Sludge bulking suppression method based on soft constraint model predictive control

Abstract

The present application provides a sludge bulking inhibition method based on soft constraint model predictive control, which adjusts the control strategy according to the cause variable of sludge bulking, so as to track the dissolved oxygen concentration and nitrate nitrogen concentration to the expected value and realize the inhibition of sludge bulking. The present application designs a sludge bulking intelligent diagnosis algorithm, calculates the relative reconstruction contribution, diagnoses the cause variable of sludge bulking, designs a soft constraint model predictive control strategy, guides the priority order of the controlled target according to the cause variable, softens the strict output constraint by using the slack variable, and obtains the control law by sequentially optimizing the controlled target. The experimental results show that the method can effectively inhibit the sludge bulking in the urban sewage treatment process.

Description

Technical Field

[0001] This invention designs a sludge bulking suppression method based on soft-constraint model predictive control, which effectively suppresses sludge bulking in constrained urban wastewater treatment processes. Sludge bulking suppression is an important link in ensuring the stable operation of urban wastewater treatment processes and is an important branch of advanced manufacturing technology, belonging to both the field of intelligent control and the field of water treatment. Background Technology

[0002] Urban wastewater treatment is a crucial measure for improving the water environment and maintaining public health. The activated sludge process is an economical, efficient, and environmentally friendly wastewater treatment technology widely used in major wastewater treatment plants. However, significant fluctuations in influent flow rate or organic load can adversely affect the growth and metabolic activities of microorganisms in the activated sludge, leading to deterioration of the sludge's settling properties and causing sludge bulking. Sludge bulking is a typical process failure, resulting in reduced wastewater treatment efficiency, deteriorated effluent quality, and increased operating costs for the entire system. Therefore, developing effective control strategies and timely diagnosis and control of sludge bulking are of great significance for ensuring the continuous and stable operation of urban wastewater treatment processes.

[0003] Urban wastewater treatment involves complex biological, chemical, and physical processes, is constrained, and involves multivariate coupling, making it a typical nonlinear control system. Due to the physical characteristics of the equipment and the requirements of system operation, input and output constraints must be considered in wastewater treatment to ensure the feasibility of control strategies. Model predictive control (MRC) methods express the control problem as an optimization problem by defining a constrained objective function and performing rolling optimization to calculate the control law, thus achieving constraint satisfaction and performance optimization. However, most MRC methods do not consider the infeasibility of controller solutions due to extreme conditions and the use of strict constraints. For example, after sludge bulking occurs in the wastewater treatment process, a feasible solution to the optimization problem may not be found under strict system output and control input constraints.

[0004] In the control of sludge bulking in urban wastewater treatment processes, dissolved oxygen and nitrate nitrogen concentrations are adjusted to suppress sludge bulking. However, the control of both dissolved oxygen and nitrate nitrogen concentrations is related to aeration intensity and internal recirculation flow rate, and these two factors have different requirements. When the dissolved oxygen concentration reaches the desired value, the nitrate nitrogen concentration may not reach the desired value, thus requiring a trade-off between these two conflicting controlled objectives. Considering strict system constraints and multiple conflicting controlled objectives, designing an effective intelligent control method to regulate dissolved oxygen and nitrate nitrogen concentrations to suppress sludge bulking and ensure the continuous and stable operation of the urban wastewater treatment process is an urgent problem to be solved.

[0005] This invention designs a sludge bulking suppression method based on constraint model predictive control. The control strategy is adaptively adjusted according to the causal variables causing sludge bulking, ensuring that dissolved oxygen and nitrate nitrogen concentrations track to desired values ​​to suppress sludge bulking. An intelligent sludge bulking diagnostic algorithm is designed to calculate the relative reconstruction contribution to diagnose the causal variables causing sludge bulking. A soft-constraint model predictive control strategy is designed, prioritizing the controlled objectives based on the causal variables, softening strict output constraints using relaxation variables, and sequentially optimizing the controlled objectives to obtain the control law. Summary of the Invention

[0006] This invention proposes a sludge bulking suppression method based on soft-constraint model predictive control. It designs an intelligent diagnostic method based on relative reconstruction contribution to diagnose the causal variables that cause sludge bulking, constructs a soft-constraint model predictive control strategy, guides the priority ranking of multiple controlled targets according to the cause of the fault, designs a soft constraint mechanism to relax strict output constraints, and optimizes the controlled targets in sequence to calculate the control law. This solves the problem of sludge bulking being difficult to effectively control in urban sewage treatment under strict system constraints and multiple conflicting controlled targets.

