Modeling and optimization of a wastewater pumping system with data ...

Applied Energy 164 (2016) 303–311

Contents lists available at ScienceDirect

Applied Energy journal homepage: www.elsevier.com/locate/apenergy

Modeling and optimization of a wastewater pumping system with data-mining methods Zijun Zhang a, Andrew Kusiak b, Yaohui Zeng b, Xiupeng Wei b,⇑ a b

Department of Systems Engineering and Engineering Management, P6600, 6F, Academic 1, City University of Hong Kong, Hong Kong Department of Mechanical and Industrial Engineering, 3131 Seamans Center, The University of Iowa, Iowa City, IA 52242-1527, United States

h i g h l i g h t s Data-mining methods are applied to wastewater pumping system modeling and optimization. Neural networks are used to model pump energy consumption and wastewater flow rate. An artificial immune network algorithm is employed to solve the bi-objective optimization problem. Six to fourteen percent of energy could be saved when balancing the energy cost and wastewater flow rate.

a r t i c l e

i n f o

Article history: Received 8 August 2015 Received in revised form 9 November 2015 Accepted 28 November 2015

Keywords: Neural network Pumping system Energy saving Artificial immune network algorithm Bi-objective optimization Data mining

a b s t r a c t In this paper, a data-driven framework for improving the performance of wastewater pumping systems has been developed by fusing knowledge including the data mining, mathematical modeling, and computational intelligence. Modeling pump system performance in terms of the energy consumption and pumped wastewater flow rate based on industrial data with neural networks is examined. A biobjective optimization model incorporating data-driven components is formulated to minimize the energy consumption and maximize the pumped wastewater flow rate. An adaptive mechanism is developed to automatically determine weights associated with two objectives by considering the wet well level and influent flow rate. The optimization model is solved by an artificial immune network algorithm. A comparative analysis between the optimization results and the observed data is performed to demonstrate the improvement of the pumping system performance. Results indicate that saving energy while maintaining the pumping performance is potentially achievable with the proposed data-driven framework. Ó 2015 Elsevier Ltd. All rights reserved.

1. Introduction Water supply and treatment processes are energy-intensive. Studies reported that their energy usage accounts for 4% of the national electricity in U.S. [1,2] and 7% of the electrical energy worldwide [3]. Pumps and aeration systems are major energy consumers in a wastewater treatment process. Singh et al. [4] studied the energy auditing of a wastewater treatment process and concluded that pumps consumed a significant share of 79% of the used electrical energy in wastewater treatments. Therefore, it is valuable to investigate the energy saving of wastewater pumps and generate emerging techniques to enhance the sustainable wastewater management. ⇑ Corresponding author. E-mail addresses: [email protected] (Z. Zhang), [email protected] (A. Kusiak), [email protected] (Y. Zeng), [email protected] (X. Wei). http://dx.doi.org/10.1016/j.apenergy.2015.11.061 0306-2619/Ó 2015 Elsevier Ltd. All rights reserved.

The improvement of the sustainability in wastewater treatments has been mainly studied from two perspectives including the advancement of the sludge management and the development of the low-energy treatment technology [5]. In studies of the sludge management, applications of novel technologies for digesting sludge and producing biogas have been widely discussed [6–8]. Two categories of studies, the innovation of the wastewater treatment method [9] and the improvement of the wastewater treatment operation [10], have been conducted to achieve a lowenergy wastewater treatment. In [9], the potential of energy saving in the nutrient removal process with the utilization of algal reactors was investigated. In [10], a fuzzy logic control was applied to reduce the energy consumption of the wastewater treatment process. Compared with studies in [6–9], the energy saving through improving treatment operations including pump operations does not require additional investments and thus is more beneficial.

304

Z. Zhang et al. / Applied Energy 164 (2016) 303–311

The previous literature majorly studied the operation of single pumps. Raggl et al. [11] presented a sensorless control approach of a permanent-magnet synchronous machine bearingless pump. DeWinter and Kedrosky [12] introduced a 3500-hp adjustable speed drive to control the oil pipeline pump. Himavathi and Umamaheswari [13] developed a fuzzy model to control a threephase induction motor driving a submergible pump. These studies [11–13] addressed the improvement of the single pump performance through the installation of new hardware. However, the wastewater is moved by the collaboration of multiple pumps in treatment processes. Thus, operations of multi-pumping systems in the wastewater treatment need to be investigated. The previous literature studied multi-pumping systems from the scheduling rather than the control perspective. Wang et al. [14] discussed a bi-objective optimization model of an urban water distribution system. Cost minimization while preventing land subsidence was achieved by optimal scheduling of the water supplying pumps. Barán et al. [15] developed a pump scheduling model with multiple objectives and presented a comparative study of different evolutionary algorithms applied to solving the scheduling model. Zhang et al. [16] proposed a mixed integer nonlinear programming model for optimizing the operational schedule of the wastewater pump system. Scheduling the operations of pumping systems typically investigates the optimal working configurations of pumps each hour while the optimal speed settings for variable speed pumps are not adequately studied. The development of information technology enables the collection of a large volume of real time pump operational data in wastewater treatment facilities. Measured parameters include the pump operational status (on/off), pump speed, power consumption, head, etc. Through mining collected data, useful knowledge could be discovered to optimize the performance of pumping systems. Compared with traditional pump researches [17–19] and energy saving research [20] conducted with physics-based models, this paper proposes a data-driven framework for modeling the wastewater pumping system and optimizing its performance. A neural network algorithm [21,22] is applied to develop models for predicting the pump energy consumption and the wastewater flow rate after pumping. The modeling capability of neural network has been demonstrated in previous studies including a pump study [23] and a study of modeling a hydro plant [24]. Two objectives, minimizing the energy consumption of the pumping system and maximizing the flow rate of wastewater after pumping (which benefits the safe control of the wet well level), are considered in the model. An adaptive mechanism for assigning weights to two objectives is designed. An artificial immune network algorithm [25,26] is introduced to solve the bi-objective optimization model. A computational study is conducted to analyze the potential of energy saving in the wastewater treatment through optimizing control settings of pump speeds.

