CN103809557A - Neural network based sewage disposal process optimal control method - Google Patents

Abstract

The invention provides a neural network based sewage disposal process optimal control method and aims to solve the problem of excessive energy consumption during a sewage disposal process. The sewage disposal process is a highly non-linear, time-varying and complicated process, and on the premise that effluent qualities meet the standard, reduction of operation energy consumption is much challenging. The method mainly includes two neural networks, wherein one neural network is used for establishing a sewage disposal process prediction model so as to achieve prediction of performance indexes, and the other neural network is used for real-timely optimizing control variable set values according to system states and predicted performance indexes. Finally, optimal control of dissolved oxygen concentration and nitrate nitrogen concentration is achieved, so that requirements of effluent qualities can met, and meanwhile, operation costs of the sewage disposal process can be effectively reduced.

Description

A kind of sewage disposal process optimal control method based on neural network

Technical field

The present invention is directed to the too high problem of sewage disposal process energy consumption, in BSM1, utilize neural network to be optimized control to the dissolved oxygen concentration in sewage disposal process and nitrate.Neural network is one of Main Branches of intelligent control technology, and the sewage disposal process optimal control based on neural network not only belongs to water treatment field, also belongs to intelligent optimization control field.

Background technology

Along with urbanization, industrialized continuous speed-raising, China's water environment has been seriously damaged and has had the trend that continues deterioration.Sewage discharge is not only having a strong impact on resident's daily life, and has destroyed the ecologic equilibrium of the Nature.In order to reduce the discharge capacity of sewage, all parts of the country have been set up sewage treatment plant one after another, but sewage disposal process power consumption is excessive, operating cost occupies high, cause wastewater treatment in China factory " afford to build and can not support ", the optimal control of research sewage disposal process realizes energy-saving and cost-reducing significant, is the inevitable development trend of following sewage treatment industry.Therefore, achievement in research of the present invention has broad application prospects.

In sewage disposal process, main control variable is the dissolved oxygen concentration of the 5th subregion and the nitrate of the second subregion, the height of dissolved oxygen concentration and nitrate not only affects the carrying out of nitrifying process and denitrification process, and the aeration energy consumption in sewage disposal process and pumping energy consumption are played a major role.Therefore, dynamically adjust the setting value of concentration of dissolved oxygen DO and nitrate nitrogen for improving effluent quality, reduce energy consumption and be necessary.

Sewage disposal process be one there is nonlinearity, large time delay, the complication system of the feature such as change when large, Multivariable Coupling, need to complete the effluent quality multiple-objection optimization that simultaneously reduces energy consumption up to standard, some scholars has been studied and has obtained interim achievement to it.Based on the optimal control method of Model Predictive Control MPC, although can reduce to a certain extent energy consumption, but MPC is take system mechanism model as core, calculate optimum controlled quentity controlled variable by definite mathematical measure, and due to the complicacy of sewage disposal process, set up its accurate mathematical model and have certain difficulty, and the accuracy of model is larger on control performance impact, the performance that can not on-line measurement also can reduce control of the crucial water quality parameter of part.Based on the optimal control method of Genetic Algorithms, its calculated amount is large, and global convergence speed is slower, and the precision of its optimum results is subject to the control of code length simultaneously.Based on the optimization control scheme of population PSO algorithm, do not need complicated cross and variation, algorithm is simple, parameter is few, be easy to realization.No matter be genetic algorithm or particle cluster algorithm, in optimizing process, need a large amount of samples as this intelligent search algorithm, can not carry out real-time update to optimizing signal, be relatively applicable to offline optimization.

Neural network has very powerful learning ability and adaptive characteristic, can carry out highly precise approach to nonlinear system.The present invention proposes a kind of sewage disposal process optimal control method based on neural network, not only can meet the requirement of effluent quality, can also reduce the energy consumption of sewage disposal process.

Summary of the invention

Sewage disposal process optimal control method based on neural network, mainly comprises three parts: the controller of performance index forecast model, Neural Network Optimization layer and bottom.The performance index function value in following moment of utility index prediction model prediction, according to the setting value of current ambient condition and the control variable in a upper moment, it is minimum that the performance index function that performance index forecast model is doped by Neural Network Optimization layer reaches, thereby produce new setting value and be sent to bottom controller, complete the optimal control of sewage disposal process.