[0007] The present invention adopts the following technical solution and implementation steps:

[0008] 1. A sludge bulking suppression method based on soft-constraint model predictive control, characterized by: designing an intelligent sludge bulking diagnostic algorithm, constructing a soft-constraint model predictive controller, and realizing sludge bulking suppression in urban wastewater treatment processes; comprising the following steps:

[0009] (1) Design of intelligent diagnostic algorithm for sludge bulking

[0010] N sets of samples were collected under the sludge expansion condition in the urban sewage treatment process, and X(k) = [x1] T (k),...,x n T (k),...,x N T (k)] T ∈R N×5 T represents the transpose of the vector, n = 1, ..., N represents the sample dimension, x n (k)=[x n1 (k),...,x nm (k),...,x n5 [(k)] represents the nth sample vector at time k, m = 1,...,5 represents the feature dimension, x nm (k) represents the m-th feature variable in the n-th sample vector at time k;

[0011] The five characteristic variables of the intelligent diagnostic algorithm for sludge bulking are: dissolved oxygen concentration, nitrate nitrogen concentration, total nitrogen concentration, suspension concentration, and sludge load. The sample vector of dissolved oxygen concentration at time k is represented by x. N_1 (k)=[x 11 (k),...,x N1 (k)] T The sample vector of nitrate nitrogen concentration at time k is represented as x. N_2 (k)=[x 12 (k),...,x N2 (k)] T The sample vector of total nitrogen concentration at time k is represented as x. N_3 (k)=[x 13 (k),...,x N3 (k)] T The sample vector of suspension concentration at time k is represented as x. N_4 (k)=[x 14 (k),...,x N4 (k)] T The sample vector of sludge load at time k is represented as x. N_5 (k)=[x 15 (k),...,x N5 (k)] T ;

[0012] The covariance matrix of sample X(k) is calculated as follows:

[0013]

[0014] Principal component analysis is used to decompose the covariance matrix into the following eigenvalues:

[0015]

[0016] Where P(k) and Let Λ(k) and Λ(k) represent the principal component loading matrix and the residual loading matrix, respectively. These represent diagonal matrices containing principal eigenvalues ​​and residual eigenvalues, respectively.

[0017] Assume sample vector x n In (k), the r-th feature variable is the fault variable, and the reconstructed sample vector is:

[0018] z r (k)=x n (k)-ξ r d nr (k) (3)

[0019] Where, d nr(k) represents the fault amplitude of the r-th feature variable in the n-th sample vector. Indicates the direction of the fault, r = 1,...,5;

[0020] The fault detection indicators are designed as follows:

[0021]

[0022] in,

[0023] Feature variable x nr (k) The contribution to the reconstruction of fault detection metrics is defined as:

[0024]

[0025] Calculate the fault detection index Index(z) r (k) Regarding the fault amplitude d nr Taking the first derivative of (k) and setting it equal to 0, we obtain... Therefore, the reconstruction contribution (5) is calculated as follows:

[0026]

[0027] The feature variables are sorted according to their contribution to the reconstruction, and the feature variable with the largest contribution value is diagnosed as the cause of sludge bulking.

[0028] (2) Constructing a soft-constraint model predictive controller

[0029] The soft-constraint model predictive controller takes the predicted values ​​of dissolved oxygen concentration and nitrate nitrogen concentration as inputs and outputs the oxygen transfer coefficient and internal recirculation flow rate. The specific design process is as follows:

[0030] ① Design the objective functions for dissolved oxygen concentration and nitrate nitrogen concentration, respectively:

[0031]

[0032] in, This represents the tracking error of the dissolved oxygen concentration at time k+i calculated at time k, where i = 0,...,3 represents the number of prediction steps, and r DO (k+i) represents the set value of dissolved oxygen concentration at time k+i. This represents the predicted dissolved oxygen concentration at time k+i from the value at time k. y DO (k) represents the measured value of dissolved oxygen concentration at time k, Δu(k)=[Δu DO (k),Δu NO [(k)] represents the control input increment at time k, Δu DO(k) represents the increase in the oxygen transfer coefficient at time k, Δu NO (k) represents the increase in return flow rate at time k. r represents the tracking error of the nitrate nitrogen concentration at time k+i calculated at time k. NO (k+i) represents the set value of nitrate nitrogen concentration at time k+i. This represents the predicted value of nitrate nitrogen concentration at time k+i from the value at time k. y NO (k) represents the measured value of nitrate nitrogen concentration at time k;

[0033] In the control of sludge bulking in urban wastewater treatment, the commonly specified operating ranges are: oxygen transfer coefficient 40-240 mg / L / day; internal recirculation flow rate 0-92230 m³ / day; dissolved oxygen concentration 1.5-2.4 mg / L / day; and nitrate nitrogen concentration 0.5-1.5 mg / L / day. Specific constraints are set as follows:

[0034] 40≤u DO (k)≤240,0≤u NO (k)≤92230 (9)

[0035]

[0036] ② Construct a fuzzy neural network prediction model, specifically as follows:

[0037] The input to the fuzzy neural network prediction model is [α1(k), α2(k), α3(k), α4(k)], and the output expression of the fuzzy neural network prediction model is:

[0038]

