Increasing the Reliability of Flood Embankments with Neural Imaging Method

This paper presents an innovative system of many artificial neural networks that enables the tomographic reconstruction of the internal structure of a flood embankment. An advantage of the proposed method is that it allows us to obtain high-resolution images, which essentially contributes to early, precise and reliable prediction of operational hazards. The method consists in training a cluster of separate neural networks, each of which generates a single point of the output image. The simultaneous and parallel application of the set of neural networks led to effective reconstruction of the internal structure of a deposition site for floatation tailings. Results obtained from the study allow us to solve the low resolution problem that usually occurs with non-invasive imaging methods. This effect was possible thanks to the design of a new intelligent image reconstruction system.


Introduction
Floods are one of the most frequent natural disasters that have disastrous consequences [1,2].One way to enclose the range of flooded areas, in the vicinity of reservoirs and rivers, is to raise the flood embankment level [3].By doing this, it is possible to reach a higher freshet level over the main river-bed, and therefore to constrain the flood.However, this produces rapidly increasing amounts of water in the valley between the flood embankment, leading to accelerated water flow and flood wave propagation.It causes erosion of the upstream face of the embankment (and of the reservoir) and may destroy it.Additionally, considering the limited filtering capability of the embankment body, high water levels can cause the partial destruction of the embankment.For these reasons, the design of flood embankments with respect to their location, shape and material is extremely complicated.Despite a significant progress in the field of design and construction of flood embankments, there unexpected events may occur.Therefore, the design of a cost-effective, and foolproof, device for the monitoring of the state of flood embankments or reservoirs is critical to prevent the destructive effects of flood events.
Methods to prevent natural disasters, such as floods and flooding, through constant monitoring and supervision of technical facilities such as flood embankments, dams and landfills, can be divided into two main groups.The first group are traditional methods, whose characteristic feature is the spot measurements.Spot measurements provide information about a small fragment of the flood dam, which makes it uncertain when assessing such threats as water seeping through the internal part of the embankment.
The group of traditional methods includes: Geodetic monitoring (detection of structural deformation by manual measurements with benchmarks and automatic using micromirrors), hydrogeological monitoring (detection of anomalies caused by soaking dams by observing piezometric pressures in piezometers installed in the dams and near and distant foreground), geotechnical monitoring (detection of anomalies in the geological structure of the native embankment and reservoir by deep drilling and push probes), seismic monitoring (detection of building stability disturbances by means of accelerometers, which are excited whenever they identify vibrations of a certain level), and visual assessment of technical condition (direct observation conducted by staff) [4].
The second group are methods enabling full visualization of cross-sections of specific flood bank.These are usually methods that use information technology.These methods include specialized IT systems for the analysis of large data sets (big data) generated by systems of many separate sensors located in various places of flood barriers.These methods include Electrical Impedance Tomography (EIT), too.Obtaining a cross-sectional image of a flood embankment with the use of spot sensor systems is very expensive.A large number of sensors requires constant maintenance, which means that the cost of maintaining such monitoring systems for flood dams is very high.In this aspect, tomographic systems are more economical solution.Until now, the main barrier to their widespread use in flood control monitoring was the insufficient resolution of the reconstructed images of the interior of the dams.The neural imaging method presented in this paper, thanks to the use of an original algorithm that uses many neural networks, enables obtaining a high resolution tomographic image.Thanks to this, the method eliminates two main barriers accompanying the problem of monitoring flood embankments-it enables obtaining a holistic image of the cross-section of the dam and generates a high resolution image.
Currently, many methods are used to model and monitor flood control dams.In most cases, the practical applications of these methods are made possible by the use of information technology and computers.Among the methods used for modeling and prediction of phenomena occurring inside the flood embankments are: deterministic methods [5], statistical methods [6], probabilistic methods [7], the Hasofer-Lind reliability index [8], harmonic analysis [9], heuristic methods based on fuzzy logic [10,11], genetic algorithms [12].Other methods used in maintenance support systems for flood protection are: Support Vector Machine [13], Non-linear Shear Strength Criterion [14], as well as artificial neural networks (ANN) [15,16].Currently, the main application area of ANNs are predictive issues, improving operational processes by identification [17] or classification of faults [18].
The most widely used algorithms for tomographic image reconstruction include deterministic methods [5], stochastic methods, artificial neural networks [19], hybrid optimization methods and topological methods (level-set methods).Deterministic methods are characterized by the fact that they look for a local minimum of the objective function that is continuous in a given variability range.Stochastic methods make use of the objective function only in test points of the examined area, without imposing additional requirements on continuity and differentiability of the function.In addition, the global minimum of the objective function is searched for in a defined set of allowable values of design variables.Artificial neural networks are used to achieve the desired solution in a very short time, practically on-line.This method consists in selecting a suitable neural network and collecting training data for the network.ANNs behave like approximation systems and have a certain capacity to generalize training data.Hybrid optimization methods combine features of deterministic and stochastic methods.In the first stage of calculations, the stochastic algorithm usually finds the global minimum of the objective function.Once this algorithm's efficiency starts to decrease, a deterministic algorithm is introduced as it can find a solution in a small number of iterations.In hybrid methods, genetic algorithms and the simulated annealing method are often used as stochastic algorithms.This paper presents a new technique for monitoring the state and performance of flood embankments by neural imaging.It is an advanced tomographic reconstruction method for flood embankments, walls and dams.The neural architecture of the proposed innovative intelligent imaging system ensures higher-resolution images of the cross-section of the scanned object.The novelty of the proposed flood embankment monitoring system that distinguishes it from previous solutions lies in the use of a unique system of interconnected neural networks.The research used the original system consisting of 2012 separately trained neural networks.By generating a reconstructed image, each of the ANNs has the same input vector, consisting of 208 measurements coming from the electrode system.

