on using the South–North Water Transfer Project slope deformation monitoring data as the training sample data, using the segmentation function as the trend term in the Fbprophet algorithm, using the dry season in the test area as the $h(t)$ term in the Fbprophet algorithm. In the program, the window value is the time window of the $h(t)$ term, the prediction duration can be customized to the length of the prediction time, the period type is divided into yearly, quarterly, monthly, and weekly options, and the data training range can be proportionally divided into training data and validation data, using the L-BFGS (limited-memory BFGS) method in PyStan to fit the posterior estimation, and using the Scikit-learn machine learning framework to complete the model construction. Furthermore, the model is used to predict the deformation of the slope for the next 365 days. Finally, the program can output upper bounds on predicted values, prediction curves, and lower bounds on predicted values. The program flow is shown in Figure 4.

3. Results

3.1. Deformation Fields

Figure 5 displays the time-series deformation field (along the LOS direction) of the study area from MT-InSAR inversion, with the time series spanning from 11 January 2017 to 27 December 2019, beginning on 11 January 2017, with the majority of time intervals being 24 days and some being 36 days.

The deep excavation section’s spatial and temporal deformation pattern varies as monitoring time increases, according to analysis of the deformation field. The slope has an upward tendency, and the total cumulative deformation from monitoring to 27 December 2019, can reach a maximum of 60 mm. The following are the causes for the elevation of the deep excavation canal’s slope.

(1)

The cross-sectional slope factor of the excavated slope is 2.5, and the soil on both sides produces extrusion pressure into the section under the action of gravity. When this force strikes on the slope surface, it splits into upward and horizontal directions, uplifting the slope of the channel.

(2)

Groundwater seepage and lateral penetration of rainfall recharge in the study area, swelling of the in situ soil beneath the canal structures after water absorption [25], also generating compressive forces into the cross-section, leading to the lifting of the channel slope.

The results of MT-InSAR inversion show that the deformation of the deep excavated section of the South–North Water Transfer Project is unevenly distributed. To analyze the deformation characteristics more visually, a 300-m buffer zone along the main canal was established by using the Buffer spatial analysis tool of ArcGIS 10.2 software. The results of the macroscopic analysis of the deformation field show that the slope of the upstream deep excavation section has an uneven uplift phenomenon, with an annual average deformation rate between 10 mm/a and 30 mm/a, while the downstream fill section shows an uneven settlement phenomenon, between −6 mm/a and 0 mm/a. The deformation of the slope of the deep excavation section is significantly larger than that of the fill section, see Figure 6.

3.2. Predicted Results

Based on the MT-InSAR monitoring data of the deep excavation section at the head of the South–North Water Transfer Project, time-series data from January 2017 to December 2019 was extracted from the time-baseline of the nine monitoring points. The Fbprophet algorithm was used to construct the prediction model through Python programming, and the normalized time-series sampling length of 15 days of data was used as the training set to predict the future 365-day canal slope deformation at the nine monitoring points. The results are shown in Figure 7. From the figure, it can be seen that:

(1)

The Figure 7a,d,g,i predicted values fluctuate widely, the predicted sudden change increment can reach about 10 mm in June–July 2020, and the probability of damage occurring at monitoring points of the A, D, G, and I drainage slopes are significantly higher than the monitoring points B, C, E, F, and G.

(2)

The deeper the excavation, the greater the slope uplift. Figure 7a,i show that near the end of the excavated section, the excavation depth at point A is 31.2 m, the accumulated monitoring value is 48 mm, and the predicted accumulated uplift is 56 mm; point I is 33.7 m deep, the accumulated monitoring value is 49 mm, and the predicted accumulated uplift is 62 mm. Figure 7b–h were excavated to a depth of about 45 m, and the monitoring accumulation and predicted values were all greater than those at points A and I. There was a strong correlation between the amount of slope uplift and the depth of excavation.

(3)

There are still seasonal fluctuations in the predicted results over the next year, but the overall growth trend remains the same. The maximum value of deformation is point C, with a predicted cumulative deformation of 73 mm, and the minimum value is point A, with a predicted cumulative deformation of 56 mm. Therefore, the deformation of the slope of the deep excavation section of the South–North Water Transfer Project shows an uneven phenomenon, and long-term deformation will damage the slope protection structure and pose a safety hazard.

4. Discussion

4.1. Slope Deformation Characteristics

To further analyze the spatial and temporal patterns of slope deformation in the deep excavation section, the Time-Series Analyzer tool of ENVI software was used to extract the time-series deformation of nine monitoring points from the deformation field. The locations of the monitoring points are shown in Figure 6 and the time-series deformation is shown in Figure 8.