2. Description of the pumping system and its data 2.1. Pump configuration A wastewater treatment plant with the following design specifications is considered in this research. The daily minimum, average, and maximum of raw wastewater flows in design are 113,652 m3/day, 227,304 m3/day, and 672,820 m3/day respectively. The daily minimum, average, and maximum of the biochemical oxygen demand (BOD) in design are 9140 kg/day, 45,722 kg/day, and 127,958 kg/day. The pumping system in the preliminary treatment area of the wastewater treatment plant includes six 55-MGD class variable speed pumps, indexed 1 through 6. Although the six pumps were supplied by the same

manufacturer, they were not identical due to the maintenance induced changes. The maximum number of operating pumps is five because one pump is always considered as a backup unit. The pumping system in the preliminary treatment is depicted as Fig. 1. As shown in Fig. 1, the wastewater is first gathered by sewers and flows into the wastewater treatment plant. A bar screen is employed to strain the solids contained in the influent, and the screened influent is retained in the wet well. The pumping system connects the wet well with the aerated grit chamber. Its main responsibility is to lift the influent from the wet well to the aerated grit chamber. Due to the change in system dynamics and the ‘‘head influence” phenomenon, the pump curve can no longer offer accurate information for its control. The research reported in this paper sheds light on the control of the pumping system from a data-driven perspective. Pumps in the pumping system are operated in five parallel configurations due to various flow rates of the influent in the wastewater preliminary treatment. Each configuration of pumps includes all combinations of operating pumps. Since the number of combinations present in the dataset available in this research is limited and the number of data points across different configurations varies, the pump configurations with the most data points are selected for analysis. Table 1 presents information on pump configurations. In this study, four configurations shown in Table 1 are considered. The configuration of five pumps working together is arbitrarily controlled by the plant operator and therefore is not considered in this study. Parameter C is used to describe the configurations of pumps, C 2 fC 1 ; C 2 ; C 3 ; C 4 g. The binary value of C (0 and 1) describes the on/off status of the configuration of pumps. 2.2. Wastewater treatment plant data The data used in this research were collected at a wastewater treatment plant with about 1400 monitored parameters and stored in an SQL server. Four parameters related to the pumping system (e.g., the pump speed, energy consumed by the pumping system, water flow rate after pumping, and wet well level) were selected as a dataset for the study. The length of the dataset is from July 20, 2010 to December 31, 2010. Values for the four parameters were collected at different sampling intervals. The pump speed and the energy consumed by the pumping system were sampled at 5 min intervals. The water flow rate after pumping was collected every 15 s. The sampling interval of the wet well level was 1 min. Since it is not feasible to analyze the dataset includes parameters with different sampling intervals, the sampling interval of each of the four parameters was synchronized at 5 min. In this study, each configuration of pumps represents a system. Therefore, the pumping system needs to be analyzed based on pump configurations. The processed dataset is separated to four sub-datasets according to the configurations of pumps. Table 2 presents the information of the four sub-datasets. More than half of the data points correspond to the single pump configuration because the influent flow rate is significantly impacted by the rainfall. The dataset contains the data points at the end of summer and fall and at the beginning of winter. In the wastewater processing plant area, rainfall significantly diminishes in late fall and early winter. Each sub-dataset is further split into training and test data sets for data analysis (Section 3). 2.3. Estimated influent flow rate The influent flow rate is a significant factor impacting the selection of pump configurations and their speed settings as it indicates the workload for pumps. However, such data are not available in the database for several reasons. First, sensors are not mounted

305


Aerated grit chamber

Sewers Bar screen

Legend Wet well Operating pump

Idle pump

Backup pump

Parameter

Configuration

Pump index

Value

C1 C2 C3 C4

Single pump Two pumps Three pumps Four pumps

1 4 and 6 2, 5, 6 2, 3, 5, 6

On = 1, On = 1, On = 1, On = 1,

Off = 0 Off = 0 Off = 0 Off = 0

Table 2 Description of the four sub-datasets. Configuration

Data point

Training data set

Test data set


11,536 3115 3197 873

9228 2492 2556 696

2308 623 641 177

Time (5-min intervals) Single pump

Two pumps

Three pumps

Four pumps

Fig. 2. Four samples of the variation of estimated influent flow rate.

on each sewer to monitor the flow rate. Although a few main sewers are equipped with sensors, the distances between the locations of the sensors and the wastewater treatment plant are unequal. Therefore, it is difficult to determine the influent flow rate to the wastewater treatment plant based on the data from these sensors. However, since the wet well level and the wastewater flow rate after the pumps are both known, the influent flow rate to the plant can be estimated based on mass balance theory if the crosssectional area of the wet well is known. In this study, the shape of the wet well is assumed to be a cuboid of 100 m2. Therefore, the mass balance shown in Eq. (1) can be utilized to estimate the influent flow rate to the plant based on the wet well level and wastewater flow rate after the pumps:

It ¼ ðOt DT þ ðLtþDT Lt Þ AÞ=DT

10 9 8 7 6 5 4 3 2 1 0

1 10 19 28 37 46 55 64 73 82 91 100 109 118 127 136 145 154 163 172 181 190 199 208 217 226 235

Table 1 Pump configurations.