[0039] in, Let k represent the prediction output vector of the fuzzy neural network prediction model at time k. This represents the first output of the fuzzy neural network prediction model at time k. w represents the second output of the fuzzy neural network prediction model at time k. l (k) represents the connection weights between the l-th regular layer neuron and the output layer neuron in the fuzzy neural network prediction model at time k, w l (k) is randomly assigned a value in the range [0,1], α j (k) represents the j-th input to the fuzzy neural network prediction model at time k, c jl (k) represents the center value of the j-th input layer neuron corresponding to the l-th radial base neuron in the fuzzy neural network prediction model at time k, c jl (k) is randomly assigned a value in the range [0,1], σ jl(k) represents the width value of the j-th input layer neuron corresponding to the l-th radial base layer neuron in the fuzzy neural network prediction model at time k, σ jl (k) is randomly assigned a value in the range [0,1], where j = 1,2,...,4 represents the number of neurons in the input layer of the fuzzy neural network prediction model, and l = 1,2,...,8 represents the number of neurons in the radial base layer and the regular layer of the fuzzy neural network prediction model. The prediction error is calculated as follows:

[0040]

[0041] Where p(k) = [p1(k), p2(k)] represents the system output vector at time k, p1(k) represents the first output of the system, and p2(k) represents the second output of the system;

[0042] Update the weights, center, and width of the fuzzy neural network prediction model at time k+1 based on the prediction error at time k:

[0043] φ(k+1)=φ(k)-[Ω T (k)Ω(k)+0.2I] -1 Ω T (k)e p (k) (13)

[0044] Where φ(k)=[w1(k),...,w8(k),c1(k),...,c8(k),σ1(k),...,σ8(k)] T c represents the parameter vector of the fuzzy neural network prediction model at time k. l (k)=[c 1l (k),c 2l (k),c 3l (k),c 4l (k)] T σ represents the center vector of the l-th radial base layer neuron in the fuzzy neural network prediction model at time k. l (k)=[σ 1l (k),σ 2l (k),σ 3l (k),σ 4l (k)] T This represents the width vector of the l-th radial base layer neuron in the fuzzy neural network prediction model at time k. Let represent the Jacobian matrix of the fuzzy neural network prediction model at time k, and let I represent the 72-row, 72-column identity matrix. φ(k+1) = [w1(k+1),...,w8(k+1),c1(k+1),...,c8(k+1),σ1(k+1),...,σ8(k+1)] Tc represents the parameter vector of the fuzzy neural network prediction model at time k+1. l (k+1)=[c 1l (k+1),c 2l (k+1),c 3l (k+1),c 4l (k+1)] T σ represents the center vector of the l-th radial base layer neuron in the fuzzy neural network prediction model at time k+1. l (k+1)=[σ 1l (k+1),σ 2l (k+1),σ 3l (k+1),σ 4l (k+1)] T This represents the width vector of the l-th radial base layer neuron in the fuzzy neural network prediction model at time k+1;

[0045] ③ Obtain the 3-step prediction value at time k using a fuzzy neural network prediction model. The specific process is as follows:

[0046] Let the input of the prediction model be [α1(k),α2(k),α3(k),α4(k)]=[y DO (k),y NO (k),u DO (k-1),u NO [(k-1)], where u DO (k-1) is the oxygen transfer coefficient at time k-1, u NO (k-1) represents the return flow rate at time k-1, and the predicted output is obtained.

[0047] Let the input of the prediction model be Get the prediction output

[0048] Let the input of the prediction model be Get the prediction output

[0049] ④ Prioritize control objectives based on the causal variables of sludge bulking, specifically as follows:

[0050] When the causal variable is dissolved oxygen concentration, the first priority control objective is J. DO When the causal variable is nitrate nitrogen concentration, the first priority control objective is J. NO When the causal variable is total nitrogen concentration, the first priority control target is J. NO When the causal variable is the suspension concentration, the first priority control objective is J. DO When the causal variable is sludge load, the first priority control objective is J. DO .

[0051] ⑤ Design an algorithm for solving the predictive control law of a soft-constraint model, specifically as follows:

[0052] Based on the diagnostic results, J was determined. DO When the first priority control objective is selected, the control law is calculated as follows:

[0053] u(k)=u(k-1)+Δu(k) (14)

[0054]

[0055] The constraints are:

[0056]

[0057] 40≤u DO (k)≤240,0≤u NO (k)≤92230 (17)

[0058]

[0059] Where arg min represents the variable that calculates the minimum value of the function, ||| represents the norm of the vector, and ε NO (i|k) represents the relaxation variable of the nitrate nitrogen concentration at time k+i calculated at time k. Let represent the optimal value of the objective function for dissolved oxygen concentration at time k, calculated as follows:

[0060]

[0061] The constraints are:

[0062] 40≤u DO (k)≤240,0≤u NO (k)≤92230 (20)

[0063]

[0064] Where min represents the minimum value of the function, ε DO (i|k) represents the relaxation variable of dissolved oxygen concentration at time k+i calculated at time k;

[0065] Based on the diagnostic results, J was determined. NO When the first priority control objective is selected, the control law is calculated as follows:

[0066] u(k)=u(k-1)+Δu(k) (22)

[0067]

[0068] The constraints are:

[0069]

