Interval estimation-based sewage treatment biological process fault detection method and system

Abstract

The present application provides a sewage treatment biological process fault detection method and system based on interval estimation, belonging to the technical field of automatic monitoring of sewage treatment process. The present application is to solve the problem that the existing sewage treatment detection is strongly dependent on model precision and noise statistical characteristics, and is easy to cause divergence and false alarm and miss alarm when facing channel fading and nonlinear uncertainty. The method comprises the following steps: S1: T-S fuzzy model modeling; S2: robust observer design; S3: interval propagation design, obtaining state interval and residual interval; S4: establishing double fault detection strategy, outputting fault category, fault size and fault occurrence time. The system comprises: modeling module, channel processing module, observer design and operation module, interval propagation module and fault detection decision module.

Description

Technical Field

[0001] This invention relates to a method and system for detecting faults in biological wastewater treatment processes based on interval estimation, belonging to the field of automated monitoring technology for wastewater treatment processes. Background Technology

[0002] The core objective of wastewater treatment plant operation is to ensure that the effluent quality consistently meets standards. However, commonly used biological treatment processes (such as the activated sludge process) face the following three main challenges:

[0003] 1. The process mechanism is highly nonlinear and the parameters are uncertain: The microbial degradation mechanism is affected by multiple factors such as substrate concentration, dissolved oxygen, sludge age, and temperature, which makes the process model complex and difficult to linearize.

[0004] 2. Key parameters are difficult to measure online: such as dissolved organic matter and microbial activity cannot be measured directly in real time and need to be inferred by state estimation models.

[0005] 3. Wireless sensor networks are susceptible to channel fading: With the widespread application of wireless transmission, measurement signals often become unreliable due to noise, packet loss and fading, which directly affects the accuracy of monitoring and fault diagnosis.

[0006] Most existing technologies employ Kalman filtering-based methods, but these are highly dependent on model accuracy and noise statistics, and are prone to divergence when faced with channel fading and nonlinear uncertainties. Furthermore, traditional fault detection methods often rely on a single residual threshold, which can lead to false alarms or missed alarms. Summary of the Invention

[0007] To address the problems in existing wastewater treatment detection methods, which heavily rely on model accuracy and noise statistics, and are prone to divergence and false alarms when faced with channel fading and nonlinear uncertainties, this invention proposes a wastewater treatment biological process fault detection method and system based on interval estimation.

[0008] The technical solution adopted by this invention to solve the above problems is: a wastewater treatment biological process fault detection method based on interval estimation, comprising: Step 1: Based on the kinetic characteristics of the wastewater treatment biological process, establish a TS fuzzy model to describe the nonlinear dynamics of the system; Step 2: Determine the range of variation of the channel coefficients based on the channel fading characteristics of the wireless sensor network; Step 3: Based on the TS fuzzy model and the range of variation of the channel coefficients, design... Robust observers are used to obtain state estimates and residuals; Step 4: Based on the state estimate and residuals, calculate the state interval and residual interval using the Zonotope ensemble propagation algorithm; Step 5: Based on the comparison results between the residual interval and the preset threshold, and the inclusion relationship between the state estimate and the state interval, jointly output the fault category, fault size, and fault occurrence time.

[0009] Furthermore, step 1 specifically includes: Based on engineering experience, the upper and lower bounds of variables are defined, including microbial growth rate, activated sludge biomass, returned activated sludge biomass, and organic substrate concentration. Each variable is divided into two intervals, high and low, to obtain multiple premise regions, where each premise region corresponds to a set of TS linear subsystems. Based on the local linearization results within each premise region, construct the corresponding TS linear subsystem; The weights of each fuzzy subsystem are calculated based on the piecewise linear membership function, and the global TS fuzzy model is obtained by weighted averaging. .

[0010] Furthermore, step 2 specifically includes: Establish an observer and define the error, receive the measurement quotes from the wireless sensor, substitute the actual system model and the observer into the defined error, and obtain the error dynamics; Introducing in error dynamics Performance constraints, establish Performance metrics determine the range of variation of the channel coefficients.

[0011] Furthermore, step 3 specifically includes: Nonlinearity in the system As an interval uncertainty parameter, a Lyapunov function is constructed to analyze the stability of the error system; the channel fading effect is transformed into a matrix inequality form based on the convexity principle of the channel coefficient interval; and the matrix inequality is transformed into a standard linear matrix inequality that can be solved numerically through the variable substitution method and Schur complement lemma. Solve the linear matrix inequalities to obtain the observer gain matrix and the fault estimator gain matrix; calculate the state estimate online based on the observer gain matrix, and extract fault feature information based on the fault estimator gain matrix.

