An efficient approach based on bi-sensitivity analysis and genetic algorithm for calibration of activated sludge models

Chemical Engineering Journal 259 (2015) 845–853

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An efficient approach based on bi-sensitivity analysis and genetic algorithm for calibration of activated sludge models Wenliang Chen a,b,c, Xiwu Lu a,c,⇑, Chonghua Yao b,⇑, Guangcan Zhu a,c, Zhuo Xu a,c a

School of Energy and Environment, Southeast University, Sipailou Road, Nanjing 210096, China School of Resources and Environmental Engineering, East China University of Science and Technology, Meilong Road, Shanghai 200237, China c ERC Taihu Lake Water Environment (Wuxi), China b

h i g h l i g h t s  An efficient approach for calibration of ASMs was proposed.  Five influential parameters were added during the second sensitivity analysis. +

 Sensitivities of K O2 , K NH4 and KALK were influenced by NH4 -N concentration.  Computational time could be reduced by using C-code and parallel computing.  Rapid convergence of the proposed approach could be observed.

a r t i c l e

i n f o

Article history: Received 10 October 2013 Received in revised form 28 July 2014 Accepted 31 July 2014 Available online 19 August 2014 Keywords: Activated sludge model Calibration Validation Sensitivity analysis Genetic algorithm Switching function

a b s t r a c t An efficient approach employing bi-sensitivity analysis and genetic algorithm was proposed for calibration of activated sludge models. The approach mainly contained twice sensitivity analyses and twice calibrations through minimizing cost function by genetic algorithm, and which was evaluated on Step A2/O activated sludge process with Commutative Multi-influent (SA2/OCM) at low temperature, where effluent COD, TN, TP and NH+4-N were used. The model was calibrated at HRT 16 h under steady state, while model validation was carried out under HRT 20 h and HRT 24 h using dynamic data. Results showed that, model with default ASM2d parameters had poor predictions of TN and NH+4-N at low temperature. Sensitivities of K O2 , K NH4 and KALK located in switching functions would be increased along with the decreasing of NH+4-N, thus these parameters were missed during the first sensitivity analysis owing to that NH+4-N was poorly predicted, however they were selected during the second sensitivity analysis based on the calibrated model 1. Consequently predictions of the calibrated model 2 were better than that of the calibrated model 1. In addition, computational time of this approach could be reduced by using the efficient C code and the parallel computing. Ó 2014 Elsevier B.V. All rights reserved.

1. Introduction Activated sludge process (ASP) is widely used for municipal and industrial wastewater treatment. Nowadays, modeling of ASP using activated sludge models (ASMs) [1] proposed by the International Water Association (IWA) is widely extended. ASMs are also incorporated in some contemporarily used commercial simulation ⇑ Corresponding authors. Addresses: School of Energy and Environment, Southeast University, Sipailou Road, Nanjing 210096, China (X. Lu), School of Resources and Environmental Engineering, East China University of Science and Technology, Meilong Road, Shanghai 200237, China (C. Yao). Tel.: +86 13795412265. E-mail addresses: [email protected] (W. Chen), [email protected] (X. Lu), [email protected] (C. Yao), [email protected] (G. Zhu), [email protected] (Z. Xu). http://dx.doi.org/10.1016/j.cej.2014.07.131 1385-8947/Ó 2014 Elsevier B.V. All rights reserved.

software, e.g., BioWin, GPS-X, WEST, ASIM, DESSAS [2–4], which can be used to design ASP [5–7], develop control strategies and optimize processes [8–13]. In order to successfully apply ASMs in simulation of wastewater treatment processes, there are several steps starting from (1) definition of modeling objective, (2) data collection and the quality check, (3) programing of the models for different units of processes, including hydraulics, (4) model calibration and to (5) model validation and model using [14]. Among them model calibration is the core, which is defined as the adjustment of specific model parameters so that model outputs can be fitted a certain set of experimental data from the process under study [15]. Several calibration guidelines have been proposed so far, particularly the WERF protocol [16], the STOWA protocol [17] and the HSG