The Study Object Description
The object of the study was generalized and comprised dams and flood banks of water reservoirs, deposition sites for liquid waste, rivers, canals, etc.Specifically, the study investigated the Żelazny Most tailings pond located in south west of Poland between the towns of Lubin and Głogów.The pond is situated in a natural valley between moraine hills in the upper basin of Rudna River.The operation of Żelazny Most is managed by Rudna-based Tailings Management Division of the Polish mining conglomerate KGHM Polska Miedź S.A.
The " Żelazny Most" tailings pond is a deposition site for flotation tailings.It is currently the sole deposition site for flotation tailings from the mines of KGHM Polska Miedź S.A. Due to its size, " Żelazny Most" is one of the largest tailings ponds in the world.It stretches over a 1410-hectare area and is surrounded by a 14.3-kilometre dam, the maximum dam height being 55 m.A topographic model of the Żelazny Most tailings pond is shown in Figure 1.This paper presents a new technique for monitoring the state and performance of flood embankments by neural imaging.It is an advanced tomographic reconstruction method for flood embankments, walls and dams.The neural architecture of the proposed innovative intelligent imaging system ensures higher-resolution images of the cross-section of the scanned object.The novelty of the proposed flood embankment monitoring system that distinguishes it from previous solutions lies in the use of a unique system of interconnected neural networks.The research used the original system consisting of 2012 separately trained neural networks.By generating a reconstructed image, each of the ANNs has the same input vector, consisting of 208 measurements coming from the electrode system.

The Study Object Description
The object of the study was generalized and comprised dams and flood banks of water reservoirs, deposition sites for liquid waste, rivers, canals, etc.Specifically, the study investigated the Żelazny Most tailings pond located in south west of Poland between the towns of Lubin and Głogów.The pond is situated in a natural valley between moraine hills in the upper basin of Rudna River.The operation of Żelazny Most is managed by Rudna-based Tailings Management Division of the Polish mining conglomerate KGHM Polska Miedź S.A.
The "Żelazny Most" tailings pond is a deposition site for flotation tailings.It is currently the sole deposition site for flotation tailings from the mines of KGHM Polska Miedź S.A. Due to its size, "Żelazny Most" is one of the largest tailings ponds in the world.It stretches over a 1410-hectare area and is surrounded by a 14.3-kilometre dam, the maximum dam height being 55 m.A topographic model of the Żelazny Most tailings pond is shown in Figure 1.Apart from its basic function of a deposition site for floatation tailings, a reservoir created in the central part of "Żelazny Most" also serves as a settling pond for clarifying supernatant waters used in the flotation cycle and, due to its high capacity, as a dosing and storage tank for excess mine and process water.Figure 2a shows the photograph of the earth embankment around the tailings pond.Figure 2b shows the measuring equipment that collects various kinds of data and thus allows for constant monitoring of the state of the embankment.To improve the safety of the reservoir, the following geophysical methods are currently applied: Apart from its basic function of a deposition site for floatation tailings, a reservoir created in the central part of " Żelazny Most" also serves as a settling pond for clarifying supernatant waters used in the flotation cycle and, due to its high capacity, as a dosing and storage tank for excess mine and process water.Figure 2a shows the photograph of the earth embankment around the tailings pond.Figure 2b shows the measuring equipment that collects various kinds of data and thus allows for constant monitoring of the state of the embankment.To improve the safety of the reservoir, the following geophysical methods are currently applied:  The measurements are made with specialist measuring instruments, and obtained data require a complex signal processing and results analysis in the form of profiles, cross sections or geophysical maps.Figure 3. shows the distribution of measurement and control equipment around the Żelazny Most tailings pond.

