A canal water level probability prediction method and system based on MC Dropout and CNN-LSTM

Abstract

The present application relates to a kind of canal water level probability prediction method and system based on MC Dropout and CNN-LSTM, belong to water level prediction technical field.The prediction method includes the following steps:s101.data acquisition;S102.model architecture building;S103.model training and inference.The present application fuses convolutional neural network (CNN) to extract the local space-time characteristics of multi-source hydro-meteorological data, long short-term memory network (LSTM) captures long time series dependency relationship, and integrates Monte Carlo Dropout (MC Dropout) variation inference mechanism and heteroscedastic loss function, realizes the accurate prediction of key water level observation station, uncertainty decomposition (Aleatoric uncertainty and Epistemic uncertainty) and the synchronous output of confidence interval.

Description

Technical Field

[0001] This invention relates to the field of water level forecasting technology, and in particular to a method and system for probabilistic forecasting of canal water levels. Background Technology

[0002] With the acceleration of urbanization and the frequent occurrence of extreme weather events, urban river network water level prediction has become a core technology for ensuring flood control and drainage safety. Among existing technologies, traditional physical models (such as SWMM and MIKE 11) rely on precise watershed parameters and physical assumptions. However, in complex river network interaction scenarios, they suffer from difficulties in parameter calibration and insufficient real-time performance, making them unable to adapt to dynamically changing environments.

[0003] Statistical methods such as the Autoregressive Integrated Moving Average (ARIMA) model are limited by the assumption of stationary sequences and have difficulty handling the nonlinear and non-stationary characteristics of water level changes, resulting in large prediction biases and delayed responses.

[0004] In recent years, data-driven deep learning methods such as Long Short-Term Memory (LSTM) networks can capture long-term dependencies, and Convolutional Neural Networks (CNN) can extract local spatiotemporal features. The CNN-LSTM model, which combines the two, has performed well in water level prediction. However, these models are essentially deterministic point predictions and cannot quantify uncertainties such as data noise, model parameter estimation errors, and environmental disturbances. This results in a lack of reliability assessment and risk quantification of the prediction results, making it difficult to meet the needs of risk-sensitive decision-making such as pump station scheduling.

[0005] While uncertainty assessment methods such as Bayesian neural networks or ensemble learning can evaluate uncertainty, they have high computational complexity, are difficult to adapt to deep models, and the assumption of constant residual variance in traditional statistical methods is not applicable to the conditional heteroscedasticity of hydrological processes, which limits their application in practical engineering.

[0006] Overall, existing water level forecasting technologies have significant shortcomings in terms of accuracy, real-time performance, and uncertainty quantification, and cannot provide comprehensive and reliable support for the intelligent operation and scientific scheduling of urban water conservancy facilities. Summary of the Invention

[0007] In view of this, it is necessary to provide a method and system for canal water level probability prediction based on MC Dropout and CNN-LSTM to address the shortcomings of existing technologies in terms of accuracy, real-time performance and uncertainty quantification.

[0008] To address the aforementioned problems, in a first aspect, this invention provides a canal water level probability prediction method based on MC Dropout and CNN-LSTM, comprising the following steps: s101. Data Acquisition: Collect multi-source data, including hourly measured data such as water level, rainfall, upstream water flow, wind speed, and temperature; s102. Model Architecture: This includes a CNN feature extraction layer, an LSTM temporal modeling layer, and an MC Dropout uncertainty model. The CNN feature extraction layer uses a one-dimensional convolutional structure to perform convolution operations on the input sequence. The LSTM temporal modeling layer feeds the convolutional output into LSTM units, controlling long-term dependencies through input gates, forget gates, and output gates. The MC Dropout uncertainty model embeds a Dropout layer between the LSTM layer and the fully connected layer, retaining random deactivation during the prediction phase. s103. Model Training and Inference: Training is performed based on the PyTorch framework and Adam optimizer, as well as an early stopping mechanism; during the inference phase, MC sampling is performed to generate probability output.

[0009] In one possible implementation, step s101 involves imputing missing values, removing outliers, and normalizing the multi-source data to generate an input sequence X. t The input window is set to a multivariate time series of the past 12 hours; the missing values ​​are filled using the sliding window mean method; the outlier removal is based on the 3σ principle and linear interpolation; the normalization process uses the minimum-maximum normalization method.

