Stoch Environ Res Risk Assess DOI 10.1007/s00477-014-0889-0

ORIGINAL PAPER

Short-term prediction of influent flow in wastewater treatment plant Xiupeng Wei • Andrew Kusiak

Ó Springer-Verlag Berlin Heidelberg 2014

Abstract Predicting influent flow is important in the management of a wastewater treatment plant (WWTP). Because influent flow includes municipal sewage and rainfall runoff, it exhibits nonlinear spatial and temporal behavior and therefore makes it difficult to model. In this paper, a neural network approach is used to predict influent flow in the WWTP. The model inputs include historical influent data collected at a local WWTP, rainfall data and radar reflectivity data collected by the local weather station. A static multi-layer perceptron neural network performs well for the current time prediction but a time lag occurs and increases with the time horizon. A dynamic neural network with an online corrector is proposed to solve the time lag problem and increase the prediction accuracy for longer time horizons. The computational results show that the proposed neural network accurately predicts the influent flow for time horizons up to 300 min. Keywords Influent flow  Radar reflectivity  Rainfall  Wastewater treatment plant  Neural networks

1 Introduction The influent flow to a wastewater treatment plant (WWTP) has a significant impact on the energy consumption (Wei et al. 2013). To maintain the required water level in the wet

X. Wei (&)  A. Kusiak Department of Mechanical and Industrial Engineering, The University of Iowa, 3131 Seamans Center, Iowa City, IA 52242, USA e-mail: [email protected] A. Kusiak e-mail: [email protected]

well, the number of running raw wastewater pumps should be scheduled according to the influent rate to the plant. The optimal selection and scheduling of pumps can greatly reduce electricity usage. In addition, the pollutants in the wastewater, including the total suspended solids (TSS) and biochemical oxygen demand (BOD), are also correlated with the influent flow (Bechmann et al. 1999). The treatment process should be adjusted based on the pollutant concentration in the influent. For example, a high BOD concentration requires a longer aeration time and greater oxygen supply (Qasim 1998). Therefore, it is important to predict the influent flow in the near future in order to improve the process efficiency and save energy use. The accurate prediction of the influent flow remains a challenge in the wastewater processing industry. Several studies have focused on developing models to predict influent flow (Kim et al. 2006; Kurz et al. 2009; Beraud et al. 2007; Keyser et al. 2010; Djebbar and Kadota 1998; Gernaey et al. 2010). Hernebring et al. (2002) presented an online system for short-term sewer flow forecasts that optimized the effects of the received wastewater. A more complex phenomenological model was built in (Gernaey et al. 2005) based on 1 year of full-scale WWTP influent data. It included diurnal phenomena, a weekend effect, seasonal phenomena, and holiday periods. Carstensen et al. (1998) reported prediction results for the hydraulic load of storm water. Three models, a simple regression model, adaptive grey-box model, and complex hydrological and full dynamic wave model, represented three different levels of complexity and showed different abilities to predict water loads 1 h ahead. Although these models accounted for temporal correlations of the influent flow, they ignored its spatial feature. The wastewater processing industry has used physicsbased deterministic models to estimate the influent flow.