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guidelines [18] and the extended protocol in BIOMATH [19,20]. A detailed comparison of the existing model guidelines can be found in Sin et al. [14]. Model calibration is usually conducted by calculating the best parameter values according to a cost function (CF), which generally describes the difference between model prediction and experimental data. However, ASMs contain many parameters, and which leads to the well-known problem of poorly identifiable parameters [21], making it hard to decide which parameters must be calibrated. The calibration procedure usually employs lots of experience obtained from activated sludge systems [22], which is difficult for newbie engineers or researchers. While some studies have presented the systematic approach based on mathematical methods to select parameters. They studied the identifiability of parameters in ASMs calculated by the sensitivity analysis [21,23– 25], where influences of parameters on model outputs can be determined, and then adequate influential parameters should be selected and estimated [26]. In fact, in most model application cases, only small number of parameters are estimated, either by manual trial and error method or combining an optimization algorithm [27,28], while most parameters are remained at their default values. Sin et al. [27] introduced an efficient approach using Monte Carlo method to complete the tedious manual trial and error way of model calibration automatically. However, there are some drawbacks in the method combining optimization algorithm. Many studies [21,29,30] revealed that these methods were time-consuming, and local optimization algorithm would get troubled easily in local minimum, while global optimization method, e.g., genetic algorithm, would require large numbers of simulations until offering the satisfying parameter estimates [27]. Therefore, there are still two difficulties in ASMs calibration, the first is how to define an unbiased parameter subset, which contains as less parameter as possible but it’s sufficient to get a satisfying calibrated model; and the second is to obtain a global optimized CF value with the minimal time-consuming demand. Having recognized these difficulties, this study proposed a systematic calibration approach based on bi-sensitivity analysis and genetic algorithm. On the one hand, sensitivity analysis of parameters were calculated twice, where the second sensitivity analysis was calculated relying on the first parameter estimation to identify the missed influential parameters caused by the poor prediction of model with the default values, on the other hand, computational time could be reduced by means of the efficient C code and with the help of parallel computing in MATLAB. All these will become clear below.

2. Material and methods 2.1. Pilot plant The pilot plant studied was the Step A2/O activated sludge process with Commutative Multi-influent (SA2/OCM, Fig. 1) developed by Southeast University of China, which combined excellent features of UNITANK and A2/O. SA2/OCM consists of five bioreactors and one clarifier for sludge-water separation. The dimension of each bioreactor is 280 * 240 * 900 mm3, and that of the clarifier is 360 * 280 * 900 mm3, the available depth is 700 mm. The pilot plant was controlled with a PLC control system. Each bioreactor fixes aerator and stirrer and conditions of anaerobic, anoxic and aerobic can be achieved by changing the process parameters. Raw wastewater can be pumped into all of the bioreactors; however the returned sludge from the bottom of clarifier can be only recycled to tank2, tank3 and tank4. The step operating time, working time of the aerators and stirrers, on and off of solenoid valves can be adjusted manually or automatically from the touch screen of PLC control system. The cycle of SA2/OCM is divided into the exactly symmetrical two periods: the first half (step 1, step 2 and step 3) and the second half (step 4, step 5 and step 6). Partial sludge distribution and recycle can be realized as a result of water flow direction changing caused by the multi-influent. 2.2. Plant settings and experimental process The pilot plant was located in Qingtan WWTP of Jiangsu, China. Raw wastewater was from sump, and the sludge was taken from the aeration tank of the WWTP directly. The SA2/OCM plant was operated for about 4 months containing 3 successive runs with different hydraulic retention time (HRT). Run1 was at HRT 16 h, operated 70 days, including the period of sludge acclimation (about 50 days), Run2 and Run3 were separately operated at HRT 20 h and 24 h, lasting 20 days. Average sludge concentration was remained at about 3000 mg/L. Sludge retention time (SRT) was kept at about 13 days by controlling the waste sludge rate. The dissolved oxygen (DO) was manually controlled by manipulating the aeration rate. Conditions of the pilot plant during the experimental periods are listed in Table 1. The analytical methods for chemical oxygen demand (COD), ammonia nitrogen (NH+4-N), total nitrogen (TN), total phosphorus (TP), and mixed liquor suspended solids (MLSS) were analyzed according to standard methods. The DO was measured by a DO meter (YSI DO200, USA).

