4.1. Experiment Data and Setting
The experiment was designed and conducted based on the practical monitoring of an industrial park in Hebei Province, China. As mentioned in Section 3.1
, it is usually tricky to set up the monitoring equipment in the factories. Moreover, the government has established a monitoring system in which the monitoring stations are located at the cross point of the rectangular grid. The sparse layout makes it challenging to analyze the atmosphere distribution with the traditional Gaussian mechanism models. The data-driven method proposed is applied in the practical monitoring problem.
The experiment area is shown in Figure 5
, in which there are eight monitoring stations settled by the government, and the location marked with a red star is the monitoring-blind area to be analyzed. For the research aim, temporal monitoring equipment was arranged in the factory under negotiation. The temporal equipment was only for the research of the modeling, and it cannot be used in routine monitoring. The model built in this paper is expected to replace the temporal equipment with “Circumjacent Monitoring-Blind Area Inference”.
Limited by the network size and calculation load, the most related circumjacent points should be selected. The correlation degree of the points was calculated with the data from 14 days, shown in Figure 6
. Then five points were selected with the correlation degree, including Points 4, 8, 2, 1, and 5. The screening of the related points can reduce the network complexity and eliminate the effect of the sparse points from the spatial view. The selected points are shown in Figure 5
, with a different mark among all the points.
For the monitoring points, the atmospheric quality data were collected with the automation monitoring system. The atmospheric quality indexes included SO2 concentration, temperature, humidity, wind speed, and wind direction. The data in the experiment were monitored in January 2017. The monitoring interval was 30 min. The total number of data was 1488 in the experiment.
For the modeling of the neural network, the data were usually divided into three parts: training, validation, and testing. The number of data in the training and validation was 1100 sets, in which the validation part was selected with the hold-out method. The others were divided into two groups for the test (one group was 288 sets, and the other was 100 sets). For validation and testing, some error indicators were introduced to evaluate the network’s training. The indicators included the mean absolute error (MAE) and root mean squared error (RMSE).
For the networks in the experiment, five time series networks were built according to the number of circumjacent points. In the time series network, the inputs included the atmospheric quality indexes. The indexes were with the different units, and they were normalized to (0,1) when importing into the network. The output of the network was reversely normalized to restore the data in the original unit. The parameters of the network are listed in Table 1
. There were five time series networks (equal to the number of circumjacent points) in the fusion network, and the parameters in the table are for each network. For each time series network, the inputs included the target index SO2
and correlated indexes of temperature, humidity, wind speed, and wind direction. Then the number of inputs was five. The numbers of neurons in hidden layers were ensured with the empiric value according to the number of inputs and outputs.
Some related models are set as contrast methods:
(1) The basic neural network (BP network) was built, in which the SO2 concentration of five circumjacent points was imported into BP network, and the output was the blind area data. This method is abbreviated to BP;
(2) In the same fusion framework of this paper, the time series network was replaced with ARIMA to realize the prediction function. The prediction results of SO2 concentration in five points based on ARIMA were imported into the full connection layer. This method is abbreviated to ARIMA-FC;
(3) In the same fusion framework, the full connection layer was replaced with the classical fusion method of weighted sum. The prediction outputs of five points based on NARX were summed directly with the trial weights. This method is abbreviated to NARX-WS.
Our method is abbreviated to NARX-FC. In the experiment, each method was adjusted to obtain the relatively optimal results.
4.2. Experiment Result
The fusion network proposed in this paper was trained and validated in the experiment. For the validation, three groups of the data were divided based on the hold-out method to calculate the output error. For the intuitive comparison with the test results, the validation result errors were reversely normalized from (0,1), and the errors are listed in Table 2
. The errors in different subsets were approximate and within the accepted level. Then, the trained network can be regarded as available without divergency and overfitting.
When the network was established, two groups of the data were tested with the proposed method and contrast methods. In the first group, 288 sets of data were predicted. The second group was 100 sets. The results are shown in Figure 7
in which the concentration of SO2
is predicted with the time step delays. The input delay means the number of historical data used, which was 24 in the experiment. The output delay means the time steps to be predicted, and it was six in the test. That is, 24 sets of the monitoring data were used to predict the future data in the next six time steps. The data were used forward circularly. In Figure 7
, the reference true value and the prediction results of various methods are presented with lines in different colors.
In the prediction results of the blind area, the methods show different performance. For the methods of BP and ARIMA-FC, they cannot trace the trend closely, especially in the apparent fluctuation (like the 210–230 steps in the first group). The other methods based on the NARX perform better in the trend tracing. The drifting of NARX-WS is severe. The proposed method NARX-FC performs reliably in general.
To evaluate the different methods, the errors are calculated and shown in Figure 8
. The error indicators MAE and RMSE are listed in Table 3
It can be found from the error indicators in Table 2
and Table 3
that the errors in validation and testing are on the similar level. It proves that the network is steady in the experiment. The exhibition of the errors can explain the different performance of the methods. Similar to the trend in Figure 7
, the errors of BP and ARIMA-FC are large in the data fluctuation. The errors of NARX-WS increase gradually, and the phenomenon is in accord with the drifting. The errors of NARX-FC are generally stable, and they are smaller than others. The performance can also be seen from the error indicators. For MAE, NARX-FC performs better than the others. MAE of results in NARX-WS is the largest in the first group, while BP and ARIMA-FC are similar. While MAE of BP is the largest in the second group of data. RMSE reflects the overall closeness of the results to the average value. It can indicate the stability of the prediction methods. The sort of RMSE in different methods is similar to the trend of MAE, and the proposed method NARX-FC is more stable than the others in the prediction.