DYNA

2.1. Data gathering and processing

In order to check the energy consumption of one train, three MSAVDC meter devices, manufactured by Mors-Smitt, were installed in the front car of the train: one in the pantograph (circuit breaker), another in the auxiliary converter input, and the third in the braking resistors. These devices will allow the measurement of not only the overall train energy consumption in real time, but also the energy consumed by each subsystem: traction, auxiliary devices and rheostatic brake.

The train’s speed was measured by a Knorr sensor (model BB0457681100), fed by a phonic wheel on one axis of another car of the train.

After verifying the correct functionality of all the devices, measurements were made on August 4^th, 2014 with passengers on board. Twelve trips were measured in line 5 of MetroValencia, between Marítim-Serrería and

Alameda stations; six trips towards Alameda and six trips towards Marítim-Serrería.

2.2 Neural networks

The structure chosen to accomplish this objective is a two-layer feed-forward neural network because it is a common and a tested scheme, with great ability to adjust functions [14,15]. In addition, these networks are known by its classification in layers and connections between the units strictly forward, and do not form cycles or loops in the network. Feed-forward neural networks are the most commonly used in practical applications that use neural networks, obtaining very satisfactory results, fundamentally as pattern classifiers and function estimators.

The first layer, called the hidden layer, has a number of neurons that it is necessary to define. The second layer (the output layer) has a single neuron with a linear transfer function. Eq. (2) shows the formula of the network:

where O_k is the network output, M is the number of output elements, I_i is the input data, N is the number of input variables, w_ji is the synaptic weight of the first layer and w2_kj is the synaptic weight of the second layer. The synaptic weight w_ji, for example, defines the strength of a synaptic connection between two neurons, the presynaptic neuron j and the postsynaptic neuron i. This structure can identify non-linear relations between input and output data [14] using the Log-Sigmoid function as a transfer function between the hidden layer and the output layer.

The training method used is called the Back-Propagation, where the network is evaluated, the results are checked based on certain criteria, and the synaptic weights are changed in an iterative loop [14]. The chosen calibration criterion is the minimization of the Mean Square Error (MSE) between the network output and the target data, which is verified by deriving the MSE with respect to the network synaptic weights. The specific training algorithm used is called the Levenberg-Marquardt algorithm, which is very efficient and widely checked [14].

The neural network presented in this paper uses speed, acceleration, gradient and traction effort as input data and measured empirical energy consumption as target data. These input data provide good accuracy, thus making it unnecessary to consider another input data to calibrate on energy consumption. Once trained, the neural network may predict the train’s energy consumption (output) data with high accuracy, as proven when compared to the measured empirical data (target data).

2.3. Simulation model development

After training the neural network, hypothetical vertical alignments are specified with their respective speed profile, considering the optimal indications for efficient driving between two stations [14-16]:

• To accelerate to maximum acceleration, to maintain maximum speed, and to reduce speed in coasting before each of the points in which it is necessary to reduce speed.

• The same strategy as above, but with the difference of the coasting not occurring until minimum speed (or until a stop), but until a greater speed to this one below which the service brake is applied to reduce speed.

• Accelerating to the maximum acceleration to recover the maximum speed and so on.

Once the hypothetical vertical alignments have been determined, the trained neural network is applied to achieve the energy consumption (output) verifying them in each alignment, comparing them and obtaining the vertical alignment with the lowest energy consumption. It is necessary to clarify that speed optimization was not considered in this paper, but for each alignment, it was verified that the travel time between both stations were the same.

The following assumptions used by Yeh [17] are considered in this simulation:

• The vertical track profile is symmetrical regarding to a central axis.

• Parabolic curvatures are applied to the vertical curves while the gradient cannot exceed the maximum climbing ability of the train.

• Horizontal curvatures are negligible for this analysis.

• A concentrated mass is used to represent trains in motion.

• A train accelerates to its full power unless it exceeds the comfort-limited acceleration.

• The braking system can provide the maximum allowable comfort-limited deceleration rate.

3.1. Introduction

MetroValencia has six subway lines and three tram lines. It also has 132 stations with a total length of 146.8 km and has 121 trains [18]. Trips along line 5 were analysed, between Marítim-Serrería and Alameda stations. As for the traction and power systems of the network, there is only a single input voltage to the substations with a magnitude of 20 kV AC. There are, however, two different output voltages: 1,500 V DC, (used in all six subway lines) and 750 V DC (used in all three tram lines), with an annual energy consumption of around 64.4 GWh and 18.1 GWh, respectively. This energy is consumed by all elements and systems of MetroValencia. Considering the energy consumption of each network component, 70% of the overall energy goes to traction (53 GWh) while 24% goes to stations. Other power consumptions from the remaining elements are negligible [19].

3.2. Input data

Four variables were chosen as input data (gradient, speed, traction effort and acceleration). During the neural network training, all input variables and their combinations were tested until the one that provided the best fit with the target data was chosen.

Focusing on Line 5 of MetroValencia, particularly between the chosen stations, it is important to consider that there are three stations in between them, namely: Ayora, Amistat and Aragón. They have a total length of 2,720 m and the chosen route has four stops. There is a maximum gradient of 2% in this route. Fig. 2 shows a diagram of the vertical track layout of the studied route, indicating the gradient profile along the five stations of Metro Valencia’s line 5.

Figure 2. Vertical: layout between Marítim Serrería and Alameda and the stations (stops) in between them.