Fig. 1. Configuration of Step A2/O activated sludge process with Commutative Multi-influent. r – influent; s – effluent; t – waste sludge; u – return sludge.

W. Chen et al. / Chemical Engineering Journal 259 (2015) 845–853 Table 1 Environmental and operational conditions used in the pilot plant throughout the study.

a

Symbol

Parameter

Value

Units

HRT SRT SRR IDR T PH DO tank1 DO tank2 DO tank3 DO tank4 DO tank5 Time.1.4 Time.2.5 Time.3.6

Hydraulic retention time Sludge retention time Sludge recycle ratio Influent distribution ratio Temperature

16/20/24 13 0.3 1:1 10–12 (11)a 7–7.5 2 3 3 3 2 3 3 2

h d – – °C – mg/L mg/L mg/L mg/L mg/L h h h

Dissolved oxygen in tank1 Dissolved oxygen in tank2 Dissolved oxygen in tank3 Dissolved oxygen in tank4 Dissolved oxygen in tank5 Operating time of step 1 and step 4 Operating time of step 2 and step 5 Operating time of step 3 and step 6

Is the average value of temperature.

Grab samples were regularly collected, and the influent and effluent data were tested every other day during the last 20 days of each run. The cyclical dynamics of the plant was analyzed through testing the grab samples from effluent with an interval of 1 h. Fermentation products (SA), readily biodegradable organic substrates (SF), inert soluble organic material (SI), slowly biodegradable substrates (XS), inert particulate organic material (XI) separately accounted for about 13.5%, 30.7%, 7.3%, 32.2% and 16.2% of COD [31]. Component concentrations are shown in Table 2. It was important to declare that model calibration was performed calculating the CF with the data from HRT 16 h under steady state (using the average concentrations), while model validation was conducted with the available dynamic data from HRT 20 h and HRT 24 h. 2.3. Model and method implemented in MATLAB Activated sludge model 2d (ASM2d) [32] was chosen because of the function for removing nitrogen and phosphorus in SA2/OCM process. Nineteen components of ASM2d were all considered in every bioreactor. The clarifier was described with a ten-layer Takács settling model [33]. Each layer contained one particulate component and nine soluble components, described by Copp [34]. The hydraulics was assumed following the tanks-in-series approach, where five CSTRs were deemed enough to describe the model of SA2/OCM. The whole SA2/OCM model was compiled by using the C code in S-function of Simulink/MATLAB, and the set of differential equations was solved by the ode23. 2.4. Sensitivity analysis Sensitivity analysis can calculate the parameter influence for model outputs. A parameter having high sensitivity is the one that a small change of its value can make a large difference in the outputs, and vice versa. Relative sensitivity of output i (yi) respecting to a parameter j (xj) is calculated as Eq. (1) [35]. Table 2 Wastewater characterization for ASM2d influent specifications under different HRTs. Components

HRT = 16 h

HRT = 20 h

HRT = 24 h

SF (mg/L) SA (mg/L) SI (mg/L) SNH4 (mg/L) SPO4 (mg/L) XI (mg/L) XS (mg/L)

105.21 ± 41.41 46.26 ± 18.21 25.02 ± 9.84 39.8 ± 9.44 1.49 ± 0.57 55.52 ± 21.85 110.35 ± 43.44