Research Problem and Objective
The motivation behind this study is the fact that the currently used systems for monitoring of the state and performance of the embankment around the investigated tailings pond can only measure the dam parameters at specified points.Despite a large number of measuring points and the use of many measurement methods, it is impossible to completely rule out the risk of dam failure.The measurements are made with specialist measuring instruments, and obtained data require a complex signal processing and results analysis in the form of profiles, cross sections or geophysical maps.Figure 3. shows the distribution of measurement and control equipment around the Żelazny Most tailings pond.The measurements are made with specialist measuring instruments, and obtained data require a complex signal processing and results analysis in the form of profiles, cross sections or geophysical maps.Figure 3. shows the distribution of measurement and control equipment around the Żelazny Most tailings pond.

Research Problem and Objective
The motivation behind this study is the fact that the currently used systems for monitoring of the state and performance of the embankment around the investigated tailings pond can only measure the dam parameters at specified points.Despite a large number of measuring points and the use of many measurement methods, it is impossible to completely rule out the risk of dam failure.

Research Problem and Objective
The motivation behind this study is the fact that the currently used systems for monitoring of the state and performance of the embankment around the investigated tailings pond can only measure the dam parameters at specified points.Despite a large number of measuring points and the use of many measurement methods, it is impossible to completely rule out the risk of dam failure.Although they store historical data in a comprehensive database, these systems do not predict an upcoming failure in advance so as to allow for taking effective measures to repair the embankment or even to evacuate people from flood risk areas.
To design a suitable device for solving the above-mentioned problem, a modified electrical impedance (electrical resistance) tomography method was used [4,19,20].The electrical resistance method consists in the analysis of propagation of generated electrical current in a body.The method is based on the determination of changes in electrical impedance (resistance) of the tested soil.The Wenner system was used in the study.With this method, you do not have to spread apart or change positions of the electrodes, which significantly reduces the time of measurements.Prior to measurements, relevant data regarding the spacing geometry, profile lengths and measurement parameters must be entered into the apparatus.
A typical electrical impedance tomography image has a relatively low resolution.In order to eliminate well-known typical defects of electrical impedance tomography, a model of an intelligent monitoring system for flood embankments was developed.The key element of the model was an electrical impedance tomography device for the image reconstruction of the embankment, inside by means of a properly designed cluster of artificial neural networks.A unique feature of the proposed solution that distinguishes it from other, well known concepts is the fact that it generates a color value of each and every pixel of the output image using a separate neural network.The primary objective was to improve the resolution of tomographic reconstruction images and to increase the system's capability to detect various types of anomalies inside dams and flood embankments.

Experimental
The experiments were performed on a material model of flood embankment.The model was provided with a system of 16 measuring electrodes that were spaced at equal distances along the profile line (Figure 4).The model also comprised an Electrical Impedance Tomography (EIT) device that was designed and constructed by the authors of this study.The role of the EIT was to:

•
Generate electric current with specific parameters (voltage, intensity, frequency, amplitude) for individual pairs of electrodes, • Read voltage between individual electrodes, • Transmit the above data to the output port in format for data analysis.Although they store historical data in a comprehensive database, these systems do not predict an upcoming failure in advance so as to allow for taking effective measures to repair the embankment or even to evacuate people from flood risk areas.
To design a suitable device for solving the above-mentioned problem, a modified electrical impedance (electrical resistance) tomography method was used [4,19,20].The electrical resistance method consists in the analysis of propagation of generated electrical current in a body.The method is based on the determination of changes in electrical impedance (resistance) of the tested soil.The Wenner system was used in the study.With this method, you do not have to spread apart or change positions of the electrodes, which significantly reduces the time of measurements.Prior to measurements, relevant data regarding the spacing geometry, profile lengths and measurement parameters must be entered into the apparatus.
A typical electrical impedance tomography image has a relatively low resolution.In order to eliminate well-known typical defects of electrical impedance tomography, a model of an intelligent monitoring system for flood embankments was developed.The key element of the model was an electrical impedance tomography device for the image reconstruction of the embankment, inside by means of a properly designed cluster of artificial neural networks.A unique feature of the proposed solution that distinguishes it from other, well known concepts is the fact that it generates a color value of each and every pixel of the output image using a separate neural network.The primary objective was to improve the resolution of tomographic reconstruction images and to increase the system's capability to detect various types of anomalies inside dams and flood embankments.

