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Prediction of Influent Flow Rate: Data-Mining Approach

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Xiupeng Wei 1; Andrew Kusiak 2; and Hosseini Rahil Sadat 3

Abstract: In this paper, models for short-term prediction of influent flow rate in a wastewater-treatment plant are discussed. The prediction horizon of the model is up to 180 min. The influent flow rate, rainfall rate, and radar reflectivity data are used to build the prediction model by different data-mining algorithms. The multilayer perceptron neural network algorithm has been selected to build the prediction models for different time horizons. The computational results show that the prediction model performs well for horizons up to 150 min. Both the peak values and the trends are accurately predicted by the model. There is a small lag between the predicted and observed influent flow rate for horizons exceeding 30 min. The lag becomes larger with the increase of the prediction horizon. DOI: 10.1061/(ASCE)EY.1943-7897 .0000103. © 2013 American Society of Civil Engineers. CE Database subject headings: Data collection; Algorithms; Flow rates; Neural networks; Radar; Rainfall; Wastewater management; Water treatment plants; Predictions. Author keywords: Data-mining algorithms; Influent flow rate; Multilayer perceptron neural networks; Radar reflectivity; Rainfall; Wastewater-treatment plant.

Introduction To maintain stable effluent characteristics in a wastewatertreatment plant (WWTP), it is desirable to know in advance the influent flow rate to the WWTP. Wastewater characteristics such as biochemical oxygen demand (BOD), total suspended solids (TSS), and pH (Tillman 1991; Qasim 1998; Vesilind 2003) are strongly correlated to the influent flow rate. Prediction of the influent flow rate is helpful in the optimal scheduling of wastewater pumps. In practice, the influent flow rates are usually estimated by the operators based on experience and local weather forecasts (Kim et al. 2006). Such estimations, however, are not accurate enough to manage WWTPs, especially for plants that treat both municipal wastewater and storm rainfalls (Kurz et al. 2009). The precipitation may cause large variability of the influent flow rate, thus reducing the efficiency of WWTPs. Heavy rainfall overwhelms the wastewatertreatment system, causing spills and overflows. Several studies have been performed to model and predict the influent flow rate to WWTPs (Young and Wallis 1985; Yen 1986; Carstensen et al. 1998; Djebbar and Kadota 1998; Vojinovic et al. 2003). Using a direct k-step predictor to forecast the wastewater flow rate, Tan et al. (1991) obtained reliable predictions up to 2 h ahead for wet-weather sewer flow. Using recursive autoregressive with exogenous input (ARX) filters, a model based on the 1 Ph.D. Student, Dept. of Mechanical and Industrial Engineering, 3131 Seamans Center, Univ. of Iowa, Iowa City, IA 52242. E-mail: [email protected] 2 Professor and Chair, Dept. of Mechanical and Industrial Engineering, 3131 Seamans Center, Univ. of Iowa, Iowa City, IA 52242 (corresponding author). E-mail: [email protected] 3 M.S. Student, Dept. of Mechanical and Industrial Engineering, 3131 Seamans Center, Univ. of Iowa, Iowa City, IA 52242. E-mail: rahilsadat [email protected] Note. This manuscript was submitted on January 17, 2012; approved on September 27, 2012; published online on September 29, 2012. Discussion period open until November 1, 2013; separate discussions must be submitted for individual papers. This paper is part of the Journal of Energy Engineering, Vol. 139, No. 2, June 1, 2013. © ASCE, ISSN 0733-9402/ 2013/2-118-123/$25.00.

flow pattern estimation was able to handle rainy conditions for prediction horizons of a few hours (Lindqvist et al. 2005). Data mining is a promising approach for building prediction models. It is the process of finding patterns from data by algorithms versed on the crossroads of statistics and computational intelligence (Witten and Frank 2005). Successful data-mining applications in weather forecasting, manufacturing, science, and engineering have been reported in the literature (Kusiak and Li 2010; He and Kusiak 1997; Agard and Kusiak 2004; Cunha et al. 2006; Kusiak et al. 2009; Song and Kusiak 2007). This paper presents a data-mining approach to predict influent flow rate in a WWTP for a short-term period (up to 180 min ahead). The prediction model is constructed by data-mining algorithms using radar reflectivity data, rainfall rate data, and the historical influent flow rate data. The presented approach considers the impact of rainfall and local geography on the influent flow rate, which has not been discussed in the literature. Data provided by weather radar are important in weather forecasting (Ganguly and Bras 2003). Radar reflectivity data can be used to forecast weather several hours or even several days ahead. Rainfall data are introduced to provide storm water information at different locations in the vicinity of the wastewater-treatment plant. A multilayer perceptron (MLP) neural network is used to build the prediction model and compare its accuracy with that of models constructed by three other data-mining algorithms. The bestperforming algorithm is selected to build the prediction model. The prediction results are evaluated by prediction metrics and discussed in detail.