101.8 ± 36.66 44.77 ± 16.12 24.21 ± 8.71 35.2 ± 11.73 1.38 ± 0.51 53.72 ± 19.34 106.78 ± 38.45

99.07 ± 36.04 43.56 ± 15.85 23.56 ± 8.57 40.7 ± 11.99 1.35 ± 0.62 52.28 ± 19.02 103.91 ± 37.81

xj dyi Si;j ¼ yi dxj

847

ð1Þ

The derivatives in Eq. (1) were determined numerically by a specific change. In this work, a 10% increase of one parameter was applied for calculating Si,j. The influence of a parameter on the outputs of model can be classified according to Table S1 (Supplementary data) [15]. Four variables (yi) representing the effluent quality were taken into account during the sensitivity calculations, specifically COD, TN, TP and NH+4-N. The temperature was very low during the experiment period, all parameter values were adjusted to that of 11 °C by Eq. (S1) in Supplementary data. There are 45 kinetic parameters and 9 stoichiometric parameters in ASM2d. Among 45 kinetic parameters, rate constant for phosphorus precipitation (kPRE), rate constant for redissolution (kRED) and saturation coefficient for alkalinity (KALK) are involved in precipitation process, which were useless in this study and thus were kept constant at their default values. Among the 9 stoichiometric parameters, fSI (production of SI in hydrolysis), fXI (fraction of inert COD in heterotrophic organisms (XH), phosphate-accumulating organism (XPAO) and nitrifying organisms (XAUT)) were maintained at the default values [26]. As a consequence, the sensitivity analysis included 47 parameters: 42 kinetic parameters and 5 stoichiometric parameters: yield coefficient for XH (YH), yield coefficient for XPAO (YPAO), PP requirement per PHA stored (Y PO4 ), PHA requirement for PP storage (YPHA) and yield coefficient of XAUT (YA). 2.5. CF evaluation The model calibration procedure was based on the minimization of a CF (Eq. (2)) calculating the absolute value of relative errors between the model predictions and experimental data of effluent COD, TN, TP and NH+4-N.

CODmod  CODmea TNmod  TNmea TPmod  TPmea þ þ CF ¼ CODmea TNmea TPmea þ þ NH -Nmod  NH4 -Nmea þ 4 NHþ -N 4

ð2Þ

mea

where CODmod, TNmod, TPmod and NH+4-Nmod are the model prediction values and CODmea, TNmea, TPmea and NH+4-Nmea are the experimental data. 2.6. Optimization algorithm The optimization algorithm employed in this study was a global optimization method: genetic algorithm in optimization toolbox of MATLAB. Genetic algorithm is multi-point search and it does not use any derivatives of problems, for example, the numerical or analytic gradients of CF, it only cares the value of CF. Generally, each parameter has its own constraint (lower and upper limits) in optimization problems. In this paper, all parameters needed to be calibrated have wide constraints, specifically the lower limits (one third of the default values) and upper limits (three times of the default values). In fact, the goal was not to constrain too much the search space so that the algorithm would not miss any promising solutions [36]. Settings for genetic algorithm are listed in Table S3 (Supplementary data). 2.7. Model calibration procedure based on sensitivity analysis The procedure of model calibration is based on the bi-sensitivity analysis and genetic algorithm. Parameters needed to be calibrated are estimated to minimize CF as far as possible. Fig. 2 shows a flowchart illustrating the methodology used in this study.

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Fig. 2. Flowchart of the proposed methodology.

First, checking the qualities of available experimental data and the process parameters is conducted, and then model for SA2/ OCM based on ASM2d is built. The prediction of the established model is examined under the condition that all kinetic and stoichiometric parameters are with their default values at temperature 11 °C. Second, the first sensitivity analysis including 47 parameters is calculated at ASM2d default values. According to the classification for sensitivity from Table S1, the first parameter subset is created containing the parameters whose sensitivities of effluent COD, TN, TP and NH+4-N are more than 0.25, then calibration model 1 employing CF calculated as Eq. (2) and the first parameter subset is established. During the calibration process, the optimization of calibration model 1 through minimizing CF using the genetic algorithm is very simple, which is conducted in the optimization toolbox of MATLAB. And then examining the prediction of the calibrated model 1 with the optimized parameters is carried out.