Experimental
The experiments were performed on a material model of flood embankment.The model was provided with a system of 16 measuring electrodes that were spaced at equal distances along the profile line (Figure 4).The model also comprised an Electrical Impedance Tomography (EIT) device that was designed and constructed by the authors of this study.The role of the EIT was to:   Specifically, the investigated cases of embankment failure were seepage and overflows of varying location, shape and intensity.The biggest hazard for tailings ponds, flood dams and embankments is micro-instability (Figure 5c).Specifically, the investigated cases of embankment failure were seepage and overflows of varying location, shape and intensity.The biggest hazard for tailings ponds, flood dams and embankments is micro-instability (Figure 5c).To validate the material model, we designed an electrical resistance tomography (TERT) device suitable for outdoor use (Figure 6).The TERT device consists of three key modules: (1) A power supply, (2) a signal modulator with protection system, as well as (3) a multiplexer with communication interface.Like in the material model, 16 electrodes were connected to the interface (Figure 7).The role of the signal modulator was to adjust AC modulation in such a way that individual electrode pairs produced the highest signal-to-noise ratio (SNR).The multiplexer was used for rapid and systematic voltage switching between individual pairs of measuring electrodes.It is vital that the switching process does not affect the measurement of AC voltage and intensity.
As with the EIT device, data obtained with the TERT system were processed by cloud computing with image reconstruction software.Figure 8 shows different layouts of the electrodes in the flood embankment enabling 2D and 3D image reconstruction.
To validate the material model, we designed an electrical resistance tomography (TERT) device suitable for outdoor use (Figure 6).The TERT device consists of three key modules: (1) A power supply, (2) a signal modulator with protection system, as well as (3) a multiplexer with communication interface.
Data obtained from the EIT material model was validated via the TERT system and was then used to develop a neural model for image reconstruction enabling the generation of several thousand training examples that can later be used to train a cluster of artificial neural networks.To validate the material model, we designed an electrical resistance tomography (TERT) device suitable for outdoor use (Figure 6).The TERT device consists of three key modules: (1) A power supply, (2) a signal modulator with protection system, as well as (3) a multiplexer with communication interface.Like in the material model, 16 electrodes were connected to the interface (Figure 7).The role of the signal modulator was to adjust AC modulation in such a way that individual electrode pairs produced the highest signal-to-noise ratio (SNR).The multiplexer was used for rapid and systematic voltage switching between individual pairs of measuring electrodes.It is vital that the switching process does not affect the measurement of AC voltage and intensity.As with the EIT device, data obtained with the TERT system were processed by cloud computing with image reconstruction software.Figure 8 shows different layouts of the electrodes in the flood embankment enabling 2D and 3D image reconstruction.Data obtained from the EIT material model was validated via the TERT system and was then used to develop a neural model for image reconstruction enabling the generation of several thousand training examples that can later be used to train a cluster of artificial neural networks.
To generate 10542 training cases (defined as historical data), a dedicated program to solve a simple problem using the finite element method was developed.In order to develop the algorithm and its validation, the numerical model and laboratory model were used.The prepared solution successfully solves the inverse problem by reconstructing the image representing the real object.Like in the material model, 16 electrodes were connected to the interface (Figure 7).The role of the signal modulator was to adjust AC modulation in such a way that individual electrode pairs produced the highest signal-to-noise ratio (SNR).The multiplexer was used for rapid and systematic voltage switching between individual pairs of measuring electrodes.It is vital that the switching process does not affect the measurement of AC voltage and intensity.As with the EIT device, data obtained with the TERT system were processed by cloud computing with image reconstruction software.Figure 8 shows different layouts of the electrodes in the flood embankment enabling 2D and 3D image reconstruction.Data obtained from the EIT material model was validated via the TERT system and was then used to develop a neural model for image reconstruction enabling the generation of several thousand training examples that can later be used to train a cluster of artificial neural networks.
To generate 10542 training cases (defined as historical data), a dedicated program to solve a simple problem using the finite element method was developed.In order to develop the algorithm and its validation, the numerical model and laboratory model were used.The prepared solution successfully solves the inverse problem by reconstructing the image representing the real object.