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Online sensors are used to provide flow data at subpumping stations. Based on empirical data such as the distance between the sub-station and WWTP, and the sewer piping size, the influent flow could be roughly estimated and calibrated using the historical data to improve the estimation accuracy (Pons et al. 1998). Such simple models did not fully consider the temporal correlations of the influent flow. In the case of a large rainfall or a lack of sensors covering large areas, the predicted influent flow involves a significant error. A WWTP usually receives municipal sewer and storm water from different areas around the plant (Vesillind 2003). The quantity of the generated wastewater or precipitation may vary in space and time. In fact, to accurately predict the influent flow to a WWTP, the spatial and temporal characteristics should be considered simultaneously. To authors’ knowledge no such research has been done. Therefore, the short-term prediction (300 min ahead) of influent flow is presented in this paper taking into account the spatial–temporal characteristics discussed above. Rainfall data measured at different tipping buckets, radar reflectivity data covering the entire area handled by the WWTP, and the historical influent data to the plant are used as input parameters to build prediction models. The rainfall data provided by tipping buckets offers valuable precipitation measurements containing spatial information. However, this kind of point based data has limitations due to physical location of tipping buckets. The actual precipitation of the whole area usually cannot be simply summed up by measurements of all tipping buckets. As weather radar offers spatial–temporal data covering a large area, including the places not covered by the tipping buckets, Kusiak et al. (2013) obtained more accurate rainfall prediction using tipping bucket data together with radar reflectivity data than only tipping bucket data. In addition, the high frequency of the radar data makes it useful for forecasting rainfall several hours ahead. The historical influent time series data contains temporal influent information that is useful for predicting the influent flow. There are other data resources, e.g., substation influent flows. They are not considered as input parameters as they are somehow redundant to above mentioned data. Data containing weather information such as temperature and humidity are not considered either due to low relevancy with the plant influent flow. The remainder of this paper is organized as follows. Section 2 describes the data collection, preparation, and preprocessing, as well as the metrics used to evaluate the accuracy of models. Section 3 presents the static multilayer perceptron (MLP) neural network that is employed to build a prediction model for the influent flow. In Sect. 4, a data-driven dynamic neural network (DNN) is proposed to solve the time lag problem appearing in the models by the

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static MLP neural network. The neural network structure and computational results are discussed. Section 5 presents the conclusions.

2 Data preparation The Wastewater Reclamation Facility (WRA) studied in this paper is located in Des Moines, Iowa. It treats the collected sewage and rainfall runoff from the surrounding areas. To build an influent flow prediction model for this WRA, historical influent data, rainfall data, and radar reflectivity data are considered. The influent flow data were collected at 15-s intervals at WRA. The data are preprocessed to find 15-min averages to match the frequency of the rainfall data. The rainfall data were measured at six tipping buckets (blue icons in Fig. 1) in the vicinity of WRA (red icon in Fig. 1). As WRA receives wastewater from a large area, including rainfall data in the model inputs satisfies the spatial characteristic of the influent flow. Figure 2 illustrates the rainfall rates at the tipping buckets over time. It shows that the rainfall is location dependent and may vary despite the proximity of the tipping buckets. This indicates the importance of the rainfall data in building the influent flow prediction model. The rainfall graphs in Fig. 2 illustrate the runoff amounts at several locations, rather than completely reflect the precipitation over the entire area covered by WRA. Therefore, the use of radar reflectivity data is proposed to provide additional input for influent flow prediction. By doing this the limitations of tipping bucket based models will be overcome due to high spatiotemporal characteristics of radar reflectivity data. The NEXRAD-II radar data used in this paper are from weather station KDMX in Des Moines, Iowa, which is located approximately 32 km from WRA. KDMX uses Doppler WSR-88D radar to collect high resolution data for each full 360° scan at 5-min intervals with a range of 230 km and a spatial resolution of about 1 by 1 km. The radar reflectivity data were collected at 1, 2, 3, and 4 km Wastewater Reclamation Facility (CAPPIs). As shown in Fig. 3, the reflectivity may be quite different at different heights for the same scanning time. The terrain and flocks of birds may produce errors in the radar readings. In addition, the reflectivity at one height may not fully describe a storm occurring at a different height. To deal with these issues, it is necessary to use radar reflectivity data from different CAPPIs. The radar reflectivity data at nine grid points surrounding each tipping bucket are selected and averaged with the center data to be the reflectivity for that tipping bucket. Null values are treated as missing values and are filled using the reflectivity at the surrounding gird points.

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Fig. 1 Location of tipping buckets and WRA

The NEXRAD radar data were collected at 5-min intervals and then processed to find 15-min averages by averaging 3 radar data reflectivity values.