[0012] Furthermore, step 4 specifically includes: Construct an initial error zonotope set based on the initial state uncertainty. ; The set of zonotope generators is obtained by iteratively calculating the shape matrix of the initial error zonotope set using the dynamic expression of the error. ; By reducing the order of the shape matrix of the initial error zonotope set, we obtain a zonotope set containing all possible values ​​of the error. ; Using zonotope generator sets and zonotope set Calculate the set of true states to obtain the final state interval and residual interval.

[0013] Furthermore, step 5 specifically includes: The residual is determined by the intersection of the residual interval and the normal operating threshold interval to detect whether the residual exceeds the limit; Detect whether the state estimate is out of bounds based on whether the state estimate is contained within the state interval; Based on the joint logical judgment of residual out-of-bounds and state estimation out-of-bounds, determine whether a fault has occurred, the fault type, and the time of fault occurrence.

[0014] Furthermore, the joint logic judgment includes: when the residual exceeds the limit and the state estimate exceeds the limit at the same time, it is determined to be a confirmed fault state; When only the residual exceeds the limit or only the state estimate exceeds the limit, it is judged as a suspected fault state and a delayed confirmation mechanism is triggered. When neither the residual nor the state estimate exceeds the limit, it is determined to be in normal operating condition.

[0015] Furthermore, this invention also proposes a wastewater treatment biological process fault detection system based on interval estimation, comprising: The modeling module, based on the activated sludge dynamics model, performs interval processing on nonlinear terms, constructs a TS fuzzy model, and outputs a unified set of linear subsystem matrices. The channel processing module receives wireless measurement signals, models and characterizes channel coefficients, and determines their intervals. Robust observer design provides robust conditions to adapt to the channel fading characteristics of wireless sensor networks. The observer design and operation module is used to design the observer gain, in order to The indicators limit the impact of disturbances, calculate the state estimate and residuals online, and extract fault information; The interval propagation module uses zonotope to represent the set of uncertainties, iteratively updates and reduces the order of the correlation matrix, and outputs the state interval and residual interval. The fault detection decision module uses a combination of residual interval out-of-bounds and state point estimation out-of-bounds criteria to make a joint judgment, and outputs the fault category, fault size and fault occurrence time to achieve fault detection with low false alarms.

[0016] The beneficial effects of this invention are: 1. This invention linearizes nonlinear biological processes based on TS fuzzy modeling, combined with... The robust observer design can still achieve accurate state estimation of key process variables such as dissolved oxygen and substrate concentration even under the presence of model errors, wireless channel fading, external disturbances and measurement noise. Moreover, the state estimation error remains bounded under the condition of bounded disturbances and is not limited by the statistical characteristics of precise noise, thus achieving high-precision and robust state estimation.

[0017] 2. This invention intervalizes the wireless channel coefficients and incorporates them into the LMI design conditions of the robust observer, making the detection method highly robust to wireless sensor network problems such as channel fading and signal packet loss. At the same time, by enveloping various uncertainties through the zonotope interval propagation technique, it effectively resists interference caused by model nonlinearity, parameter fluctuations and external disturbances, ensuring the stability of estimation under channel fading conditions.

[0018] 3. This invention utilizes the zonotope interval propagation technique to generate strict upper and lower bound intervals for states and residuals, providing an accurate envelope description of measurement offsets caused by nonlinear errors, noise, and channel fading. This achieves quantification and constraint of various uncertainties, providing a bounded and provable reliable basis for fault detection. At the same time, the size of the generating matrix is ​​controlled by a reduction-order algorithm, ensuring the real-time performance of interval calculations.

[0019] 4. This invention adopts a dual-criteria fault decision mechanism, which is based on residual interval detection as the main criterion and state point estimation over-limit detection as the auxiliary criterion. Residual interval detection can effectively distinguish between random noise disturbances and equipment abnormalities, and is sensitive to faults of sudden changes, small offsets, and slow drifts. State point estimation over-limit detection can provide early warning for chronic offset faults. The combination of the two enables rapid fault identification, and the decision strategy of dual-condition joint confirmation greatly reduces the false alarm rate caused by sensor noise and instantaneous jitter, and can also accurately output the fault type, size, and occurrence time.