[0010] In one possible implementation, the formula for the convolution operation in step s102 is: F=Relu(X*W+b), where * represents the convolution operation, W is the convolution kernel matrix, b is the bias term, and Relu is the activation function; wherein the convolution kernel size is 3, the number of output channels is 64, and it captures local time dependence and short-term change trends.

[0011] In one possible implementation, the calculation formulas for the input gate, forget gate, and output gate in step s102 are as follows: Forgotten Gate: f t =σ(W f ·[h t-1 ,x t ]+b f ); Input gate: i t =σ(W i ·[h t-1 ,x t ]+b i ); Cell state update: C t =f t *C t-1 +i t *tanh(W C ·[h t-1 ,x t ]+b C ); Output gate: o t =σ(W o ·[h t-1 ,x t ]+b o ); Hidden state: h t =o t *tanh(C t The LSTM has 128 cells.

[0012] In one possible implementation, the MC Dropout uncertainty model in step s102 obtains the prediction set μ through T random forward propagation samplings. i ,log(σ i 2 ), where T=1000, μ i For the mean, log(σ) i 2 The variance is logarithmic; the predicted mean μ = (1 / T)Σμ i Epistemic uncertainty variance Var ep =(1 / T)Σ(μ i -μ) 2 Aleatoric uncertainty variance Var al =(1 / T)Σexp(log(σ i 2 The total uncertainty standard deviation σ = sqrt(Var ep +Var al The 95% confidence interval is [μ-1.96σ, μ+1.96σ]. Heteroscedasticity loss function: Loss = (1 / 2)exp(-log(σ) 2 ))(y-μ) 2 +(1 / 2)log(σ 2 ), where y is the true value, μ is the predicted mean, and σ is the predicted mean. 2 To estimate the variance; the heteroscedasticity loss function is used to adaptively adjust for noise heterogeneity.

[0013] Secondly, the present invention also provides a canal water level probability prediction system based on MC Dropout and CNN-LSTM, comprising the following modules: Data acquisition module: Collects multi-source data, including hourly measured data such as water level, rainfall, upstream water flow, wind speed, and temperature; The model architecture module includes a CNN feature extraction layer, an LSTM temporal modeling layer, and an MC Dropout uncertainty model. The CNN feature extraction layer uses a one-dimensional convolutional structure to perform convolution operations on the input sequence. The LSTM temporal modeling layer feeds the convolutional output into LSTM units, controlling long-term dependencies through input gates, forget gates, and output gates. The MC Dropout uncertainty model embeds a Dropout layer between the LSTM layer and the fully connected layer, retaining random deactivation during the prediction phase. Model training and inference module: Training is performed based on the PyTorch framework and Adam optimizer, as well as the early stopping mechanism; during the inference phase, MC sampling is performed to generate probability output.

[0014] As described above, the beneficial effects of the present invention are: (1) High prediction accuracy: In extreme rainfall scenarios, the prediction accuracy is significantly better than the benchmark models ARIMA, LSTM, CNN-LSTM and LSTM-MC Dropout, and it can better capture nonlinear changes.

[0015] (2) Excellent uncertainty quantification: PICP reaches 96.9%, MPIW is 0.082m, realizing dynamic response and uncertainty decomposition, with narrow confidence interval and high coverage, avoiding overconfidence or too wide interval.

[0016] (3) Strong risk quantification capability: It reveals the driving mechanism of upstream water level as the main factor and rainfall as the key fluctuation source, and supports the reliability and economy of pump station scheduling decisions.

[0017] (4) High computational efficiency: MC Dropout does not require training multiple models, but achieves Bayesian approximation through sampling, which is suitable for engineering deployment; the heteroscedasticity loss function improves noise adaptability.

[0018] (5) Stable multi-step prediction: Supports 1-24 hour prediction, with a gradual increase in error and R² maintained above 0.956.

