Wavelet–ANN hybrid model evaluation in seepage prediction in nonhomogeneous earthen dams

Building earthen dams is essential in countries with specific climatic conditions and a need for storing water. These dams act as surface water retention structures and control floods, providing the opportunity for increased use of river water. Prior to construction, studies are conducted, but accurately predicting the hydraulic behavior of the dam body and surrounding geological formations is not always possible. Therefore, seepage after construction is almost certain. The intensity of seepage is acceptable as long as dam safety is not endangered, but assessing the risks associated with seepage and infiltration due to their inherent complexity is crucial for safety. Many dams have seepage from geological formations at the construction site, downstream of the dam or the dam body itself, which can lead to adverse consequences such as economic issues, high hydraulic gradients leading to erosion or boiling, and increased pore pressure that reduces effective stress. Therefore, addressing seepage from the downstream and dam body is important during study phases, implementation operations, and post-construction. Precisely calculating the amount of seepage flow and investigating methods to control or reduce it is essential to prevent potential life and financial hazards. Research on dams and water seepage is crucial due to the growing need for water resources and the importance of optimal resource use. Given the water shortage in Iran and the effects of climate change, research in this area can greatly assist in planning water resources, agriculture, drinking water supply, and economic development. Ersayin (2006) employed a feed-forward neural network (FF-NN) with a sigmoid activation function and one hidden layer to model seepage in earthen dams. The findings indicated that the model's accuracy did not improve and, in fact, the network became unstable when increasing the number of hidden layers. Miao et al. (2012) employed a genetic algorithm (GA) and a novel neural network model to predict seepage from the ‘Diaoli’ earthen dam in China. The findings indicated that the Genetic Algorithm and Levenberg-Marquardt (GA-LM) model had the ability to accurately predict seepage from the dam and outperformed conventional neural networks in extrapolation and interpolation. Nourani et al. (2012) analyzed the piezometric head in the core of an earthen dam in Sattarkhan, Iran, using artificial neural networks (ANNs). The study showed a strong agreement between predicted and measured values with an R² of 0.798 for the single ANN model. For the integrated ANN models of feed-forward backpropagation and radial basis function (RBF), the R² was found to be 0.87 and 0.67, respectively. Poorkarimi et al. (2013) introduced a new approach for estimating seepage flow from the foundation and body of an earthen dam based on data mining techniques. Soil permeability of the dam was estimated through the use of SEEP/W software. The results demonstrated that ANNs performed well as a tool for detecting patterns in data and accurately predicting seepage flow from the Fileh-Khase earthen dam's foundation and body. Kamanbedast & Delvari (2013) conducted a study on the Maroun earthen dam located in the Maroun River in Northern Bahaman. The study aimed to investigate the behavior of the dam's soil and seepage phenomenon using ANSYS software and comparing results with Geo-Studio software. Researchers found that the value of pore water pressure is influenced by several factors, including material stiffness, moisture, soil permeability, and applied loads. Pore water pressure can also reduce the shear strength of the soil, which may cause soil particles to move and result in piping and erosion of finer particles from the dam's body if the rate of reduction in pore water pressure caused by leakage is greater than the resistance of the soil particles. Jafari (2014) employed ANNs as a data mining method to predict seepage from the earthen dam body of Sattarkhan. The dataset consisted of 1,684 piezometric data points, which were divided into training and validation sets at an 80:20 ratio. Using appropriate statistical parameters, the neural network was effectively trained and showed a high capability for predicting seepage. Parkam Shadbad et al. (2023) conducted a study on seepage from the body of the Sattarkhan dam in Ahar, using the finite difference method through Flac3D software. The results revealed that the ratio of permeability between the shell and core had a significant effect on the seepage behavior of the dam, and reducing it led to a more uniform and homogeneous dam behavior, which was observed by examining the trend of changes in pore water pressure in the shell and core while moving from upstream to downstream. With a constant ratio, the seepage pattern in the dam remained unchanged, and only the time of occurrence of generated pore water pressure changed based on the permeability values of the materials. Ranković et al. (2014) developed a FNN model using an improved resilient backpropagation algorithm to predict the piezometric water