Results and Discussion
The innovative concept of neural algorithm for tomographic image reconstruction was dictated by the need to improve reconstructed image resolution, as well as to increase the sensitivity of the monitoring To generate 10542 training cases (defined as historical data), a dedicated program to solve a simple problem using the finite element method was developed.In order to develop the algorithm and its validation, the numerical model and laboratory model were used.The prepared solution successfully solves the inverse problem by reconstructing the image representing the real object.

Results and Discussion
The innovative concept of neural algorithm for tomographic image reconstruction was dictated by the need to improve reconstructed image resolution, as well as to increase the sensitivity of the monitoring system to changes occurring inside the flood embankment.The array of 16 electrodes generates a vector of 208 voltage measurements between individual pairs of the electrodes.If voltage values are known, it is therefore possible to calculate both the impedance and conductivity of soil between the electrodes.
During the testing of many variants of neural networks, it was found that the classification networks are too imprecise and not capable of covering all possible cases that might occur inside flood embankments and dams.To eliminate this problem, a neural model was designed based on the following assumptions:

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Every point of the output image is generated by a separate neural network with 208 values of output voltage.

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There is an interdependence individual points of the output image.As a result, every neural network generating values of a single point of the image can be trained independently using randomly-generated initial weights and bias.

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The neural networks assigned to the output image points can solve both classification and regression problems.In the case of a classification problem, the generated image may be monochrome or have several colors/shades, and then the classifier assigns a given point to a specific color.
Due to a high number of both data and neural networks for training, the realization of the assumptions required the use of supercomputers.
The input vector consisted of 208 measurement cases, as shown in Equation (1).Each element contained a voltage between an individual pair of the electrodes. (1) The output vector of each of 2012 neural networks contained only one element corresponding to the color of a single pixel.
Figure 9 shows the schema of the applied neural network model.The network has 208 inputs, 10 neurons in the hidden layer and 1 neuron in the output layer.The hidden layer uses a logistic transfer function.In the output layer, the transfer function is linear.During the testing of many variants of neural networks, it was found that the classification networks are too imprecise and not capable of covering all possible cases that might occur inside flood embankments and dams.To eliminate this problem, a neural model was designed based on the following assumptions:

•
Every point of the output image is generated by a separate neural network with 208 values of output voltage.

•
There is an interdependence between individual points of the output image.As a result, every neural network generating values of a single point of the image can be trained independently using randomly-generated initial weights and bias.