[0019] (6) High interpretability: By analyzing the importance of permutation features, the contribution of input variables is quantified, which conforms to the laws of hydrophysical analysis and improves the credibility of the model. Attached Figure Description

[0020] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0021] Figure 1A schematic diagram of the layout of the Hangzhou Hangjiahu Plain water conservancy system and drainage project provided in an embodiment of the present invention; Figure 2 A forecasting model structure diagram provided in an embodiment of the present invention; Figure 3 A schematic diagram of an LSTM cyclic cell structure provided in an embodiment of the present invention; Figures 4(a)-4(c) are comparison charts of the mean water level prediction and uncertainty quantification performance of different models provided in the embodiments of the present invention under typical rainfall events; Figure 5 An uncertainty decomposition and quantification analysis diagram of a water level prediction model based on MC Dropout is provided for an embodiment of the present invention; Figure 6 This invention provides a dynamic response diagram of uncertain components during a typical rainfall event, as shown in an embodiment of the invention. Figure 7 This is a trend diagram of the model prediction error variation under different prediction step sizes provided in the embodiments of the present invention; Figure 8 This is a permutation feature importance analysis diagram provided in an embodiment of the present invention. Detailed Implementation

[0022] Preferred embodiments of the present invention will now be described in detail with reference to the accompanying drawings, which form part of this application and are used together with the embodiments of the present invention to illustrate the principles of the present invention, but are not intended to limit the scope of the present invention.

[0023] In this document, the term "embodiment" means that a particular feature, structure, or characteristic described in connection with an embodiment may be included in at least one embodiment of the invention. The appearance of this phrase in various places throughout the specification does not necessarily refer to the same embodiment, nor is it a mutually exclusive, independent, or alternative embodiment. It will be explicitly and implicitly understood by those skilled in the art that the embodiments described herein can be combined with other embodiments.

[0024] A specific embodiment of the present invention, such as Figure 1 As shown, in order to meet the major needs of urban flood control and drainage in the river network area of ​​Hangzhou-Jiaxing-Huzhou Plain, the Gongchenqiao water level station in the river network of Hangzhou Plain is taken as the research object, aiming to overcome the challenge of accurate water level forecasting.

[0025] like Figure 2 As shown, this is a forecasting model structure diagram provided by an embodiment of the present invention. Based on this, a method for predicting canal water levels based on MC Dropout and CNN-LSTM is specifically disclosed, including the following steps: s101. Data Acquisition: Collect multi-source data, including hourly measured data such as water level, rainfall, upstream water flow, wind speed, and temperature; for example, collect hourly data from 2020 to 2024, such as water level, rainfall, upstream water level, wind speed, and temperature.

[0026] After data collection is completed, preprocessing is performed. Input the past 12-hour sequence, and finally output the water level probability forecast results and confidence intervals for the next 1, 3, 6, 12 and 24 hours.

[0027] s102. Model Architecture: This includes a CNN feature extraction layer, an LSTM temporal modeling layer, and an MC Dropout uncertainty model. The CNN feature extraction layer uses a one-dimensional convolutional structure to perform convolution operations on the input sequence. The LSTM temporal modeling layer feeds the convolutional output into LSTM units, controlling long-term dependencies through input gates, forget gates, and output gates. The MC Dropout uncertainty model embeds a Dropout layer between the LSTM layer and the fully connected layer, retaining random deactivation during the prediction phase. Figure 3 As shown, it is a structural diagram of an LSTM cyclic unit used in an embodiment of the present invention.

[0028] s103. Model Training and Inference: Training is performed using the PyTorch framework and Adam optimizer, along with an early stopping mechanism; during the inference phase, McLeod sampling is executed to generate probability outputs. Specifically, the learning rate can be set to 0.001, batch size to 64, maximum 100 epochs, and early stopping to 20 epochs.

[0029] To demonstrate the beneficial effects of the forecasting method of this invention, as shown in Table 1, the performance indicators of different models on the test set are compared, in conjunction with Figure 4- Figure 8 As can be seen, in typical rainfall events, the forecasting method described in this invention produces a prediction curve that closely fits the measured values, with the confidence interval covering extreme fluctuations. In multi-step forecasting, the 6-hour RMSE is 0.029m, and the 24-hour RMSE is 0.048m. Furthermore, it can be integrated into pump station scheduling systems, providing integrated support for "prediction-uncertainty assessment-decision making".

