CN102249411B - Method for optimizing sewage treatment process - Google Patents

Method for optimizing sewage treatment process Download PDF

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CN102249411B
CN102249411B CN 201110127239 CN201110127239A CN102249411B CN 102249411 B CN102249411 B CN 102249411B CN 201110127239 CN201110127239 CN 201110127239 CN 201110127239 A CN201110127239 A CN 201110127239A CN 102249411 B CN102249411 B CN 102249411B
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俞汉青
方芳
倪丙杰
盛国平
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University of Science and Technology of China USTC
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Abstract

The invention discloses a method for optimizing a sewage treatment process in an urban sewage treatment factory, which comprises the following steps of: 1) generating n operating conditions of an anaerobic-anoxic-oxic (A<2>O) process in the urban sewage treatment factory by a stochastic simulation method; 2) simulating effluent quality under the n stochastically generated process operating conditions by using an activated sludge mathematical model of the A<2>O process; 3) establishing a relationship between the operating conditions obtained in the step 1) and the effluent quality obtained in the step 2) by using a support vector machine to obtain a support vector machine model; and 4) optimizing the support vector machine model obtained in the step 3) by using an accelerated genetic algorithm to obtain the optimal operating condition of the sewage treatment process. Under the optimal process operating condition obtained by the method, the internal reflux ratio is reduced, and the hydraulic retention time of an anoxic tank is shortened simultaneously, so that operating cost is saved while the requirement on the effluent quality is met.

Description

A kind of optimization method of sewage treatment process
Technical field
The invention belongs to the biological wastewater treatment technology field, relate to a kind of sewage disposal A 2The optimization method of O technique.
Background technology
A 2O technique (also claims A-A-O technique, the abbreviation (biological carbon and phosphorous removal) of English Anaerobic-Anoxic-Oxic first letter, also referred to as the anaerobic-anoxic-oxic method) function of denitrogenation dephosphorizing becomes the widely used biological process of wastewater treatment in present municipal sewage plant owing to having simultaneously.Due to A 2The effluent quality of O technique and working cost are subject to the impact of a plurality of factors, as internal reflux ratio, hydraulic detention time, sludge retention time, aeration speed etc., therefore need to seek the process operation condition of optimizing, make guaranteeing that effluent quality can reduce working cost again in up to standard.The general method of seeking optimal conditions is the experiment of a series of different process operational conditionss of design, obtains by experiment A under the different process operational conditions 2Then the effluent quality of O technique obtains A by optimization method 2The optimum operating condition of O technique.But due to A 2O technique more complicated if the method for design obtains optimum operating condition by experiment, needs to consume a large amount of time and expense.
Summary of the invention
The purpose of this invention is to provide a kind of sewage disposal A 2The optimization method of O technique.
Sewage disposal A provided by the invention 2The optimization method of O technique comprises the steps:
1) adopt the method for stochastic simulation to produce n sewage disposal A 2The operational conditions of O technique;
2) adopt A 2The activated sludge model of O technique obtains step 1) each sewage disposal A of gained 2Effluent quality under O process operation condition;
3) with step 1) gained operational conditions and step 2) relation between the gained effluent quality is optimized, and obtains described sewage disposal A 2The optimum operating condition of O technique.
Described step 1) in, obtain municipal sewage plant A owing to testing by series of optimum 2The optimum operating condition of O technique is difficult to realize, therefore adopts the method for computer simulation to seek the optimised process operational conditions.In this step, described operational conditions comprises the hydraulic detention time (HRT) of anaerobic pond, the hydraulic detention time of anoxic pond, hydraulic detention time, internal reflux ratio, Aerobic Pond oxygen mass transfer coefficients and the solid retention time (SRT) of Aerobic Pond.In described stochastic simulation step, can set according to the actual treatment ability of different cities sewage work the different range of above-mentioned operational conditions, so that the operational conditions after optimizing is within reasonable process range.