Next step is sensitivity calculation for the second time, which is analyzed with the optimized parameters obtained from calibration model 1. Then the same procedures including selection of parameters whose sensitivities are more than 0.25, building calibration model 2 and optimization are calculated. The reason for conducting the second time sensitivity analysis with the optimized parameters was that this study found the prediction of model using ASM2d default values under low temperature was very poor, especially for the nitrification, as showed in Fig. 3. The big differences between experimental data and model calculation might have great influence on sensitivity analysis, results of which were varied with different situations [21]. At last, differences between the first optimized parameter subset and the second optimized parameter subset were analyzed, and predictions of model with these two optimized parameter subsets were compared.

3. Results and discussion 3.1. Prediction of model with ASM2d default values

Fig. 3. Effluents comparison between experimental data with the model outputs at HRT 16 h. Measured is the experimental data, Model_default is model output with default values, Model_1 is results of calibration 1, while Model_2 is result of calibration 2. Confidence bounds were calculated by standard deviation.

Prediction of model with ASM2d default values was examined and comparison between experimental and model outputs is shown in Fig. 3. The prediction for COD is passable, while the predictions of other three components are too outrageous, especially for effluent NH+4-N, the difference of which is 28.16 mg/L, consequently, the fitness for effluent TN is also not good, indicating that the model with ASM2d default values has poor nitrification and denitrification at low temperature. The measured effluent TP is 1.0 mg/L, however the output TP of model is 0.34 mg/L, where good performance of phosphorus removal can be observed. Comparing the performances of effluent NH+4-N, TN and TP, nitrification and denitrification reactions are much more easily influenced by low temperature than phosphorus removal. Therefore, the model with default ASM2d parameters predicted a higher PAO activity and a lower autotrophic biomass activity [26]. Based on the above analysis, there was a strong need for model calibration.

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W. Chen et al. / Chemical Engineering Journal 259 (2015) 845–853 Table 3 Values of Si,j for the most influential (Si,j P 0.25) parameters at HRT 16 h (the first). Parameters

Si,j

Table 5 Values of Si,j for the most influential (Si,j P 0.25) parameters at HRT 16 h (the second). Parameters

COD

TN

NH+4-N

TP

Kinetic PAO qpp

0.51 0.85 0.31

lPAO KPS AUT

lAUT

0.32

1.12 0.44

Stoichiometric YPAO Y PO4

COD

TN

Kinetic PAO qPP

0.66 0.93

0.31

bPP KPS AUT

lAUT

3.2.1. The first sensitivity analysis In Table 3, values of the relative sensitivity (Si,j) more than 0.25 are shown. It occurred that 7 out of 47 parameters should be regarded as influential. Specifically, maximum growth rate of AUT (lAUT) could be classified as very influential, six parameters including rate constant for storage of PHA (qpp), maximum growth rate of PAO (lPAO), saturation coefficient for phosphorus in storage of PP (KPS), decay rate of AUT (bAUT), YPAO and Y PO4 were influential according to the classification shown in Table S1. However, for effluent COD, no parameter is influential. 3.2.2. Calibration 1 According to the results of the first sensitivity analysis, seven parameters were selected to make up the first parameter subset, including qpp, lPAO, KPS, lAUT, bAUT, YPAO and Y PO4 . The calibration was conducted through minimizing the CF using genetic algorithm in MATLAB. Estimated values (calibration 1) for the 7 parameters are listed in Table 4. For the purpose of comparing conveniently, all values are based on temperature of 20 °C. It seemed insignificance to analyze the differences between estimated values and the default, but this comparison was necessary for a further understanding of ASM2d. For PAO, five parameters were estimated. qpp was sharply decreased from default (1.5 g(Xpp)/g(XPAO)/d) to 0.60 g(Xpp)/g(XPAO)/d, while lPAO was increased from default (1 d1) to 1.91 d1, which guaranteed a sufficient growth rate for PAO at low temperature, and there was another parameter having the same effect, YPAO, being increased by 42.4% compared with default. KPS locating at switching function