[0030] Table 1 Performance metrics of different models on the test set Model RMSE / m MAE / m R² PICP / % MPIW / m ARIMA 0.061 0.047 0.929 0.966 0.235 LSTM 0.024 0.019 0.987 — — CNN-LSTM 0.017 0.012 0.994 — — LSTM-MC Dropout 0.025 0.021 0.988 0.848 0.079 CNN-LSTM-MC Dropout 0.016 0.012 0.995 0.969 0.082 In this embodiment of the invention, step s101 involves imputing missing values, removing outliers, and normalizing the multi-source data to generate an input sequence X. t The input window is set to a multivariate time series of the past 12 hours; the missing values ​​are filled using the sliding window mean method; the outlier removal is based on the 3σ principle and linear interpolation; the normalization process uses the minimum-maximum normalization method.

[0031] In this embodiment of the invention, the formula for the convolution operation in step s102 is: F=Relu(X*W+b), where * represents the convolution operation, W is the convolution kernel matrix, b is the bias term, and Relu is the activation function; wherein the convolution kernel size is 3, the number of output channels is 64, and the local time dependence and short-term change trend are captured.

[0032] In this embodiment of the invention, the calculation formulas for the input gate, forget gate, and output gate in step s102 are as follows: Forgotten Gate: f t =σ(W f ·[h t-1 ,x t ]+b f ); Input gate: i t =σ(W i ·[h t-1 ,x t ]+b i ); Cell state update: C t =f t *C t-1 +i t *tanh(W C ·[h t-1 ,x t ]+b C ); Output gate: o t =σ(W o ·[h t-1 ,x t ]+b o ); Hidden state: h t =o t *tanh(C t The LSTM has 128 cells.

[0033] In this embodiment of the invention, the MC Dropout uncertainty model in step s102 obtains the prediction set μ through T random forward propagation samplings. i ,log(σ i 2 ), where T=1000, μ i For the mean, log(σ) i 2 The variance is logarithmic; the predicted mean μ = (1 / T)Σμ i Epistemic uncertainty variance Var ep =(1 / T)Σ(μ i -μ) 2Aleatoric uncertainty variance Var al =(1 / T)Σexp(log(σ i 2 The total uncertainty standard deviation σ = sqrt(Var ep +Var al The 95% confidence interval is [μ-1.96σ, μ+1.96σ]. Heteroscedasticity loss function: Loss = (1 / 2)exp(-log(σ) 2 ))(y-μ) 2 +(1 / 2)log(σ 2 ), where y is the true value, μ is the predicted mean, and σ is the predicted mean. 2 To estimate the variance; the heteroscedasticity loss function is used to adaptively adjust for noise heterogeneity.

[0034] Another specific embodiment of the present invention provides a canal water level probability prediction system based on MC Dropout and CNN-LSTM, comprising the following modules: Data acquisition module: Collects multi-source data, including hourly measured data such as water level, rainfall, upstream water flow, wind speed, and temperature; The model architecture module includes a CNN feature extraction layer, an LSTM temporal modeling layer, and an MC Dropout uncertainty model. The CNN feature extraction layer uses a one-dimensional convolutional structure to perform convolution operations on the input sequence. The LSTM temporal modeling layer feeds the convolutional output into LSTM units, controlling long-term dependencies through input gates, forget gates, and output gates. The MC Dropout uncertainty model embeds a Dropout layer between the LSTM layer and the fully connected layer, retaining random deactivation during the prediction phase.

[0035] Model training and inference module: Training is performed based on the PyTorch framework and Adam optimizer, as well as the early stopping mechanism; during the inference phase, MC sampling is performed to generate probability output.

[0036] In this embodiment of the invention, the system further includes a preprocessing module, which performs missing value imputation, outlier removal, and normalization on the multi-source data to generate an input sequence X. t The input window is set to a multivariate time series of the past 12 hours; the missing values ​​are filled using the sliding window mean method; the outlier removal is based on the 3σ principle and linear interpolation; the normalization process uses the minimum-maximum normalization method.

