An interval observer-based state interval estimation method for activated sludge treatment process

Abstract

The application discloses a state interval estimation method for activated sludge treatment process based on an interval observer. Considering a large amount of uncertainty existing in a sewage treatment process, the application studies state interval estimation of an activated sludge system composed of an aeration tank and a sedimentation tank. Firstly, a mathematical model is established for a dynamic process of activated sludge reaction. Secondly, a T-S (Takagi-Sugeno) fuzzy method is used to perform pseudo-linearization processing on the established nonlinear model, so that a T-S fuzzy system is obtained, and the complexity of the model is reduced. Finally, an interval observer is designed for the T-S fuzzy model, the interval observer has interference robustness, and through the interval observer, the upper limit and the lower limit of the state of the activated sludge treatment process can be estimated, thereby providing a new thought and method for state monitoring of the activated sludge treatment process.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of wastewater treatment process fault diagnosis, and particularly relates to a state interval estimation method for activated sludge treatment process based on an interval observer. BACKGROUND

[0002] As an artificial kidney of the city, the wastewater treatment plant can effectively treat domestic sewage and industrial wastewater, and has important significance for improving the ecological environment and enhancing the city grade.

[0003] At present, wastewater treatment mainly adopts the activated sludge method, which is an aerobic biological treatment method for wastewater. The process is a complex dynamic biochemical reaction engineering, and involves many mechanical equipment, electrical equipment and automatic instruments. Due to the complexity of the actual wastewater treatment process, many online monitoring indexes are complex, and many water quality indexes need to be detected by the laboratory, which has low accuracy and large time lag, etc., which brings certain difficulties to the practical application of intelligent feature modeling methods. For example, the commonly used water quality monitoring indexes, such as biological oxygen demand BOD, chemical oxygen demand COD, ammonia nitrogen NH3-N, etc. are difficult to realize online accurate measurement, and need to be estimated or predicted.

[0004] However, most of the existing methods are based on the ASM series model to study the state estimation of the activated sludge treatment process in wastewater treatment. The method usually takes water quality indexes, sludge volume index, foam scum index, microbial content index and other parameters as process variables, and estimates the above variables based on Kalman filtering, observer, particle filtering and its extended methods, and other traditional control theory technologies. However, due to the influence of factors such as inflow, inflow composition, pollutant concentration and environmental changes, the wastewater treatment process shows characteristics such as multivariable, strong coupling, nonlinearity, large time delay, randomness, uncertainty, etc. If these uncertainties are not considered, the reliability of the model will be seriously reduced, resulting in a large difference between the actual water quality and quantity and the design value, and the raw water quality cannot be effectively controlled to the design water quality range. Therefore, it is of great research significance and value to fully consider the uncertainty of the activated sludge treatment process, analyze it, and realize the state interval estimation of the activated sludge treatment process on this basis. SUMMARY

[0005] The present application aims to solve the problem of system state interval estimation in wastewater treatment process. For this problem, the present application proposes a state interval estimation method for activated sludge reaction process based on an interval observer.

[0006] The present application proposes an interval state estimation method for activated sludge treatment process based on an interval observer, which includes the following three steps:

[0007] Step S1: In order to be more realistic for the activated sludge treatment process of the sewage treatment plant, considering the kinetic process of the activated sludge reaction and its application scene, the microbial amount X, the reflux microbial amount X r , the organic substrate concentration C S and the dissolved oxygen concentration C O are selected as the system state variables, and a nonlinear activated sludge mass balance model is established.

[0008] Step S2: The T-S fuzzy method is used for the T-S fuzzy modeling of the nonlinear activated sludge treatment process, and the T-S fuzzy system of the activated sludge treatment process is obtained. The model is a pseudo-linear model, which helps to reduce the complexity of the model and facilitate the state interval estimation.