[0020] 5. The method proposed in this invention has controllable computational complexity, and the design of each module takes into account the requirements of real-time online operation. It can be engineered and deployed in the intelligent monitoring system of sewage treatment plants. At the same time, it is compatible with various sewage treatment biological treatment units such as activated sludge systems, oxidation ditches, and biological filters. It is also suitable for new sewage treatment plant architectures such as wireless sensor networks and low-power monitoring systems, and has a wide range of practical application scenarios. Attached Figure Description

[0021] Figure 1 This is a flowchart of a wastewater treatment biological process fault detection method based on interval estimation; Figure 2 A plot showing the point estimation results for the state estimation; Figure 3 The graph shows the interval estimation results for state variable 1; Figure 4 The graph shows the interval estimation results for state variable 2; Figure 5 The graph shows the interval estimation results for state variable 3; Figure 6 The point estimation results for fault 1 are shown in the image. Figure 7 This is a diagram showing the fault detection results estimated using state points. Figure 8 The image shows the residual detection results for fault 1. Figure 9 The image shows the residual detection results for fault 2. Figure 10 This is a structural block diagram of a wastewater treatment biological process fault detection system based on interval estimation. Detailed Implementation

[0022] like Figure 1 As shown in the figure, the steps of the wastewater treatment biological process fault detection method based on interval estimation described in this embodiment include: S1: TS fuzzy modeling; S101: Determine the prerequisite variables and define their upper and lower bounds based on engineering experience: Microbial specific growth rate: (1); Activated sludge biomass: (2); Returned activated sludge biomass: (3); Organic substrate concentration: (4); In formulas (1)-(4), Let be the time-varying range variable of the specific growth rate of microorganisms. For the time-varying range of activated sludge biomass, The time-varying range of the biomass of the returned activated sludge is a variable. For the time-varying range of organic substrate concentration, , , and All of these are key state variables that can be estimated for the wastewater treatment system. , , and These are the upper and lower bounds of each prerequisite variable under normal operating conditions, determined by the operating experience and historical data of the wastewater treatment process. They are used to divide the interval of the fuzzy membership function and are the basic boundary constraints for constructing the TS fuzzy model.

[0023] By dividing each variable into two intervals (high / low), we can obtain 2³=8 premise regions, each region corresponding to a unique set of TS linear subsystems.

[0024] S102: Linearize the system model for each combination of premise variables, and obtain: (5); In formula (5), and This is the system matrix after linearization within the given region. Represents the premise variable under the e-th rule. Fuzzy membership degree, p This indicates a fuzzy membership relationship between the premise variables. This indicates the number of fuzzy rules.

[0025] S103: Fuzzy weight design; The T–S model combines multiple sub-models using a weighted average method, with weights... satisfy: (6); In this implementation, a piecewise linear membership function is used: (7); In formula (7), Prerequisite variables The upper realm, Prerequisite variables The lower bound.

[0026] The final combined weight of each rule is the product of the membership degrees of each component: (8); As can be seen from the above, the design of the TS fuzzy model has the advantages of low computational cost and easy real-time implementation.

[0027] S104: The final T–S model takes the form of: (9); In formula (9), For the first The state matrix corresponding to each fuzzy rule describes the state. State at the next moment The dynamic impact, For the first The input matrix corresponding to each fuzzy rule describes the control input. State at the next moment The function, This is a fuzzy antecedent variable used to trigger fuzzy rules and determine the activation level of each rule. To control the input vector, at time... External control signals applied to the system are used to regulate the system state.

[0028] This form facilitates integration with robust observers and can be directly used as the output of the modeling module of this invention.

[0029] S2: Robust observer design; S201: Observer design objectives; Channel fading exists in wireless sensor networks Measurement noise, model uncertainty, disturbance In this case, the device needs to construct an observer that can simultaneously satisfy the following conditions: The state estimation error remains bounded under the condition that the disturbance is bounded; The magnitude of the error relative to the disturbance satisfies Maximum gain constraint in the sense of the case; For channel fading parameters The changes are robust; It can still work stably without relying on precise noise statistics; It can run online in real time with controllable computational complexity.

[0030] To achieve the above objectives, the following observer is constructed: (10); In formula (10), To output the estimation error vector That is, representing the actual system output. With observer estimated output The deviation between them is used to correct the state estimate. The system state estimation vector represents the true system state. The real-time estimate is generated iteratively by the observer. The fuzzy antecedent variable estimation vector is the basis for estimating the premise variables of the TS model. The estimate is used to calculate the activation weights of each fuzzy rule. This is the actual fault vector, representing an unknown fault occurring in the system. The fault estimation vector is the observer's estimate of the actual fault. Real-time estimates, The nominal state matrix, This is the nominal input matrix.