[0070] 40≤u DO (k)≤240,0≤u NO (k)≤92230 (25)

[0071]

[0072] in, Let represent the optimal value of the objective function for nitrate nitrogen concentration at time k, calculated as follows:

[0073]

[0074] The constraints are:

[0075] 40≤u DO (k)≤240,0≤u NO (k)≤92230 (28)

[0076]

[0077] (3) Sludge bulking inhibition in urban wastewater treatment process

[0078] The soft-constraint model predictive control law u(k) includes the oxygen transfer coefficient and internal recirculation flow rate at time k. The programmable logic controller controls the frequency of the frequency converter based on the calculated oxygen transfer coefficient. The frequency converter controls the aeration rate by adjusting the speed of the blower. The electric regulating valve controls the internal recirculation flow rate by adjusting the valve opening. Finally, the sludge bulking in the urban wastewater treatment process is suppressed by controlling the dissolved oxygen concentration and nitrate nitrogen concentration.

[0079] The inventiveness of this invention is mainly reflected in:

[0080] (1) The present invention designs an intelligent diagnostic algorithm to identify the causal variables that cause sludge bulking, and guides the priority ranking of control targets based on the causal variables, thus solving the problem of conflict of control targets in the inhibition of sludge bulking in urban sewage treatment process;

[0081] (2) The present invention designs a soft-constraint model predictive controller, which uses slack variables to relax strict output constraints, improves the flexibility of controller solution, effectively suppresses sludge bulking, and ensures the continuous and stable operation of the sewage treatment process.

[0082] Special note: This invention is also applicable to self-healing and fault-tolerant control of other abnormal operating conditions in wastewater treatment processes. Without departing from the core of this invention, any simple modifications, alterations, or equivalent substitutions are within the scope of protection of the claims of this invention. Attached Figure Description

[0083] Figure 1 This is a diagram showing the sludge bulking diagnosis results of the present invention.

[0084] Figure 2 This is a graph showing the results of the dissolved oxygen concentration tracking and control according to the present invention.

[0085] Figure 3 This is a graph showing the tracking and control results of nitrate nitrogen concentration according to the present invention.

[0086] Figure 4 This is a diagram showing the results of the operation variables in this invention.

[0087] Figure 5 This is the sludge volume index diagram of the present invention. Detailed Implementation

[0088] A sludge bulking suppression method based on soft-constraint model predictive control is characterized by: designing an intelligent sludge bulking diagnostic algorithm and constructing a soft-constraint model predictive controller to suppress sludge bulking in urban wastewater treatment processes; including the following steps:

[0089] (1) Design of intelligent diagnostic algorithm for sludge bulking

[0090] N sets of samples were collected under the sludge expansion condition in the urban sewage treatment process, and X(k) = [x1] T (k),...,x n T (k),...,x N T (k)] T ∈R N×5 T represents the transpose of the vector, n = 1, ..., N represents the sample dimension, x n (k)=[x n1 (k),...,x nm (k),...,x n5 [(k)] represents the nth sample vector at time k, m = 1,...,5 represents the feature dimension, x nm (k) represents the m-th feature variable in the n-th sample vector at time k;

[0091] The five characteristic variables of the intelligent diagnostic algorithm for sludge bulking are: dissolved oxygen concentration, nitrate nitrogen concentration, total nitrogen concentration, suspension concentration, and sludge load. The sample vector of dissolved oxygen concentration at time k is represented by x. N_1 (k)=[x 11 (k),...,x N1 (k)] T The sample vector of nitrate nitrogen concentration at time k is represented as x. N_2 (k)=[x 12 (k),...,x N2(k)] T The sample vector of total nitrogen concentration at time k is represented as x. N_3 (k)=[x 13 (k),...,x N3 (k)] T The sample vector of suspension concentration at time k is represented as x. N_4 (k)=[x 14 (k),...,x N4 (k)] T The sample vector of sludge load at time k is represented as x. N_5 (k)=[x 15 (k),...,x N5 (k)] T ;

[0092] The covariance matrix of sample X(k) is calculated as follows:

[0093]

[0094] Principal component analysis is used to decompose the covariance matrix into the following eigenvalues:

[0095]

[0096] Where P(k) and Let Λ(k) and Λ(k) represent the principal component loading matrix and the residual loading matrix, respectively. These represent diagonal matrices containing principal eigenvalues ​​and residual eigenvalues, respectively.

[0097] Assume sample vector x n In (k), the r-th feature variable is the fault variable, and the reconstructed sample vector is:

[0098] z r (k)=x n (k)-ξ r d nr (k) (32)

[0099] Where, d nr (k) represents the fault amplitude of the r-th feature variable in the n-th sample vector. Indicates the direction of the fault, r = 1,...,5;

[0100] The fault detection indicators are designed as follows:

[0101]

[0102] in,

[0103] Feature variable x nr(k) The contribution to the reconstruction of fault detection metrics is defined as:

[0104]

[0105] Calculate the fault detection index Index(z) r (k) Regarding the fault amplitude d nr Taking the first derivative of (k) and setting it equal to 0, we obtain... Therefore, the reconstruction contribution (5) is calculated as follows:

[0106]

[0107] The feature variables are sorted according to their contribution to the reconstruction, and the feature variable with the largest contribution value is diagnosed as the cause of sludge bulking.