Described step 2) in, the activated sludge model of described sewage treatment process is any one or the revised mathematical model of following any one mathematical model in following mathematical model: No. 1 model of active sludge, activated sludge model No.2, No. 3 models of active sludge and active sludge 2d model.Above-mentioned four kinds of models are the conventional activated sludge mathematical model, referring to " activated sludge model ", and international water association's biological wastewater treatment design and operation mathematical model problem group work, Zhang Yalei, Li Yongmei translates.In actual applications, can above-mentioned four kinds of mathematical models be revised according to the different situations of the sewage technique of concrete processing, various modification methods commonly used all are applicable to the present invention.The detection index of described effluent quality comprises water outlet COD value, NH 4 +Concentration, the concentration of total nitrogen (TN) and the concentration of total phosphorus (TP).This step is specially: with a said n different process operation conditions difference substitution A used 2The activated sludge model of O technique obtains A under the different process operational conditions by corresponding mathematical model 2The effluent quality of O technique.
Described step 3) in, the method for optimization comprises the steps:
1) adopt SVMs to set up described step 1) gained operational conditions and step 2) relation between the gained effluent quality, supported vector machine model;
2) adopt the described supporting vector machine model of acceleration genetic algorithm optimization, obtain described sewage disposal A 2The optimum operating condition of O technique.
Described step 1) gained operational conditions and described step 2) pass between the gained effluent quality is nonlinear function; In SVMs, the nonlinear function of setting up between input variable and output variable is to solve regression problem, for this A 2The optimization method of O technique, input variable is step 1) the gained operational conditions, output variable is step 2) the gained effluent quality.
By introducing slack variable ξ iAnd ξ i *, regression problem can be converted into formula (1):
min w , b , &xi; , &xi; * 1 2 w 2 + C &Sigma; i = 1 l &xi; i + C &Sigma; i = 1 l &xi; i * - - - ( 1 )
Constraint condition is: ( w &CenterDot; &phi; ( x i ) + b ) - z i &le; &epsiv; + &xi; i ( z i - w &CenterDot; &phi; ( x i ) ) - b &le; &epsiv; + &xi; &xi; i , &xi; i * &GreaterEqual; 0 , i = 1 , . . . , l
Lagrange function face is incorporated into above-mentioned protruding double optimization problem, and formula (1) becomes:
min &alpha; , &alpha; * 1 2 &Sigma; i , j = 1 l ( &alpha; i - &alpha; i * ) ( &alpha; i - &alpha; i * ) K ( x i , x j ) + &epsiv; &Sigma; i = 1 l ( &alpha; i + &alpha; i * ) - &Sigma; i = 1 l z i ( &alpha; i - &alpha; i * ) - - - ( 2 )
Constraint condition is: &Sigma; i = 1 l ( &alpha; i - &alpha; i * ) = 0 0 &le; &alpha; i , &alpha; i * &le; Ci = 1 , . . . , l
Wherein: K (x i, x j)=φ (x i) φ (x j) be kernel function, generally get polynomial kernel function or RBF kernel function etc.
By finding the solution formula (2), the nonlinear function between the different process operational conditions of can supported vector machine setting up and effluent quality.
The present invention also provides a kind of sewage treatment process of optimization, comprise following process operation condition: the Aerobic Pond oxygen mass transfer coefficients is 32/h, solid retention time is 15 days, internal reflux ratio is 2.6, and the hydraulic detention time of Aerobic Pond, anaerobic pond and anoxic pond was respectively 10.8 hours, 1.5 hours and 2.9 hours.
In addition, supporting vector machine model and the application of acceleration genetic algorithm in the optimization method of sewage treatment process also belong to protection scope of the present invention.
The present invention obtains municipal sewage plant A by the method for mathematical model and computer simulation 2The optimised process operational conditions of O technique.The process operation condition of gained the best has reduced internal reflux ratio, has shortened simultaneously the hydraulic detention time of anoxic pond, makes and save working cost when satisfying effluent quality.The method has important practical value.
Description of drawings
Fig. 1 is municipal sewage plant A 2O technique Inlet and outlet water water quality (former processing condition) (A)-(D) is followed successively by COD value, NH into water and water outlet 4 +The concentration of concentration, total nitrogen (TN) and the concentration of total phosphorus (TP) with the variation relation figure of the working time of sewage work.
Fig. 2 be the different process operational conditions set up of SVMs and effluent quality between nonlinear function, (A) be water outlet COD value, (B) be NH 4 +Concentration, (C) be the concentration of total nitrogen (TN), be (D) concentration of total phosphorus (TP).