NH+4-N

0.33

1.55 0.65 0.30 0.29 0.26

bAUT K O2 K NH4 KALK Stoichiometric YH YPAO Y PO4

3.2. The first calibration circle

TP

2.58 6.72 0.31 0.82

lPAO

0.68 0.27

bAUT

Si,j

0.27

0.93 2.74 6.43

0.35

SPO4 =ðK PS þ SPO4 Þ, was increased by 60% compared with default value, which will minimize the role of SPO4 at low concentration. Y PO4 was lower than its default value, which was close to the values in Makinia et al. [24] and Machado et al. [26], where they considered the reason was the presence of GAO bacteria (glycogen accumulation organisms), because a lower anaerobic P release vs. VFA (volatile fatty acid) uptake would be observed due to the simultaneous VFA uptake by GAO and PAO. Thereby, GAO could be considered as an external unmeasured process disturbance that affected the optimized values of the PAO parameters [21,26]. For AUT, two kinetic parameters (lAUT and bAUT) were estimated, and these two parameters for calibration activity of AUT could be found commonly in literatures. Fig. 3 shows that model with ASM2d default values have a poor nitrification compared with experimental data at low temperature. For the sake of obtaining a good fitness for effluent NH+4-N, optimized value for lAUT was more than two times (2.21 d1) than the default (1 d1), while value of bAUT (0.12 d1) was lower than the default (0.15 d1), and lAUT and bAUT had the same effect to guarantee an enough growth rate for AUT at low temperature. Using the optimized parameters to replace the default values, concentrations of effluent for the calibrated model 1 are shown in Fig. 3. It could be observed that model outputs were in good agreement with the experimental data, the CF is 0.62.

Table 4 Estimated values for parameters in calibration 1 and calibration 2. Parameters Kinetic PAO qpp

lPAO bpp KPS AUT

lAUT bAUT K O2 K NH4 KALK

Units

Default

Calibration 1

Calibration 2

g(Xpp)/g(XPAO)/d d1 d1 g(P)/m3

1.5 1 0.2 0.2

0.60 1.91 – 0.32

0.68 1.90 0.57 0.49

d1 d1 g(O2)/m3 g(N)/m3 3 mol(HCO 3 )/m

1 0.15 0.5 1 0.5

2.21 0.12 – – –

2.75 0.10 0.60 0.76 1.14

0.625 0.625 0.4

– 0.89 0.18

0.73 1.84 0.37

Stoichiometric YH g(COD)/g(COD) YPAO g(COD)/g(COD) Y PO4 g(P)/g(COD)

Fig. 4. Variation of sensitivity correspond to different concentrations of effluent NH+4-N. the dash line represents boundary for parameters that should be calibrated or not.

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Fig. 5. Variation of switching function correspond to different concentrations of effluent NH+4-N. SNH4 is concentration of NH+4-N, value of K NH4 is constant of 1.0 mg(N)/L.

3.3. The second calibration circle 3.3.1. The second sensitivity analysis After calibration 1, there was an optimized parameter subset containing 7 parameters. On the basis of these optimized values, another sensitivity analysis was carried out, the most influential (Si,j P 0.25) parameters under HRT 16 h are listed in Table 5. It occurred that 12 out of 47 parameters could be regarded as influential, where 7 parameters were the same with that in the first sensitivity analysis (Table 3), and the other 5 were: rate for lysis of Xpp (bpp), saturation coefficient for oxygen (K O2 ), saturation coefficient for ammonium (K NH4 ), saturation coefficient for alkalinity (KALK), YH. Among them qpp, lPAO, YPAO, Y PO4 could be regarded as extremely influential; lAUT was very influential, while the others were influential according to Table S1.