Table 1 summarizes the dataset used in this paper. In addition to 4 historical influent flow inputs at 15, 30, 45, and 60 min ahead, 6 rainfall and 24 radar reflectivity inputs

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Stoch Environ Res Risk Assess Fig. 2 Rainfall at six tipping buckets

Fig. 3 Radar reflectivity at different CAPPIs

35

CAPPI1 CAPPI2 CAPPI3 CAPPI4

30

Reflectivity

25 20 15 10 5 0 1

11

21

31

41

51

61

71

81

91

Time (15min)

Table 1 Data set description Inputs

Description

Unit

x1 - x6

Rainfall at 6 tipping buckets

Inch

x7 - x30

Radar reflectivity at 6 tipping buckets at 4 CAPPI

Number

x31 - x34

Historical influent flow

MGD

provide temporal and spatial parameters for the model. The data were collected from January 1, 2007, through March 31, 2008. The data from January 1, 2007, through November 1, 2007, containing 32,697 data points, are used to train the neural networks. The remaining 11,071 data points are used to test the performance of the constructed models. Three commonly used metrics, the mean absolute error (MAE), mean squared error (MSE), and correlation

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coefficient (R2) are used to evaluate the performance of the prediction models (Eq. (1)–(3)).

MAE ¼

n 1X jfi  yi j n i¼1

ð1Þ

n 1X jfi  yi j2 n i¼1 P ðfi  yi Þ2 i 2 R ¼1P P ðfi  yi Þ2 þ ðfi  yi Þ2

MSE ¼

i

ð2Þ

ð3Þ

i

where fi is the predicted value produced by the model, yi is the observed value, yi is the mean of the observed value, and n represents the number of test data points.

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3 Modeling by static multi-layer perceptron neural network Successful applications of neural networks (NNs) based prediction models have been reported in the literature. Singh and Borah (2013) used feed-forward back-propagation (BP) NN to forecast of Indian summer monsoon rainfall and obtained more accurate results than the existing model. Two models using NN (Paleologos et al. 2013) were developed to simulate spring flow. The results showed less 3 % of under/over of the observed values. Wu et al. (2008) found that BP-NN showed an advantage in heavy snow risk evaluation compared to the conventional method of evaluation criteria equation. As neural network based models are capable of forecasting with satisfactory prediction results, NNs are applied in the research reported in this paper to build prediction models. To build the influent flow prediction model, a static MLP neural network is developed. The MLP neural network has been one of the most widely used network topologies since its introduction in 1960 (Gurney 1997). It overcomes the limitations of the single-layer perceptron to handle model nonlinearity. Prediction and classification applications of MLP neural networks have been reported in a variety of scientific and engineering fields. Kusiak and Wei (2012) employed MLP NNs to model and predict methane production during sludge treatment and obtained better accuracy rather than other data-mining algorithms. In addition, MLP NN has been showing good performance in non-linear prediction. Verma et al. (2013) had similar conclusion that MLP NN outperforming other algorithms when predicting TSSs in wastewater. Therefore, MLP NN has been selected to build the influent flow prediction models in this paper. The structure of the MLP neural network reported in this paper is shown in Fig. 4. It is a supervised BP network with three layers. Each layer has one or more neurons, which are interconnected to each neuron of the previous and next layers. The connections between two neurons are parameterized using a weight and bias. Different activation functions, including the logistic, hyperbolic tangent, identity, sine, and exponential functions, are used for the hidden and output layers. In the MLP in Fig. 4, output y1 is calculated as shown in Eq. (4): ! ! X X y1 ¼ fo ð4Þ fh xi wij þ bj wj1 þ b1 j

neuron, and wj1 is the weight between the jth neuron in the hidden layer and the neuron in the output layer. bj and b1 are the bias values of neuron j and the output neuron. Weights wij are calculated in the training process based on Eq. (5), minimizing the target output, 1X ðTðnÞ  y1 ðnÞÞ2 ð5Þ eðnÞ ¼ 2 k where e is the mean of the square error, n denotes the nth data point, k is the kth output neuron (in this paper k ¼ 1), and T represents the targeted output value. Automated network search was employed to create a variety of different networks and choose the network with the best performance in all networks. In total, 200 MLP neural networks were trained to obtain a generalized network structure. The number of neurons in the hidden layer varied from 3 to 30. The weights were randomly initialized between -1 and 1 and iteratively improved by minimizing the mean of the square error. Different hidden and output activation functions were used, including logistic, exponential, tanh, identity, hyperbolic, etc. To improve the convergence speed of the training process, the BFGS (Broyden-Fletcher-Goldfarb-Shanno) algorithm (Saini 2002) was used. The influent flow prediction model at current time t was built first. The dataset described in Sect. 2 was used to train and test the MLP neural networks. The best MLP had 25 neurons in the hidden layer with the logistic hidden activation function and the exponential output activation function. The calculated MAE, MSE, and correlation coefficient were 1.09 MGD, 4.21 MGD2, and 0.988, respectively. These metrics indicate that the prediction model is accurate. The first 300 observed and predicted influent flow values from the test dataset are shown in Fig. 5. Most of the predicted values are very close to the observed ones, and the predicted influent flow follows the trend of the observed flow rate.