level in dams. The measured data were compared with the results obtained from both the FNN models and multiple linear regression models, which are commonly used for analyzing the structural behavior of dams. These models were developed and tested on experimental data collected over a period of 9 years. The study findings suggest that FNN models can serve as powerful and essential tools for evaluating dams. Zhang et al. (2020) employed backpropagation neural network (BPNN) theories in conjunction with a GA to model and predict water overflow at dams. They compared the prediction results of the BPNN-GA model with those of a statistically guided model that used supervised values, using a sample dam in China. The findings revealed that the improved model enhanced nonlinear visualization and generalization capabilities, accurately predicting future water overflow with an acceptable level of precision. Using the established criterion, the safety status of the dam during flood season was evaluated. Ishfaque et al. (2022) developed a deep learning model to predict the leakage rate of Tarbela Dam in Pakistan, which is the world's second largest earth-filled dam. The dataset consisted of hydroclimatological, geophysical, and engineering features related to water inflow to the dam from 2014 to 2020. The data were organized as a time series, and recurrent neural network (RNN) and long short-term memory (LSTM) algorithms were applied for time series neural networks. The RNN-LSTM model showed an average mean squared error (MSE) of 0.12 and a performance score of 0.9451, with the lowest errors and high accuracy, leading to the best predicted results for dam leakage. Beiranvand & Rajaee (2022) conducted a review in which they revealed that machine learning models (37.53%), neural networks (27.63%), and hybrid models (21.05%) are the most common techniques for predicting infiltration. Among single models, ANNs, support vector regression, random forests (RF), and FF-NN have been used more frequently than other models. In addition, 81.25% of the hybrid models utilized neural network models, and 31.25% of the hybrid models used GAs. They reviewed a total of 46 research articles from 2005 to 2022. Duong & Tran (2023) developed ANN models for primary prediction of soil sediment velocity and resistance based on fiber type, soil type, fiber length, and fiber content. They utilized an extensive dataset of input parameters to develop the ANN models and compared their performance to that of regression models. In addition, sensitivity analyses were performed using the Garson algorithm and connection weight method to rank the effective input parameters in the ANN formulas. The results demonstrated that the ANN models had excellent prediction performance, with high coefficient of determination (DC) values (R² = 0.995 for sediment velocity and R² = 0.998 for resistance), indicating their potential for predicting these issues. Emami et al. (2019) analyzed water infiltration in the earthen dam of Shahid Kazemi in Boukan, Iran, using RBF and FF-NN models from ANNs. The results revealed good agreement between predicted and observed values, and it was concluded that the RBF model trained by the Levenberg–Marquardt algorithm with four hidden layers had high potential for predicting infiltration. In addition, the statistical parameter values of R² and root mean squared error (RMSE) were 0.81 and 33.12, respectively. Parsaie et al. (2021) utilized various soft computing models, including multilayer perceptron neural network (MLPNN), support vector machine, multiple adaptive regression splines (MARS), genetic programming, M5 algorithm, and group method of data handling, to predict piezometric pressure in the dam core and infiltration flow from the earthen dam body. The dataset collected from the absolute instrument mechanism during the past 94 months at the Shahid Kazemi Dam in Boukan were used for this purpose. The results showed that all models used for predicting piezometric pressure had an acceptable level of accuracy, with average error indices of R² = 0.957 and RMSE = 0.806 in the training phase and R² = 0.949 and RMSE = 0.932 in the testing phase. Moreover, the performance of all models, except for M5 and MARS algorithms, in predicting infiltration flow was almost similar. However, the MARS method exhibited the best performance, while the M5 algorithm had the weakest performance. Rehamnia et al. (2021) developed an efficient data-information artificial intelligence paradigm that combined an extended Kalman filter with a feed-forward ANN (EKF-ANN) to accurately estimate daily infiltration flow through earthen dams at the Fontaine Gazelles dam in Algeria. The study examined three powerful machine learning methods, including MLPNNs, RBF neural networks (RBF-NN), and RF, to assess the capability of EKF-ANN in predicting infiltration flow. The results showed that the EKF-ANN paradigm outperformed MLP, RF, and RBF-NN. In addition, the leverage approach was utilized to report the range of application of the presented models. Zhang et al. (2021) introduced a supervised infiltration flow monitoring model for concrete dams by