A polyhedral-based thermal reactor fault detection method

Abstract

The application belongs to the technical field of fault detection and analysis in control system, and discloses a kind of hot reactor fault detection method based on polytope. Through the discretization analysis of the nonlinear model of hot reactor, the system dynamics under the condition of hot reactor failure is described by T-S fuzzy 2-D model. To solve the problem of unknown antecedent variables, a T-S fuzzy state observer is designed to calculate the estimated value of the antecedent variables using state estimation. On this basis, a T-S fuzzy fault detector is designed to generate a residual signal. Using the estimated-based method, a fault detection mechanism based on polytope is established to determine whether a fault has occurred according to the residual signal. Finally, the feasibility and effectiveness of the application are verified through simulation. The application first designs a T-S fuzzy 2-D model fault detector for hot reactor, and conducts fault detection based on polytope under the condition of unknown antecedent variables.

Description

Technical Field

[0001] This invention relates to the field of fault detection and analysis technology in control systems, and in particular to a fault detection method for thermal reactors based on multicellular structures. Background Technology

[0002] Thermal reactors are crucial containers in chemical production, widely used in modern chemistry, petroleum, and pesticide industries. Controlling the internal temperature of a thermal reactor is key to ensuring the expected chemical reactions of raw materials. As a real-world system, nonlinearity and uncertainty are unavoidable in thermal reactor models. The TS fuzzy model, a fuzzy dynamic approximation for complex nonlinear systems, is widely used in nonlinear control. Antecedent variables reflect the dynamic changes of the TS fuzzy model; previous studies often assumed known antecedent variables, significantly limiting the practicality of the TS fuzzy model. The central multiple cell can be used to depict the feasible set of states and is an important tool in set membership estimation. This invention uses a TS fuzzy 2-D model to model and analyze a thermal reactor, and designs a state observer and fault detector for the reactor under unknown antecedent variables, achieving fault detection based on the central multiple cell. Finally, simulations verify the feasibility and effectiveness of the invention. To date, no patents disclose designs for fault detection in thermal reactors based on multiple cells. Summary of the Invention

[0003] This invention proposes a fault detection method for thermal reactors based on multicellular structures, designs a fault detector for chemical thermal reactors based on central multicellular structures, and verifies the fault detector through simulation.

[0004] The technical solution of the present invention is as follows: A fault detection method for a thermal reactor based on multiple cells is proposed, which involves establishing a TS fuzzy 2-D model of the internal temperature change of the thermal reactor; designing a TS fuzzy state observer based on the TS fuzzy 2-D model when the antecedent variables are unknown, and calculating the antecedent variable estimates through the state estimates; designing a TS fuzzy fault detector based on the antecedent variable estimates, generating residual signals, and determining whether a fault has occurred through a fault detection mechanism based on multiple cells.

[0005] The specific steps for establishing the TS fuzzy 2-D model of temperature change inside the thermal reactor are as follows:

[0006] Establish the nonlinear equations for the temperature dynamics inside the thermal reactor:

[0007]

[0008] W(s,t) represents the temperature in the thermal reactor, s represents the spatial dimension of the temperature, t represents the time dimension of the temperature, f(s,t) represents the fault in the thermal reactor, and d(s,t) represents the disturbance experienced by the thermal reactor, satisfying the following conditions: It is the square of the upper bound of the disturbance signal amplitude, a1, a2, b0, c0 are constant parameters of the nonlinear equation (1), and α0=cos(W(s,t)) are the nonlinear parameters of the nonlinear equation (1) in the spatial and temporal dimensions.

[0009] Discretization analysis of the nonlinear equations for the temperature dynamics inside the thermal reactor; definition For partial differential terms Discretization: replace replace Define x h (i,j)=R(i*Δs,j*Δt),x v (i,j)=W(i*Δs,j*Δt), where Δs is the spatial dimension sampling interval and Δt is the time dimension sampling interval; the nonlinear equation in equation (1) is represented as a 2-D system model:

[0010]

[0011] Take the antecedent variable θ(i,j) = x v (i,j), applying the sector nonlinearity method to the nonlinear term a0, the weighting coefficients of each subsystem in the 2-D system model are: Simultaneously considering the output equation (3.2), the 2-D system model can be written as a TS fuzzy 2-D model:

[0012]

[0013] y(i,j)=Cx(i,j)+Ed(i,j) (3.2)

[0014] x + (i,j)=[x h (i+1,j),x v (i,j+1)] T , x(i,j)=[x h (i,j),x v (i,j)] T Let f(i,j) represent the system state, f(i,j) represent the fault signal, d(i,j) represent the disturbance signal, y(i,j) represent the measurement output, and A represent the system state. n D, F, C, E are the parameter matrices of the TS fuzzy 2-D model, h n(θ(i,j)) is the weighting coefficient of the nth subsystem, n=1,…N, where N is the number of subsystems and N=2.

[0015] The TS fuzzy state observer is established as follows:

[0016] Design a fuzzy state observer for TS when the antecedent variables are unknown:

[0017]

[0018]

[0019]

[0020] in, Represents the state estimate. These are estimates of the antecedent variables calculated using the state estimates. This is an estimated value measured and output from the thermal reactor. It is an estimate of the fault signal, k = i + j; K n and G n Let n be the matrix of the TS fuzzy state observer to be designed, n = 1, 2;

[0021] h n (θ(i,j)) is abbreviated as h n , Abbreviated as definition Analyzing the state-space equations of formulas (3.1), (3.2), (4.1), (4.2), and (4.3), we obtain the augmented error system:

[0022]

[0023]

[0024] Define m(i,j) = [e x (i,j) T e f (k) T ] T K n G n Let K be the parameter matrix; under the condition that the external disturbance signal d(i,j) = 0, by adjusting K... n G n The augmented error system gradually stabilizes.

[0025] The designed fault detector is specifically as follows:

[0026] Based on state observation results Calculate the estimated values ​​of the weighting coefficients for each subsystem. Based on this, a fault detector is designed:

[0027]

[0028] Where, x f (i,j) represents the fault detector state, and r(i,j) represents the actual residual signal; the fault detector iteration uses the estimated values ​​of the antecedent variables, obtained from the TS fuzzy state observer; A fn B fn C fn D fn This is the parameter matrix of the fault detector to be designed, n = 1, 2.

[0029] Based on the state estimate provided by formula (4.1), the fault detector parameter matrix is ​​designed; combining formulas (3.1), (3.2) and (6), the augmented system (7) is obtained:

[0030]

[0031]

[0032]

[0033] in The parameter matrix of the augmented system (7) is composed of the parameter matrices of the TS fuzzy 2-D model and the fault detector (6); the asymptotic stability of the augmented system (7) and the L value under the condition f(i,j)=0 are analyzed. ∞ Performance, constructing Lyapunov functions Design the parameter matrix A of the fault detector. fn B fn C fn D fn , n = 1, 2.

[0034] The asymptotic stability of the augmented error system (5), the asymptotic stability of the augmented system (7), and L were respectively examined. ∞ The performance was analyzed, and a series of matrix inequalities were obtained as sufficient conditions for the performance to hold. The matrix inequalities were used as constraints to establish an optimization problem. After solving the optimization problem, the parameter matrices of the state observer (4) and the fault detector (6) were obtained. The fault detection mechanism based on polycellular structures was used to determine whether a fault had occurred.

[0035]

[0036]

[0037] r(i,j) is the actual residual signal; r (i,j)] u , These represent the lower and upper bounds of the u-th element of the residual signal, respectively.

[0038] A Matlab simulation program was developed for a 2-D model of a thermal reactor to verify the feasibility of the invention. Fault signals were added to the reactor model, and a fault detector was used to determine whether a fault occurred. Simulation results show that the invention can detect faults when they occur, achieving its design objective.

[0039] The beneficial effects of this invention are:

[0040] 1) Based on the nonlinear equations describing the temperature dynamics of the thermal reactor, a TS fuzzy 2-D model of the thermal reactor is established through discretization and sector nonlinearization. Based on this model, a state observer and fault detector for the thermal reactor are designed.

[0041] 2) Based on the traditional Luneburger observer, considering the estimation of the fault signal itself, a thermal reactor state observer is designed that can achieve state estimation in both fault-free and faulty scenarios when the antecedent variables are unknown.