Embodiment
The invention will be further described below in conjunction with specific embodiment, but the present invention is not limited to following examples.In following embodiment No. 3, activated sludge model used is referring to " activated sludge model ", the biological wastewater treatment design of international water association and operation mathematical model problem group work, and Zhang Yalei, Li Yongmei translates; EAWAG biological phosphorus model is referring to Rieger L, Koch G, Kuhni M, Gujer W, Siegrist H.The EAWAG Bio-P module for activated sludge model No.3.Water Research 35 (2001) 3887-3903.
Embodiment 1
Municipal sewage plant A 2In O technique, the hydraulic detention time of anaerobic pond, anoxic pond and Aerobic Pond was respectively 1.5 hours, 3.2 hours and 10.8 hours, solid retention time is 13 days, external reflux ratio (return sludge ratio) is 80%, and internal reflux ratio (return current ratio of the mixed liquid) is 3.0.The Inlet and outlet water water quality of sewage work is (in Fig. 1, the X-coordinate time is the working time of sewage work) as shown in Figure 1.Municipal sewage plant A 2The step of O process optimization technology is as follows:
Step 1: adopt the method for stochastic simulation to produce 100 groups of different municipal sewage plant A 2the operational conditions (table 2) of O technique, the process operation condition comprises the Aerobic Pond oxygen mass transfer coefficients, solid retention time (SRT), internal reflux ratio, Aerobic Pond, the hydraulic detention time of anaerobic pond and anoxic pond (HRT), wherein, the setting range of Aerobic Pond oxygen mass transfer coefficients is 10-60/h, the setting range of solid retention time (SRT) is 5-50 days, the setting range of internal reflux ratio is 0.5-5, Aerobic Pond, the setting range of the hydraulic detention time of anaerobic pond and anoxic pond (HRT) was respectively 1.5-10.5 hour, 0.5-1.5 hour, 1.5-3 hour.
Step 2: with step 1) No. 3,100 groups of different process operational conditionss difference substitution activated sludge models and the EAWAG biological phosphorus model of random generation, obtain A under each process operation condition by this mathematical model 2The effluent quality of O technique comprises water outlet COD, NH 4 +, TN and TP concentration (as shown in table 3).
In No. 3, this activated sludge model, consider 4 kinds of living microorganisms: common heterotrophic bacterium (X H), ammonia oxidizing bacteria (X AOB), nitrite-oxidizing bacteria (X NOB) and polyP bacteria (X PAO).In addition, this model also comprises common heterotrophism mycetocyte internal memory storing (X STO), polyP bacteria born of the same parents internal memory storing (X PHA) and polyphosphoric acid salt (X PP), and the inert particle organic matter (X that produces due to the microorganism endogenous respiration I).This model comprises 32 biochemical reaction dynamic processes.Due to the sewage treatment plant inflow complicated component, at first consider hydrolytic process (1 process); For heterotrophic bacterium (X H), comprise 11 processes in model; For ammonia oxidizing bacteria (X AOB) and nitrite-oxidizing bacteria (X NOB), comprise altogether 6 processes in model; For polyP bacteria (X PAO), comprise 14 processes in model.In model, the kinetic equation of 4 kinds of living microorganisms and hydrolytic process sees Table 1.
Step 3: adopt SVMs to set up process operation condition (hydraulic detention time (HRT) of Aerobic Pond oxygen mass transfer coefficients, solid retention time (SRT), internal reflux ratio, Aerobic Pond, anaerobic pond and anoxic pond) and effluent quality (water outlet COD, NH 4 +, TN and TP concentration) between nonlinear function, obtain supporting vector machine model.
In SVMs, the nonlinear function of setting up between input variable and output variable is the solution regression problem.Herein, input variable is process operation condition (hydraulic detention time (HRT) of Aerobic Pond oxygen mass transfer coefficients, solid retention time (SRT), internal reflux ratio, Aerobic Pond, anaerobic pond and anoxic pond), amounts to 6 input variables; Output variable is effluent quality (water outlet COD, NH 4 +, TN and TP concentration), amount to 4 output variables.