[0031] S202: Derivation of the dynamic error model; Define error: (11); Substituting the actual system model and the observer into the equation, we can obtain the error dynamics: (12); In formula (12), , The weighted error term for the fuzzy rules is obtained by weighted summation of the state estimation errors and input estimation errors of each fuzzy subsystem. It reflects the impact of fuzzy antecedent variable estimation bias on the dynamics of the state error. For the fault estimation error vector, For the output matrix, for An identity matrix of order 1. The dimension of the fault vector is used to ensure the structural integrity of the fault error dynamic equation. For the first The state-weighted error term of a fuzzy rule consists of the weighted difference between the actual state and the estimated state under their respective fuzzy membership degrees, i.e. , For the first The input weighted error term of the fuzzy rule is obtained by weighting the difference between the control input and the estimated membership degree, i.e. .

[0032] S203: Performance metric settings; To enhance the device's immunity to disturbances and channel uncertainties, this embodiment introduces... Performance constraints: (13); This performance metric indicates that the error must be bounded under finite disturbances.

[0033] S204: The robustness condition is transformed into LMI, where LMI is a linear matrix inequality; To avoid directly analyzing nonlinear terms The complexity will Treating it as an interval-determined parameter, the channel fading effect is transformed into the following matrix inequality form using the convexity principle: This matrix inequality represents that the system satisfies stability and [condition] under all channel conditions. performance.

[0034] To transform matrix inequalities into standard LMIs, the variable substitution method can be used: For the system, the following matrix inequalities should be satisfied: (14); (15); In formulas (14) and (15), , Let be the observer gain matrix that needs to be solved. The observer gain matrix is ​​solved by solving the above matrix inequalities, and then the state-space estimation result is output.

[0035] The principle behind the above conversion is as follows: Constructing Lyapunov functions: (16); According to the Lyapunov function, we can obtain... Since the perturbations studied here are bounded, therefore, By giving a positive definite constant The increment of the Lyapunov function can be obtained as follows: (17); Right now ,in, ,and , ; Next, let , Applying Schul's complement lemma to linear matrix inequalities can transform them into... and .

[0036] Furthermore because It is positive, so we can obtain it. Based on this, we can recursively derive the following: .

[0037] Finally, multiply the left and right sides of the LMI infinitive respectively. , And its transpose, we can obtain Therefore, it can be concluded that the error dynamic system in step three satisfies... Performance, proof complete.

[0038] S205: The matrix to be solved and the solution method; Given the LMI, solve the following matrix: P1: Lyapunov matrix of the error system; P2: stability matrix used for the fault estimator; H: Intermediate variable corresponding to observer gain L; S: Intermediate variable corresponding to fault estimation Γ; Final result: Observer gain matrix and .

[0039] S3: Interval propagation design to obtain the state interval and residual interval; This step comprehensively details the mathematical foundation, set operation rules, error propagation process, and engineering implementation of the interval propagation module, enabling the device to obtain a rigorous, bounded, and provable state interval estimate under conditions of model uncertainty, channel fading error, and noise, providing a reliable basis for subsequent fault detection.

[0040] To facilitate subsequent fault detection, when no fault exists, the system state error is... satisfy: (18); The following Lipschitz condition is proposed for nonlinear systems. Furthermore, it is assumed that both the disturbance and the nonlinear effects are unknown but bounded.

[0041] Next, the initial interval set is used to construct the initial state of the system. The initial state is usually uncertain and can be represented using zonotope, let... , The initial error is contained within the area specified below: Therefore, the error is included in zonotope. .

[0042] Using the known dynamic expression of the error, the shape matrix of the error is then iteratively calculated. After order reduction, its zonotope can be expressed as

[0043] The method for calculating the final state interval is by and The set of actual states can be obtained as follows: (19); S4: Establish a dual fault detection strategy and output the fault category, fault size, and fault occurrence time; This step comprehensively expands the logical structure, detection criteria, interval fusion method, and final alarm mechanism of the fault detection module, so that the detection results still have high reliability, low false alarm rate, and engineering availability under complex conditions such as model uncertainty, channel fading, and external disturbances.

[0044] S401: Residual interval detection; Residual interval detection is the primary detection method, which uses the generated residual intervals. It can provide an envelope description of the measurement offset caused by nonlinear errors, noise, and channel fading. If the actual residual given by the observer... If it exists This indicates that the actual residual exceeds "all possible fluctuation ranges under normal operating conditions"; the out-of-bounds error cannot be explained by noise, disturbance, or modeling error; and a persistent structural deviation has occurred, which is a strong indication of a fault.