The present invention has adopted following technical scheme and performing step:

Sewage disposal process optimal control method based on neural network, is characterized in that, comprises the following steps:

1. the foundation of performance index

Sewage disposal process is a nonlinearity system with Multivariable Coupling, serious interference, large time delay characteristic, and neural network can, with its very powerful non-linear approximation capability, be carried out modeling to complicated control system.The optimization problem of sewage disposal process need to consider the targets such as effluent quality, aeration energy consumption and pumping energy consumption, is a multi-objective optimization question.Therefore the performance index function that, definition is optimized is

J(k)=α ₁E(k)+α ₂E _Q(k) (1)

α ₁, α ₂for weighing energy consumption E and effluent quality E _qweight factor, α ₁, α ₂∈ [0,1], and α ₁+ α ₂=1, E is a total energy consumption in optimization cycle, is aeration energy consumption E _awith pumping energy consumption E _psum, E _qrepresent that an optimization cycle discharges pollutants and needs the fine of payment to receiving water body.E, E _a, E _p, E _qexpression formula respectively as shown in (2), (3), (4), (5).

E(k)=E _A(k)+E _P(k) (2)

$E_A\left(k\right)=\frac{S_{o,\mathrm{sat}}}{T\·1.8\·1000}\underset{\mathrm{kT}}{\overset{(k+1)T}{\∫}}\underset{i=1}{\overset{i=5}{\mathrm{\Σ}}}{V}_i\·K_L{a}_i\left(t\right)\mathrm{dt}---\left(3\right)$

$E_P\left(k\right)=\frac{1}{T}\underset{\mathrm{kT}}{\overset{(k+1)T}{\∫}}0.004Q_a\left(t\right)+0.008Q_r\left(t\right)+0.05Q_w\left(t\right)\mathrm{dt}---\left(4\right)$

$E_Q\left(k\right)=\frac{1}{T\·1000}\underset{\mathrm{kT}}{\overset{(k+1)T}{\∫}}(B_{\mathrm{SS}}\·{\mathrm{SS}}_e\left(t\right)+B_{\mathrm{COD}}\·{\mathrm{COD}}_e\left(t\right)+B_{\mathrm{NO}}\·S_{\mathrm{NO},e}\left(t\right)+{B_{\mathrm{Nkj}}\·S}_{\mathrm{Nkj},e}\left(t\right)+B_{\mathrm{BOD}5}\·{\mathrm{BOD}}_e\left(t\right))\mathrm{dt}---\left(5\right)$

K is the moment, and T is optimization cycle, S _{o, sat}for the saturation concentration of dissolved oxygen DO, S _{o, sat}=8mg/L, V _i, K _la _i(i=1,2,3,4,5) are respectively first volume to the 5th reaction tank and oxygen transfer coefficient, wherein, and V ₁=V ₂=1000m ³, V ₃=V ₄=V ₅=1333m ³, K _la ₁=K _la ₂=0, K _la ₃=K _la ₄=240d ^-1, K _la ₅and Q _abeing respectively and controlling in the 5th reaction tank the performance variable of nitrate in dissolved oxygen concentration and second reaction tank, is the output of controller, is two variablees, K _la ₅variation range is 0～240d ^-1, Q _avariation range is 0～5Q ₀, Q ₀for flow of inlet water, Q _rfor sludge reflux amount, Q _wfor sludge discharge, B _sS, B _cOD, B _nO, B _nKj, B _bOD5for water outlet SS _e, COD _e, S _{nO, e}, S _{nKj, e}, BOD _eto effluent quality E _qthe weight factor of impact, B _sS=2, B _cOD=1, B _nO=10, B _nKj=30, B _bOD5=2.