Data Collection and Preprocessing The historical values of influent flow rate, rainfall rate, and radar reflectivity are used to construct the prediction model. The influent flow rate data was collected at the Des Moines Wastewater Reclamation Facility (WRF) in Iowa. The WRF processed wastewater from 16 metropolitan-area municipalities, counties, and sewer districts in the Des Moines area. By recycling wastewater, the WRF supports public health and enhances the environment; it is also the preferred treatment facility for hauled liquid wastes.

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Table 1. Location Data for Tipping Buckets Name

Latitude

Tipping Tipping Tipping Tipping Tipping Tipping WRF

bucket bucket bucket bucket bucket bucket

1 2 3 4 5 6

N N N N N N N

Longitude

41.6230° 41.6005° 41.5694° 41.6147° 41.5060° 41.6008° 41.5713°

W W W W W W W

93.5515° 93.6091° 93.7020° 93.7801° 93.6712° 93.5245° 93.5555°

(denoted as −99) were present, implying that the radar signal was not detected. These null values are treated as missing values. When the reflectivity at the center and nine surrounding cells were all nulls, the average value of the preceding and succeeding neighbor values were used as the reflectivity for this particular tipping bucket. The radar data are also averaged over 15-min intervals. To improve prediction accuracy, the reflectivity at 1-, 2-, 3-, and 4-km constant altitude plan position indication (CAPPI) heights is used in this paper. The CAPPI (Doviak and Zrnic 1993) refers to a horizontal cross-section of data at a constant altitude. Using the reflectivity data at different heights allows prediction problems attributable to the plan position indicator (PPI) to be avoided; PPI is influenced by the ground geometry because the reflectivity data are considered at one constant height (Fabry et al. 1992; Baeck and Smith 1998). In total, six rainfall rate parameters and 24 reflectivity parameters around the six tipping buckets were used in this paper. In addition, influent flow rates of 30, 60, 90, and 120 min were used as inputs to construct the prediction model. All the data used in this research were collected in the period from January 1, 2007, to March 31, 2008. The preprocessed data set includes 43,768 data points and is divided into a training set with 32,697 data points (from January 1, 2007, to November 1, 2007) to build a prediction model by data-mining algorithms, and a test set with 11,071 data points (from November 1 to March 31, 2008) to evaluate the performance of the model. The description of the data set is summarized in Table 2. Different data-mining algorithms are used to build the prediction model for prediction of the influent flow rate. Two metrics, the mean absolute error (MAE) and mean square error (MSE), are used to measure prediction accuracy. In time-series analysis, MAE is commonly used to measure how closely the predictions come to the observations. Meanwhile, MSE is a way to quantify the difference between the values implied by the prediction method and the true values; it is a risk function corresponding to the expected value of the squared error loss. The expressions to calculate MAE and MSE are shown in Eqs. (1) and (2): n 1X jf − yi j n i¼1 i

ð1Þ

n 1X jf − yi j2 n i¼1 i

ð2Þ

MAE ¼ 0.5

MSE ¼

0.4 Rainfall rate (inch)


The influent flow rate data are measured at 15-s intervals. These data are then converted into 15-min averages to bring them to the same frequency as the rainfall rate data. The upper and lower limits on the influent flow rate are 0 and 260 million gallons per day, respectively. Values beyond these limits are considered outliers and are removed in preprocessing the data. The rainfall rate data (15 min) was collected at six tipping buckets in the vicinity of the WRF. Table 1 presents the detailed values of the latitude and longitude for these tipping buckets. Because the WRF facility handles wastewater and storm water from its north and west areas, the tipping buckets provide data useful for prediction of influent flow. Fig. 1 demonstrates that the rainfall rates vary among the tipping buckets despite the short distances between them. This is the main reason for using the data from all tipping buckets to build the prediction model. The radar data were recorded in Des Moines, Iowa, at the KDMX radar station located at latitude 41.7311° and longitude 93.7228°, approximately 32 km from the WRF. Because the radar image covers the locations of all tipping buckets, the reflectivity data at nine surrounding cells (the dimension of each cell is 1 × 1 km) around the center of the tipping bucket on the radar map and the reflectivity at the center are extracted and averaged for each tipping bucket. In the original data set, some null values

0.3

where fi = predicted value produced by model; yi = measured value; and n = number of test data points.

