# Increasing the Reliability of Flood Embarments with Neural Imaging Method
## 5 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:  
* 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. \[I=[x_{1},\ x_{2},\ x_{3},\ \ldots,\ x_{208}] \tag{1}\]  
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, 1  
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. 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. 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). Mean Squared Error is the average squared difference between outputs and targets. Lower values are better.