[0037] In this embodiment of the invention, the formula for the convolution operation is: F=Relu(X*W+b), where * represents the convolution operation, W is the convolution kernel matrix, b is the bias term, and Relu is the activation function; wherein the convolution kernel size is 3, the number of output channels is 64, and the convolution kernel size is 3, capturing local time dependence and short-term change trends.

[0038] In this embodiment of the invention, the calculation formulas for the input gate, forget gate, and output gate are as follows: Forgotten Gate: f t =σ(W f ·[h t-1 ,x t ]+b f ); Input gate: i t =σ(W i ·[h t-1 ,x t ]+b i ); Cell state update: C t =f t *C t-1 +i t *tanh(W C ·[h t-1 ,x t ]+b C ); Output gate: o t =σ(W o ·[h t-1 ,x t ]+b o ); Hidden state: h t =o t *tanh(C t The LSTM has 128 cells.

[0039] In this embodiment of the invention, the MC Dropout uncertainty model obtains the prediction set μ through T random forward propagation samplings. i ,log(σ i 2 ), where T=1000, μ i For the mean, log(σ) i 2 The variance is logarithmic; the predicted mean μ = (1 / T)Σμ i Epistemic uncertainty variance Var ep =(1 / T)Σ(μ i -μ) 2 Aleatoric uncertainty variance Var al=(1 / T)Σexp(log(σ i 2 The total uncertainty standard deviation σ = sqrt(Var ep +Var al The 95% confidence interval is [μ-1.96σ, μ+1.96σ]. Heteroscedasticity loss function: Loss = (1 / 2)exp(-log(σ) 2 ))(y-μ) 2 +(1 / 2)log(σ 2 ), where y is the true value, μ is the predicted mean, and σ is the predicted mean. 2 To estimate the variance; the heteroscedasticity loss function is used to adaptively adjust for noise heterogeneity.

[0040] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for probabilistic prediction of canal water levels based on MC Dropout and CNN-LSTM, characterized in that, Includes the following steps: s101. Data Acquisition: Collect multi-source data, including hourly measured data such as water level, rainfall, upstream water flow, wind speed, and temperature; s102. Model Architecture: This includes a CNN feature extraction layer, an LSTM temporal modeling layer, and an MC Dropout uncertainty model. The CNN feature extraction layer uses a one-dimensional convolutional structure to perform convolution operations on the input sequence. The LSTM temporal modeling layer feeds the convolutional output into LSTM units, controlling long-term dependencies through input gates, forget gates, and output gates. The MC Dropout uncertainty model embeds a Dropout layer between the LSTM layer and the fully connected layer, retaining random deactivation during the prediction phase. s103. Model Training and Inference: Training is performed based on the PyTorch framework and Adam optimizer, as well as an early stopping mechanism; during the inference phase, MC sampling is performed to generate probability output.

2. The forecasting method according to claim 1, characterized in that, In step s101, the multi-source data undergoes missing value imputation, outlier removal, and normalization to generate the input sequence X. t The input window is set to a multivariate time series of the past 12 hours; the missing values ​​are filled using the sliding window mean method; the outlier removal is based on the 3σ principle and linear interpolation; the normalization process uses the minimum-maximum normalization method.

3. The forecasting method according to claim 1, characterized in that, The formula for the convolution operation in step s102 is: F=Relu(X*W+b), where * represents the convolution operation, W is the convolution kernel matrix, b is the bias term, and Relu is the activation function; wherein the convolution kernel size is 3, the number of output channels is 64, and it captures local time dependence and short-term change trends.

4. The forecasting method according to claim 3, characterized in that, The calculation formulas for the input gate, forget gate, and output gate in step s102 are as follows: Forgotten Gate: f t =σ(W f ·[h t-1 ,x t ]+b f ); Input gate: i t =σ(W i ·[h t-1 ,x t ]+b i ); Cell state update: C t =f t *C t-1 +i t *tanh(W C ·[h t-1 ,x t ]+b C ); Output gate: o t =σ(W o ·[h t-1 ,x t ]+b o ); Hidden state: h t =o t *tanh(C t The LSTM has 128 cells.

