La integración de los conceptos revolucionarios en el sistema

The problem is predicting the flow of a typical urban basin from a sensor: the rain collected by a sensor located in the city sewer. And the goal is to predict the flow rate resulting from the rain. Usually, these two signals (rainfall and flow due to rain) have a relationship which is shown in another signal that turns the pluviometer signal into that of the flow (Figure 2). This signal has the shape of decreasing exponential functions, acting as a response to the stimulus of a system which relates both signals.

The flow level signal has two distinct causes, so it can be decomposed into two signals, one representing the daily pattern of water use by inhabitants of the city, and the other which is due to rainfall (Figure 3). Therefore, the system can be divided into two parts:

• The modeling of the daily flow rate.

• The prediction of the flow level caused by the rain.

The oscillatory behaviour of the periodic flow level signal (daily flow) depends on the quantity of water consumed by the citizens. For instance, the volume is lower at night and increases during the day with certain peak hours. The runoff caused by sporadic rainfall is added. Normally, both flows are studied separately since their origins differ, and this is the methodology used in the present study.

Modeling of the Daily Flow Rate by ANN

In the field of hydrology, despite the success in results ANNs have obtained (Govindaraju Figure 2. Rain collector sensor and flow rate sensor

Rain Collector Measured Flow Rate

a short hydrological history. The black box nature of ANNs has also contributed to the reluctance in using these tools despite the existence of techniques that can aid in model interpretation (Rabuñal, 2004).

We can obtain a representative signal of the mean flow in a day by taking only those samples which were not affected by the rain signal, and finding the average value of the samples corresponding to each moment in the day. Given that the samples were taken every 5 minutes, there are 288 samples per day. Therefore, this signal will have that length, as can be seen in Figure 4, where the central plain corresponds to the night hours. Peaks corresponding to the morning shower (about 10:00), lunch (15:00), and dinner (about 22:00) also can be seen. The first point corresponds to 15.00 (lunchtime). The measure- ment unit of the rain collected by the pluviometer is millimetres (mm) or litres per square metre (l/m2_).

Now, we can extract this signal from the whole runoff signal, so that the resulting signal will only be due to rain. As the signal extracted is an average value of the daily flow signal, there is a small error in the resulting signal. A second type of error is associated with samples affected by rain because flow due to rain and flow due to human activity are not independent. Weather (and, in this case, rain) affects the behaviour of the citizens (for example, people tend to stay at home), and so we cannot extract the real value of the flow due to human activity from the whole flow in the samples affected by rain. We can only extract the daily flow in normal conditions, and therefore there will be a small error. These errors will be corrected with the use of an ANN.

We use a feedforward ANN with a temporal window of length L as input and with a single output: The following sample is of the window, as shown in Figure 5.

Most of the ANN’s approaches to the prediction problem use a multilayer network trained with the backpropagation algorithm (Atiya et al., 1999). Consider a time series X₁, X₂, X_n, where it is required to forecast the value of X_n+1. The inputs to the ANN are typically chosen as the previous values and the output will be the prediction. Inputs and outputs Figure 3. Flow rate signal with the daily flow and the flow level caused by the rain

0 0.5 1 1.5 2 2.5 Daily flow

are pre-processed, this means extracting features from the inputs and transforming the target outputs in a way that might make it easier for the network to extract useful information from the inputs and associate it with the required outputs. The parameters used for the ANN and this creation are described in detail in Dorado et al. (2003). Without considering the effect of rain, the daily flow can be modeled with an ANN taking input values between 0 and 287 (a whole day), and in comparison to the average daily flow, as observed in Figure 6.

Figure 4. Average daily flow

Xn Xn-1 Xn-2 Xn-L X n+1 . . .

It must be noted that no analytical expressions exist that predict the shape of the daily curve, since it depends on a variety of factors linked to the usage of water — the numerous factors unmeasured which can drive the behaviour of this signal: industrial or commercial activity in the area, permanent or weekend residence, hygiene or alimentary habits, and so forth. Generally speaking, there is a curve formed by a high level (day) and a low one (night). In this way, the approach obtained fulfills the usual calculation standards. It is better to temper the adjustment of the average flow in order to take an average point, due to possible fluctuations in the flow variation depending on external circumstances, that is, to average out the influence of the many unmeasured drivers.