Estimated influent flow rate (m3/s)

Fig. 1. The pumping system of the wastewater preliminary process.

ð1Þ

In (1), It is the influent flow rate at time t, Ot is the wastewater flow rate after pumping at t, Lt is the wet well level at t, A is the area of the wet well, t is the current time, and DT is the data sampling interval (5 min). Fig. 2 provides the daily sample of the estimated influent flow rate from four sub-datasets described in Table 2. 3. Data-driven pump system performance prediction models The performance of the pumping system is described by two parameters, the energy consumed by pumps and the wastewater flow rate after pumping. Therefore, to analyze performance of the

pumping system, models for predicting the energy consumed by four pump configurations and the corresponding pumped wastewater flow rate need to be developed. In this section, a neural network (NN) [21,22] is used to build the pump energy model and the wastewater flow rate model for four pump configurations. In a previous pump study [23] reported in literature, the NN algorithm has been compared with other data mining algorithms, such as random forest (RF), support vector machine (SVM), and knearest neighbor (k-NN). The results showed that NN algorithm tends to outperform other data mining algorithms in constructing accurate predictive models for complex, nonlinear wastewater pumping systems. 3.1. Pump energy model The pump energy model predicts the energy consumed by the four pump configurations at time t. Parameters, such as pump energy consumption at time t DT (Energy consumed by pumps from t DT to t), pump speeds at time t, pump speeds at time t DT; the wet well level at t and the wet well level at t DT are considered as the inputs of the pump energy model for predicting the energy consumed by the pumping system from t to t + DT. The influent flow rate is not included in models because it is estimated and might include errors which could impair the quality of data-driven models. In inputs, the speed setting of each pump at time t is considered a controllable parameter. Table 3 lists all parameters used in the model.


Parameter

Description

Parameter

Description

EC,t

Power consumed by pump configuration C at time t The speed of pump with pump index b at time t Level of junction chamber at time t Pump configurations C 2 {C1, C2, C3, C4}

EC,tDT

Power consumed by pump configuration C at time t DT The speed of pump with pump index b at time t DT Level of junction chamber at time t DT Index set of pumps b 2 {1, 2, 3, 4, 5, 6}

Sb,t

Lt C

Sb,tDT

LtDT b

800 750 700 650 600 550 500 450 400

1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69 73 77 81 85 89 93 97

Table 3 Parameter description of the pump energy model.

The 5-min averaged power (kW)

306

Time (5-min intervals) Observed value

The pump energy models are formulated in (2)–(5).

Fig. 3. First 100 test points of the observed and predicted power using model C2.

EC1 ;t ¼ f C 1 ðEC 1 ;tDT ; S1;t ; S1;tDT ; Lt ; LtDT Þ

ð2Þ

EC2 ;t ¼ f C 2 ðEC 2 ;tDT ; S4;t ; S6;t ; S4;tDT ; S6;tDT ; Lt ; LtDT Þ

ð3Þ

EC3 ;t ¼ f C 3 ðEC 3 ;tDT ; S2;t ; S5;t ; S6;t ; S2;tDT ; S5;tDT ; S6;tDT ; Lt ; LtDT Þ

ð4Þ

EC 4 ;t ¼ f C 4 ðEC 4 ;tDT ; S2;t ; S3;t ; S5;t ; S6;t ; S2;tDT ; S3;tDT ; S5;tDT ; S6;tDT ; Lt ; LtDT Þ ð5Þ

where fC(), C 2 fC 1 ; C 2 ; C 3 ; C 4 g, describes NN based pump energy prediction models for four pump configurations. The data mentioned in Section 2 are used in this section to establish data-driven models. The training datasets are utilized to develop NN based pump energy models of the four pump configurations. Four metrics (6)–(9), the mean absolute error (MAE), standard deviation of absolute error (SDofAE), mean absolute percentage error (MAPE), and standard deviation of absolute percentage error (SDofAPE), are employed to validate the models. n 1X b MAE ¼ y i yi n i¼1

ð6Þ

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 Xn 2 1 Xn b b SDofAE ¼ y y y y i i i i i¼1 i¼1 n n

ð7Þ

ð8Þ

i

ffi vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u !2 n u1 Xn X b b y i yi 1 y i yi 100% SDofAPE ¼ t y i¼1 n y n i

The first 100 test points of the energy consumed by the configuration of two pumps are provided in Fig. 3 to demonstrate the prediction accuracy visually. 3.2. Wastewater flow rate model The wastewater flow rate model predicts the flow rate of the wastewater after the pumps. A modeling approach similar to that in Section 3.1 is applied in this section. Pump speeds at t and t DT, the wet well level at t and t DT, and the pumped wastewater flow rate at t DT are considered as inputs, and the flow rate of pumped wastewater at t is the output of models. Table 5 lists the parameters used to develop the wastewater flow rate model. The wastewater flow rate models of the four pump configurations are formulated as Eqs. (10)–(13) using the notations in Table 5:

F C1 ;t ¼ hC 1 ðF C 1 ;tDT ; S1;t ; S1;tDT ; Lt ; LtDT Þ

ð10Þ

F C2 ;t ¼ hC 2 ðF C 2 ;tDT ; S4;t ; S6;t ; S4;tDT ; S6;tDT ; Lt ; LtDT Þ

ð11Þ

F C3 ;t ¼ hC 3 ðF C 3 ;tDT ; S2;t ; S5;t ; S6;t ; S2;tDT ; S5;tDT ; S6;tDT ; Lt ; LtDT Þ

ð12Þ

F C 4 ;t ¼ hC 4 ðF C 4 ;tDT ; S2;t ; S3;t ; S5;t ; S6;t ; S2;tDT ; S3;tDT ; S5;tDT ; S6;tDT ; Lt ; LtDT Þ ð13Þ

n b 1X y i yi 100% MAPE ¼ y n i¼1

Predicted value

i¼1

ð9Þ

i

In (6)–(9), b y is the value estimated by data-driven models, y is the observed value, i is the index of data points, and n is the total number of data points. Table 4 presents the test results of the NN pump energy models for four pump configurations. As shown in Table 4, the NN models accurately predict the energy consumed by the pumping system at time t. The MAPE of the four models is less than 0.04, which indicates that the prediction accuracy is above 96%.