[0042] 3) Based on the state estimates, a fault detector for the thermal reactor is designed, and a multicellular fault diagnosis mechanism is used to determine whether an internal fault has occurred in the reactor. Matlab simulations of the model and the designed fault detector show that this invention can detect internal faults in the thermal reactor. This fault detector can be used for nonlinear models of thermal reactors and operates under conditions where the antecedent variables are unknown, exhibiting significant universality. Attached Figure Description

[0043] Figure 1 This is a schematic diagram of the fault detector and the condition observer working together;

[0044] Figure 2 The state observer designed in this invention is for state x h The estimation effect of (i,j);

[0045] Figure 3 yes Figure 2 The planar image after fixing i = 25.

[0046] Figure 4 This invention demonstrates the effectiveness of the fault detector in estimating faults. Detailed Implementation

[0047] The following details the derivation process, specific design, and implementation of this invention.

[0048] This invention designs a TS fuzzy fault detector to meet the fault detection requirements of thermal reactors. Through discretization analysis of the nonlinear model of the thermal reactor, the system dynamics of the reactor under fault conditions are depicted using a TS fuzzy 2-D Roesser system. Sector nonlinearization is used to convert the nonlinear terms in the nonlinear model into a weighted sum of linear terms to construct the various subsystems in the TS fuzzy system. To address the problem of unknown antecedent variables, a TS fuzzy state observer is designed to calculate the estimated antecedent variables using the state estimates. Based on this, a TS fuzzy fault detector is designed to perform multicellular-based fault detection in the model. Finally, numerical simulation is used to model the state observer and fault detector to verify the feasibility and effectiveness of this invention.

[0049] Step 1: Describe the nonlinear equations for the temperature dynamics inside the thermal reactor:

[0050]

[0051] E(s,t) represents the temperature in the thermal reactor, where s and t represent the spatial and temporal dimensions of the temperature, f(s,t) represents the fault in the thermal reactor, and d(s,t) represents the disturbance experienced by the thermal reactor, satisfying the following conditions:

[0052] definition Discretization of partial differential terms: Define x h (i,j)=R(i*Δs,j*Δt),x v (i,j)=W(i*Δs,j*Δt), Δs=0.5, Δt=0.5, (1) The partial differential equation is expressed as a 2-D system model:

[0053]

[0054] Given system parameters a2=a1=-3, b0=0.066, c0=0.02, a0=0.5*cos(W(s,t))-8.5, where a0 is a nonlinear term.

[0055] Applying the sector nonlinearity method to the nonlinear term a0, we take θ(i,j) = x v Given (i,j), L=1, N=2, the parameter matrix of the TS fuzzy 2-D system is as follows:

[0056]

[0057]

[0058] C = [0.8 0.2], E = 0.02

[0059] This represents the weighting coefficients of each subsystem calculated using the antecedent variable θ(i,j).

[0060] Step 2: Design the parameter matrix K of the state observer when the antecedent variables are unknown. n G n (n = 1, 2).

[0061] This step uses two assumptions, assumption 1 of which is as follows:

[0062] Assumption 1: The fault signal f(i,j) is a constant.

[0063] Based on assumption 1, two properties of f(i,j) can be derived:

[0064]

[0065]

[0066] Based on these two properties, in the state observer, use estimate But this means that each iteration of (i,j) will produce a Ultimately, you will get multiple This stipulates that during the iteration of the state observer, for a certain... Pick h n (θ(i,j)) is abbreviated as h n , Abbreviated as definition The state-space equations of the TS fuzzy 2-D model and the TS fuzzy state observer are analyzed to obtain the augmented error system:

[0067]

[0068]

[0069] Define m(i,j) = [e x (i,j) T e f (k) T ] T Abbreviated as m, under the condition that the external disturbance signal d(i,j)=0, design the parameter matrix K. n G n (n=1,2) makes the augmented error system asymptotically stable.

[0070]

[0071] Where I nx I nf It is an identity matrix of appropriate dimension.