3.3.2. Calibration 2 Optimization for minimizing the CF was calculated based on the second parameter subset, where the same procedures as calibration 1 in Section 3.2.2 were carried out. The results are listed in Table 4. Comparing calibration 2 with calibration 1, the same parameters almost had the same optimized values except YPAO and Y PO4 , which had larger values. For PAO, value of bpp was adjusted from 0.2 d1 to 0.57 d1, while for AUT, two newly added parameters (K O2 , KALK) were increased, and the other new parameter K NH4 was decreased, lower values of which are commonly encountered in pilot plant, which could be justified by a lower diffusion limitation due to high turbulence and small flocs with comparison to full scale conditions [1,24]. Stoichiometric parameter YH had a slight bigger value (0.73 g(COD)/g(COD)) than default (0.625 g(COD)/g(COD)). The reasons leading to different parameter subsets had also been discussed. Effluent COD, TN and TP were composited components, e.g., COD was the sum of SA, SF, SI, XI, XS, XH, XPAO, polyhydroxy-alkanoates (XPHA), and XAUT. It was very difficult to analyze the specific reasons. However, effluent NH+4-N was a single component, and in addition, Fig. 3 have shown the prediction of model with ASM2d default values is very poor compared with the experimental data, especially for effluent TN and NH+4-N. How to get a low concentration of effluent NH+4-N at ASM2d default values was the key point for a further research, and this study overcame it by means of reducing the concentration of NH+4-N in influent, from 39.8 mg/L to 29.8 mg/L, then to 19.8 mg/L and the last to 9.8 mg/L, the corresponding concentrations of NH+4-N in effluent were 30.46 mg/L, 21.06 mg/L, 12.56 mg/L and 5.90 mg/L, respectively. During this process, only parameters relating to AUT was analyzed and all calculations were carried out under HRT 16 h. Fig. 4 shows the sensitivity of K O2 ; K NH4 and KALK at different concentrations of effluent NH+4-N. Parameter K NH4 is located in the switching function SNH4 =ðK NH4 þ SNH4 Þ, and it can be seen from Fig. 5 that the larger value of SNH4 is, the more approximate 1 of the

Fig. 6. Comparison of measured and simulated concentrations in effluent under HRT 20 h and HRT 24 h. Measured is the experimental data, Model_1 is result of calibration 1, while Model_2 is result of calibration 2, sample time of model is 8 h.

W. Chen et al. / Chemical Engineering Journal 259 (2015) 845–853

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Fig. 7. Measured and simulated components in the effluent during one operating cycle (16 h) under HRT 20 h. Measured is the experimental data, Model_1 is result of calibration 1, while Model_2 is result of calibration 2, sample time is 1 h.

Fig. 8. Values of cost function during the optimization process. (a) Calibration 1 and (b) calibration 2.

switching function equals, and at this situation, the role of K NH4 is very slight, while when SNH4 is getting smaller (less than 5), value of switching function will be decreased sharply and the role of K NH4 is getting more important. Sensitivity could reflect the importance of parameters to outputs, therefore, sensitivity value of K NH4 would get larger and larger with the decreasing of NH+4-N concentrations (Fig. 4). K O2 is located in the switching function SO2 =ðK O2 þ SO2 Þ while KALK is located in the switching function SALK/(KALK + SALK), they also have the similar tendency as K NH4 perhaps owing to that during nitrification reaction, oxygen and alkalinity are also consumed. Outputs of COD, TN, TP and NH+4-N for the calibrated model 2 under HRT 16 h are drawn in Fig. 3. The predictions of TN, TP and NH+4-N were all better than that of calibration 1, and the CF was 0.25. Calibrated models were long-term simulated for validation using the dynamic data under HRT 20 h and HRT 24 h. Fig. 6 is