The 2.k moment, the prediction optimization control of dissolved oxygen concentration and nitrate

The forecast model of 2.1 model performance index, the performance index value J'(k in prediction k moment), adopt echo state network ESN to build forecast model, input layer, the output layer of prediction ESN, dynamically lay in pond DR and comprise respectively K, L, a N neuron, W _p ⁱⁿfor prediction ESN input layer is to the connection weight value matrix in internal state deposit pond, W _pfor prediction, ESN dynamically lays in the weight matrix of inside, pond, between its neuron, be sparse connection, definition degree of rarefication SD be the ratio of dynamically laying in interconnective neuron number and total neuron number in pond, the general value 2%～5% of SD, to guarantee that dynamically laying in pond enriches dynamic perfromance, W _p ^backfor prediction ESN output layer is to the connection weight value matrix in internal state deposit pond, W _p ⁱⁿ, W _p, W _p ^backdimension is respectively N × K, N × N, N × L, and initial value is random generation, once generation, just no longer changes, and the power spectral radius of prediction ESN is less than 1, to guarantee the stability of network.The input of prediction ESN is k moment dissolved oxygen concentration r ₁and nitrate r (k) ₂(k) setting value, output is the performance index value of prediction, prediction ESN is input as:

R(k)=[r ₁(k)r ₂(k)] ^T (6)

Dynamically deposit pond is output as:

$x_P\left(k\right)=f(W_P^{\mathrm{in}}R\left(k\right)+W_P{x}_P(k-1)+W_P^{\mathrm{back}}{J}^{\′}(k-1))---\left(7\right)$

J'(k-1) be the output of upper moment prediction ESN, f is intrinsic nerve unit activation function, is taken as Sigmoid function.

ESN is output as performance index function:

$J^{\′}\left(k\right)=f^{\mathrm{out}}\left(W_P^{\mathrm{out}}{x}_P\left(k\right)\right)---\left(8\right)$

In formula, W _p ^outfor prediction ESN internal state deposit pond is to the connection weight value matrix of output, dimension is L × N, is the weights that in network training process, unique needs are adjusted, f ^outfor output layer transport function, be taken as linear function, output J'(k) be the performance index function value in k moment.

2.2 by k moment dissolved oxygen concentration r ₁and nitrate r (k) ₂(k) setting value is as the input of sewage disposal process, the actual performance target function value J (k) obtaining in the k moment.The target function of revising forecast model network weight is:

$g\left(k\right)=\frac{1}{2}{[J^{\′}\left(k\right)-J\left(k\right)]}^2---\left(9\right)$

Weights are adjusted publicity:

$\mathrm{\Δ}{W}_P^{\mathrm{out}}\left(k\right)=-{\mathrm{\η}}_P\left(k\right){\left(\frac{\∂g\left(k\right)}{\∂W_P^{\mathrm{out}}\left(k\right)}\right)}^T---\left(10\right)$

Wherein, η _pfor learning rate.

2.3 optimization neural networks adopt ESN equally, input layer, the output layer of optimization, dynamically lay in pond DR and comprise respectively K ', L ', the individual neuron of N ', W _o ⁱⁿfor optimizing the connection weight value matrix of ESN input layer to internal state deposit pond, W _odynamically laying in the weight matrix of inside, pond for optimizing ESN, is sparse connection between its neuron, and degree of rarefication keeps 2%～5% equally, guarantees that network has abundant dynamic perfromance, W _o ^backfor optimizing the connection weight value matrix of ESN output layer to internal state deposit pond, W _o ⁱⁿ, W _o, W _o ^backdimension is respectively N ' × K ', N ' × N ', N ' × L ', and initial value is random generation, once generation, just no longer changes, and the power spectral radius of optimizing ESN should be less than 1 equally, and to guarantee the stability of network, f is taken as Sigmoid function.

It is input as

h(k+1)=[R ^T(k-1),S(k)] ^T (11)

R ^t(k-1) be the setting value of k-1 moment dissolved oxygen concentration and nitrate, S (k) is the ambient condition in k moment, can be expressed as:

S(k)=[S _O(k),S _NO(k),S _NH(k),S _ND(k),X _ND(k),Q ₀(k)] (12)

S _o(k) be k moment intake dissolved oxygen concentration, S _nO(k) be k moment intake nitrate, S _nH(k) be k moment intake ammonia concentration, S _nD(k) be k moment intake soluble organic nitrogen, X _nD(k) be k moment intake insolubility organic nitrogen, Q ₀(k) be k moment flow of inlet water.