considering delays in input factors and proposed an effective identification method for the delay process. The results indicated that the improved harmony search global optimization (HGWO) has stronger global optimization capability, and the HGWO-XGBoost model performs well for predicting infiltration flow in concrete dams. Moreover, compared to the traditional trial-and-error method, the proposed delay process calculation method in this study provides better effectiveness, which has significant value for monitoring and controlling infiltration flow in concrete dams. Markovic et al. (2021) developed a new method for predicting permeation pressure in incompatible cells using multiple sequential ANNs to address the issue of an incompatible cell with a small available dataset. The results showed that this approach achieved high accuracy in predicting values, which were more precise than those obtained using only one ANN for prediction. Chen et al. (2020) developed a framework for data mining and monitoring to control the safety of dam leakage. The study first investigated the effective factors in dam leakage, followed by training a kernel extreme learning machine (KELM) to predict dam leakage. Finally, an innovative global sensitivity analysis was provided to evaluate the relative importance of each input variable based on KELM. The simulation results from the case study demonstrated that KELM provides an acceptable prediction of leakage flow. Furthermore, water level fluctuations and precipitation were found to have a significant impact on the size of leakage. The sensitivity analysis offers a useful qualitative criterion for dam leakage, which has high value for monitoring and safety operations of dams. Ersayin (2006) studied seepage in a body of earthfill dam by ANNs. Seepage is investigated since both in the dam's body and under the foundation, it adversely affects dam's stability. This study specifically investigated seepage in the dam's body. Seepage in the dam's body follows a phreatic line. To understand the degree of seepage, it is necessary to measure the level of the phreatic line. This measurement is called piezometric measurement. Piezometric datasets that were collected from the Jeziorsko earthfill dam in Poland were used for training and testing the developed ANN model. Sazzad & Islam (2019) have studied about different seepage control methods in earthen dams, and the objective of that paper is to perform a comprehensive study of the incorporation of different seepage control measures to an earthen dam using a finite element method (FEM). SEEP/W, an FEM-based software, has been used for modeling and analysis of different seepage control measures. From the numerical analysis, it is observed that the use of rock toe combined with a horizontal filter is more beneficiary than they are used alone. The length of a horizontal blanket filter is a controlling factor to reduce the pore water pressure rather than its thickness. Attia et al. (2021) studied seepage through earthen dams with internal cut-off, Seepage through an earthen dam with internal cut-off is experimentally studied in the laboratory of Irrigation Engineering and Hydraulics Department, Faculty of Engineering, Alexandria University, Egypt, on a Hele-Shaw model. The effect of the relative penetration depth (d/D) and the relative distance of cut-off (X/D_w) on both the relative drop in the total head upstream (ΔH/H) and relative length of filter (L_f/H) is studied. The pervious layer thickness beneath the dam is also studied to investigate its effect on the filter length and total seepage discharge. The optimum position of the cut-off also is obtained from analysis of the experimental results. Experimental results are drawn in dimensionless form. Salem et al. (2019), in their research, studied seepage passing through the body of the earthen dam with/without an internal core experimentally and numerically, It is concluded that by increasing the side slopes (H:V), a noticeable drop of seepage line is observed with increasing downstream slope stability; by decreasing core permeability, increasing core thickness, base core thickness, and core penetration, the quantity of seepage and exit gradient decreased the upstream slope stability and increased the downstream slope stability. To explore the multifrequency mode of the stock, this paper proposes an adaptive wavelet transform model (AWTM). AWTM integrates the advantages of XGBoost algorithm, wavelet transform, LSTM, and adaptive layer in feature selection, time–frequency decomposition, data prediction, and dynamic weighting (Liu et al. 2020). Zhu et al. (2023) investigated the combined method of variational mode decomposition (VMD)-wavelet packet denoising method and the improved temporal convolutional network model to predict seepage in dams. Consequently, this paper combines the advantages of VMD decomposition and wavelet packet analysis. First, the contaminated signals are decomposed into several components by VMD, and the components with more noise are denoised by the wavelet packet threshold. Finally, the signal pieces are reconstructed to obtain the denoised signal.

