Subwaveform classification by using neural networks

4.2 Subwaveform classification by using neural networks

Until now, it could be seen that there are only limited improvements if one uses the basic neural network and do retracking with it. Thus, a different approach will be tested for this task.

Thereby, an algorithm is applied which uses the input data from a neural network to define the best peak of the waveform. Thus, not the whole waveform is regarded by the algorithm but only a smaller part of it, which is defined by a window. Thus, the algorithm is only analysing the pattern which is in the current field of view. In this algorithm, the output of the neural network is used, which gives the probability of the label, which is tested. This information is then used for the computations of the new retracking algorithm. In the first step, the algorithm is explained in detail and shown, how it can be used to find the best peak position for the leading edge. The second step concern the neural network which is used in this algorithm and how the data sets have to be prepared for it.

4.2.1 A new retracking algorithm

In this approach, one uses the fact that neural networks provide the probability of each label.

The probability is calculated in this case now for a predefined window, which means that the neural network estimates which area has the highest probability to contain the leading edge.

The needed steps are explained in the following:

1. Window size: In the first step, the size of the window has to be defined, which is then used to detect the best peak inside the waveform. Thereby, the window has to be big enough to include a characteristic pattern, but at the same time, it should be small enough, that the preferred peak is distinguished. With a total length of 104 bins, two different window sizes can be tested which are 10 and 30 bins. In the following figures both windows compared to each other are shown:

(a) (b)

Figure 4.14: Examples of waveforms with the search window of 30 bins

As it can be seen in Figure 4.14, the search window of 10 bins only covers the leading edge itself and a small area around it, whereas the 30 bin window covers a more significant area so that the neural network can also learn characteristic pattern around the peak. However, it can be tested if it is already enough to use a small area around the peak and, which would help to distinguish the best area. At the same time, it can be useful that a wider area is used to

improve the possibilities to learn the characteristic pattern. Thus, further studies will show the best option.

2. Step size: After the size of the window, also the size of the steps have to be defined. This step size is used to move the window along the waveform. In this case, the step size 1 is chosen to make sure, that the algorithm misses no part of the waveform.

3. Neural network step: After the previous parameter is determined, the first area inside the window at its first position is used as input data for the network. Thus, one will receive the label and the probability of the area which is analysed. These two values will be stored for further calculations. However, besides these two values, the maximum peak n_k inside the window is counted. Hence, also the number, how often the same peak is inside a window with the labelled peak is stored. By this, additional information can be provided, because it is assumed that the peak with the leading edge is labelled more often as peak then a smaller one.

4. Calculate the mean Probability ¯P_k: After going through the whole waveform with the window, the same peaks are tracked multiple times. Thus, it is now possible to calculate a mean probability ¯P_kof each peak k:

¯P_k = ¹ n_k

nk

∑

P_k,i (4.10)

where P_k,iis the probability of the peak k at the ith time it is tracked. After this step, the mean probability of each peak inside the waveform is known and as additional information, it is recorded, how often it is labelled as a peak.

5. Estimating the best peak: A small peak may be labelled with a high probability as a peak, and the peak with the leading edge is labelled with a lower probability as a peak. Thus, the smaller peak would be chosen for the retracking approach instead of the other one. This prob-lem is tackled by the number, how often the peak is inside an area labelled as a peak. That means the mean probability ¯P_kis multiplied with the number n_k, how often it is labelled, which can be seen as a weight factor. Therefore, not only the probability value is regarded, but also how often the network regard this area as a peak is included:

p_k = max(¯P_k·n_k) (4.11)

where p_k is the position of the best peak according to the algorithm. After this step, the For-mulas (4.7) until (4.9) are used to estimate the position of the leading edge. In the diagram in Figure 4.15, the discussed steps are shown, and it provides a better overview of the whole al-gorithm. In Section 4.1.1 it was discussed, how the data has to be prepared for the use in neural networks. Also in Section 4.1.1 it was shown, how the parameters of the neural networks can be chosen. However, in the case of this algorithm, some differences have to be regarded which are explained in the next section.