i

where i denotes the ith neuron in the input layer, j is the jth neuron in the hidden layer, and fo and fh are the activation functions for output layer and hidden layer, respectively. wij is the weight connecting the ith neuron to the jth

Fig. 4 Structure of MLP neural network

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Stoch Environ Res Risk Assess Table 2 Prediction accuracy

Fig. 5 Predicted and actual influent flows at current time t

Fig. 6 Predicted and actual influent flows at time t ? 30 min

Prediction horizon

MAE (MGD)

t

1.09

MSE (MGD2) 4.21

Correlation coefficient 0.98

t ? 15

1.48

5.83

0.98

t ? 30

1.89

8.20

0.97

t ? 60

2.75

14.59

0.95

t ? 90

3.61

22.95

0.93

t ? 120

4.46

33.21

0.90

t ? 150 t ? 180

5.26 6.02

44.88 57.39

0.87 0.83

MLP neural network models were also built at t ? 15 min, t ? 30 min, t ? 60 min, t ? 90 min, t ? 120 min, t ? 150 min, and t ? 180 min with the same procedure as the model built at time t. As shown in Fig. 6, the predicted influent flow is similar to the observed value, and the predicted trend is the same as the observed one. However, a small time lag appears between the predicted and observed influent flows. This lag increases over time and can be clearly observed in Fig. 7, which shows the predicted influent flow at t ? 180 min ahead. Table 2 summarizes the accuracy of the prediction results at current time t through t ? 180 min. The prediction accuracy decreases with longer time horizon. The MAE and MSE increase quickly after t ? 30 min, while the correlation decreases as well. The prediction models for horizons smaller than t ? 150 min have acceptable accuracy when the threshold of the correlation coefficient is set at 0.85 which is still more accurate than the estimations by WWTP. However, the time lag is too large to provide a useful real-time influent flow rate even though the trend can be well predicted.

4 Modeling by dynamic neural network

Fig. 7 Predicted and actual influent flows at time t ? 180 min

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The computational results in Sect. 3 indicated that a static MLP neural network is unable to capture the dynamics in the dataset at long time horizons. As DNN is an effective and suitable method to predict dynamic system and has been successful applied in scientific and engineering problems (Chiang et al. 2010; Shaw et al. 1997; Hussain et al. 2009), it is then used in this research to improve the prediction accuracy. Considering the increasing time lag issue which has not appeared in DNN applications, a DNN with an online corrector is proposed and tested in this section. A DNN involves a memory structure and predictor. As the memory captures the past time series information, it can be used by the predictor to learn the temporal patterns of the time series. This paper uses a focused time-delay

Stoch Environ Res Risk Assess Fig. 8 Structure of dynamic neural network

Hidden layer H1

y(t-1) y(-2)

weights

Input layer

Output layer

D

y(t)

yp(t)

D

y(t-3) D

y(t-4)

D

radar(t) + Hm

rain(t)

yo(t) -

e(t)

Fig. 11 MAE values of prediction models with two neural networks

Fig. 9 Predicted and actual influent flows at time t ? 30 min

Fig. 12 MSE values of prediction models with two neural networks

Fig. 10 Predicted and actual influent flows at time t ? 180 min for two models

neural network (FTDNN) as the predictor (Velasquez et al. 2009). To address the time lag issue of the static MLP neural network, an online corrector is proposed. The

structure of the final FTDNN is shown in Fig. 8. The memory structure is a time delay line containing several most recent input values generated by the delay element shown as operator D in Fig. 8 to hold on the relevant past information. The predictor is the conventional feed-forward network to predict the future output. Four past values of influent flow are used to provide temporal information and reduce the time lag. The boosting tree algorithm has been employed to reduce the dimensionality of memories