0.2 0.1

Multilayer Perceptron Neural Network

0 6 5

25 4

20 15

3 Tipping buckets

2 1

5 0

10 Time ( 15 min)

Fig. 1. Rainfall rates at six tipping buckets

To predict the influent flow rate, the multilayer perceptron neural network is used. The MLP is a feed-forward neural network algorithm that maps the input data into a desired output using historical data (Parlos et al. 1994a, b). A MLP consists of multiple layers of nodes in a directed graph, with each layer fully connected to the next. Except for the input nodes, each node is a neuron using

Table 2. Data Set Description Data set 1 2 3

Start time stamp (date)

End time stamp (date)

Description

2:00:00 a.m. (January 1, 2007) 2:00:00 a.m. (January 1, 2007) 12:30:00 a.m. (November 1, 2007)

11:45:00 p.m. (March 31, 2008) 12:15:00 a.m. (November 1, 2007) 11:45:00 p.m. (March 31, 2008)

Total data set: 43,768 observations Training data set: 32,697 observations Test data set: 11,071 observations

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Output layer

Input layer x1-6:rainfall x7-30:radar


y

x-31-34:history

Hidden layers Fig. 2. Architecture of MLP neural network

a nonlinear activation function (Gurney 1997). Generally, the multilayer perceptron consists of an input layer, an output layer, and one or more hidden layers. Each node in one layer connects, is assigned a certain weight, and connects to every node in the following layer. The specific architecture of the MLP used in this paper is shown in Fig. 2. There are 34 inputs in the input layer and one output in the output layer. The number of hidden layers is one or two, and it is determined in the training process. Learning in MLP occurs in the perceptron by changing connection weights as the training data get processed on the basis of the error in the output compared with the measured result (Haykin 1999). In science and engineering, MLPs are commonly applied to solve complex problems involving classification, regression, and time series (Hassoun 1995; Parlos et al. 1994a, b; Chaudhuri and Bhattacharya 2000). To compare performance of the MLP-generated models, datamining algorithms such as random forest, boosted tree, and support vector machine (SVM) have been used. The random forest algorithm was proposed by Breiman et al. (1984). It can be used for both regression and classification, and for parameter selection, interaction detection, and clustering. The random forest algorithm learns quickly and produces highly accurate classifiers for many applications (Liaw and Wiener 2002). The boosted tree algorithm usually improves performance of a single model by fitting many models and combining them for prediction. It uses the classification and regression tree to build a collection of models. Both variance and bias can significantly be reduced by boosting (Roe et al. 2005). The SVM is a supervised learning algorithm used in classification and regression. By mapping the original parameters through a nonlinear kernel function, SVM can construct a hyperplane or a set of hyperplanes in a high- or infinite-dimensional space. This feature makes SVM suitable for solving complex nonlinear classification problems (Wang 2005).

The data set described in Table 2 is used to train and test the prediction model. Table 3 summarizes the performance of all four algorithms tested in this paper. The MAE in Eq. (1) and MSE in Eq. (2) are used to select the most suitable algorithm. Of the MAE and MSE values, a smaller one indicates a more accurate and stable model. The computational results demonstrate that the MLP neural network model outperforms other algorithms. The MAE and MSE of MLP are the smallest among all the algorithms, and the correlation coefficient of MLP is also the highest. The SVM performs better than random forest and boosted tree, and random forest performs worst. Therefore, MLP is finally selected for building the prediction models at all time stamps. Fig. 3 shows the first 300 observed and predicted influent flow rates from data set 3 of Table 2. Most predicted values are very close to the observed values, and the predicted influent flow rate follows the trend of the observed flow rate. To obtain a generalized MLP network structure, 500 networks were trained with Broyden–Fletcher–Goldfarb–Shanno) algorithm (Becerikli et al. 2003). The number of hidden neurons was varied between five and 60, and five activation functions (namely, identity, logistic, hyperbolic, exponential, and sine function) were used. The sum squared error was used to determine the network error. The best-performing five networks are presented in Table 4. By building seven MLP prediction models at t þ 15, t þ 30, t þ 60, t þ 90, t þ 120, t þ 150, and t þ 180 min, respectively, the influent flow rate can be predicted up to 180 min ahead. Figs. 4 and 5 illustrate the first 300 predicted influent flow rates and the observed influent flow rate at t þ 30 and t þ 180 min ahead. In Fig. 5, it is shown that the predicted influent flow rate is close to the observed influent flow rate, and the trend for both predicted and observed values is the same. There is, however, a slight lag for the predicted values. This lag increases as the prediction horizon

Results and Discussion

Table 3. Prediction Accuracy of Four Algorithms

The influent flow rates at current time t, t þ 15, t þ 30, t þ 60, t þ 90, t þ 120, t þ 150, and t þ 180 min are predicted by data-mining algorithms. To identify the best-performing algorithm for the eight prediction horizons, prediction models at the current time t are selected to investigate the four data-mining algorithms.