5. The forecasting method according to claim 1, characterized in that, The MC Dropout uncertainty model in step s102 obtains the prediction set μ through T random forward propagation samplings. i ,log(σ i 2 ), where T=1000, μ i For the mean, log(σ) i 2 The variance is logarithmic; the predicted mean μ = (1 / T)Σμ i Epistemic uncertainty variance Var ep =(1 / T)Σ(μ i -μ) 2 Aleatoric uncertainty variance Var al =(1 / T)Σexp(log(σ i 2 The total uncertainty standard deviation σ = sqrt(Var ep +Var al The 95% confidence interval is [μ-1.96σ, μ+1.96σ]. Heteroscedasticity loss function: Loss = (1 / 2)exp(-log(σ) 2 ))(y-μ) 2 +(1 / 2)log(σ 2 ), where y is the true value, μ is the predicted mean, and σ is the predicted mean. 2 To estimate the variance; the heteroscedasticity loss function is used to adaptively adjust for noise heterogeneity.

6. A canal water level probability prediction system based on MC Dropout and CNN-LSTM, characterized in that, Includes the following modules: Data acquisition module: Collects multi-source data, including hourly measured data such as water level, rainfall, upstream water flow, wind speed, and temperature; The model architecture module includes a CNN feature extraction layer, an LSTM temporal modeling layer, and an MC Dropout uncertainty model. The CNN feature extraction layer uses a one-dimensional convolutional structure to perform convolution operations on the input sequence. The LSTM temporal modeling layer feeds the convolutional output into LSTM units, controlling long-term dependencies through input gates, forget gates, and output gates. The MC Dropout uncertainty model embeds a Dropout layer between the LSTM layer and the fully connected layer, retaining random deactivation during the prediction phase. Model training and inference module: Training is performed based on the PyTorch framework and Adam optimizer, as well as the early stopping mechanism; during the inference phase, MC sampling is performed to generate probability output.

7. The forecasting system according to claim 6, characterized in that, The system also includes a preprocessing module, which performs missing value imputation, outlier removal, and normalization on the multi-source data to generate an input sequence X. t The input window is set to a multivariate time series of the past 12 hours; the missing values ​​are filled using the sliding window mean method; the outlier removal is based on the 3σ principle and linear interpolation; the normalization process uses the minimum-maximum normalization method.

8. The forecasting system according to claim 6, characterized in that, The formula for the convolution operation is: F=Relu(X*W+b), where * represents the convolution operation, W is the convolution kernel matrix, b is the bias term, and Relu is the activation function; the convolution kernel size is 3, the number of output channels is 64, and it captures local time dependence and short-term change trends.

9. The forecasting system according to claim 8, characterized in that, The calculation formulas for the input gate, forget gate, and output gate are as follows: Forgotten Gate: f t =σ(W f ·[h t-1 ,x t ]+b f ); Input gate: i t =σ(W i ·[h t-1 ,x t ]+b i ); Cell state update: C t =f t *C t-1 +i t *tanh(W C ·[h t-1 ,x t ]+b C ); Output gate: o t =σ(W o ·[h t-1 ,x t ]+b o ); Hidden state: h t =o t *tanh(C t The LSTM has 128 cells.

10. The forecasting system according to claim 6, characterized in that, The MC Dropout uncertainty model obtains the prediction set μ through T random forward propagation samplings. i ,log(σ i 2 ), where T=1000, μ i For the mean, log(σ) i 2 The variance is logarithmic; the predicted mean μ = (1 / T)Σμ i Epistemic uncertainty variance Var ep =(1 / T)Σ(μ i -μ) 2 Aleatoric uncertainty variance Var al =(1 / T)Σexp(log(σ i 2 The total uncertainty standard deviation σ = sqrt(Var ep +Var al The 95% confidence interval is [μ-1.96σ, μ+1.96σ]. Heteroscedasticity loss function: Loss = (1 / 2)exp(-log(σ) 2 ))(y-μ) 2 +(1 / 2)log(σ 2 ), where y is the true value, μ is the predicted mean, and σ is the predicted mean. 2 To estimate the variance; the heteroscedasticity loss function is used to adaptively adjust for noise heterogeneity.

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