4.2 Subwaveform classification by using neural networks 65

Waveforms

Creating window and define step size i

Waveform sample

Label and probability of the

sample Neural network

Save the maximum peak and count how often

it is labeled

End of waveform reached?

Move window i bins foreward

Yes

Calculate mean probability for each peak and calculate

the best peak Peaks with label,

probability and how often they are

labeled

Best peak position No

Figure 4.15: Diagramm of the developed algorithm

Preprocessing steps

Proprocessing the data: The main work is the same as explained for the network approach, which means that first the data has to be normalised and in a second step, the waveforms have to be labelled. The only difference now is, that not the whole waveform is used. Thus, only the area which is covered by the window is taken into account, which leads to the fact, that the whole area will get the same label. Therefore, two cases have to be distinguished:

1. Wanted peak is inside the window→label is peak 2. Wanted peak outside inside the window→label is noise

With this, one can now train and test the neural network. However, regarding the data, the pre-vious analysis has to be regarded. There, three sets are used with 600, 720 and 900 waveforms for training. However, the improvement is limited, and the best results are reached with 900 waveforms. However, because now smaller areas for analyses are used, it could be possible to reach also good results also with a smaller number of training data. Hence, in the next analysis 600 and 900 waveform samples are used for the analysis with 10 and 30 bin input windows.

With this, it will be possible to test all variations. Additionally, it can be seen, if the neural network can reach good results also with a smaller number of training data if the input area is smaller.

Network parameters: In a first step, the basic structure of the neural network can be defined.

Thus, it can already be said, that the input layer contains 10 or 30 neurons respectively. The output layer only contains now two neurons, one representing the peak and the other no peak.

This already leads to a much smaller neural network, compared to the previous ones. However, the other network parameter will be analysed in chapter A.2 as done before. In this chapter, the learning rate, the number of neurons of the hidden layer and the number of epochs will be defined. For the sake of convenience, these analyses are no further explained in this chapter, and only the resulting parameter is used.

4.2.2 Comparing the results with in situ data Using 10 input neurons

The parameters, which are used in this chapter are estimated in Appendix A.2. Thus, in the following table are the parameters for the neural networks which use the 10 bin input win-dow:

Table 4.7: Neural network parameters for a network with 10 input neurons Parameter 600 waveforms 900 waveforms

Hidden neurons 5 10

Learning rate 0.005 0.0075

Epochs 55 10

4.2 Subwaveform classification by using neural networks 67 After applying these parameters from Table 4.2.2 to the neural network, the time series in Figure 4.16 are gained. There it can be seen clearly, that the usage of 10 input neurons is not sufficient enough to capture the leading edges. In both cases either with 600 waveforms (a), (c) or with 900 waveforms (b) and (d), are significant differences between in situ water height and the calculated ones visible. However, in the second approach, an improvement can be seen, and the two graphs match better to each other.

(a) (b)

(c) (d)

Figure 4.16: Time series and residuals after using 10 neurons in the input layer and using 600 (a), (c) and 900 (b), (d) waveforms for training respectively

A look at the statistics fosters this assumption. In Table 4.2.2 it can be seen that there is a big improvement by increasing the number of training data sets. However, even the improved results are worse compared to the results in Table 4.1.3. At least it could be shown here, how significant the influence of the increase of training data is. Thus, it can be concluded that the usage of 10 input neurons is not able to detect the wanted peaks. In the next step, one can have a closer look at the 30 input neurons approach.

Table 4.8: The accuracy, mean and RMSE for tests with 600 and 900 training waveforms with 10 input neurons 600 waveforms 900 waveforms

Accuracy NN 72.4 % 87.8%

Mean 3.91 m 1.49 m

RMSE 4.79 m 1.84 m