The dynamic deposit pond of optimizing ESN is output as:

$x_o(k+1)=f(W_o^{\mathrm{in}}h(k+1)+W_o{x}_o\left(k\right)+W_o^{\mathrm{back}}R\left(k\right))---\left(13\right)$

ESN is output as setting value:

$R(k+1)=f^{\mathrm{out}}\left(W_o^{\mathrm{out}}{x}_o(k+1)\right)---\left(14\right)$

W _o ^outfor optimizing the connection weight value matrix of ESN internal state deposit pond to output layer, dimension is L ' × N ', needs to adjust f in learning process ^outbe taken as linear function.

2.4 are input to R (k+1) in performance index forecast model, obtain predicting that the dynamic deposit pond that ESN is new is output as:

$x_P(k+1)=f(W_P^{\mathrm{in}}R(k+1)+W_P{x}_P\left(k\right)+W_P^{\mathrm{back}}{J}^{\′}\left(k\right))---\left(15\right)$

Performance index predicted value when k+1 is:

$J^{\′}(k+1)=f^{\mathrm{out}}\left(W_P^{\mathrm{out}}{x}_P(k+1)\right)---\left(16\right)$

Optimize ESN to carry out weights adjustment formula as follows for 2.5 pairs:

$\mathrm{\Δ}{W}_o^{\mathrm{out}}(k+1)=-\mathrm{\η}\left(k\right){\left(\frac{\∂J^{\′}(k+1)}{\∂W_o^{\mathrm{out}}(k+1)}\right)}^T---\left(17\right)$

The setting value of 2.6 new generations after optimizing is input in P I D controller as the value in k+1 moment, obtain actual output of sewage disposal process k+1 moment J (k+1), performance index forecast model weights are readjusted, and the target function of weights adjustment is:

$g(k+1)=\frac{1}{2}{[J^{\′}(k+1)-J(k+1)]}^2---\left(18\right)$

3. step 2.1 is added to n to the k in step 2.6, become k+n, repeating step 2.1 is to step 2.6,

N=1,2,3,4 ..., circulate, until no longer include into water data.

Creativeness of the present invention is mainly reflected in:

The present invention has designed the optimization method on sewage disposal process upper strata, and the method can be according to the setting value of ambient condition real-time optimization control variable.One, utilizes ESN to set up the relation between setting value R (k) and performance index J (k), i.e. performance index intelligent forecast model can obtain the performance index value in following moment by forecast model; Its two, utilize equally ESN to be optimized the performance index of prediction, make it reach minimum, and then obtain performance index value control variable setting value hour.The prediction optimization method that above two parts enough become, belongs to protection scope of the present invention.

The sewage disposal process optimal control method based on ESN that the present invention proposes, has solved the mechanism model out of true problem of setting up in Model Predictive Control, has overcome that intelligent optimization algorithm computation complexity is large, shortcoming that can not real-time update optimal control signal.

Accompanying drawing explanation

Fig. 1. sewage disposal process benchmark model

Fig. 2 .ESN network topology structure figure

Fig. 3. prediction optimization control structure figure

Fig. 4. dissolved oxygen DO effect of optimization

Fig. 5. nitrate nitrogen effect of optimization

Fig. 6. the effect comparison of water outlet BOD

Fig. 7. the effect comparison of water outlet COD

Fig. 8. the effect comparison of water outlet TSS

Fig. 9. the effect comparison of water outlet ammonia nitrogen

Figure 10. the effect comparison of water outlet total nitrogen

Embodiment

Experiment in literary composition is that the data based under the sunny weather of BSM1 model are carried out, and concrete steps are as follows:

1. set up performance index forecast model

In the performance index of setting up, α ₁, α ₂be taken as respectively 0.8,0.2, the input of forecast model is the setting value of dissolved oxygen concentration and nitrate, is output as performance index value, intrinsic nerve unit number is 45, the structure that is forecast model is 2-45-1, and the weights of initialization network are input to the weights W of internal state _p ⁱⁿdimension be 45 × 2, the connection weights W between internal state _pdimension be 45 × 45, internal state to output weights W _p ^outdimension be 1 × 45, output to the weights W of internal state _p ^backdimension be 45 × 1, degree of rarefication SD is 5%, power spectral radius be 0.48.