Accurate estimation of seepage from earthen dams has always been an important challenge in the design of these huge structures. The use of instrumentation may provide an accurate estimate of this phenomenon to some extent, but the upcoming problems such as the failure of the instruments due to time, expenditure of money and manpower for reading, and so on, greatly reduce the efficiency of this method. It is common to use analytical solution methods proposed by different researchers to evaluate the amount of seepage from the body of earthen dams located on an impermeable bed due to their ease of use. However, in these analytical methods, assumptions are used to simplify the construction of equations, which may lead to big errors. Therefore, according to the stated content, the aim of this study is to provide a combined wavelet–ANN model to more accurately predict the amount of seepage from the body of earthen dams and eliminate the above problems, which is actually an accurate smart method to determine the amount of seepage in the body of nonhomogenous earthen dams. So, it has been tried to predict the phenomenon of seepage based on the data of the precise instruments of a specific dam and using the above method, and this method, the problems in the discussion of accurate estimation of seepage that existed in the previous methods have been solved. In this research, the capabilities of the ANN model as a black box model, as well as the wavelet soft calculations, which is a suitable tool for the preprocessing of unstable data, have been discussed; using the combined wavelet–ANN models, the amount of percolation in earthen dams has been predicted, and finally the results have been compared with the ANN model. In general, this method can be used in the future to determine the exact amount of seepage in porous media such as the body of earthen dams. One of the innovations of the present research is the use of the wavelet transform, unlike Fourier transformation (FT), which decomposes the signal or information series into sine and cosine functions and their harmonics; the signal is depicted on a group of functions called wavelets, which are derived from the mother wave. In this research, artificial intelligence and soft computing tools such as ANNs and wavelet transform are used to predict the piezometric pressure. Also, the combined neural wavelet method is able to provide a more accurate prediction of a phenomenon with uncertainty such as seepage in the porous medium, so the range and scope of using this method in engineering problems can be very wide. Hence, at the beginning of the work, the input data are extracted and then normalization and preprocessing of the data are done. Then, prediction is done in two cases, with wavelet transformation and without wavelet transformation. In the case of wavelet transformation, the data are divided into sub-data; these analyzed data are entered into the ANN model and prediction data are extracted. In the case without wavelet transformation, the data without decomposition is entered into the mentioned models and the output is obtained. In the next step, the results obtained from the different models of this research are validated. Regionally and globally, the phenomenon of leakage in all hydraulic structures that can be eroded is a natural phenomenon. How to predict leakage with advanced models is important, which is discussed in this study. The problems that are more visible in the past research are one-dimensional in terms of the research method, while in the present research, the combined method of ANNs and wavelet transform has been discussed, which is mentioned previously. The neural wavelet model is an advanced method in machine learning, which is a combination of wavelet transform and neural networks. One of the reasons the combined model was used for this research is its high efficiency in predicting the amount of leakage in earthen dams; previously where only one type of model was used, the accuracy level of the model was compared to the known models. It was low and not reliable, but in the combined model of this research, which is based on the neural wavelet and considered a hybrid model, it can practically be used to predict the amount of leakage in the body of all earthen dams.