[0009] Step S3: Considering that a large amount of uncertainty in the sewage treatment process makes it difficult to obtain accurate real-time state indicators, the T-S system of the activated sludge treatment process is designed to generate interval estimations of the model state variables X, X r , C S and C O . In the present application, a T-S fuzzy interval observer with H ∞ disturbance attenuation performance is designed to estimate the state interval in real time, thereby improving the accuracy of the prediction. BRIEF DESCRIPTION OF DRAWINGS

[0010] The drawings accompanying the specification of the present application are used to provide a further understanding of the present application, the illustrative embodiments of the present application and the description thereof serve to explain the present application, and do not constitute an improper limitation on the present application.

[0011] Figure 1 The flowchart of the application scene of the present application is shown in the drawings;

[0012] Figure 2 The block diagram of the overall system design steps of the present application is shown in the drawings; DETAILED DESCRIPTION

[0013] The present application will be described in detail below in combination with the drawings and specific embodiments.

[0014] The present application mainly studies the state estimation of an activated sludge system composed of an aeration tank and a sedimentation tank. The aeration tank is considered as a fully stirred container, in which suspended microorganisms react with organic matter in wastewater and dissolved oxygen in water to produce more cells, carbon dioxide and water, removing carbon in wastewater. Oxygen is injected into the aeration tank by compressed air, and suspended microorganisms are completely separated in the sedimentation tank, part of which is recycled to the aeration tank, and the rest is discharged to maintain a certain microorganism concentration in the biological reactor. It should be noted that the application scenario applied in the present application only considers the process of removing organic matter in wastewater by microorganisms, i.e. removing carbon and hydrogen elements, and does not consider the processes of removing nitrogen and phosphorus in wastewater treatment.

[0015] In step S1, according to the kinetic process of activated sludge, a nonlinear kinetic model is established for the biological treatment process of the activated sludge treatment process based on three microbial kinetic equations, i.e. the monod equation, the Lawrence-McCarty first equation and the Lawrence-McCarty second equation, to reflect the mass balance changes of the microbial amount in the activated sludge in the wastewater treatment process.

[0016] The three basic microbial kinetic equations used are specifically introduced as follows:

[0017] Monod equation:

[0018]

[0019] Wherein, μ is the specific growth rate of microbial amount, C S is the substrate concentration, μ max is the maximum specific growth rate, K a is the half-saturation coefficient, i.e. the substrate concentration when μ = 0.5 μ max . The equation can be used to describe the relationship between the substrate concentration and the specific proliferation rate of microorganisms, and also can be used to describe the growth rate of activated sludge in the aeration tank.

[0020] Lawrence-McCarty first equation:

[0021]

[0022] Wherein, X is the microbial content, C S is the organic substrate concentration, Y is the microbial yield coefficient, reflecting the relationship between the substrate consumption rate and the cell growth rate; K d is the internal endogenous metabolism coefficient, which is used to represent the amount of microbial amount consumed by endogenous metabolism per unit of microbial amount per unit of time.

[0023] Lawrence-McCarty second equation:

[0024]

[0025] Where r is the specific substrate degradation rate. The Lawrence-McCarty basic equation is a kinetic relationship established according to the Monod equation, which is used to represent the average residence time of unit mass of microorganisms in the activated sludge biological treatment process, so as to reflect the average sludge age of the activated sludge.

[0026] On the basis of the Monod equation, the influence of substrate concentration on the reaction rate of microorganisms in the enzymatic reaction is considered, and the influence of oxygen concentration on the reaction rate of microorganisms in the aerobic microbial oxidation reaction is also considered. The specific growth rate equation of the microorganism used is as follows:

[0027]

[0028] Where C O is the dissolved oxygen concentration, C S is the substrate concentration, μ max is the maximum specific growth rate, K a is the affinity coefficient, and K s is the saturation coefficient.

[0029] The present application is aimed at the assumption of dissolved oxygen concentration C O when modeling the microbial kinetics principle of activated sludge. S The system constant and parameter are all known, but the microbial amount X, the substrate concentration C r and the recovered microbial amount X S cannot be obtained online.