Algorithm MLP Random forest Boosted tree SVM


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MAE (%)

MSE (%)

Correlation coefficient

1.09 3.04 1.77 1.47

4.21 20.69 11.16 5.46

0.988 0.945 0.97 0.985

70

65

55

50

45

40

35 Observed value 30

1

51

101

151 Test data (15 min)

Predicted value

201

251

Fig. 3. Prediction of influent flow rate at current time t

Table 4. MLP Network Structure Index

Network name

Training algorithm

1 2 3 4 5

MLP 34-58-1 MLP 34-19-1 MLP 34-8-1 MLP 34-19-1 MLP 34-11-1

BFGS 82 BFGS 48 BFGS 55 BFGS 131 BFGS 53

Error function

Hidden activation

Output activation

SOS SOS SOS SOS SOS

Tanh Tanh Logistic Tanh Logistic

Exponential Identity Exponential Logistic Logistic

lengthens. The lag can be clearly observed in Fig. 6, which predicts the influent flow rate at time t þ 180 min ahead. Even though the trend was successfully predicted, the response for the prediction model is slow. Figs. 6 and 7 illustrate the MAE and MSE, two metrics of prediction accuracy, for all eight prediction models at different prediction horizons. It is shown that both MAE and MSE slowly increase before t þ 30 min and then rapidly increase after this prediction

horizon. This means that the prediction accuracy of the model decreases after t þ 30 min. It is believed that the prediction model has acceptable accuracy before t þ 150 min. The performance of the prediction model is not of sufficient quality beyond t þ 150 min, even if the MAE is small. Predicting the influent flow rate 150 min ahead is valuable because this may provide enough time to arrange operators and schedule wastewater booster pumps. Considering longer prediction horizons would offer an added benefit. The time lag between the observed and the predicted influent flow rate needs to be addressed. It appears, and it increases in prediction horizon. It is the systematic error attributable to the temporal inputs and training process. As the previously predicted influent flow values are used as inputs, the error accumulates and grows. Reducing the time lag needs research attention. Optimizing the neural network structure with a pre- or postcorrector of the error may be a potential solution. Using dynamic neural networks could be another approach.

70

65

60 Influent flow rate (MGD)


Influent flow rate (MGD)

60

55

50

45

40

35 Observed vale 30

1

51

101

151

201

Predicted value 251

Test data (15 min)

Fig. 4. Prediction of influent flow rate at time t þ 30 min JOURNAL OF ENERGY ENGINEERING © ASCE / JUNE 2013 / 121

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70 65

55 50 45 40 35 30

1

51

101

Observed vale

Predicted value

201

251

151 Test data (15 min)

Fig. 5. Prediction of influent flow rate at time t þ 180 min

7

MAE (%)

6 5 4 3 2 1 0

t

t+15

t+30

t+60 t+90 Time (min)

t+120 t+150 t+180

Fig. 6. MAE of model for prediction of influent flow rate

60 50 MSE (%)


Influent flow rate (MGD)

60

40 30 20

Among the four data-mining algorithms used in this paper, the MLP neural network performed better than the other algorithms applied to build the prediction model. The MLP was selected to construct the prediction model of influent flow rate for all prediction horizons from t to t þ 180 min. The results showed that the prediction model predicted the influent flow rate well until t þ 150 min. The predicted influent flow rate was close to the measured influent flow rate, and the trend for predicted and observed values was the same. In addition, there was a lag between predicted and observed influent flow rate after t þ 30 min, and the lag became larger with longer time horizons. At t þ 180 min (i.e., 3 h ahead), the prediction accuracy metrics indicated that the prediction model performed inadequately. Prediction of the influent flow rate 150 min ahead might provide sufficient time for wastewater-treatment plants to arrange operators and schedule pumps; however, the prediction accuracy of the prediction model should be improved by future research to provide long-term predictions with more acceptable accuracy. In the case of heavy rainfall, long-term predictions will give wastewatertreatment plants more time to make necessary operation plans.

10 0

Acknowledgments This research was supported by funding from the Iowa Energy Center (Grant No. 10-1).

Time (minute)

Fig. 7. MSE of model for prediction of influent flow rate

References Conclusions To maintain stable effluent and optimally arrange wastewater booster pumps, it is helpful to know in advance the influent flow rate to the wastewater-treatment plant. In this paper, a model was built to predict influent flow rate up to 180 min ahead using rainfall rate, radar reflectivity, and influent flow rate as inputs. The influent flow rate data were collected at the WRF; the rainfall rate data were recorded by six tipping buckets surrounding the WRF; and the radar reflectivity data were obtained from the radar map through a nearby radar station. The data were transformed to the same frequency by computing the average over higher-frequency data.

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