•
The neural networks assigned to the output image points can solve both classification and regression problems.In the case of a classification problem, the generated image may be monochrome or have several colors/shades, and then the classifier assigns a given point to a specific color.
Due to a high number of both data and neural networks for training, the realization of the assumptions required the use of supercomputers.
The input vector consisted of 208 measurement cases, as shown in Equation (1).Each element contained a voltage between an individual pair of the electrodes.
The output vector of each of 2012 neural networks contained only one element corresponding to the color of a single pixel.
Figure 9 shows the schema of the applied neural network model.The network has 208 inputs, 10 neurons in the hidden layer and 1 neuron in the output layer.The hidden layer uses a logistic transfer function.In the output layer, the transfer function is linear.Figure 10 shows the model of a cluster of 2012 neural networks generating output image of a 2012-point resolution.Each of the neural networks (N1, N2, N2012) is described by the same input vector but trained independently of the other networks.For the model to operate correctly, all the 2012 neural networks must be trained and simultaneously generate single points that create first the output vector and then the output image.The output vector is converted to a grid of points with the cross-section of the investigated flood embankment.Figure 10 shows the model of a cluster of 2012 neural networks generating output image of a 2012-point resolution.Each of the neural networks (N1, N2, N2012) is described by the same input vector but trained independently of the other networks.For the model to operate correctly, all the 2012 neural networks must be trained and simultaneously generate single points that create first the output vector and then the output image.The output vector is converted to a grid of points with the cross-section of the investigated flood embankment.
Figure 10 shows the model of a cluster of 2012 neural networks generating output image of a 2012-point resolution.Each of the neural networks (N1, N2, N2012) is described by the same input vector but trained independently of the other networks.For the model to operate correctly, all the 2012 neural networks must be trained and simultaneously generate single points that create first the output vector and then the output image.The output vector is converted to a grid of points with the cross-section of the investigated flood embankment.The EIT neural model was built by designing a physical model based on the research and observation of the real object.This process was as follows: 1.
Developing an algorithm for simulating teaching case generation.In order to develop the algorithm, the physical model and the finite element method were used.Training of 2012 separate neural networks.The output of each ANN is a real number, corresponding to the conductance of a single pixel of the reconstructed output image.The input of each of the 2012 neural networks is a vector of 208 measurements for a given case. 5.
To visualize one reconstruction, 2012 neural networks with an identical input vector were used, however each of ANN has a different output.Each of the 2012 ANN generates the real value of the pixel of reconstructed image.
In the discussed case, the neural network outputs were real numbers, which means that each of the networks had to solve a regression problem.Results given below concern network training by the Levenberg-Marquardt algorithm.The total number of historical cases was 10542.All cases were randomly divided into three datasets: Training, validation and test, in the following percentages: 70%, 15%, and 15% (Figure 11a).The highest Mean Squared Error (MSE) was found in the validation set and amounted to 0.000525.A smaller error of 0.00045 was observed for the training set.The level of regression for the three sets was very high and equal to 0.999.These values prove high quality of the trained neural network (Figure 11b).The EIT neural model was built by designing a physical model based on the research and observation of the real object.This process was as follows: 1. Developing an algorithm for simulating teaching case generation.In order to develop the algorithm, the physical model and the finite element method were used.In the discussed case, the neural network outputs were real numbers, which means that each of the networks had to solve a regression problem.Results given below concern network training by the Levenberg-Marquardt algorithm.The total number of historical cases was 10542.All cases were randomly divided into three datasets: Training, validation and test, in the following percentages: 70%, 15%, and 15% (Figure 11a).The highest Mean Squared Error (MSE) was found in the validation set and amounted to 0.000525.A smaller error of 0.00045 was observed for the training set.The level of regression for the three sets was very high and equal to 0.999.These values prove high quality of the trained neural network (Figure 11b).Another tested network quality indicator was a regression, R. When R is equal to 1, this means a close relationship, while 0 indicates a random relationship.As it can be observed in Figure 12b, the value of R in the three cases is close to 1.This can particularly be observed in the test and validation sets, which is very favorable.When the values are close to 1, this indicates good fitting of ANN results (output vectors) to patterns in individual datasets (training, validation and test).
Figure 12 shows the correlation diagrams for the analyzed network.It can be observed that the number of results that go beyond the reference lines is small, and their correlation is high.This is proved by the overlapping correlation lines for all the examined cases: The training, validation, and test sets, and for the total of all three sets.The gradient plot shows that the gradient value was stable for several preceding epochs (the dynamics of change was close to zero).Examining a similar point in the momentum-plot one can observe that-it reaches its minimum value at Epoch 37 and that the value does not change over successive six epochs.The last (bottom) curve in the plot denotes the number of preceding epochs that did not improve the validation deviation.It was assumed that if the validation error does not decrease after six successive epochs, then the training process should be stopped.That is why, the training process ended at Epoch 43.The gradient plot shows that the gradient value was stable for several preceding epochs (the dynamics of change was close to zero).Examining a similar point in the momentum-plot one can observe that-it reaches its minimum value at Epoch 37 and that the value does not change over successive six epochs.The last (bottom) curve in the plot denotes the number of preceding epochs that did not improve the validation deviation.It was assumed that if the validation error does not decrease after six successive epochs, then the training process should be stopped.That is why, the training process ended at Epoch 43. Figure 14 shows the plot of mean squared error recorded during artificial neural network training.It can be observed that the MSE values are low and there are no major variations in plot shape, which points to the lack of network overfitting and, at the same time, to high effectiveness of the designed system for tomographic image reconstruction.Figure 14 shows the plot of mean squared error recorded during artificial neural network training.It can be observed that the MSE values are low and there are no major variations in plot shape, which points to the lack of network overfitting and, at the same time, to high effectiveness of the designed system for tomographic image reconstruction.Figure 14 shows the plot of mean squared error recorded during artificial neural network training.It can be observed that the MSE values are low and there are no major variations in plot shape, which points to the lack of network overfitting and, at the same time, to high effectiveness of the designed system for tomographic image reconstruction.Comparing the output images with their patterns one can clearly notice a high convergence of details.The concentration of colors in specified pixels allows for the assessment of location, size, intensity, range and expansion direction of the overflow.Figure 16 shows a comparison between the patterns and the outputs generated by the designed neural tomographic system.Reconstructed images are shown on the right.Comparing the output images with their patterns one can clearly notice a high convergence of details.The concentration of colors in specified pixels allows for the assessment of location, size, intensity, range and expansion direction of the overflow.Comparing the output images with their patterns one can clearly notice a high convergence of details.The concentration of colors in specified pixels allows for the assessment of location, size, intensity, range and expansion direction of the overflow.