[0108] (2) Constructing a soft-constraint model predictive controller

[0109] The soft-constraint model predictive controller takes the predicted values ​​of dissolved oxygen concentration and nitrate nitrogen concentration as inputs and outputs the oxygen transfer coefficient and internal recirculation flow rate. The specific design process is as follows:

[0110] ① Design the objective functions for dissolved oxygen concentration and nitrate nitrogen concentration, respectively:

[0111]

[0112] in, This represents the tracking error of the dissolved oxygen concentration at time k+i calculated at time k, where i = 0,...,3 represents the number of prediction steps, and r DO (k+i) represents the set value of dissolved oxygen concentration at time k+i. This represents the predicted dissolved oxygen concentration at time k+i from the value at time k. y DO (k) represents the measured value of dissolved oxygen concentration at time k, Δu(k)=[Δu DO (k),Δu NO [(k)] represents the control input increment at time k, Δu DO (k) represents the increase in the oxygen transfer coefficient at time k, Δu NO (k) represents the increase in return flow rate at time k. r represents the tracking error of the nitrate nitrogen concentration at time k+i calculated at time k. NO (k+i) represents the set value of nitrate nitrogen concentration at time k+i. This represents the predicted value of nitrate nitrogen concentration at time k+i from the value at time k. y NO (k) represents the measured value of nitrate nitrogen concentration at time k;

[0113] In the control of sludge bulking in urban wastewater treatment, the commonly specified operating ranges are: oxygen transfer coefficient 40-240 mg / L / day; internal recirculation flow rate 0-92230 m³ / day; dissolved oxygen concentration 1.5-2.4 mg / L / day; and nitrate nitrogen concentration 0.5-1.5 mg / L / day. Specific constraints are set as follows:

[0114] 40≤u DO (k)≤240,0≤u NO (k)≤92230 (38)

[0115]

[0116] ② Construct a fuzzy neural network prediction model, specifically as follows:

[0117] The input to the fuzzy neural network prediction model is [α1(k), α2(k), α3(k), α4(k)], and the output expression of the fuzzy neural network prediction model is:

[0118]

[0119] in, Let k represent the prediction output vector of the fuzzy neural network prediction model at time k. This represents the first output of the fuzzy neural network prediction model at time k. w represents the second output of the fuzzy neural network prediction model at time k. l (k) represents the connection weights between the l-th regular layer neuron and the output layer neuron in the fuzzy neural network prediction model at time k, w l (k) is randomly assigned a value in the range [0,1], α j (k) represents the j-th input to the fuzzy neural network prediction model at time k, c jl (k) represents the center value of the j-th input layer neuron corresponding to the l-th radial base neuron in the fuzzy neural network prediction model at time k, c jl (k) is randomly assigned a value in the range [0,1], σ jl (k) represents the width value of the j-th input layer neuron corresponding to the l-th radial base layer neuron in the fuzzy neural network prediction model at time k, σ jl (k) is randomly assigned a value in the range [0,1], where j = 1,2,...,4 represents the number of neurons in the input layer of the fuzzy neural network prediction model, and l = 1,2,...,8 represents the number of neurons in the radial base layer and the regular layer of the fuzzy neural network prediction model. The prediction error is calculated as follows:

[0120]

[0121] Where p(k) = [p1(k), p2(k)] represents the system output vector at time k, p1(k) represents the first output of the system, and p2(k) represents the second output of the system;

[0122] Update the weights, center, and width of the fuzzy neural network prediction model at time k+1 based on the prediction error at time k:

[0123] φ(k+1)=φ(k)-[Ω T (k)Ω(k)+0.2I] -1 Ω T (k)e p (k) (42)

[0124] Where φ(k)=[w1(k),...,w8(k),c1(k),...,c8(k),σ1(k),...,σ8(k)] T c represents the parameter vector of the fuzzy neural network prediction model at time k. l (k)=[c 1l (k),c 2l (k),c 3l (k),c 4l (k)] T σ represents the center vector of the l-th radial base layer neuron in the fuzzy neural network prediction model at time k. l (k)=[σ 1l (k),σ 2l (k),σ 3l (k),σ 4l (k)] T This represents the width vector of the l-th radial base layer neuron in the fuzzy neural network prediction model at time k. Let represent the Jacobian matrix of the fuzzy neural network prediction model at time k, and let I represent the 72-row, 72-column identity matrix. φ(k+1) = [w1(k+1),...,w8(k+1),c1(k+1),...,c8(k+1),σ1(k+1),...,σ8(k+1)] T c represents the parameter vector of the fuzzy neural network prediction model at time k+1. l (k+1)=[c 1l (k+1),c 2l (k+1),c 3l (k+1),c 4l (k+1)] T σ represents the center vector of the l-th radial base layer neuron in the fuzzy neural network prediction model at time k+1. l (k+1)=[σ 1l (k+1),σ 2l(k+1),σ 3l (k+1),σ 4l (k+1)] T This represents the width vector of the l-th radial base layer neuron in the fuzzy neural network prediction model at time k+1;