By introducing slack variable ξ iAnd ξ i *, regression problem can be converted into formula (1):
min w , b , &xi; , &xi; * 1 2 w 2 + C &Sigma; i = 1 l &xi; i + C &Sigma; i = 1 l &xi; i * - - - ( 1 )
Constraint condition is: ( w &CenterDot; &phi; ( x i ) + b ) - z i &le; &epsiv; + &xi; i ( z i - w &CenterDot; &phi; ( x i ) ) - b &le; &epsiv; + &xi; &xi; i , &xi; i * &GreaterEqual; 0 , i = 1 , . . . , l
Wherein, C is penalty coefficient, gets 10, x iBe input, z iBe work output, ε, w and b are coefficient.Lagrange function face is incorporated into above-mentioned protruding double optimization problem, and formula (1) becomes:
min &alpha; , &alpha; * 1 2 &Sigma; i , j = 1 l ( &alpha; i - &alpha; i * ) ( &alpha; i - &alpha; i * ) K ( x i , x j ) + &epsiv; &Sigma; i = 1 l ( &alpha; i + &alpha; i * ) - &Sigma; i = 1 l z i ( &alpha; i - &alpha; i * ) - - - ( 2 )
Constraint condition is: &Sigma; i = 1 l ( &alpha; i - &alpha; i * ) = 0 0 &le; &alpha; i , &alpha; i * &le; Ci = 1 , . . . , l
Wherein, α iWith
Figure BDA0000061697370000045
Be Lagrange's multiplier; K(x i, x j)=φ (x i) φ (x j) be kernel function, select the RBF kernel function herein.
By finding the solution formula (2), can be supported the different process operational conditions set up of vector machine and effluent quality between 4 nonlinear functions, as shown in Figure 2, wherein, Training refers to be used to the data of setting up the supporting vector machine model employing, Testing refers to for the data that adopt of test SVMs, the effluent quality that the effluent quality that Stimulated Values refers to adopt aforesaid activated sludge model to obtain, Predicted Values refer to adopt the supporting vector machine model of foundation to obtain.As shown in Figure 2, supporting vector machine model can be set up the correlationship between process operation condition and effluent quality preferably.
Step 4: adopt and accelerate genetic algorithm optimization above-mentioned steps 3) 4 supporting vector machine models setting up are to obtain municipal sewage plant A 2The optimised process operational conditions of O technique.
Adopt and accelerate in the genetic algorithm optimization step, parameter setting is as follows: population size 400,20 of excellent individual numbers accelerate cycle index 100 times.This optimization step of accelerating genetic algorithm is as follows:
1) coding.Utilize formula to correspond to real number y (j) on [0,1] interval for [a (j), b (j)] interval j optimization variable x (j) initial change is interval.Through coding, the span of all optimization variable all unifies to be [0,1] interval.
x(j)=a(j)+y(j)[b(j)-a(j)] (3)
2) initialize of parent colony.If population size is n, generation n organizes the uniform random number on [0,1] interval, and every group has p, i.e. and { u (j, i) } (j=1~p, i=1~n), each { u (j, i) } the parent individual values y (j, i) as initial population.Y (j, i) substitution formula (3) the variate-value x (j, i) that is optimized, then substitution optimization aim function obtains corresponding target function value f (i).F (i), and i=1~n} sorts from small to large, and corresponding individual y (j, i) is and then sequence also.Claim that rear top ns the individuality of sequence is excellent individual.
3) fitness evaluation of parent colony.This individual fitness value of the less expression of target function value f (i) value is higher, and vice versa.Based on this, after the definition sequence, the fitness function value F (i) of i parent individuality is:
F(i)=1/[f(i)×f(i)+0.001] (4)
0.001 be wherein that experience arranges in denominator, to avoid the situation of f (i) value as 0.
4) select.First progeny population { y 1(j, i) | j=1~p, i=1~n} produces by selection operation.Get the ratio selection mode, the selection Probability p s (i) of the individual y of parent (j, i) is:
P (2)] ..., [p (n-1), p (n)], these sub-ranges and n the individual y of parent (j, i) sets up one-to-one relationship.
5) intersect.Second filial generation { y of colony 2(j, i) | j=1~p, i=1~n} produces by selection operation.The purpose of intersecting is that to seek the parent parents existing but fail the gene information rationally utilized.The GA of standard, its interlace operation is to be divided at random several sections on a pair of parent parents chromosome chain, then mutual exchange forms.But in AGA, in order to keep the diversity of colony, its interlace operation is select a pair of parent individual y random according to the selection probability of formula (5) 2(j, i 1) and y 2(j, i 2) as parents, and carry out following random combine, produce the individual y of a filial generation 2(j, i):
y 2 ( j , i ) = u 1 y ( j , i 1 ) + ( 1 - u 1 ) y ( j , i 2 ) , u 3 < 0.5 y 2 ( j , i ) = u 2 y ( j , i 1 ) + ( 1 - u 2 ) y ( j , i 2 ) , u 3 &GreaterEqual; 0.5 - - - ( 6 )
Wherein: u 1, u 2And u 3It is all randomized number.