Conclusions
The study presented a new non-destructive method for flood embankment condition assessment based on electrical impedance tomography and artificial neural network.The proposed solution was effectively applied to the model described in the study, yielding promising results.The use of a system of 2012 simultaneously operating neural networks produced accurate output images of the preset patterns.The quality of these images was good enough to correctly identify the nature of potential failure, as well as to assess the rate of changes taking place inside the embankment.
Considering the fact that, with the proposed method, measurements are taken at regular time intervals, the solution is a useful tool for determining the rate of overflow propagation.Not only does this information enable accurate condition assessment of the flood embankment, it also ensures effective prediction of the moment of embankment failure.As a result, one can take appropriate measures to prevent embankment failure.
During the tests, the electrodes were arranged in one row, which led to obtaining 2D cross-sections.It can be assumed that by arranging the electrodes on a triangular or square grid, it will be possible to obtain high-quality solid (3D) cross-sections.Thanks to 3D imaging with one visualization, you can obtain spatial information about the technical condition of a flood bank part with a specific length.
The described in this paper neural imaging method can be used to monitor the protections of the tailings ponds, flood embankments, dams and many technical objects of similar construction and purpose.

• 14 •
Ground-penetrating radar (GPR), • Seismic engineering, • Electrical resistance tomography, • Gravimetric methods, • Electromagnetic methods.Each of the above methods is based on a different geophysical phenomenon depending on the expected results and on undesired conditions such as factors that distract wave propagation and wave intensity measurement.Appl.Sci.2018, 8, x FOR PEER REVIEW 4 of Ground-penetrating radar (GPR), • Seismic engineering, • Electrical resistance tomography, • Gravimetric methods, • Electromagnetic methods.Each of the above methods is based on a different geophysical phenomenon depending on the expected results and on undesired conditions such as factors that distract wave propagation and wave intensity measurement.

Figure 2 .
Figure 2. Photographs of earth embankment: (a) the earth embankment around the tailings pond, (b) the measuring equipment.

Figure 3 .
Figure 3. Distribution of measurement and control equipment around the pond.

Figure 2 .
Figure 2. Photographs of earth embankment: (a) the earth embankment around the tailings pond, (b) the measuring equipment.

14 •
Appl.Sci.2018, 8, x FOR PEER REVIEW 4 of Ground-penetrating radar (GPR), • Seismic engineering, • Electrical resistance tomography, • Gravimetric methods, • Electromagnetic methods.Each of the above methods is based on a different geophysical phenomenon depending on the expected results and on undesired conditions such as factors that distract wave propagation and wave intensity measurement.

Figure 2 .
Figure 2. Photographs of earth embankment: (a) the earth embankment around the tailings pond, (b) the measuring equipment.

Figure 3 .
Figure 3. Distribution of measurement and control equipment around the pond.

Figure 3 .
Figure 3. Distribution of measurement and control equipment around the pond.

•
Generate electric current with specific parameters (voltage, intensity, frequency, amplitude) for individual pairs of electrodes, • Read voltage between individual electrodes, •Transmit the above data to the output port in format for data analysis.

Figure 4 .
Figure 4. Flood embankment model with electrodes and EIT (Electrical Impedance Tomography) device.The cross section of the flood embankment model was designed in such a way as to reflect key parameters of the real object as closely as possible.Different types of embankment damage were investigated.Examples of flood embankment failure types are shown in Figure 5.

Figure 4 .
Figure 4. Flood embankment model with electrodes and EIT (Electrical Impedance Tomography) device.

Figure 5 .
Figure 5. Examples of flood embankment failure types.

Figure 5 .
Figure 5. Examples of flood embankment failure types.

Figure 5 .
Figure 5. Examples of flood embankment failure types.

Figure 9 .
Figure 9. Model of a neural network generating single output image.

Figure 9 .
Figure 9. Model of a neural network generating single output image.

Figure 10 .
Figure 10.Model of a neural network cluster generating 2012-point resolution output image.Figure 10.Model of a neural network cluster generating 2012-point resolution output image.

Figure 10 .
Figure 10.Model of a neural network cluster generating 2012-point resolution output image.Figure 10.Model of a neural network cluster generating 2012-point resolution output image.