the comparison of measured and models simulated concentrations in effluent. Fig. 7 is the effluent dynamics during one operating cycle under HRT 20 h. It could be concluded that calibrated model 2 had a better agreement with the measured data than calibrated model 1, especially for effluent TP and NH+4-N. The dynamic of all effluent components were more drastic than the measured data, which indicated that the clarifier had a good buffering effect in practice. However, the tendencies of model simulated were all similar with the measured data. 3.4. Efficiency of the calibration procedure The calculated process could be completed by a computer without user intervention, so considerable time for researcher could be reduced, which was the ultimate aim of using a model [27]. Fig. 8 shows values of CF during the optimization processes, which are the results of genetic algorithm calculation. It could be found that

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the best values of CF were minimized quickly and CF could get almost the ultimate values at about generation 8 or generation 6, respectively. The mean fitness represented the convergence during the optimization process. Calibration 1 took about 21 generations while calibration 2 required approximate 36 generations before reaching convergence. Calibration 2 consumed more generations probably because that 12 parameters were needed to be estimated, while it was 7 in calibration 1. A shortage of the proposed method was the requirement of computational time, because large numbers of model simulations were still needed before providing a calibrated model. With the author’s computer (Intel Core i7-2600, 3.40 GHz, Quad-Core with 12G RAM PC), one simulation run of SA2/OCM model written by M-file required about 400 seconds, while it just consumed 30 s written by C code in S-function of Simulink. Another way to reduce computational time was the parallel computing in MATLAB. With these techniques, model calibration based on the proposed approach could be completed within 12 h. 4. Conclusions In this contribution, the authors have proposed and evaluated a systematic approach based on bi-sensitivity analysis and genetic algorithm to replace manual trial and error methods for calibration of activated sludge models. The approach contains step as: (1) sensitivity analysis with ASM2d default values, (2) selecting parameters whose sensitivities are more than 0.25, (3) building calibration model to estimate the selected parameters employing CF, (4) using the genetic algorithm to optimize the calibration model, (5) the second sensitivity analysis based on the optimized parameters and recalculating from step (2) to step (4). The proposed systematic approach was successfully used to calibrate a model for a pilot plant named Step A2/O activated sludge process with Commutative Multi-influent (SA2/OCM) at low temperature. The calibration was calculated under HRT 16 h, while validation of the calibrated model was carried out under HRT 20 h and HRT 24 h. Two calibrated models with two parameter subsets were obtained. Comparing these two subsets, subset 1 contained 7 parameters while subset 2 contained 12 parameters, so 5 parameters were newly added during the second sensitivity analysis. Sensitivities of K O2 ; K NH4 and KALK located in switching functions would be increased along with the decreasing of NH+4-N, owing to that NH+4-N was poorly predicted with ASM2d default values, these parameters were missed during the first sensitivity analysis, however they were selected during the second sensitivity analysis based on the calibrated model 1. As a consequence, calibrated model 2 had better prediction in effluent TN and NH+4-N than calibrated model 1. The shortage of calibration process using genetic algorithm could be overcame by the high-efficiency C code and the parallel computing in MATLAB. More importantly, rapid convergence of the proposed approach could be observed. Overall, the proposed systematic approach employing bi-sensitivity analysis and genetic algorithm can replace the manual trial and error calibration method for calibration of activated sludge models. Acknowledgements This research has been supported by the Major Program on Scientific Research of Ministry of Education (308010), the National Twelfth Five-year Major Projects (No. 2012ZX07101-005), Key Technology R&D program of Jiangsu Province (BS2008667) and Nature Science Foundation of Jiangsu (BK2011142). The authors wish to thank the anonymous reviewers for their constructive comments that improved the manuscript.

Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.cej.2014.07.131.

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