[0030] In summary, the activated sludge biochemical reaction process of wastewater treatment is modeled by a kinetic system, and an activated sludge mass balance model is obtained. The state equation of the mass balance model is:

[0031]

[0032]

[0033]

[0034]

[0035] The above four state space equations respectively represent the activated sludge microbial mass balance equation of the aeration tank, the recovered activated sludge microbial mass balance equation of the secondary sedimentation tank, the mass balance equation of the organic substrate, and the mass balance equation of the dissolved oxygen concentration. Among them, X, C S , Xr and C O respectively represent biomass, substrate concentration, recycled biomass and dissolved oxygen concentration. D represents dilution rate, which is used to represent the proportion of biomass reduced in the process. r and β respectively represent the ratio of recycle flow to influent flow and the ratio of effluent flow to influent flow, and respectively correspond to the concentrations of substrate and dissolved oxygen in the influent. K0 is a given constant, represents the maximum dissolved oxygen concentration, K La represents the oxygen transfer coefficient.

[0036] In step S2, for the mass balance equation of the activated sludge biological treatment process described above, the T-S (Takagi-Sugeno) fuzzification method is used to convert it into a nonlinear T-S fuzzy system. The process includes the following steps:

[0037] In the model, the state variables are: microbial content X, substrate concentration C S , recycled microbial content X r and dissolved oxygen concentration C O , the oxygen transfer coefficient K La and the dilution rate D are selected as input variables, and the nonlinear equation is arranged into a linear variable parameter system form with pseudo-linear properties. At the same time, considering the unknown disturbance input existing in the process, the following linear variable parameter system system can be obtained:

[0038]

[0039] Where x=[X X r C S C O ] T is the state vector, u=[D K La ] T is the input vector, and the unknown bounded disturbance d existing in the influent organic substrate is considered in this scenario, G=[0 0 1 0] T .

[0040] To build a T-S fuzzy model, the premise variables needed for fuzzification need to be selected. In order to reduce the complexity of the T-S fuzzy system, the number of premise variables needs to be as small as possible, each premise variable equation needs to depend on the minimum number of state variables, and the selected premise variables need to ensure the controllability and observability of the LPV system. The present application selects the following six premise variables, which are represented by z(x):

[0041]

[0042] z2(x) = X

[0043] z3(x) = X r

[0044] z4(x) = C O

[0045]

[0046] z6(x) = C S

[0047] After selecting the above premise variables, according to the fuzzy transformation rule, the linear variable parameter system is subjected to a convex polyhedron transformation, and membership functions corresponding to two time-varying matrices in the system are obtained, at this time, the time-varying matrix of the system can be rewritten as a form of a plurality of linear sub-matrices containing only the upper and lower bounds of the premise variables and other parameters and the weights formed by multiplying and adding the corresponding membership degrees. The formulas of the transformation rule are as follows:

[0048]

[0049] Wherein, F represents the membership function, F j,max and F j,min respectively represent the membership degree of the jth premise variable when it is biased to the upper bound and the membership degree of the premise variable when it is biased to the lower bound.

[0050]

[0051] Wherein, σ = 1, 2 respectively represent max and min, the multiplication of the membership functions of n premise variables can obtain the total weight h i (z) of the premise variables, i = 1, …, 2 n There are 2 n sub-models in total;

[0052]

[0053] The formula represents the convexity of the weight, that is, each sub-weight is non-negative and the sum is 1.

[0054] In the present application, there are 6 premise variables (n = 6), according to the transformation rule, there are 64 sub-models (r = 2 6 ), each sub-system model can be determined by the parameters of each premise variable at the vertex of the convex polyhedron and the corresponding membership function. Due to the excessive number of sub-models in the present application, only the expression form of the sub-model of the T-S fuzzy matrix obtained after the convex polyhedron transformation is shown:

[0055] A(z) = A(z1, z2, z3, z4, z5) = F 1,1 F2,1 F 3,1 F 4,1 F 5,1 F 6,1

[0056]

[0057]

[0058] B(z)=B(z2,z3,z4,z6)=F 1,1 F 2,1 F 3,1 F 4,1 F 5,1 F 6,1

[0059]

[0060]

[0061] The global T-S fuzzy model is obtained by multiplying each sub-model with the corresponding membership function, and the pseudo-linearization of the complex nonlinear system is completed.