6) variation.The 3rd the filial generation { y of colony 3(j, i) | j=1~p, i=1~n} produces by mutation operation.The purpose of variation is in order to introduce new gene, to strengthen the diversity of colony.The GA of standard, its mutation operation are that genic value to any 1 or any 2 on the karyomit(e) of each parent individuality is with a small probability p m(probability namely makes a variation) overturns.And in AGA, the individual y (j, i) of any one parent, if its fitness function value F (i) is less, namely it selects Probability p s(i) less, as this individuality to be made a variation Probability p m(i) larger.The variation probability is calculated by formula (7):
p m(i)=1-p S(i) (7)
Adopt p randomized number with p m(i) probability replaces individual y (j, i), thereby obtains the 3rd filial generation individuality, also namely:
y 3 ( j , i ) = u ( j ) , u m < p m ( i ) y 3 ( j , i ) = y ( j , i ) , u m &GreaterEqual; p m ( i ) - - - ( 8 )
Wherein: u (j) (j=1~p) and u mBe randomized number.
7) evolution iteration.Individual by 3n the filial generation that step 4 to the step 6 of front obtains, sort from big to small according to its fitness function value, get and come top n filial generation individuality as new parent colony.Algorithm changes step 3 over to, carries out next round evolution iteration, again parent colony is estimated, selects, hybridizes and makes a variation, and so repeatedly develops.
8) accelerate circulation.The corresponding variable change of this sub-group of excellent individual that the iteration of accelerating circulation and be to develop with for the first time, for the second time produces is interval, and interval as the initial change that variable is new, then algorithm changes step 1 over to.So accelerate circulation, the constant interval of excellent individual will progressively be adjusted and shrink, with optimum point the distance will be more and more nearer, until the target function value of optimum individual reaches predetermined (circulation) number of times that accelerates less than a certain set(ting)value or algorithm operation, finish the operation of whole algorithm, and the mean value of optimized individual or excellent individual in current colony is decided to be the optimum result of AGA.
The optimised process operational conditions that solves is: the Aerobic Pond oxygen mass transfer coefficients is 32/h, and solid retention time (SRT) is 15d, and internal reflux ratio is 2.6, and the hydraulic detention time of Aerobic Pond, anaerobic pond and anoxic pond is respectively 10.8h, 1.5h and 2.9h.In No. 3, this process operation condition substitution activated sludge model used, obtain A under this optimised process operational conditions 2The effluent quality of O technique is: water outlet COD, NH 4 +, TN and TP concentration is respectively 23.1mg/L, 4.75mg/L, 5.95mg/L and 0.04mg/L.Compare with former process operation condition, utilize the process operation condition of the best that optimization method provided by the invention obtains, reduced internal reflux ratio, shortened simultaneously the hydraulic detention time of anoxic pond, make and save working cost when satisfying effluent quality.