2 .
Generating a set of 10542 historical cases.Each case consists of two vectors: Input and output.The input vectors consist of 208 voltage measurements.The output vectors are equal to the cardinality of the output image and count the 2012 actual values corresponding to the conductance of each pixel.3. Division of the data set into three sets: Teaching, validation, and test.4.

2 .
Generating a set of 10542 historical cases.Each case consists of two vectors: Input and output.The input vectors consist of 208 voltage measurements.The output vectors are equal to the cardinality of the output image and count the 2012 actual values corresponding to the conductance of each pixel.3. Division of the data set into three sets: Teaching, validation, and test.4. Training of 2012 separate neural networks.The output of each ANN is a real number, corresponding to the conductance of a single pixel of the reconstructed output image.The input of each of the 2012 neural networks is a vector of 208 measurements for a given case. 5. To visualize one reconstruction, 2012 neural networks with an identical input vector were used, however each of ANN has a different output.Each of the 2012 ANN generates the real value of the pixel of reconstructed image.

Figure 11 .
Figure 11.Training data division and single neural network training results: (a) training, validation and test samples, (b) mean squared error and the level of regression values.

Figure 11 .
Figure 11.Training data division and single neural network training results: (a) training, validation and test samples, (b) mean squared error and the level of regression values.

Figure 12 .
Figure 12.Data correlation in ANN (artificial neural networks) training, testing and validation.

Figure 13 shows
Figure 13 shows three plots for ANN training parameters versus epochs (pass of all the training data through one iteration loop).It can be seen that network training process ended with Epoch 43.The gradient plot shows that the gradient value was stable for several preceding epochs (the dynamics of change was close to zero).Examining a similar point in the momentum-plot one can observe that-it reaches its minimum value at Epoch 37 and that the value does not change over successive six epochs.The last (bottom) curve in the plot denotes the number of preceding epochs that did not improve the validation deviation.It was assumed that if the validation error does not decrease after six successive epochs, then the training process should be stopped.That is why, the training process ended at Epoch 43.

Figure 12 .
Figure 12.Data correlation in ANN (artificial neural networks) training, testing and validation.

Figure 13
Figure 13 shows three plots for ANN training parameters versus epochs (pass of all the training data through one iteration loop).It can be seen that network training process ended with Epoch 43.The gradient plot shows that the gradient value was stable for several preceding epochs (the dynamics of change was close to zero).Examining a similar point in the momentum-plot one can observe that-it reaches its minimum value at Epoch 37 and that the value does not change over successive six epochs.The last (bottom) curve in the plot denotes the number of preceding epochs that did not improve the validation deviation.It was assumed that if the validation error does not decrease after

14 Figure 13 .
Figure 13.Plots of selected parameters in ANN training.

Figure 14 .
Figure 14.Plot of mean squared error in neural network training.

Figure 15
Figure 15 shows the error histogram plot for the network outputs and the patterns.The vertical bars in the plot represent deviations from the pattern.It can be noted that the highest deviations are very low, close to zero.The shape of the histogram resembles that of a normal distribution curve.In addition, this indicates a high quality of the produced solution.

Figure 13 .
Figure 13.Plots of selected parameters in ANN training.

14 Figure 13 .
Figure 13.Plots of selected parameters in ANN training.

Figure 14 .
Figure 14.Plot of mean squared error in neural network training.

Figure 15
Figure 15 shows the error histogram plot for the network outputs and the patterns.The vertical bars in the plot represent deviations from the pattern.It can be noted that the highest deviations are very low, close to zero.The shape of the histogram resembles that of a normal distribution curve.In addition, this indicates a high quality of the produced solution.

Figure 14 .
Figure 14.Plot of mean squared error in neural network training.

Figure 15
Figure 15 shows the error histogram plot for the network outputs and the patterns.The vertical bars in the plot represent deviations from the pattern.It can be noted that the highest deviations are

Figure 16
Figure16shows a comparison between the patterns and the outputs generated by the designed neural tomographic system.Reconstructed images are shown on the right.

Figure 16 .
Figure 16.Comparison of patterns and outputs.

Figure 16
Figure16shows a comparison between the patterns and the outputs generated by the designed neural tomographic system.Reconstructed images are shown on the right.

Figure 16 .
Figure 16.Comparison of patterns and outputs.

Figure 16 .
Figure 16.Comparison of patterns and outputs.
measurements between individual pairs of the electrodes.If voltage values are known, it is therefore possible to calculate both the impedance and conductivity of soil between the electrodes.