[0062] For the sake of simplicity, the system is written as

[0063]

[0064] Wherein, y is an output vector, and C = [0 0 0 1].

[0065] In step S3, in order to obtain the real-time state value of the sludge biochemical reaction process, considering that the process will continue to exist bounded disturbance and the uncertainty generated after T-S fuzzy modeling, interval estimation is performed on the model state variable, so that the state change range after disturbance can be better found. Step S3 is the key of the present application, in step S3, a T-S fuzzy interval observer with H ∞ Disturbance attenuation performance is designed for the nonlinear T-S fuzzy model obtained in step S2, so as to estimate the state interval in real time. The design process of the T-S fuzzy interval observer is as follows:

[0066] For the design of interval observer for continuous system, it is necessary to ensure that the system matrix is Metzler matrix, that is, all non-diagonal elements of the system matrix are non-negative, and such design form can ensure that the state error system is a positive system. Therefore, the following theorem is used for the design of interval observer:

[0067] Lemma 1: for an n-dimensional vector x belonging to the real number field, and satisfying If matrix A is a constant matrix, then: If matrix A is a variable matrix and also satisfies then: where x + = max{0, x}, x - = x + -x, matrix A + , A - Similarly.

[0068] According to the lemma, the T-S fuzzy observer state equation is designed as follows:

[0069]

[0070] where and and and d are the upper and lower bounds of the state estimation value and the unknown bounded disturbance, respectively,

[0071] In order to find the appropriate T-S fuzzy gain matrix The first step is to determine the error equation of the T-S fuzzy observer. Define the state error upper and lower bounds as:

[0072]

[0073] where, e (t)≤0

[0074] The error equation of the T-S fuzzy observer is:

[0075]

[0076] where, and ω are the upper and lower bounds of the disturbance, respectively, and their specific expressions are as follows:

[0077]

[0078]

[0079] where,

[0080] After obtaining the error equation, the H ∞ decay error disturbance ω(t) is introduced, and the following linear matrix inequality (LMI) is solved using Matlab to obtain the T-S fuzzy parameter matrix

[0081]

[0082] The design steps of the specific interval observer are as follows:

[0083] Consider a positive definite upper bound error Lyapunov function:

[0084]

[0085] Where the matrix P > 0 is a symmetric positive definite matrix. At the same time, its derivative Must be negative, as shown below:

[0086]

[0087] Lemma 2: If there exist matrices x, y with appropriate dimensions and a positive definite matrix Q, then the following conditions are satisfied: T y + y T x ≤ x T Qx + y T Q -1 y.

[0088] With the help of Lemma 2, It can be converted to:

[0089]

[0090] Introduce a H ∞ Form disturbance attenuation parameter γ and a positive definite matrix M, with the following relationship:

[0091]

[0092] Through the above formula, the range of Can be further scaled:

[0093]

[0094] Thus the LMI design condition can be obtained:

[0095]

[0096] Let According to the Schur complement lemma, the LMI design condition can finally be rewritten in the following standard form:

[0097]

[0098] With the above constraints, the fuzzy parameter matrix is solved by using YALMIP toolbox The design of the T-S fuzzy interval observer is completed.

[0099] The above examples are only used to illustrate the technical solutions of the present application, but not to limit it; although the present application has been described in detail with reference to the foregoing examples, those skilled in the art should understand that the technical solutions recorded in the foregoing examples can be modified, or some technical features can be replaced by equivalents; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present application.