Table 4 Test results of pump energy models.

where hC(), C 2 fC 1 ; C 2 ; C 3 ; C 4 g, is the NN based wastewater flow rate prediction model for four pump configurations. The datasets discussed in Section 2 are applied to train and validate the NN models in this section. The four metrics of Section 3.1 (see (6)–(9)) are also used to examine the accuracy of the models. Table 6 shows the test results of the models predicting the pumped wastewater flow rate at t. The prediction accuracy of the model for the configuration with four pumps (C4) is slightly inferior to that of other three models corresponding to configurations with a single pump, two pumps, or three pumps. This is understandable as a

Table 5 Parameter description of the wastewater flow rate model. Parameter

Description

Parameter

Description

FC,t

Wastewater flow rate at time t when pump configuration is C The speed of pump with pump index b at time t Level of junction chamber at time t Pump configurations C 2 {C1, C2, C3, C4}

FC,tDT

Wastewater flow rate at time t DT when pump configuration is C The speed of pump with pump index b at time t DT Level of junction chamber at time t DT Index set of pumps b 2 {1, 2, 3, 4, 5, 6}

Sb,t

Configuration

MAE

SDofAE

MAPE

SDofAPE


11.66824 22.45111 20.99458 51.99877

8.953406 14.15732 15.31311 38.30398

0.027054 0.035068 0.022019 0.034757

0.01941 0.024937 0.01799 0.023876

Lt C

Sb,tDT

LtDT b

307


80 6 Sb;t 6 102;

Table 6 Test results of the wastewater flow rate models. Configuration

MAE

SDofAE

MAPE

SDofAPE


0.017389 0.022192 0.022791 0.147183

0.020183 0.025755 0.026935 0.140637

0.007866 0.00598 0.004204 0.01828

0.010489 0.006238 0.004384 0.01565

system with more pumps exhibits more complicated inherent system dynamics. More training data points are helpful to better characterize the system thus lead to higher prediction accuracy. The first 100 prediction results of wastewater flow rate of the pump configuration C4 are shown in Fig. 4. 4. Pump system performance optimization model 4.1. Control strategies of pump configurations The pump configuration is determined by rules considering the level of the raw wastewater in the wet well. These rules are described as follows: (1) When C = C1, C is switched to C2, if L P 1.524 m. (2) When C = C2, C is switched to C3, if L P 1.676 m, and C is changed to C1 if L 6 1.219 m. (3) When C = C3, C is switched to C4, if L P 1.981 m, and C is changed to C2 if L 6 1.524 m. (4) When C = C4, C is switched to C3, if L 6 1.676 m. (5) C5 is activated based on the operator’s decision. The notation used in the rules is the same as that of Section 2.1. The value of wet well levels considered in rules (1)–(5) is supplied by plant experts. A graphical illustration of the pump configuration selection rules is provided in Fig. 5.

b ¼ 1; 2; . . . ; 6

ð14Þ

Another type of constraint is the limitation of the wet well level after optimization. The wet well level constraints for four pump configurations, C1, C2, C3, and C4, are expressed in Eqs. (15)–(18).

0:8 6 LC 1 6 1:524

ð15Þ

1:219 6 LC 2 6 1:676

ð16Þ

1:524 6 LC 3 6 1:981

ð17Þ

1:676 6 LC 4 6 2:5

ð18Þ

Here, lower and upper bounds of the wet well level are assigned to pump configurations C1 through C4 according to the control logic employed by plant experts and the range of the wet well level in the dataset. The upper bound of C4 is used to prevent overflow of the wastewater, as the maximum height of the wet well is 3.6 m. The lower bound of C1 is established to ensure pressure for pumping. 4.3. Optimization model formulation The optimization model has two objectives: minimizing the energy consumed by the pumps and maximizing the flow rate of the pumped wastewater. These objective functions are expressed in (19)–(23), where the wet well level constraints are integrated to the objective function following the Lagrangian multipliers [27,28].

J ¼ Ið1Þ ðC 1 ÞJ 1 þ Ið1Þ ðC 2 ÞJ 2 þ Ið1Þ ðC 3 ÞJ 3 þ Ið1Þ ðC 4 ÞJ 4

ð19Þ

J 1 ¼ w1 g 1 ðEC 1 ;t Þ þ w2 g 2 ðF C 1 ;t Þ þ kðmaxf0; LtþT 1:524g þ maxf0; 0:8 LtþT gÞ

ð20Þ

J 2 ¼ w1 g 1 ðEC 2 ;t Þ þ w2 g 2 ðF C 2 ;t Þ þ kðmaxf0; LtþT 1:676g þ maxf0; 1:219 LtþT gÞ

ð21Þ

4.2. Constraints Two types of constraints are considered in the performance optimization model. The first set of the constraints is concerned with the limited solution space (range of pump speeds) based on the dataset. Since pump speed is the only controllable parameter in the models discussed in Section 3, it becomes the decision variable scaled between 0% and 100%. In the dataset of Section 2.2, the minimum of pump speed is about 80%, and the maximum of pump speed is around 102%. Therefore, the pump speed can only be optimized between 80 and 102. The pump speed constraint is expressed in (14).