Source: The authors

Speed was measured using an odometer placed in one of the wheels of the monitored train. Acceleration is directly derived from the speed. Fig. 3 shows these two variables of the first trip.

Figure 3. Speed: (blue) and acceleration (orange) of the first trip between Marítim-Serrería and Alameda

Source: The authors

3.3. Target data

The monitored train was a Metro Series 4300 (Vossloh) with 4 cars, a maximum speed of 80 km/h, a nominal tension of 1,500 V DC and a power of 1,480 kW.

The energy consumption in the pantograph (measured in the circuit breaker) was monitored real time while the train performed conventional services with passengers on board. The measured energy consumption was used as target data.

The measuring devices provide the energy consumption measured in the circuit breaker of the train every second, as shown in Fig. 4. The Fig. 4 represents the training target of the neural network on the first trip.

Figure 4. Example: of the energy consumption measured in the circuit breaker on the first trip between Marítim-Serrería - Alameda stations

Source: The authors

4.1. Training of the Artificial Neural Network

Two different criteria were used to assess the performance of the network and to decide whether its training was successful. The first of which was the Pearson correlation coefficient (R) between the neural network output (modelled energy consumption) and the target data (measured energy consumption), which needs to be equal or greater than 90% for all the three subsets (training, validation and testing).

The second criterion was the relative Mean Square Error (rMSE), which is defined as follows in eq. (3):

where MSE is the Mean Square Error, and Var(Q) is the variance of the measured consumption data (target). The rMSE needs to be lower than 20% of the variance of the data for all three subsets (training, validation and testing) [20], in order to control the dependence of the neural network to the specific data used for training. The process of the creation, training, and validation of the neural network was performed using the Neural Fitting Tool, from MATLAB R2014a (The MathWorks, Inc.)

Different tests were performed by combining the four input variables previously defined so as to identify which fits the energy consumption data better. If the input variables are speed, acceleration, gradient and traction effort, the neural network satisfies all the criteria; with the rMSE being lower than 20% and the R coefficient being greater than 90% [21]. Those input variables were, therefore, chosen for the analysis due its significant impact on energy consumption.

The results (Fig. 5) show an average measured energy consumption of 7.29 kWh per km, while the network estimated an energy consumption of 7.11 kWh per km, which has a small deviation of 0.176 kWh per km (2.42%). Every trip was the same: each with four stops between the first station and the last, and in terms of train load.

Figure 5. Energy: consumption by trip

Source: The authors

4.2. Application of artificial neural networks on hypothetical vertical alignments

For applying the trained artificial neural network on alignments, three hypothetical vertical alignments scenarios between two stations with a length of 1,000 m were considered: the first scenario is a flat alignment; the second is the SVSA profile with a maximum depth d halfway between two stations of δ = 5 m (0.5% of total length) having the same elevation. The last is the SVSA profile with a maximum depth d halfway between two stations of δ = 10 m (1.0% of total length) having the same elevation. Fig. 6 shows the three hypothetical scenarios.

Figure 6. Hypothetical: scenarios of vertical alignments between two stations oft the same elevation

Source: The authors

After which, the trained neural network was implemented to estimate the energy consumption for every case using the input variables for each hypothetical scenario.

The results show a total energy consumption of 5.81 kWh per km for the flat alignment between two stations, 4.74 kWh per km for the SVSA with a maximum depth of δ = 5 m between two stations, and 4.94 kWh per km for the SVSA with a maximum depth of δ = 10 m between two stations. It was observed that the SVSA with a maximum depth of δ = 5 m between two stations recorded the lowest energy consumption, reducing it by 18.41% in comparison to the flat alignment (Fig. 7). Each trip had a duration of 86 seconds, which did not affect the travel time element of one trip from the other.

Figure 7. Total: energy consumption in the hypothetical vertical alignments

Source: The authors

Fig. 8 shows the energy consumption estimated by the neural network for the three cases in every location in the alignment.

Figure 8. Energy: consumption in the hypothetical alignments in every step

Source: The authors

4.3. Discussion

Fig.5 shows that the network adjusts the energy consumption, measured in the circuit breaker, reasonably well, reproducing the peaks from traction and valleys, where the train is coasting. However, the network omitted small oscillations in consumption, and indeed shows small oscillations and negative peaks that do not correspond to the registration. This shows that there is still room to further refine the training of the network, possibly with a post-processing of the output.

In any case, the trained network as shown above, with four input variables, provides a good estimation of the energy consumption of the train, and since it is always within the range considered for every variable, the network could be used to test other alternatives like other hypothetical vertical alignments so as to reduce energy consumption and improve efficiency.

The results of applying the neural network on the hypothetical vertical alignments scenarios between two stations oft the same elevation, with a length of 1,000 m, show that the SVSA with a maximum depth of δ = 5 m between two stations yields the lowest energy consumption, reducing it by 18.41% as compared to a flat alignment. This technical advantage is facilitated by gravity, both as the train accelerates at the first station and as it decelerates at the steep final station.

As for the flat alignment, Fig. 8 shows a peak of energy consumption at the beginning of the route when the train accelerates to reach cruising speed. Then, when the train coasts, energy consumption is reduced. Finally, when service brake is applied, a traction energy consumption of almost zero results.

As for both SVSA alignments, Fig. 8 shows a peak of energy consumption at the beginning of the route when the train accelerates to reach cruising speed. Then, when the train coasts, energy consumption is reduced. Later, while the train is coasting, it arrives to a slope which gradually increases energy consumption. Finally, there is a point where energy consumption presents another peak just before service brake is applied to stop at the next station.