Claims

1. A method for estimating the state interval of an activated sludge treatment process based on an interval observer, characterized in that: The state interval estimation method for the activated sludge treatment process based on interval observers includes the following steps: S1: Considering the kinetics of the activated sludge reaction, we first select the microbial biomass X and the return microbial biomass X. r Organic substrate concentration C S and dissolved oxygen concentration C O A nonlinear activated sludge mass balance model was established as a system state variable. S2: For the nonlinear system of activated sludge treatment process, the TS fuzzification method is used to perform TS fuzzy modeling on the activated sludge mass balance model to obtain the TS fuzzy system of activated sludge treatment process. S3: Considering the significant uncertainties in the wastewater treatment process that make it difficult to obtain accurate real-time state indicators, an interval observer is designed for the TS system in the activated sludge treatment process. This interval observer is used to generate the model state variables X and X'. r C S and C O The upper and lower bounds provide a basis for monitoring the status of the activated sludge treatment process.

2. The state interval estimation method for activated sludge treatment process based on interval observer as described in claim 1, characterized in that: In step S1, considering the kinetic process of activated sludge reaction, a nonlinear kinetic model is established for the biological treatment process of activated sludge treatment based on the three microbial kinetic equations: the Monod equation, the Lawrence-McCarty first equation, and the Lawrence-McCarty second equation. This model is used to reflect the mass balance changes of microbial biomass in activated sludge during wastewater treatment.

3. The state interval estimation method for activated sludge treatment process based on an interval observer as described in claim 2, characterized in that: The three microbial kinetic equations are described in detail below: Monod equation: Where μ is the microbial biomass specific growth rate, and C S The substrate concentration is μ. max For the maximum ratio growth rate, K a The half-saturation coefficient is μ = 0.5μ. max The equation describes the relationship between substrate concentration and microbial specific proliferation rate, and can also describe the growth rate of activated sludge in an aeration tank. Lawrence-McCarty's first equation: Where X represents the microbial content, and C S K represents the organic substrate concentration, Y represents the microbial yield coefficient, reflecting the relationship between substrate consumption rate and cell growth rate; d This is the internal endogenous metabolism coefficient, used to represent the amount of microorganisms consumed by endogenous metabolism per unit of microbial biomass per unit time. Lawrence-McCarty's second equation: Where r is the substrate-specific degradation rate; the Lawrence-McCarty basic equation is a kinetic relationship established based on the Monod equation, used to represent the average residence time of a unit mass of microorganisms in the activated sludge biological treatment process, thereby reflecting the average sludge age of the activated sludge. Based on the monod equation, the influence of substrate concentration on the microbial reaction rate in enzymatic reactions is considered, as well as the influence of oxygen concentration on the microbial reaction rate in aerobic microbial oxidation reactions; the specific growth rate equation used is shown below: Where C O C represents the dissolved oxygen concentration. S The substrate concentration is μ. max For the maximum specific growth rate, K a K is the affinity coefficient. s The saturation coefficient; The assumed dissolved oxygen concentration C when modeling the microbial kinetics of activated sludge O It is the only measurable state of the process, and all system constants and parameters are known, but the microbial biomass X and substrate concentration C are unknown. S and recovered microbial biomass X r Unavailable online; In summary, a kinetic system model was performed on the biochemical reaction process of activated sludge in wastewater treatment, resulting in an activated sludge mass balance model. The state equation of the mass balance model is as follows: The four equations of state above represent the mass balance equations for activated sludge microorganisms in the aeration tank, the secondary sedimentation tank for recovered activated sludge microorganisms, the organic substrate, and the dissolved oxygen concentration, respectively; where X(t), C S (t), X r (t) and C O (t) represent biomass, substrate concentration, recirculated biomass, and dissolved oxygen concentration, respectively; D(t) represents the dilution rate, indicating the proportion of biomass reduction during the process; β represents the ratio of wastewater flow rate to influent flow rate. and These correspond to the concentrations of the substrate and dissolved oxygen in the influent, respectively; K0 is a given constant. K represents the maximum dissolved oxygen concentration. La (t) represents the oxygen mass transfer coefficient.

4. The state interval estimation method for activated sludge treatment process based on interval observer as described in claim 1, characterized in that: In step S2, for the nonlinear system of the activated sludge treatment process, the TS (Takagi-Sugeno) fuzzification method is used to convert it into a nonlinear TS fuzzy system.

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