The list and specifications of the installed piezometers in the Zonouz dam are provided in Table 1.

Two famous mother wavelets with explicit mathematical relationships are presented (Addison et al. 2006).

• (A) Mexican Hat wavelet, which is the second derivative of the Gaussian function (Equation (8)):

  

  (8)
• (B) Morlet wavelet, which consists of a Gaussian term and a sinusoidal term (Equation (9)):

  

  (9)

ANNs are one of the oldest methods used in data mining. In recent years, the application of ANNs has greatly extended in various engineering fields. A review of the technical literature reveals that ANNs have been successfully utilized for predicting the load-bearing capacity of piles, modeling soil behavior, site characterization, retaining wall design, settlement analysis, slope stability, tunnel and cavern design, groundwater flow, soil permeability, soil compaction, soil swelling, and soil classification.

As the learning rate α decreases, the number of required trial-and-error iterations to reach the desired performance index increases, but the problem-solving accuracy improves.

The wavelet–ANN and ANN have similarities and differences in their methodologies and applications. Both wavelet–ANNs and ANNs are widely used for prediction in various fields, such as hydraulic phenomena, meteorology, climatology, and hydrology.

The similarities are as follows:

• Both wavelet–ANNs and ANNs are used for prediction in diverse areas.

• They involve the processing of data to make predictions or classifications.

• Both networks can be trained using data to improve their predictive capabilities.

The differences are as follows:

• wavelet–ANNs specifically incorporate wavelet functions as activation functions, allowing for time-dependent spectral analysis and time–frequency decomposition of time series data.

• ANNs have a broader scope and can encompass various architectures beyond wavelet-based approaches.

To use data mining methods such as neural networks and fuzzy models, having an appropriate dataset is one of the basic requirements, and for each dataset, three features are necessary.

• 1. Reliability: This means being real and accurate.

• 2. Sufficient data: Having enough data based on the dimensions and complexities of the problem.

• 3. Comprehensive coverage: In an audit environment, reliability of data means that data are applicable for audit purpose and are sufficiently complete and accurate.

The text explains that Table 2 presents the normalized value, actual value, and maximum and minimum values of the data for input and output variables used in the ANN model. In addition, the table includes statistical parameters related to the two sets of training and testing data. The purpose of this presentation is to provide a clear understanding of the data used in the ANN model. Data normalization is a technique used to normalize the range of features in a dataset so that no feature is dominated by the others. This technique is used to improve the performance of the ANN model. The input and output variables are preprocessed using normalization or standardization techniques before training the ANN model. These techniques are used to improve the stability and performance of the ANN model.

The aim of this study is to predict the piezometric pressure in the Zonouz dam using ANN models and a combined wavelet–ANN model. The modeling system involves examining different models with different memories. In this modeling system, the best input pattern is determined first, followed by comparing the best pattern of each model with the other models to determine the most accurate model. Two important graphical criteria used in this study are.

• (a) a scaled linear plot between observed and computed data for verification and validation stages and

• (b) a scatter plot between observed and computed data for verification and validation stages.

In addition, the performance of the models can be examined using five numerical criteria, including the DC, MSE, RMSE, mean absolute error (MAE), and standard error of prediction (SEP). Among these criteria, the DC has a wide range of applications in evaluating predictive models.

In the above relationships, the value of N represents the number of observed, are computed data, are predicted values, and are mean of observed data.

The most common method for finding the optimal combination of weights in FF-NN is the backpropagation algorithm, which works based on reducing the first derivative. Since the backpropagation algorithm uses the minimization of the first derivative to determine the connection weights of the network, if the initial weight guesses are not suitable, the optimization process may get stuck in a local minimum. Therefore, in this study, the training phase has been repeated several times with different specifications for the layer or hidden layers to find the optimal network. The results of the seven input patterns are shown in Table 3.