[0125] ③ Obtain the 3-step prediction value at time k using a fuzzy neural network prediction model. The specific process is as follows:

[0126] Let the input of the prediction model be [α1(k),α2(k),α3(k),α4(k)]=[y DO (k),y NO (k),u DO (k-1),u NO [(k-1)], where u DO (k-1) is the oxygen transfer coefficient at time k-1, u NO (k-1) represents the return flow rate at time k-1, and the predicted output is obtained.

[0127] Let the input of the prediction model be Get the prediction output

[0128] Let the input of the prediction model be Get the prediction output

[0129] ④ Prioritize control objectives based on the causal variables of sludge bulking, specifically as follows:

[0130] When the causal variable is dissolved oxygen concentration, the first priority control objective is J. DO When the causal variable is nitrate nitrogen concentration, the first priority control objective is J. NO When the causal variable is total nitrogen concentration, the first priority control target is J. NO When the causal variable is the suspension concentration, the first priority control objective is J. DO When the causal variable is sludge load, the first priority control objective is J. DO .

[0131] ⑤ Design an algorithm for solving the predictive control law of a soft-constraint model, specifically as follows:

[0132] Based on the diagnostic results, J was determined. DO When the first priority control objective is selected, the control law is calculated as follows:

[0133] u(k)=u(k-1)+Δu(k) (43)

[0134]

[0135] The constraints are:

[0136]

[0137] 40≤u DO (k)≤240,0≤u NO (k)≤92230 (46)

[0138]

[0139] Where arg min represents the variable that calculates the minimum value of the function, ||| represents the norm of the vector, and ε NO (i|k) represents the relaxation variable of the nitrate nitrogen concentration at time k+i calculated at time k. Let represent the optimal value of the objective function for dissolved oxygen concentration at time k, calculated as follows:

[0140]

[0141] The constraints are:

[0142] 40≤u DO (k)≤240,0≤u NO (k)≤92230 (49)

[0143]

[0144] Where min represents the minimum value of the function, ε DO (i|k) represents the relaxation variable of dissolved oxygen concentration at time k+i calculated at time k;

[0145] Based on the diagnostic results, J was determined. NO When the first priority control objective is selected, the control law is calculated as follows:

[0146] u(k)=u(k-1)+Δu(k) (51)

[0147]

[0148] The constraints are:

[0149]

[0150] 40≤u DO (k)≤240,0≤u NO (k)≤92230 (54)

[0151]

[0152] in, Let represent the optimal value of the objective function for nitrate nitrogen concentration at time k, calculated as follows:

[0153]

[0154] The constraints are:

[0155] 40≤u DO (k)≤240,0≤u NO (k)≤92230 (57)

[0156]

[0157] (3) Sludge bulking inhibition in urban wastewater treatment process

[0158] The soft-constraint model predictive control law u(k) includes the oxygen transfer coefficient and internal recirculation flow rate at time k. The programmable logic controller controls the frequency of the frequency converter based on the calculated oxygen transfer coefficient. The frequency converter controls the aeration rate by adjusting the speed of the blower. The electric regulating valve controls the internal recirculation flow rate by adjusting the valve opening. Finally, the sludge bulking in the urban wastewater treatment process is suppressed by controlling the dissolved oxygen concentration and nitrate nitrogen concentration. Figure 1 Displays the sludge bulking diagnosis results. X-axis: time, in days; Y-axis: reconstruction contribution value of each variable. Figure 2 The display shows the tracking results of dissolved oxygen concentration. X-axis: time, in days; Y-axis: dissolved oxygen concentration value, in milligrams per liter. Figure 3 The display shows the tracking results of nitrate nitrogen concentration. X-axis: time, in days; Y-axis: nitrate nitrogen concentration value, in milligrams per liter. Figure 4 Displays oxygen transfer coefficient and internal recirculation flow rate; X-axis: time, unit: days; Y-axis: oxygen transfer coefficient and internal recirculation flow rate; sludge volume index as shown... Figure 5 X-axis: time, in days; Y-axis: sludge volume index. The results demonstrate the effectiveness of this method in inhibiting sludge bulking.