As described in Section 3.1, the uplift of the slope of the deep excavated section of the channel occurs mainly due to gravity and expansive soil deformation. As slip deformation under gravity is a continuous occurrence, it should be the trend term $g(t)$ in the model. Swelling soil deformation is closely related to rainfall, which is evident in the study area during the wet season, and therefore, swelling soil deformation is the periodic term $s(t)$ in the model. To analyze the correlation between deformation and rainfall, rainfall data with the same time baseline as the monitoring data was selected for comparison and analysis. As shown in Figure 8, The monitoring period is from January 2017 to December 2019, with a cumulative period of 3 years, and can be divided into three time periods. The deformation variables at all nine monitoring points gradually increased in time, with the cumulative deformation variables lying between 40 and 60 mm. With the change of seasons, the shape of the curve fluctuates slightly after the wet season, with peaks and troughs. The slope of the growth curve increases with a certain lag as rainfall increases from May to July each year, and the dry season occurs from November to around March, with a trough in the deformation curve around February each year. The periodic fluctuations are mainly due to the periodic deformation of the expansive soil below the structure in the deep excavation section. Although a 1.5-m-thick replacement fill was made during construction and the replacement soil was less affected by rainfall, the original soil below the replacement soil will still swell when it encounters groundwater runoff and the lateral infiltration of rainfall. This situation is due to the change in the groundwater environment and increases in the water content under the conditions of regional groundwater runoff and the lateral infiltration of rainfall, which induces the deformation of the original soil below the replacement soil and increases the volume of the original soil, thus causing the slope of the canal to be lifted.

4.2. Analysis of the Applicability of the Fbprophet

We decomposed the deformation of the drainage slopes at the monitoring sites by a quarter, and the three-year time-series curves show a gradual increase in deformation with seasonal changes and no crossover. As shown in Figure 9, the deformation in each quarter of each year was higher than the previous quarter, reaching a maximum in the fourth quarter. It can be concluded that fluctuations in the amount of drainage slope deformation occur in the short term because of seasonal variations. The long-term growth trend of the gradual cumulative increase in the deformation of the canal slope in the excavated section over time applies to the trend term $g(t)$ in Fbprophet. The deformation of the channel slope of the excavated section shows fluctuating uplift, which is influenced by rainfall, and there is a certain lag. Also, because rainfall is seasonally related and has a certain periodicity, the deformation is considered to be influenced by the seasonal turnover. Therefore, the seasonal factor is an important factor to be considered in the prediction of the deformation of the drainage slopes, applying to the periodic term $s(t)$ in Fbprophet. As shown in Figure 8, there are multiple peaks and troughs in each deformation curve, with troughs of different sizes occurring in February each year. The peaks and troughs are mutation anomalies, so the mutation values apply to the holiday term $h(t)$ in Fbprophet. In summary, the Fbprophet algorithm is suitable for predicting the temporal deformation of the canal slope shape in the deep excavation section of the South–North Water Transfer Project.

4.3. Accuracy Evaluation

(1)

Reliability verification

To verify the reliability of the prediction model, we compared the predicted values with the measured values. The reliability of the model prediction results was tested by counting the absolute value of the most-valued error between the predicted and monitored values for the nine monitoring sites from 2017–2019. The maximum errors are shown in

Table 1. Maximum and minimum error for sample points.

	Sample Point Number	A	B	C	D	E	F	G	H	I
Value (mm)
maximum		8.2	9.5	3.5	3.1	2.5	2.8	2.0	2.7	3.7
minimum		0	0.1	0	0	0	0	0	0.1	0

.

(2)

Accuracy Assessment

To evaluate the prediction accuracy of the prediction model for drainage slope deformation, the MT-InSAR monitoring values were used as the actual measured values and compared with the predicted values. Two evaluation indexes, the correlation coefficient and $RMSE$, were used, and the indexes were calculated by Equations (6) and (7), respectively. The index evaluation results are shown in

Table 2. Results of accuracy evaluation.