J 3 ¼ w1 g 1 ðEC 3 ;t Þ þ g 2 ðw2 F C 3 ;t Þ þ kðmaxf0; LtþT 1:981g þ maxf0; 1:524 LtþT gÞ J 4 ¼ w1 g 1 ðEC 4 ;t Þ þ w2 g 2 ðF C 4 ;t Þ þ kðmaxf0; LtþT 2:5g þ maxf0; 1:676 LtþT gÞ

Flow rate (m3/s)

8.0

x= maxfxg

i¼1

ðmaxfxg xÞ= maxfxg i ¼ 2

ð24Þ

where x is the input of the function. In the objective function, weights need to be determined. In many optimization problems, equal values are assigned to weights, or weights are arbitrarily set. In this paper, an adaptive approach is developed to automatically adjust the value of weights according to the external information, change rate of junction chamber level, and influent flow rate. The adaptive approach is formulated as

7.5 7.0 6.5 6.0

1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69 73 77 81 85 89 93 97

5.5 5.0

ð23Þ

In (19)–(22), J is the objective to be minimized, I() is the indicator function, w is the weights of the objective functions, k is the Lagrangian multiplier, and g() is a function normalizing the value of objectives to [0, 1]. The remaining notations are the same as the parameters in Sections 2 and 3.The function g() is formulated as

g i ðxÞ ¼

8.5

ð22Þ

Time (5-min intervals) Observed value

Predicted value

Fig. 4. First 100 test points of observed and predicted wastewater flow rate after pumps using model C4.

u1 ¼ w1 cððLt LtT Þ= maxfLgÞ

ð25Þ

u2 ¼ w2 þ ðIt ItT Þ=ðmaxfIg minfIgÞ

ð26Þ

w1 ¼ u1 =ðu1 þ u2 Þ

ð27Þ

308


Fig. 5. The diagram of the pump configuration selection logic.

w2 ¼ u2 =ðu1 þ u2 Þ

ð28Þ

where c is a constant scaling the change of the junction chamber level to the range compatible with the influent flow rate. The remaining notation is listed in Section 2. The initial values of w1 and w2 are set to 0.5. As shown in (25)–(28), the weight associated the pump energy consumed increases as the junction chamber level and influent flow rate decrease. Similarly, if the junction chamber level and influent flow increase, then the weight associated with maximizing pumped wastewater flow rate also increases. By integrating (19)–(28) with the pump speed constraints in Section 4.2, the model for performance optimization of the pumping system is expressed in (29).

minSb;t J s:t: J ¼ Ið1Þ ðC 1 ÞJ 1 þ Ið1Þ ðC 2 ÞJ 2 þ Ið1Þ ðC 3 ÞJ 3 þ Ið1Þ ðC 4 ÞJ 4 J 1 ¼ w1 g 1 ðEC1 ;t Þ þ w2 g 2 ðF C1 ;t Þ þ kðmaxf0; LtþT 1:524g þ maxf0; 0:8 LtþT gÞ J 2 ¼ w1 g 1 ðEC2 ;t Þ þ w2 g 2 ðF C2 ;t Þ þ kðmaxf0; LtþT 1:676g þ maxf0; 1:219 LtþT gÞ J 3 ¼ w1 g 1 ðEC3 ;t Þ þ w2 g 2 ðF C3 ;t Þ þ kðmaxf0; LtþT 1:981g þ maxf0; 1:524 LtþT gÞ J 4 ¼ w1 g 1 ðEC4 ;t Þ þ w2 g 2 ðF C4 ;t Þ þ kðmaxf0; LtþT 2:5g

ð29Þ

þ maxf0; 1:676 LtþT gÞ LtþT ¼ ððIt Ot Þ TÞ=A þ Lt Ot ¼ Ið1Þ ðC 1 ÞF C 1 ;t þ Ið1Þ ðC 2 ÞF C 2 ;t þ Ið1Þ ðC 3 ÞF C3 ;t þ Ið1Þ ðC 4 ÞF C4 ;t u1 ¼ w1 c1 ððLt LtT Þ= maxfLgÞ u2 ¼ w2 þ ðIt ItT Þ=ðmaxfIg minfIgÞ w1 ¼ u1 =ðu1 þ u2 Þ w2 ¼ u2 =ðu1 þ u2 Þ 80 6 Sb;t 6 102;

for b ¼ 1; 2; 3; . . . ; 6

The notations are the same as in (19)–(28) and in Section 4.2.

4.4. Artificial immune network algorithm Solving model (29) with traditional optimization tools is challenging due to its nonlinearity and complexity. In this research, the Artificial Immune Network Algorithm (aiNet) [25,26] is applied. Computational intelligence methods including the evolutionary algorithm (EA) and particle swarm optimization (PSO) are also applicable to solve model (29). However, according to previous studies [29,30], we observed that the aiNet is more powerful than EA and PSO in boosting the solution diversity during search so that more robust search results can be obtained and faster computational speed can be achieved. The concept of an artificial immune system (AIS) was inspired by the principles and processes of the human immune system. The theory used in AIS mimics the biological functions in the human immune system, and this simulation transforms to a new computational approach that exploits the adaptive and memory mechanisms of the immune system. The AIS was developed in the mid-1980s. Farmer et al. [31] and Bersini and Varela [32] were the first researchers to publish their work on immune networks. In the following years, research related to AISs gradually expanded, and various AIS algorithms were developed and applied in different fields. Two versions of the clonal selection principle were derived by de Castro and Von Zuben [33] and applied to machine learning, pattern recognition, and multimodel optimization. Timmis et al. [34] presented the application of an immune network model of AIS in data analysis. Dasgupta [35] developed a multi-agent decision support system by examining the recognition and response mechanisms of the immune system. Forrest et al. [36] combined a genetic algorithm and an immune system algorithm to study the pattern recognition process. The steps of the aiNet algorithm [25] are as follows: Step 1. Population initialization: Randomly generate an initial population of the network parent antibodies with size N. Repeat Steps 2–6 until the stopping criterion (number of iterations) of aiNet algorithm is met.