Claims

1. A method for inhibiting sludge bulking based on soft-constraint model predictive control, characterized in that: Design an intelligent diagnostic algorithm for sludge bulking and construct a soft-constraint model predictive controller to suppress sludge bulking in urban wastewater treatment processes; including the following steps: (1) Design of intelligent diagnostic algorithm for sludge bulking N sets of samples were collected under the sludge expansion condition in the urban sewage treatment process, and X(k) = [x1] T (k), ..., x n T (k), ...,x N T (k)] T ∈R N×5 T represents the transpose of the vector, n=1, ..., N represents the sample dimension, x n (k)=[x n1 (k), ..., x nm (k), ..., x n5 [(k)] represents the nth sample vector at time k, m=1, ..., 5 represents the feature dimension, x nm (k) represents the m-th feature variable in the n-th sample vector at time k; The five characteristic variables of the intelligent diagnostic algorithm for sludge bulking are: dissolved oxygen concentration, nitrate nitrogen concentration, total nitrogen concentration, suspension concentration, and sludge load. The sample vector of dissolved oxygen concentration at time k is represented by x. N_1 (k)=[x 11 (k), ..., x N1 (k)] T The sample vector of nitrate nitrogen concentration at time k is represented as x. N_2 (k)=[x 12 (k), ..., x N2 (k)] T The sample vector of total nitrogen concentration at time k is represented as x. N_3 (k)=[x 13 (k), ..., x N3 (k)] T The sample vector of suspension concentration at time k is represented as x. N_4 (k)=[x 14 (k), ..., x N4 (k)] T The sample vector of sludge load at time k is represented as x. N_5 (k)=[x 15 (k), ...,x N5 (k)] T ; The covariance matrix of sample X(k) is calculated as follows: (1) ； Principal component analysis is used to decompose the covariance matrix into the following eigenvalues: ； Where P(k) and P̃(k) represent the principal component loading matrix and the residual loading matrix, respectively, and Λ(k) and Λ̃(k) represent the diagonal matrices containing the principal eigenvalues ​​and the residual eigenvalues, respectively; Assume sample vector x n In (k), the r-th feature variable is the fault variable, and the reconstructed sample vector is: (3) ； Where, d nr (k) represents the fault amplitude of the r-th feature variable in the n-th sample vector. Indicates the direction of the fault, r=1, ..., 5; The fault detection indicators are designed as follows: (4) ； Among them, W(k) = P̃(k)P̃ T (k); Feature variable x nr (k) The contribution to the reconstruction of fault detection metrics is defined as: (5) ； Calculate the fault detection index Index(z) r (k) Regarding the fault amplitude d nr Taking the first derivative of (k) and setting it equal to 0, we obtain d. nr (k)=(ξ T r W(k)ξ r ) -1 ξ T r W(k)x n Therefore, the reconstruction contribution (5) is calculated as follows: (6) ； The feature variables are sorted according to their contribution to the reconstruction, and the feature variable with the largest contribution value is diagnosed as the cause of sludge bulking. (2) Constructing a soft-constraint model predictive controller The soft-constraint model predictive controller takes the predicted values ​​of dissolved oxygen concentration and nitrate nitrogen concentration as inputs and outputs the oxygen transfer coefficient and internal recirculation flow rate. The specific design process is as follows: ① Design the objective functions for dissolved oxygen concentration and nitrate nitrogen concentration, respectively: (7) ； (8) ； Among them, e DO (i|k)=r DO (k+i)−ŷ DO (i|k) represents the tracking error of dissolved oxygen concentration at time k+i calculated at time k, where i=0, ..., 3 represents the number of prediction steps, r DO (k+i) represents the set value of dissolved oxygen concentration at time k+i. DO (i|k) represents the predicted dissolved oxygen concentration at time k+i at time k. DO (0|k)=y DO (k), y DO (k) represents the measured value of dissolved oxygen concentration at time k, ∆u(k)=[∆u DO (k), ∆u NO [(k)] represents the control input increment at time k, ∆u DO (k) represents the increment of the oxygen transfer coefficient at time k, ∆u NO (k) represents the increment of the return flow rate at time k, e NO (i|k)=r NO (k+i)−ŷ NO (i|k) represents the tracking error of the nitrate nitrogen concentration at time k+i calculated at time k, r NO (k+i) represents the set value of nitrate nitrogen concentration at time k+i. NO (i|k) represents the predicted value of nitrate nitrogen concentration at time k+i at time k. NO (0|k)=y NO (k), y NO (k) represents the measured value of nitrate nitrogen concentration at time k; In the sludge bulking control of urban wastewater treatment, the specified operating ranges are: oxygen transfer coefficient 40-240 / day; internal return flow rate 0-92230 cubic meters / day; dissolved oxygen concentration 1.5-2.4 mg / L / day; and nitrate nitrogen concentration 0.5-1.5 mg / L / day. Specific constraints are set as follows: (9) ； (10) ； ② Construct a fuzzy neural network prediction model, specifically as follows: The input to the fuzzy neural network prediction model is [α1(k), α2(k), α3(k), α4(k)], and the output expression of the fuzzy neural network prediction model is: (11) ； Where p̂(k)=[p̂1(k), p̂2(k)] represents the prediction output vector of the fuzzy neural network prediction model at time k, p̂1(k) represents the first output of the fuzzy neural network prediction model at time k, p̂2(k) represents the second output of the fuzzy neural network prediction model at time k, and w l (k) represents the connection weights between the l-th regular layer neuron