NO.	R	RMSE/mm
A	0.989	2.38
B	0.988	2.87
C	0.997	1.34
D	0.997	1.18
E	0.998	0.94
F	0.998	0.89
G	0.998	0.72
H	0.997	1.04
I	0.996	1.29

.

$$R=\frac{Cov(y,\overline{y})}{\sqrt{Var\left|y,\overline{y}\right|Var\left|y,\overline{y}\right|}}$$

(6)

$$RMSE=\sqrt{\frac{1}{n}{\displaystyle \sum _{i=1}^n{(y-\overline{y})}^2}}$$

(7)

As can be seen from Table 2, the maximum value of R is 0.998 and the minimum is 0.988, indicating that the predicted values have a high correlation with the measured values. The minimum and maximum values of RMSE are 0.72 mm and 2.87 mm, respectively. Therefore, the prediction model in this paper applies to the prediction of slope deformation in the deep excavation section of the South–North Water Transfer Project.

4.4. Comparison with Other Predictive Algorithms

Amid nine points from point A to point E, we chose point A, with the most remarkable fluctuation, and point E, with the least unnoticeable amplitudes, as the typical test points based on the InSAR monitoring data to further verify the efficiency of the Fbprophet algorithm and assess the model’s predictive ability. We chose two classical types of algorithms, i.e., the decision tree [26] and ARIMA [27] as the subjects of comparison. The data set obtained over point A and point E from 2017 to 2018 was first the training set to determine the parameters for three different predictive models. Afterwards, the deformation values in 2019 were forecasted with the abovementioned three models. The contrast between the predictive results and observed ones is shown in Figure 10.

It can be shown from Figure 10a,d that when the decision tree algorithm is used to predict the deformation at points A and E in 2019, the predictive curve is horizontal and the discrepancy between the measured and predicted values is significant, indicating that the algorithm is unsuitable for the predicting of volatile time-series data. The prediction curve displays a horizontal shape when the ARIMA algorithm is used to predict point A, in which the amplitude of the fluctuation is noticeable. However, the prediction curve displayed a linear growth trend when predicting point E, where the fluctuation is weak. As can be seen in Figure 10b,e, there were also clear discrepancies between the measured and predicted values. When the Fbprophet algorithm is employed for prediction as opposed to the decision tree and ARIMA algorithms, the prediction results are in greater agreement with the measured findings and can reflect the fluctuation of future deformation, shown in Figure 10c,f. For the time-series prediction of the slope deformation of the South–North Water Transfer Project, the Fbprophet algorithm performs better and has stronger robustness.

5. Conclusions

This paper proposes a new idea for adopting the joint prediction of MT-InSAR and Fbprophet to quickly and efficiently monitor and predict the slope deformation at the head. Firstly, MT-InSAR monitoring technology was used to invert the deformation field of the head of the South-to-North Water Transfer Project using the 88-view Sentinel-1A uplift images with a time baseline of 2017 to 2019. The Buffer spatial analysis tool of ArcGIS was used to establish a 300 m buffer zone along the main canal in the deformation field, and the macroscopic deformation field results were analyzed. It was found that there was uneven uplift of the canal slope in the upstream deep excavation section, and the average annual deformation rate ranged from 10 mm/a to 25 mm/a. The time-series deformation curves of nine monitoring points were extracted from the deformation field through ENVI’s Time-Series Analyzer tool, and the time-series curves showed a fluctuation phenomenon. To address the difficulty of predicting fluctuating time-series curves, this paper uses the Fbprophet algorithm to program a prediction model in Python and uses it to predict the slope deformation for the next 365 days. The minimum and maximum deformations of the nine points predicted using the model are 56 mm and 73 mm, respectively. When comparing the predicted values with the MT-InSAR monitoring values, the correlation coefficient is up to 0.998 and the minimum is 0.988. The minimum and maximum values of RMSE are 0.72 mm and 2.87 mm, respectively. The prediction idea proposed in this paper applies to the prediction of slope deformation in the deep excavation section of the South–North Water Transfer. It can provide a data reference for the sustainable development of the South–North Water Transfer Project. It may offer an early warning for its deformation catastrophe, analyze the risk using the projected findings, and uncover hidden risks, improving the technology and capability of the slope disaster’s complete prevention and control, and effectively reducing the risk of disaster. In our study, the combined method of MT-InSAR and Fbprophet is mainly used for the prediction of river slope deformation. The method is not limited to the prediction of river slope deformation. In addition, it can also be used for the prediction of dam deformation, the prediction of landslide deformation, and the prediction of surface subsidence. It can also be used for the deformation prediction of heritage conservation, and the monitoring and prediction of the deformation of monuments, ancient buildings, ancient city walls, etc. Although the prediction approach in this study predicts river slope deformation with excellent accuracy, it is still only marginally suitable for rapid changes in the data. Neural networks and seasonal indices will probably need to be combined in order to target the data’s seasonality and make future advancements.