309


5. Optimization results In this section, the optimization results are discussed in two parts: single point optimization and continuous optimization. In the first part, the convergence of aiNet algorithm is discussed. In

5.1. Single point optimization The single point optimization is applied to evaluate the convergence speed of aiNet. Since the pumping system has four configurations (C1, C2, C3, and C4), four optimization scenarios (X1, X2, X3 and X4) are considered. Four data points 12/7/2010 3:06:06 AM, 9/19/2010 10:01:29 PM, 8/20/2010 2:42:55 AM and 8/5/2010 6:57:50 PM are selected to study the convergence of aiNet algorithm for each single point optimization scenario. The aiNet algorithm was run for 1500 iterations. Fig. 6 shows the convergence of aiNet algorithm for all four scenarios. In Fig. 6, the fitness of each iteration is standardized by dividing the largest fitness obtained through 1500 iterations. As shown in Fig. 6, the aiNet algorithm converges at the 22nd iteration in the X1 scenario. In the X2 and X3 scenarios, the aiNet algorithm converges at the 8th iteration. In X4, the aiNet algorithm converges at the 188th iteration. Based on this observation, a conservative setting for the stopping criterion of the aiNet algorithm is determined. In scenarios X1 through X3, the stopping criteria are set to 100 iterations. In X4, the stopping criterion is set to 300 iterations. 5.2. Continuous optimization In this section, four sets of data points are selected from the test dataset of the four pump configurations described in Table 2. These data points are used for continuous optimization of four scenarios, and each data set contains eleven data points. The data set for optimization in X1 includes data points from 11/5/2010 11:16:06 PM to 11/6/2010 12:06:06 AM. Data points in the data set for optimization in the X2 scenario are from 10/1/2010 10:11:29 AM to 10/1/2010 11:01:29 AM. In X3, the data points from 8/20/2010 5:57:55 PM to 8/20/2010 6:47:55 PM are selected. The data set for X4 includes data points from 8/17/2010 10:32:55 PM to 8/17/2010 11:22:55 PM. The optimized results are repeatedly treated as the inputs of the next step in optimization. Two weights, w1 and w2, are adaptively adjusted from one data point to another in the optimization. Table 7 quantitatively summarizes the optimization results of the pumping system performance for X1–X4. The mean of the computed and observed power for eleven data points from X1 to X4 is computed. Similarly, the mean of optimized and observed flow rate is also computed. The gain in energy savings and the pumped wastewater is calculated. As shown in Table 7, it is obvious that energy savings are achieved in all four scenarios, and the wastewater pumping performance is not degraded. In X2, the wastewater pumping performance can be improved while energy is saved. 1.02 1 0.98 0.96 0.94 0.92 0.9 0.88 0.86 0.84 0.82

1 9 17 25 33 41 49 57 65 73 81 89 97 105 113 121 129 137 145 153 161 169 177 185 193 1500

Here, f is the average fitness value of a clone, i is the iteration index, f is the threshold to determine the convergence of local search, a is the constant to control the decay of the inverse exponential function, f⁄ denotes the fitness value of parent antibody, and N(0, 1) is a standard normal distribution. The parameter e determines the number of parent antibodies that can remain after suppression. It also accepts partially impaired solutions in support of diversification. In the aiNet algorithm, the local search identifies potential solutions around the parent antibody by clonal expansion and antibody mutation. The termination of local search is determined by f, which is the difference between the average fitness of antibodies in the clone and in aiNet. After the local search, the parent antibody is updated to improve the quality of solutions. Once an antibody in the clone has a fitness value better than the fitness of the corresponding parent antibody, it is replaced by the parent antibody. The global nature of the aiNet algorithm results in the best solutions among parent antibodies. A memory mechanism of the aiNet algorithm is handled by the network interactions and the suppression step. In the suppression step, only a portion of the parent antibodies survive and remain for next iteration by examining their fitness values. The aiNet algorithm requires settings of four parameters: f, a, e, and the stopping criterion. In this study, f, is set to 0.01, which indicates that the local search is terminated when the average fitness of a clone cannot be further improved. Then, a and e are set to 10 and 0.05, respectively. Parameters, f, a, and e are usually set arbitrarily based on the type of optimization problem and user preference. The stopping criterion for the aiNet algorithm is discussed in Section 5.1.

the second part, comparative analysis of the optimized and the observed pumping system performance is presented.

Standardized fitness

Step 2. Clonal expansion: Create a clone of size n for each network parent antibody. The antibodies contained in the clone are exact copies of their network parent antibody. Step 3. Local search: Search until the stopping criterion of local search, f i f i1 6 f, is met. Step 3.1. Determine the fitness of each parent antibody, and normalize the fitness values. Step 3.2. Mutate each antibody of every clone based on the fitness value of the parent antibody. The equation for anti body mutation is S0 ¼ S þ ð1=aÞ expðf ÞNð0; 1Þ. The S denotes the antibody (the pump speed) and the S’ denotes the mutated antibody (the modified pump speed). Step 3.3. Compare the network parent antibody with the antibody with the highest fitness in the clone. If the fitness value of the antibody in the clone is better than that of network parent antibody, replace the network parent antibody with this antibody from the clone. Step 3.4. Compute the average fitness of each clone. Step 4. Network interactions and suppression: Compare the fitness value of the network parent antibodies, and eliminate network parent antibodies with fitness values larger than a threshold. The threshold is calculated as the minimal fitness of the network parent antibodies multiplied by (1 + e). Step 5. Diversity: Introduce a number of new randomly generated network parent antibodies into the network, which is the network parent antibody set. Step 6. Go back to Step 2.

