4.1. Case Background
(1) Overview of the J Reservoir Project
J Reservoir was built in February 1969 and completed in December 1976. The watershed area controlled above the dam site is 240 km2; the length of the main river above the dam site is 28 km, and the average slope drop of the main river is 5.5%, which is a mountainous river with good vegetation in the watershed; the reservoir watershed is in the low-latitude and -longitude area, and the average rainfall for many years is 1897.7 mm, and the distribution of rainfall is not uniform within the year. Reservoir hub buildings mainly include one main dam, one sub-dam, one spillway dam, two water conveyance culverts, power house, tailwater channel, etc. The upstream of J Reservoir is 41 km away from the urban area, with a population of more than 25,000 people in the town, and a total area of 265 km2. There are local villagers living in the vicinity of the reservoir, and a number of towns and villages downstream of the J Reservoir have an impact on the population of more than 200,000 people, and the affected cultivated land covers an area of 150,000 acres.
(2) J Reservoir Risk Event
From 20:00 on 18 August 2013 to 8:00 on 19 August 2013, heavy rain fell in the reservoir area, and the automatic rainfall observatory around the reservoir measured 274.9 mm, while other rainfall observatories measured more than 170 mm, and the maximum value of rainfall at the rainfall observatory reached 477.4 mm. The water level of the reservoir rose sharply due to the torrential rain, and the water level of the reservoir was 97.65 m at 7:50 p.m. on 19 August, and the water level of the reservoir reached 102.20 m at 10:20. The reservoir water level reached 102.20 m, exceeding the flood limit level of 4.6 m, exceeding the calibration level of 0.88 m, and when the power plant has been flooded, there was grid power interruption. At 11:40, the reservoir water level reached 102.50 m, at this time 0.50 m away from the top of the dam, and in this emergency decisive order to break the sub-dam to increase the release of flood water, the flood discharge was up to 2250 m
3/s at this time. At 19:00, the water level in the reservoir dropped to the flood limit level, due to the appropriate measures taken to ensure that J Reservoir’s main water level, with a flood limit of 478.4 mm, the maximum rainfall observed at the station, remained at 478.4 mm. Appropriate measures were adopted to ensure the safety of the main dam of J Reservoir, to avoid greater losses of life and property of the downstream groups. On 19 August 2013, the J Reservoir overflow flood inundation situation was as shown in
Figure 3.
With the aim of studying the effectiveness of the probabilistic radial-based neural network model for risk early warning, this article validates the case of J Reservoir and compares the genuine circumstances of the safety events and the model prediction outcomes of J Reservoir.
4.2. J Reservoir Inflow Forecast
- (1)
Observational Data Smoothness Test
Missing data points within the collected reservoir data series (denoted as J) were estimated through the application of the sliding average interpolation method. Subsequent to the data handling, ADF tests were conducted on the rainfall time series , barometric pressure time series , relative humidity time series , and inlet flow time series . This examination aimed to assess the data’s smoothness and stationarity.
Based on the test outcomes, presented in
Table 3 are the outcomes of unit root analysis for variables
,
,
, and
.
The following are hence indicated by the test results:
The time series for rainfall , barometric pressure , relative humidity , and inlet flow all exhibit smooth patterns.
- (2)
Causality Tests for Variables
Because the series are smooth series, there is no need to carry out an additional cointegration test considering the series data can be directly applied to the Granger causality test; variable
, variable
, and variable Z were subjected to a causality test on variable Y; the original hypothesis is ‘not established causality’; and the results of the test are presented in
Table 4.
The test outcomes reveal that the -values for and stand at 0.3641 and 0.9389, respectively. These values surpass the 5% critical threshold, leading to the acceptance of the null hypothesis. Consequently, it can be concluded that variables and do not serve as Granger causes for variable , so the barometric pressure time series and the relative humidity time series do not have the ability of predicting the inbound flow time series .
- (3)
Granger Test for the Variable
Using the Akaike Information Criterion to determine the maximum lag order of rainfall time series
on the incoming flow time series
is 24, according to the adjusted lag order Granger test, and the results of the test are displayed in
Table 5.
The test findings reveal that with a maximum lag order of 24, the -value for making a type 1 error in rejecting the null hypothesis ‘ does not Granger Cause ’ during the hypothesis test is 0.0948, placing it at the 5% significance level. Conversely, the -value for making a type 1 error in rejecting the null hypothesis ‘ does not Granger Cause ’ during the hypothesis test is 0.0163, which is below the 5% significance threshold. Consequently, it can be concluded that variable serves as the Granger cause of variable , and the time series of rainfall has the ability to predict the time series of the inlet flow .
Through the Granger causality test, rainfall time series , barometric pressure time series , and relative humidity time series were screened, and the results show that only rainfall time series was a valid influence factor on the inlet flow time series .
The BP neural network is used to train and simulate the inlet flow time series using the effective influence factor rainfall time series .
- (4)
Data Accuracy Check
The precision of the neural network data prediction is assessed using the recorded rainfall and inflow data from J Reservoir. Given the constraints of the available data, ensuring the neural network model’s effectiveness required the selection of data from a time period with comprehensive and abundant rainfall records. The data are further processed using the digital twin method proposed by Li et al. [
37], to supplement and enhance the quality and availability of training data in deep learning methods. Accordingly, a dataset spanning 1836 h, from 31 May 2018 to 15 August 2018, is chosen for training, while a separate 24 h dataset is employed to evaluate the model’s predictive capabilities.
For predicting the inflow of J Reservoir, a three-layer BP network is employed. The specific number of neurons in the hidden layer is fine-tuned through practical curve-fitting assessments. The ultimate network topology adopted is 3-8-1. Model development is carried out using the MATLAB 2021 neural network toolbox, and the transfer function employed is purely, known for its linearity. The precision for the error term, denoted as E, is configured at 0.01. The maximum number of training cycles is capped at 30,000 iterations, with the network designed to output hourly inflow rates.
The forecasting accuracy of the results is assessed in compliance with the ‘Hydrological Information Forecasting Specifications (GB/T 22482-2008)’ [
38].
- (5)
Evaluation of the J Reservoir Inflow Prediction Results
The comparison between measured and predicted inflow flow values using multiple input parameters before data screening, and the comparison between measured and predicted inflow flow values with a single input parameter after data screening are shown in
Figure 4. The evaluation of prediction result accuracy is presented in
Table 6. The Nash–Sutcliffe efficiency (
) index offers the advantage of versatility, as it can be applied to various types of models. Therefore, the article uses this indicator for prediction accuracy evaluation. The equation is as follows:
where
and
represent the observed and computed flow values at time t, respectively, and
represents the mean of the observed and computed flow values corresponding to different patterns.
In
Table 6, the prediction results’ accuracy assessment is presented, with the following comparative analysis:
(1) The application of the Granger causality test method for data screening led to substantial improvements in the quality of the BP neural network predictions. This resulted in an 83.23% increase in prediction accuracy, a 45.05% reduction in average relative error, a 38.46% decrease in average error, a 97.06% enhancement in the Nash–Sutcliffe efficiency, and a significant improvement in the alignment between predicted and actual values. Furthermore, employing filtered data for generalization testing within the prediction process substantially lowered the incidence of fitting failures in the results.
(2) In this case, the success rate of J Reservoir inflow predictions falls below 60%. This outcome can be ascribed to the limited quantity of network training samples and the lower data accuracy. The number of training samples will be increased in subsequent research. And improving the accuracy of sample data can enhance the precision of predictions.