Table 3

The results of the coefficient and the errors of the ANN model

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The results indicate that the input pattern four with three neurons in the input layer, eight neurons in the hidden layer, and only one output neuron representing piezometric pressure had the best performance among other input patterns (shown in bold in Table 3). The results also indicate that the proposed ANN model has been properly trained and can be used to predict seepage.

In ANN training, emphasis is placed on the scale with the greatest impact. Subsequently, to enhance model accuracy, preprocessed data utilizing DWT is utilized as input for the neural network. This approach ensures that key features are represented across both the detailed and coarse scales of the time series, enabling the neural network to assign distinct weights to each decomposed subseries.

A summary of the modeling results using this method can be seen in Table 4. As seen in the table, the best structure in the input pattern 1 is obtained with six neurons in the hidden layer and 130 iterations using the mother wavelet coif1 (shown in bold in Table 4). The comparative results of two prediction methods are given in Table 5.

Table 4

The results of the DC and errors obtained from the wavelet–ANN model are summarized

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As can be seen in the results of MSE and explanation coefficient for the two methods of ANN and wavelet–ANN, the result of test and training in both statistical communities shows the appropriate and high efficiency of the wavelet method. From Figure 5, it can be seen that the combined wavelet–ANN method has an extremely high accuracy compared to the ANN model. The observational versus computational figures and the scatter of observational and computational data for the optimal state of both the wavelet–ANN and ANN models are shown in Figures (6)–(8).

In this research, an attempt was made to simulate piezometric pressure in the body of the Zonouz dam using ANN and wavelet–ANN models. The simulation was performed based on the dataset obtained from the piezometers installed in the body of the dam. In this paper, the first step was to ensure the accuracy of the piezometers and the recorded data, and then to use the data. The accuracy of the piezometers was investigated to make sure that the data collected were reliable. The model carried out in this research was based on a combined wavelet–ANN model, in which the amount of seepage in the body of earthen dams can be accurately predicted to a great extent, and this method is considered a fundamental method.

The use of these methods for model training and evaluation based on appropriate statistical parameters led to significant results:

• 1. Randomly dividing the data for model training and testing showed that the 80–20%, which is recommended in many references, is the optimal state.

• 2. Due to the multiscale structure of the wavelets, the used hybrid model has the ability to extract local and partial features, and in general, it provides a better understanding of the data structure in problems where there is uncertainty; in this research, it provided a more accurate prediction.

• 3. Using appropriate statistical parameters to evaluate the presented models can significantly help in identifying their accuracy and capability. Each of the statistical parameters used evaluates a specific criterion of the model. Based on such comprehensive and complete validation, it can be stated that the above models have good usability in predicting piezometric pressure in earthen dams.

• 4. Using the presented models and replacing them with the available precise tools, it is possible to witness a reduction in the costs associated with instrumentation in the body of earthen dams, a reduction in the significant costs of human resources for continuous reading of piezometers, and predicting seepage for the future.

• 5. Using the presented models and assigning more weight to the scale that has the most effect during the training of the ANN model, preprocessed data by the DWT has been considered as the input to the neural network. In this way, all the main features are visible in the fine and coarse time series scales, and the neural network assigns a specific weight to each of the decomposition subseries, leading to an improvement in the results of the wavelet–ANN model compared to ANN model.

• 6. According to the modeling done, it was found that the proposed model is well trained and has a high capability in predicting the seepage phenomenon, and this method can be introduced as a basic method for predicting the seepage phenomenon in porous media.

• 7. Due to the difference in geometric and physical specifications in earthen dams, in this study, such specifications were not considered as input to only investigate the exact amount of seepage through the combined intelligent model in a dam. Therefore, the results of this study can be used for all earthen dams.

For future research, this method can be introduced as a basic method for predicting the seepage phenomenon in porous media.

Data cannot be made publicly available; readers should contact the corresponding author for details.

The authors declare there is no conflict.