2. the foundation of Neural Network Optimization layer

The setting value that is input as a moment of optimization neural network and the state of current time, comprising: water inlet dissolved oxygen concentration S _o, water inlet nitrate S _nO, water inlet ammonia concentration S _nH, water inlet soluble organic nitrogen S _nD, water inlet insolubility organic nitrogen X _nDwith flow of inlet water Q ₀, being output as setting value, intrinsic nerve unit number is similarly 45, and the structure of optimization neural network is 8-45-2, and the weights of initialization network are input to the weights W of internal state _o ⁱⁿdimension be 45 × 8, the connection weights W between internal state _odimension be 45 × 45, internal state to output weights W _o ^outdimension be 2 × 45, output to the weights W of internal state _o ^backdimension be 45 × 2, degree of rarefication SD is 5%, power spectral radius be 0.57.

3. bottom controller

Bottom control is PID controller, and its parameter is taken as respectively: KP _o=200, KI _o=150, KD _o=5, KP _nO=80000, KI _nO=7000, KD _nO=400.

4. pass through iteration optimization, can obtain the optimum results of dissolved oxygen concentration and nitrate as shown in the red line in Fig. 3 and Fig. 4, can find out, the setting value of control variable is along with discharge and enter water component (being the state of system) and changes in real time, the PID control effect that blue line is control variable.By PID closed-loop control default in Neural Network Optimization control and BSM1, (setting value of dissolved oxygen concentration and nitrate nitrogen is fixed value, be respectively 2mg/L and 1mg/L) compare, water outlet BOD, water outlet COD, water outlet TSS, the contrast of water outlet ammonia nitrogen and water outlet total nitrogen is respectively as Fig. 5, 6, 7, 8, shown in 9, as seen from the figure, water outlet BOD, water outlet COD and water outlet TSS front and back in two kinds of control situations change little, and along with the real-time optimization to dissolved oxygen concentration and nitrate, the average setting value of dissolved oxygen concentration has reduced compared with fixing setting value 2mg/L, the average setting value of nitrate has raise compared with fixing setting value 1mg/L.Optimal control is compared with PID closed-loop control, although EQ has increased 0.881%, but effluent quality still meets discharging standards, optimal control has increased by 12.77% than the pumping energy consumption PE of PID closed-loop control, aeration energy consumption AE has reduced 4.958%, cause total energy consumption (AE and PE sum) to reduce 3.906%, reached good energy conservation and consumption reduction effects.

Claims (1)

1. the sewage disposal process optimal control method based on neural network, is characterized in that, comprises the following steps:

1) foundation of performance index forecast model

The performance index function that definition is optimized is

J(k)=α ₁E(k)+α ₂E _Q(k) (1)

α ₁, α ₂for weighing energy consumption E and effluent quality E _qweight factor, α ₁, α ₂∈ [0,1], and α ₁+ α ₂=1, E is a total energy consumption in optimization cycle, is aeration energy consumption E _awith pumping energy consumption E _psum, E _qrepresent that an optimization cycle discharges pollutants and needs the fine of payment to receiving water body; E, E _a, E _p, E _qexpression formula respectively as shown in (2), (3), (4), (5);

E(k)=E _A(k)+E _P(k) (2)

$E_A\left(k\right)=\frac{S_{o,\mathrm{sat}}}{T\·1.8\·1000}\underset{\mathrm{kT}}{\overset{(k+1)T}{\∫}}\underset{i=1}{\overset{i=5}{\mathrm{\Σ}}}{V}_i\·K_L{a}_i\left(t\right)\mathrm{dt}---\left(3\right)$

$E_P\left(k\right)=\frac{1}{T}\underset{\mathrm{kT}}{\overset{(k+1)T}{\∫}}0.004Q_a\left(t\right)+0.008Q_r\left(t\right)+0.05Q_w\left(t\right)\mathrm{dt}---\left(4\right)$