and the output layer neuron in the fuzzy neural network prediction model at time k, w l (k) is randomly assigned a value in the range [0, 1], α j (k) represents the j-th input to the fuzzy neural network prediction model at time k, c jl (k) represents the center value of the j-th input layer neuron corresponding to the l-th radial base neuron in the fuzzy neural network prediction model at time k, c jl (k) is randomly assigned a value in the range [0, 1]. Let represent the width value of the l-th radial base layer neuron corresponding to the j-th input layer neuron in the fuzzy neural network prediction model at time k. Random values ​​are assigned within the range [0, 1], where j = 1, 2, ..., 4 represents the number of neurons in the input layer of the fuzzy neural network prediction model, and l = 1, 2, ..., 8 represents the number of neurons in the radial base layer and the regular layer of the fuzzy neural network prediction model. The prediction error is calculated as follows: (12) ； Where p(k)=[p1(k), p2(k)] represents the system output vector at time k, p1(k) represents the first output of the system, and p2(k) represents the second output of the system; Update the weights, center, and width of the fuzzy neural network prediction model at time k+1 based on the prediction error at time k: (13) ； in, Let represent the parameter vector of the fuzzy neural network prediction model at time k. This represents the center vector of the l-th radial base layer neuron in the fuzzy neural network prediction model at time k. This represents the width vector of the l-th radial base layer neuron in the fuzzy neural network prediction model at time k. Let I represent the Jacobian matrix of the fuzzy neural network prediction model at time k, and let I represent the 72-row, 72-column identity matrix. This represents the parameter vector of the fuzzy neural network prediction model at time k+1. This represents the center vector of the l-th radial base layer neuron in the fuzzy neural network prediction model at time k+1. This represents the width vector of the l-th radial base layer neuron in the fuzzy neural network prediction model at time k+1; ③ Obtain the 3-step prediction value at time k using a fuzzy neural network prediction model. The specific process is as follows: Let the input to the prediction model be [α1(k), α2(k), α3(k), α4(k)]=[y DO (k), y NO (k), u DO (k-1), u NO [(k-1)], where u DO (k-1) is the oxygen transfer coefficient at time k-1, u NO (k-1) represents the return flow rate at time k-1. The predicted output is [p̂1(k), p̂2(k)]=[ŷ DO (1|k), ŷ NO (1|k)]; Let the input to the prediction model be [α1(k), α2(k), α3(k), α4(k)]=[ŷ DO (1|k), ŷ NO (1|k), u DO (k-1),u NO (k-1)], obtain the predicted output [p̂1(k), p̂2(k)]=[ŷ DO (2|k), ŷ NO (2|k)]; Let the input to the prediction model be [α1(k), α2(k), α3(k), α4(k)]=[ŷ DO (2|k), ŷ NO (2|k), u DO (k-1),u NO (k-1)], obtain the predicted output [p̂1(k), p̂2(k)]=[ŷ DO (3|k), ŷ NO (3|k)]; ④ Prioritize control objectives based on the causal variables of sludge bulking, specifically as follows: When the causal variable is dissolved oxygen concentration, the first priority control objective is J. DO When the causal variable is nitrate nitrogen concentration, the first priority control objective is J. NO When the causal variable is total nitrogen concentration, the first priority control target is J. NO When the causal variable is the suspension concentration, the first priority control objective is J. DO When the causal variable is sludge load, the first priority control objective is J. DO ; ⑤ Design an algorithm for solving the predictive control law of a soft-constraint model, specifically as follows: Based on the diagnostic results, J was determined. DO When the first priority control objective is selected, the control law is calculated as follows: (14) ； (15) ； The constraints are: (16) ； (17) ； (18) ； Where arg min represents the variable that calculates the minimum value of the function, ||| represents the norm of the vector, and ε NO (i|k) represents the relaxation variable of the nitrate nitrogen concentration at time k+i calculated at time k, and J*DO(k) represents the optimal value of the objective function for the dissolved oxygen concentration at time k, calculated as follows: (19) ； The constraints are: (20) ； (21) ； Where min represents the minimum value of the function, ε DO (i|k) represents the relaxation variable of dissolved oxygen concentration at time k+i calculated at time k; Based on the diagnostic results, J was determined. NO When the first priority control objective is selected, the control law is calculated as follows: (22) ； (23) ； The constraints are: (24) ； (25) ； (26) ； Where J*NO(k) represents the optimal value of the objective function for nitrate nitrogen concentration at time k, and is calculated as follows: (27) ； The constraints are: (28) ； (29) ； (3) Sludge bulking inhibition in urban wastewater treatment process The soft-constraint model predictive control law u(k) includes the oxygen transfer coefficient and internal recirculation flow rate at time k. The programmable logic controller controls the frequency of the frequency converter based on the calculated oxygen transfer coefficient. The frequency converter controls the aeration rate by adjusting the speed of the blower. The electric regulating valve controls the internal recirculation flow rate by adjusting the valve opening. Finally, the sludge bulking in the urban wastewater treatment process is suppressed by controlling the dissolved oxygen concentration and nitrate nitrogen concentration.

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