Table 1, reaction kinetics equation
Figure BDA0000061697370000062
Figure BDA0000061697370000081
Parameter declaration:
S S: the readily biodegradable organic concentration
S O: the concentration of oxygen
S NH4: the concentration of ammonia nitrogen
S NO2: the concentration of nitrite
S NO3: the concentration of nitrate
S PO4: phosphatic concentration
X H: the concentration of heterotrophic bacterium
X AOB: the concentration of nitrite bacteria
X NOB: the concentration of nitrobacteria
X PAO: the concentration of polyP bacteria
X STO: the concentration of stock in born of the same parents in heterotrophic bacterium
X PHA: the concentration of intracellular PHA in polyP bacteria
X PP: the concentration of PP in born of the same parents in polyP bacteria
k STO: X STOMemory rate
K H, S: S SThe semi-saturation constant (to X H)
K H, O: S OThe semi-saturation constant (to X H)
η H, NOx: X HThe anoxic correction factor
K NOx: S NOxThe semi-saturation constant (to X H)
K H, NO2: S NO2The semi-saturation constant (to X H)
K H, NO3: S NO3The semi-saturation constant (to X H)
K H, NH4: S NH4The semi-saturation constant (to X H)
K H, PO4: S PO4The semi-saturation constant (to X H)
μ H: X HMaximum specific growth rate
b H, O: X HRate of decay under aerobic condition
b H, NOx: X HRate of decay under anoxia condition
b STO, O: X STORate of decay under aerobic condition
b STO, NOx: X STORate of decay under anoxia condition
μ AOB: X AOBMaximum specific growth rate
μ NOB: X NOBMaximum specific growth rate
K AOB, O: S OThe semi-saturation constant (to X AOB)
K NOB, O: S OThe semi-saturation constant (to X NOB)
K AOB, NH4: S NH4The semi-saturation constant (to X AOB)
K AOB, NO2: S NO2The semi-saturation constant (to X AOB)
K NOB, NO2: S NO2The semi-saturation constant (to X NOB)
K NOB, NO3: S NO3The semi-saturation constant (to X NOB)
K AOB, PO4: S PO4The semi-saturation constant (to X AOB)
K NOB, PO4: S PO4The semi-saturation constant (to X NOB)
b AOB, O: X AOBRate of decay under aerobic condition
b AOB, NO2: X AOBRate of decay under anoxia condition
b NOB, O: X NOBRate of decay under aerobic condition
b NOB, NO3: X NOBRate of decay under anoxia condition
q PHA: X PHAThe memory rate constant
q PP: X PPThe memory rate constant
μ PAO: X PAOMaximum specific growth rate
η PAO, NOx: X PAOThe anoxic correction factor
b PAO: X PAORate of decay
b PP: X PPRate of decay
b PHA: X PHARate of decay
K PAO, S: S SThe semi-saturation constant (to X PAO)
K PAO, O: S OThe semi-saturation constant (to X PAO)
K PAO, PP: X PP/ X PAOThe semi-saturation constant
K Max, PAO: X PP/ X PAOMaximum value
K IPP, PAO: (k Max, PAO-X PP/ X PAO) the semi-saturation constant
K PHA: X PHA/ X PAOThe semi-saturation constant
K PAO, NH4: S NH4The semi-saturation constant (to X PAO)
K PAO, NOx: S NOxThe semi-saturation constant (to X PAO)
K PAO, PO4: S PO4The semi-saturation constant (to X PAO)
Table 2,100 groups of different municipal sewage plant A 2The operational conditions of O technique
Figure BDA0000061697370000101
Figure BDA0000061697370000111
Figure BDA0000061697370000121
A under table 3, each process operation condition 2The effluent quality of O technique
Figure BDA0000061697370000122
Figure BDA0000061697370000131
Figure BDA0000061697370000141

Claims (3)

1. sewage disposal A 2The optimization method of O technique comprises the steps:
1) adopt the method for stochastic simulation to produce n sewage disposal A 2The operational conditions of O technique;
2) adopt A 2The activated sludge model of O technique obtains each sewage disposal A of step 1) gained 2Effluent quality under O process operation condition;
3) with step 1) gained operational conditions and step 2) relation between the gained effluent quality is optimized, and obtains described sewage disposal A 2The optimum operating condition of O technique;
In described step 1), described operational conditions comprises the hydraulic detention time of anaerobic pond, the hydraulic detention time of anoxic pond, hydraulic detention time, internal reflux ratio, Aerobic Pond oxygen mass transfer coefficients and the solid retention time of Aerobic Pond;
The method of described step 3) optimization comprises the steps:
3.1) adopt SVMs to set up described step 1) gained operational conditions and step 2) relation between the gained effluent quality, supported vector machine model;
3.2) adopt and accelerate the described supporting vector machine model of genetic algorithm optimization, obtain described sewage disposal A 2The optimum operating condition of O technique.
2. method according to claim 1, it is characterized in that: described step 2), the detection index of described effluent quality comprises water outlet COD value, NH 4 +Concentration, the concentration of total nitrogen and the concentration of total phosphorus.
3. method according to claim 1 and 2, it is characterized in that: described step 2), described activated sludge model is any one or the revised mathematical model of following any one mathematical model in following mathematical model: No. 1 model of active sludge, activated sludge model No.2, No. 3 models of active sludge and active sludge 2d model.
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