$E_Q\left(k\right)=\frac{1}{T\·1000}\underset{\mathrm{kT}}{\overset{(k+1)T}{\∫}}(B_{\mathrm{SS}}\·{\mathrm{SS}}_e\left(t\right)+B_{\mathrm{COD}}\·{\mathrm{COD}}_e\left(t\right)+B_{\mathrm{NO}}\·S_{\mathrm{NO},e}\left(t\right)+{B_{\mathrm{Nkj}}\·S}_{\mathrm{Nkj},e}\left(t\right)+B_{\mathrm{BOD}5}\·{\mathrm{BOD}}_e\left(t\right))\mathrm{dt}---\left(5\right)$

K is the moment, and T is optimization cycle, S _{o, sat}for the saturation concentration of dissolved oxygen DO, S _{o, sat}=8mg/L, V _i, K _la _i(i=1,2,3,4,5) are respectively first volume to the 5th reaction tank and oxygen transfer coefficient, wherein, and V ₁=V ₂=1000m ³, V ₃=V ₄=V ₅=1333m ³, K _la ₁=K _la ₂=0, K _la ₃=K _la ₄=240d ^-1, K _la ₅and Q _abeing respectively and controlling in the 5th reaction tank the performance variable of nitrate in dissolved oxygen concentration and second reaction tank, is the output of controller, is two variablees, K _la ₅variation range is 0～240d ^-1, Q _avariation range is 0～5Q ₀, Q ₀for flow of inlet water, Q _rfor sludge reflux amount, Q _wfor sludge discharge, B _sS, B _cOD, B _nO, B _nKj, B _bOD5for water outlet SS _e, COD _e, S _{nO, e}, S _{nKj, e}, BOD _eto effluent quality E _qthe weight factor of impact, B _sS=2, B _cOD=1, B _nO=10, B _nKj=30, B _bOD5=2;

2) the k moment, the prediction optimization control of dissolved oxygen concentration and nitrate

The forecast model of 2.1 model performance index, the performance index value J'(k in prediction k moment), adopt echo state network ESN to build forecast model, input layer, the output layer of prediction ESN, dynamically lay in pond DR and comprise respectively K, L, a N neuron, W _p ⁱⁿfor prediction ESN input layer is to the connection weight value matrix in internal state deposit pond, W _pfor prediction, ESN dynamically lays in the weight matrix of inside, pond, between its neuron, be sparse connection, definition degree of rarefication SD be the ratio of dynamically laying in interconnective neuron number and total neuron number in pond, SD value 2%～5%, to guarantee that dynamically laying in pond enriches dynamic perfromance, W _p ^backfor prediction ESN output layer is to the connection weight value matrix in internal state deposit pond, W _p ⁱⁿ, W _p, W _p ^backdimension is respectively N × K, N × N, N × L, and initial value is random generation, once generation, just no longer changes, and the power spectral radius of prediction ESN is less than 1, to guarantee the stability of network; The input of prediction ESN is k moment dissolved oxygen concentration r ₁and nitrate r (k) ₂(k) setting value, output is the performance index value of prediction, prediction ESN is input as:

R(k)=[r ₁(k)r ₂(k)] ^T (6)

Dynamically deposit pond is output as:

$x_P\left(k\right)=f(W_P^{\mathrm{in}}R\left(k\right)+W_P{x}_P(k-1)+W_P^{\mathrm{back}}{J}^{\′}(k-1))---\left(7\right)$

J'(k-1) be the output of upper moment prediction ESN, f is intrinsic nerve unit activation function, is taken as Sigmoid function;

ESN is output as performance index function:

$J^{\′}\left(k\right)=f^{\mathrm{out}}\left(W_P^{\mathrm{out}}{x}_P\left(k\right)\right)---\left(8\right)$ In formula, W _p ^outfor prediction ESN internal state deposit pond is to the connection weight value matrix of output, dimension is L × N, is the weights that in network training process, unique needs are adjusted, f ^outfor output layer transport function, be taken as linear function, output J'(k) be the performance index function value in k moment;

2.2 by k moment dissolved oxygen concentration r ₁and nitrate r (k) ₂(k) setting value is as the input of sewage disposal process, the actual performance target function value J (k) obtaining in the k moment; The target function of revising forecast model network weight is:

$g\left(k\right)=\frac{1}{2}{[J^{\′}\left(k\right)-J\left(k\right)]}^2---\left(9\right)$

Weights are adjusted publicity:

$\mathrm{\Δ}{W}_P^{\mathrm{out}}\left(k\right)=-{\mathrm{\η}}_P\left(k\right){\left(\frac{\∂g\left(k\right)}{\∂W_P^{\mathrm{out}}\left(k\right)}\right)}^T---\left(10\right)$

Wherein, η _pfor learning rate;

2.3 optimization neural networks adopt ESN equally, input layer, the output layer of optimization, dynamically lay in pond DR and comprise respectively K ', L ', the individual neuron of N ', W _o ⁱⁿfor optimizing the connection weight value matrix of ESN input layer to internal state deposit pond, W _odynamically laying in the weight matrix of inside, pond for optimizing ESN, is sparse connection between its neuron, and degree of rarefication keeps 2%～5% equally, guarantees that network has abundant dynamic perfromance, W _o ^backfor optimizing the connection weight value matrix of ESN output layer to internal state deposit pond, W _o ⁱⁿ, W _o, W _o ^backdimension is respectively N ' × K ', N ' × N ', N ' × L ', and initial value is random generation, once generation, just no longer changes, and the power spectral radius of optimizing ESN should be less than 1 equally, and to guarantee the stability of network, f is taken as Sigmoid function;

It is input as

h(k+1)=[R ^T(k-1),S(k)] ^T (11)

R ^t(k-1) be the setting value of k-1 moment dissolved oxygen concentration and nitrate, S (k) is the ambient condition in k moment, is expressed as:

S(k)=[S _O(k),S _NO(k),S _NH(k),S _ND(k),X _ND(k),Q ₀(k)] (12)

S _o(k) be k moment intake dissolved oxygen concentration, S _nO(k) be k moment intake nitrate, S _nH(k) be k moment intake ammonia concentration, S _nD(k) be k moment intake soluble organic nitrogen, X _nD(k) be k moment intake insolubility organic nitrogen, Q ₀(k) be k moment flow of inlet water;

The dynamic deposit pond of optimizing ESN is output as:

$x_o(k+1)=f(W_o^{\mathrm{in}}h(k+1)+W_o{x}_o\left(k\right)+W_o^{\mathrm{back}}R\left(k\right))---\left(13\right)$

ESN is output as setting value:

$R(k+1)=f^{\mathrm{out}}\left(W_o^{\mathrm{out}}{x}_o(k+1)\right)---\left(14\right)$

W _o ^outfor optimizing the connection weight value matrix of ESN internal state deposit pond to output layer, dimension is L ' × N ', needs to adjust f in learning process ^outbe taken as linear function;

2.4 are input to R (k+1) in performance index forecast model, obtain predicting that the dynamic deposit pond that ESN is new is output as:

$x_P(k+1)=f(W_P^{\mathrm{in}}R(k+1)+W_P{x}_P\left(k\right)+W_P^{\mathrm{back}}{J}^{\′}\left(k\right))---\left(15\right)$

Performance index predicted value when k+1 is:

$J^{\′}(k+1)=f^{\mathrm{out}}\left(W_P^{\mathrm{out}}{x}_P(k+1)\right)---\left(16\right)$

Optimize ESN to carry out weights adjustment formula as follows for 2.5 pairs:

$\mathrm{\Δ}{W}_o^{\mathrm{out}}(k+1)=-\mathrm{\η}\left(k\right){\left(\frac{\∂J^{\′}(k+1)}{\∂W_o^{\mathrm{out}}(k+1)}\right)}^T---\left(17\right)$

The setting value of 2.6 new generations after optimizing is input in P I D controller as the value in k+1 moment, obtain actual output of sewage disposal process k+1 moment J (k+1), performance index forecast model weights are readjusted, and the target function of weights adjustment is:

$g(k+1)=\frac{1}{2}{[J^{\′}(k+1)-J(k+1)]}^2---\left(18\right)$

3) step 2.1 is added to n to the k in step 2.6, become k+n, repeating step 2.1 is to step 2.6, n=1,2,3,4 ..., circulate, until no longer include into water data.

Images