No. of iterations X1

X2

X3

X4

Fig. 6. Convergence of the aiNet algorithm in four optimization scenarios.

310


Table 7 Summary of the continuous optimization results. Scenarios

Computed power (kW5-min)

Observed power (kW5-min)

Savings (%)

Computed flow rate (m3/s)

Observed flow rate (m3/s)

Gain (%)

X1 X2 X3 X4

375.82 594.04 1185.07 1377.52

438.75 664.81 1257.89 1848.82

14 11 6 25

2.33 3.83 6.63 9.29

2.33 3.37 6.62 9.29

0 14 0 0

0.65

Value of w1 and w2

Based on Table 7, several interesting findings can be further explored. First, the results of X2 demonstrate that the intuitive tradeoff between saving energy and pumping more wastewater does not strictly exist. Through the optimization of pump speed settings of pumps, it is possible to achieve a win–win game. Figs. 7 and 8 compare the optimized and observed value of the power and flow rate for X2. Figs. 9–12 demonstrate the change of w1 and w2 in continuous optimization for X1–X4. The weights are adjusted

0.6 0.55 0.5 0.45 0.4

0.3

3

4

5

6

w1

800 700

7

8

9

10

11

w2

Fig. 10. Value of w1 and w2 in the optimization for X2.

600 500 400 300

1

2

3

4

5

6

Computed value

7

8

9

10

11

Observed value

Fig. 7. Optimized vs. observed consumed energy for X2.

5.5

0.6 0.58 0.56 0.54 0.52 0.5 0.48 0.46 0.44 0.42 0.4

5

Flow rate (m3/s)

2

Data points

Data points

1

2

3

4

5

6

7

8

9

10

11

Data points 4.5

w1

4

w2


3.5 3 2.5

0.65 1

2

3

4

5

6

7

8

9

10

11

Data points Computed value

Observed value

Fig. 8. Computed vs. observed pumped wastewater flow rate for X2.

0.392

0.388 0.386 0.384 0.382 0.38 1

2

3

4

5

6

7

8

9

10

11

Data points w1

w2


0.378

0.55 0.5 0.45 0.4 0.35 0.3 1

0.39

2

3

4

5

6

7

8

9

10

11

Data points Value of w2

0.62 0.618 0.616 0.614 0.612 0.61 0.608 0.606 0.604 0.602 0.6

0.6

Value of w1 and w2

2

Value of w1

1

900

Value of w1 and w2

The 5- min averaged power (kW)

0.35 1000

w1

w2


based on the change of the wet well level and influent flow rate. In Fig. 10, it is observable that w1 and w2 slightly declined and increased at the first half period but suddenly boosted and reduced in the next half. The possible reason is that a strategy of accumulating wastewater in the wet well first and saving more energy by increasing head is applied. Next, the high energy consumption


is observed in Fig. 8 because pumping more water becomes the priority in the optimization. It is applicable because the influent flow rate in Fig. 2 is low. The proposed data-driven framework is able to be implemented in real applications. The plant experts informed us that the pump speed settings in the PI controller can be overwritten by our generated settings through matlab commands. In addition, as the influent flow rate in the optimization is assumed known, an accurate model for predicting the influent flow rate needs to be developed. 6. Conclusion This paper presented a data-driven approach to control a pumping system in a wastewater processing plant. Four configurations of the pumps were analyzed. A neural network was applied to develop models for predicting energy consumed by the pumping system and flow rate of the pumped wastewater for the four pump configurations. To train and validate the developed NN models, industrial data collected from a wastewater processing plant was utilized. The developed NN models were integrated with constraints to form a bi-objective optimization model for optimizing performance of the pumping system. The two objectives of the optimization model were minimizing energy consumption while maximizing wastewater flow rate. In the optimization model, the change rate of junction chamber level and influent flow rate were considered as the reference to adaptively adjust the importance of objectives in the continuous optimization. The solutions of the model provided optimized settings for the pump speeds. In the continuous optimization, better settings of pump speeds were provided by the optimization model. The energy consumption could be reduced while the pumping performance of the pumping system was maintained based on the computed settings of pump speeds. The optimization results indicated that the efficiency of the pumping system could be improved through appropriate settings of the pump speeds. References [1] Goldstein R, Smith W. Water & sustainability (vol. 4): U.S. Electricity consumption for water supply & treatment—the next half century. Electric Power Research Institute, Inc. (EPRI), Palo Alto, California, 2002 [technical report]. [2] Daw J, Hallett K, DeWolfe J, Venner I. Energy efficiency strategies for municipal wastewater treatment facilities. National Renewable Energy Laboratory, Golden, Colorado; 2012 [technical report]. [3] Plappally AK, Lienhard JHV. Energy requirements for water production, treatment, end use, reclamation, and disposal. Renew Sustain Energy Rev 2012;16:4818–48. [4] Singh P, Carliell-Marquet C, Kansal A. Energy pattern analysis of a wastewater treatment plant. Appl Water Sci 2012;2(3):221–6. [5] Zakkour PD, Gaterell MR, Griffin P, Gochin RJ, Lester JN. Developing a sustainable energy strategy for a water utility. Part II: a review of potential technologies and approaches. J Environ Manage 2002;66(2):115–25. [6] Zhang X, Yan S, Tyagi R, Surampalli R, Valéro J. Wastewater sludge as raw material for microbial oils production. Appl Energy 2014;135:192–201. [7] Holbrook G, Davidson Z, Tatara R, Ziemer N, Rosentrater K, Scott Grayburn W. Use of the microalga Monoraphidium sp. grown in wastewater as a feedstock for biodiesel: cultivation and fuel characteristics. Appl Energy 2014;131: 386–93.