[0072] Construct the Lyapunov function ΔV m =m + (i,j) T Pm + (i,j)-m(i,j) T Pm(i,j), P>0, defined as:

[0073]

[0074]

[0075] Assumption 2: There exists ρ>0 such that Δ es satisfy

[0076] Based on assumption 2, define The following inequalities hold:

[0077]

[0078] Analyzing the Lyapunov function, we have:

[0079]

[0080] definition ΔV m Sufficient condition for (i,j) to be less than 0:

[0081]

[0082] definition The sufficient condition for the above matrix inequality to hold is (n∈[1,N]):

[0083]

[0084] When (10) holds, the estimation error of the state observer asymptotically stabilizes.

[0085] Step 3: Based on the state estimates provided by the state observer, design the fault detector parameter matrix. Combine the system model and the fault detector model to obtain the augmented system;

[0086]

[0087]

[0088]

[0089] in:

[0090]

[0091]

[0092] definition:

[0093]

[0094]

[0095]

[0096] Analyze the stability of the augmented system and L ∞ Performance (when f(i,j)=0), constructing the Lyapunov function Design the parameter matrix A of the fault detector. fm B fm C fm D fm (m∈[1,N]). Suppose there exists a positive number λ, μ such that:

[0097]

[0098] definition The sufficient condition for inequality (11) to hold is (n,m∈[1,N]):

[0099]

[0100] Define the ellipsoidal region:

[0101]

[0102] in It is the amplitude boundary of the perturbation signal d(i,j), for any We can conclude that ΔV(i,j)≤0, which means that V(i,j) decreases as i+j increases. Therefore, we know... It is the attraction domain of the augmenting system.

[0103] Analysis of augmented system L ∞ Performance, assuming there exists a positive number γ such that the following inequality holds:

[0104]

[0105] Consider the attraction domain (13) and the amplitude boundary of the disturbance signal. have:

[0106]

[0107]

[0108] When (11) and (14) hold, the augmented system is asymptotically stable and satisfies L. ∞ Performance, that is, the robustness of the fault detector to disturbance signals. Using matrix transformation, the sufficient condition for (14) is (n,m∈[1,N]):

[0109]

[0110] Step 4: Solving for the parameter matrix and simulation verification;

[0111] Using the matrix inequalities from steps 2 and 3 as constraints, we can establish the optimization problem:

[0112]

[0113] After solving the optimization problem and obtaining the parameter matrices of the state observer and fault detector, a fault detection mechanism based on set member estimation is established.

[0114] Depend on It can be seen that the perturbation signal is in a bounded and known multicell, satisfying d(i,j)∈Z d =<0,H d > The reactor system status, the feasible set of measured outputs, and the results expressed using Z-coordinates. x = <p x H x >,Z y = <p y H y > indicates that the feasible sets of fault detector states and residual signals are represented by Z. xf = <p xf H xf >,Z r = <p r H r > indicates that, given that the initial values ​​of each cellular element are bounded, the cellular iterations corresponding to the system and the fault detector are as follows:

[0115]

[0116]

[0117]

[0118]

[0119] Residual feasible set for each fault-free condition <P r (i,j),G r(i,j)>, calculate its upper and lower bounds, and compare them with the actual fault signal r(i,j).

[0120]

[0121] Where u represents P r The u-th element of (i,j), v represents G. r (i,j) column number, [G r (i,j)] u,v Representing G r The element in row u and column v of (i,j). The specific fault detection mechanism is as follows:

[0122]

[0123]

[0124] Under this fault detection mechanism, Matlab simulation was performed to verify the effectiveness of the invention.

[0125] Figure 1 The main process of this invention for multicellular-based fault detection is demonstrated.

[0126] Figure 2 , Figure 3 , Figure 4 The simulation image was obtained under the fault signal f(i,j)=0.42, (20≤i≤30,20≤j≤30). Figure 2 It is for state x h The estimation effect of (i,j) shows that the state estimate can follow the actual state changes. To illustrate the estimation effect more clearly, we will... Figure 2 The value of i is fixed at 25, resulting in Figure 3 .from Figure 3 As can be seen, when the actual state changes due to a fault, the state estimate also changes after a certain delay. Figure 4 The detection effect of the fault detector is shown. It can be seen that the detector can achieve the purpose of fault detection at all points (i,j) except when the fault occurs or disappears.

[0127] The above-described embodiments are merely illustrative of the implementation methods of the present invention, but should not be construed as limiting the scope of the present invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the protection scope of the present invention.