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Fig. 13 Correlation coefficient of prediction models with two neural networks

by identifying the appropriate number of past values. It has been found that the prediction accuracy could not be improved but the computation time would significantly increase when more than five past influent flows are used as memories. The most recent four past values also have the highest rankings that contribute to the prediction accuracy. The radar reflectivity data and tipping bucket data are also used to provide spatial–temporal information to the network. Therefore, the inputs of the prediction model include four past values of influent flow (as memory values), radar reflectivity, rainfall, and the online corrector, eðtÞ (Eq. 6), at current time t. eðtÞ ¼ jyp ðtÞ  yo ðtÞj

ð6Þ

where yp ðtÞ and yo ðtÞ are the predicted and actual influent flows at current time t. In fact, the online corrector provides the time lag information back to the input layer to calibrate the prediction results during training. Similar to MLP neural network, therefore, the output of the neuron in hidden layerHi is calculated by X 4 yi ðt  kÞwi ðkÞ þ radarðtÞwi ð5Þ H i ¼ fh k



þrainðtÞwi ð6Þ þ bj þ eðtÞ

ð7Þ

where k means the synaptic weight for neuron i, t means current time, radarðtÞ and rainðtÞ are the input radar reflectivity and rainfall tipping bucket data at time t. Other symbols in above formula have the same meaning as described in Eq. 4. The final output of the FTDNN can be given in Eq. 8. j is the neuron in output layer, aj is the output bias. ! m X Hi wji þ aj yj ðtÞ ¼ fo ð8Þ i¼1

The same approach presented in Sect. 3 was applied to train the FTDNN. As shown in Fig. 9, the influent flow is

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well predicted at time t ? 30. There is a slight time lag. Figure 10 shows the predicted influent flow and the observed values at time t ? 180 min for the dynamic and static networks. It clearly shows that the time lag of the predictions by the DNN is much smaller than that of the predictions by the static MLP neural network. The values of MAE, MSE, and the correlation coefficient for the results produced by the two neural networks are illustrated in Figs. 11, 12, and 13, respectively. The prediction model constructed using the DNN outperforms the model with the static MLP neural network. Its MAE and MSE values increase slowly with longer time horizons. The correlation coefficient decreases slowly and is still acceptable at time t ? 300 min (R2 [ 0.85). The results indicate that the DNN is capable of modeling the influent flow. The static MLP neural network is effective at handling complex non-linear relationships rather than a temporal time series. On the other hand, a DNN is suitable for temporal data processing. The online corrector provides additional time series information as an input to correct the time lag generated in the model. The accuracy gain comes at the cost of the additional computation time needed to construct the DNN. Because knowing the future values of influent flow is important for the management of WWTPs, the 300-minahead predictions provided by the DNN offer ample time to schedule the pumps and adjust the parameters of the treatment process. However, even the 150-min-ahead predictions offered by the static MLP neural network are acceptable for lower precipitation seasons (for example, spring and winter) because it need shorter computational time.

5 Conclusion This paper focused on predicting the influent flow to a wastewater processing plant using two data-driven neural networks. To satisfy the spatial and temporal characteristics of the influent flow, rainfall data collected at six tipping buckets, radar data measured by a radar station, and historical influent data were used as model inputs. The static MLP neural network provided good prediction up to 150 min ahead with 85 % accuracy. The MAE and MSE increased quickly while the correlation decreased as well with longer time horizon. The increasing time lag generated the problem of providing a useful real-time influent flow. To solve this issue and extend the time horizon of the predictions, to 300 min, a DNN with an online corrector was proposed. The online corrector provided additional time series information as an input to correct the time lag generated in the model. The time lag that appeared in the MLP neural network model was significantly reduced. The proposed method could provide good prediction up to 300 min ahead with 85 % accuracy. This extended time

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horizon would be useful for managing the energy efficiency of wastewater processing plants. Acknowledgments This research was supported by funding from the Iowa Energy Center Grant No. 10-1.

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