311

[8] Chen G, Zhao L, Qi Y. Enhancing the productivity of microalgae cultivated in wastewater toward biofuel production: a critical review. Appl Energy 2015;137:282–91. [9] Sturm B, Lamer S. An energy evaluation of coupling nutrient removal from wastewater with algal biomass production. Appl Energy 2011;88 (10):3499–506. [10] Fiter M, Guel D, Comas J, Colprim J, Poch M, Rodriguez-Roda I. Energy saving in a wastewater treatment process: an application of fuzzy logic control. Environ Technol 2005;26:1263–70. [11] Raggl K, Warberger B, Nussbaumer T, Burger S, Kolar JW. Robust anglesensorless control of a PMSM bearingless pump. IEEE Trans Industr Electron 2009;56(6):2076–85. [12] DeWinter FA, Kedrosky BJ. Application of a 3500-hp variable frequency drive for pipeline pump control. IEEE Trans Ind Appl 1989;25(6):1019–24. [13] Himavathi S, Umamaheswari B. Fuzzy modelling and control of a three phase induction motor driven pump. Modell Meas Contr A 2002;75(3–4):33–47. [14] Wang J, Chang T, Chen J. An enhanced genetic algorithm for bi-objective pump scheduling in water supply. Expert Syst Appl 2009;36(7):10249–58. [15] Barán B, Von Lücken C, Sotelo A. Multi-objective pump scheduling optimisation using evolutionary strategies. Adv Eng Softw 2005;36(1):39–47. [16] Zhang Z, Zeng Y, Kusiak A. Minimizing pump energy in a wastewater processing plant. Energy 2012;47(1):505–14. [17] Welsby P, Pezzani M, Devotta S, Diggory PJ, Guy JJ. Steady- and dynamic-state simulations of heat-pumps. Part II: modelling of a motor driven water-towater heat-pump. Appl Energy 1988;31(4):239–62. [18] Lian Z, Park S, Qi H. Analysis on energy consumption of water-loop heat pumping system in China. Appl Therm Eng 2005;25(1):73–85. [19] Al-Haddad AA, Enaya E, Fahim MA. Performance of a thermodynamic water pump. Appl Therm Eng 1996;16(4):321–34. [20] Favoino F, Overend M, Jin Q. The optimal thermos-optical properties and energy saving potential of adaptive glazing technologies. Appl Energy 2015;156:1–15. [21] Siegelmann H, Sontag E. Analog computation via neural networks. Theoret Comput Sci 1994;131(2):331–60. [22] Smith M. Neural networks for statistical modelling. New York: Van Nostrand Reinhold; 1993. [23] Zhang Z, Kusiak A. Models for optimization of energy consumption of pumps in a wastewater processing plant. ASCE J Energy Eng 2011;137(4):159–68. [24] Zamaniyan A, Joda F, Behroozsarand A, Ebrahimi H. Application of artificial neural networks (ANN) for modeling of industrial hydrogen plant. Int J Hydrogen Energy 2013;38(15):6289–97. [25] de Castro LN, Timmis J. Artificial immune systems: a new computational intelligence approach. London: Springer-Verlag; 2002. [26] de Castro LN, Timmis J. An artificial immune network for multimodal optimization. Proc Congr Evolut Comput 2002:699–704. [27] Everett H. Generalized Lagrange multiplier method for solving problems of optimum allocation of resources. Oper Res 1963;11(3):399–417. [28] Kiwiel KC, Larsson T, Lindberg PO. Lagrangian relaxation via ballstep subgradient methods. Math Oper Res 2007;32(3):669–86. [29] Nanas N, De Roeck A. Multimodal dynamics optimization: from evolutionary algorithms to artificial immune system. In: Proceedings of the 6th international conference on artificial immune systems; 2007. p. 13–24. [30] Zelenka J, Kasanicky T. Comparison of artificial immune systems with the particle swarm optimization in job-shop scheduling problem. In: Proceedings of the 9th IEEE international symposium on applied machine intelligence and informatics; 2011. p. 129–35. [31] Farmer J, Packard N, Perelson A. The immune system, adaptation and machine learning. Physica D 1986;2(1–3):187–204. [32] Bersini H, Varela F. Hints for adaptive problem solving gleaned from immune network. In: Proceedings of the first conference on parallel problem solving from nature; 1990. p. 343–54. [33] de Castro LN, Von Zuben FJ. Learning and optimization using the clonal selection principle. IEEE Trans Evol Comput 2002;6(3):239–51. [34] Timmis J, Neal M, Hunt J. An artificial immune system for data analysis. Biosystems 2000;55(1–3):143–50. [35] Dasgupta D. An artificial immune system as a multi-agent decision support system. In: Proceedings of the IEEE international conference on systems, man and cybernetics; 1998. p. 3816–20. [36] Forrest S, Javornik B, Smith RE, Perelson AS. Using genetic algorithms to explore pattern recognition in the immune system. Evol Comput 1993;1 (3):191–211.