Claims

1. A method for detecting faults in a thermal reactor based on multicellular structures, characterized in that, A TS fuzzy 2-D model of internal temperature change in a thermal reactor is established. Given unknown antecedent variables, a TS fuzzy state observer is designed based on the TS fuzzy 2-D model to calculate antecedent variable estimates using state estimates. A TS fuzzy fault detector is designed based on the antecedent variable estimates to generate residual signals. A multi-cell-based fault detection mechanism is then used to determine whether a fault has occurred. The TS fuzzy state observer is established as follows: Design a fuzzy state observer for TS when the antecedent variables are unknown: in, Represents the state estimate. These are estimates of the antecedent variables calculated using the state estimates. This is an estimated value measured from the output of the thermal reactor. It is an estimated value of the fault signal. ; and The matrix of the TS fuzzy state observer to be designed is... ; Will Abbreviated as , Abbreviated as ,definition , By analyzing formulas (3.1), (3.2), (4.1), (4.2), and (4.3), the augmented error system is obtained: definition , , For parameter matrices; under external disturbance signals Under the condition of adjustment , The augmented error system gradually stabilizes; The TS fuzzy fault detector design specifically refers to: Based on state observation results Calculate the estimated values ​​of the weighting coefficients for each subsystem. Based on this, a fault detector was designed: (6) in, This is the status of the fault detector. It is the actual residual signal; the iteration of the fault detector uses the estimated values ​​of the antecedent variables, which are obtained from the TS fuzzy state observer. , , , This is the parameter matrix of the fault detector to be designed. ; Based on the state estimate provided by formula (4.1), the fault detector parameter matrix is ​​designed; combining formulas (3.1), (3.2) and (6), the augmented system (7) is obtained: in , , , , , , The parameter matrix of the augmented system (7) is composed of the parameter matrices of the TS fuzzy 2-D model and the fault detector (6); the asymptotic stability of the augmented system (7) is analyzed. In the case of Performance, constructing Lyapunov functions Design the parameter matrix of the fault detector , , , .

2. The method for detecting faults in a thermal reactor based on multicellular structures according to claim 1, characterized in that, The specific steps for establishing the TS fuzzy 2-D model of temperature change inside the thermal reactor are as follows: Establish the nonlinear equations for the temperature dynamics inside the thermal reactor: Represents the temperature in the hot reactor. The spatial dimension representing temperature, The time dimension representing temperature This indicates a malfunction in the thermal reactor. This represents the disturbance experienced by the thermal reactor, satisfying... ; It is the square of the upper bound of the disturbance signal amplitude. , , , These are the constant parameters of the nonlinear equation (1). These are the nonlinear parameters of the nonlinear equation (1) in the spatial and temporal dimensions; Discretization analysis of the nonlinear equations for the temperature dynamics inside the thermal reactor; definition For partial differential terms Discretization: replace , replace ;definition , , The sampling interval is the spatial dimension. The sampling interval is the time dimension; the nonlinear equation in equation (1) is represented as a 2-D system model: Get the predecessor variable For nonlinear terms Applying the sector nonlinear method, the weighting coefficients of each subsystem in the 2-D system model are: , Meanwhile, considering the output equation (3.2), the 2-D system model is written as a TS fuzzy 2-D model: , Represents the system state. This represents a fault signal. This represents a disturbance signal. Represents the measurement output. , , , , The parameter matrix of the TS fuzzy 2-D model. It is the first The weighting coefficients of each subsystem , Let be the number of subsystems, and .

3. The method for detecting faults in a thermal reactor based on multicellular structures according to claim 1, characterized in that, The asymptotic stability of the augmentation error, the asymptotic stability of the augmented system (7), and the asymptotic stability of the augmented system (7) are respectively discussed. The performance was analyzed, and a series of matrix inequalities were obtained as sufficient conditions for the performance to hold. The matrix inequalities were used as constraints to establish an optimization problem. After solving the optimization problem, the parameter matrices of the state observer (4) and the fault detector (6) were obtained. The fault detection mechanism based on polycellular structures was used to determine whether a fault had occurred. This is the actual residual signal; , Representing the residual signals respectively The lower and upper bounds of each element.

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