[0045] The advantages of this method are: it is based on set reasoning and does not rely on the statistical characteristics of noise; it is sensitive to abrupt changes, small offsets, and slow drifts; and it can distinguish between "random noise disturbances" and "equipment malfunctions". Therefore, residual interval detection is used as the main fault judgment basis of this device.

[0046] S402: State point estimation out-of-bounds detection; State point estimation and out-of-bounds detection are used as auxiliary detection methods to enhance robustness, while the interval propagation module generates state intervals. , and state point estimation Comparison: If If the following conditions are met, it is considered that: the state point estimation is inconsistent with the error range; the deviation exceeds the allowable range of error dynamics; the system may have sensor bias, actuator malfunction, process instability, or other issues.

[0047] The characteristics of this auxiliary detection method are: it is extremely sensitive to "chronic drift faults"; it can provide early warning when the residual is relatively stable but the state estimation drifts slowly; and it can be used as a supplement to residual detection to improve overall reliability.

[0048] S403: Final multi-criteria decision-making strategy; To avoid false alarms caused by sensor noise, momentary jitter, etc., this device adopts the following comprehensive decision-making mechanism: simultaneous abnormality of two conditions → immediate fault confirmation. If the residual interval exceeds the limit and the state estimate also exceeds the limit, then both independent signals point to an anomaly, which is a strong confidence fault and does not require delayed confirmation.

[0049] In addition, such as Figure 10 The embodiment shown also proposes a wastewater treatment biological process fault detection system based on interval estimation, including: a modeling module, a channel processing module, an observer design and operation module, an interval propagation module, and a fault detection decision module.

[0050] The modeling module uses an activated sludge kinetic model, which involves processes such as substrate degradation, microbial proliferation, and oxygen consumption. Nonlinear terms (such as Monod dynamics) are intervalized; Multiple T–S fuzzy sub-models were constructed based on key process variables (dissolved oxygen, substrate concentration, sludge concentration, etc.); Output a set of linear subsystem matrices with a uniform output form. .

[0051] The channel processing module receives measurement signals from the wireless sensor. ; Channel coefficient Represented by periodic or stochastic models, such as ; Determine the channel interval based on the maximum / minimum value. ; Robust design conditions for subsequent L∞ observers.

[0052] The observer design and operation module designs a unified observer gain L based on the averaging model; The maximum impact of disturbances on the estimation error is limited by the L∞ index; Online calculation of state estimates and residual ; Introducing a fault estimator Extract fault information.

[0053] The interval propagation module uses zonotope (center O and generating matrix Z) to represent the set of uncertainties; Establish a dynamic interval mapping relationship for the error to achieve iterative updates of the centroid and the generating matrix; The size of the generated matrix is ​​controlled by a reduction-order algorithm to ensure real-time computing capabilities; Output state range and residual range.

[0054] If the residual interval does not intersect with the normal threshold, the fault detection decision module will trigger an anomaly. If state point estimation Exceeding the upper / lower bound of the interval also triggers an exception; Both are used together to give the final conclusion; Output the fault type, fault size, and fault occurrence time.

[0055] To verify the effectiveness of the proposed method, the following simulation experiments were conducted, and the state estimation point estimation results are as follows: Figure 2 As shown, Figure 2 The comparison between the actual system state and the observer's estimate is shown in the figure, demonstrating that the robust observer designed in this invention can still quickly track the actual state under conditions of channel fading, model uncertainty and external disturbances, and has high-precision and robust state estimation capabilities.

[0056] The interval estimation results for state variable 1 are as follows: Figure 3 As shown, Figure 3It includes the true state value, the point estimate, and the upper and lower bound intervals of the state obtained by propagation from the Zonotope interval. This indicates that under normal operating conditions, the true state is always contained within the estimation interval. The interval can effectively enclose noise, disturbances, and modeling errors, providing a reliable boundary basis for fault detection.

[0057] The interval estimation results for state variable 2 are as follows: Figure 4 As shown, by Figure 4 The estimation results show that the interval estimation method proposed in this invention can stably constrain the range of state fluctuations and maintain interval compactness and effectiveness under the uncertainty of wireless sensing measurement.

[0058] The interval estimation results for state variable 3 are as follows: Figure 5 As shown, Figure 5 The model presents the correspondence between the true state, point estimate, and interval boundary, demonstrating that the proposed Zonotope interval propagation algorithm can accurately describe the impact of uncertainty and achieve bounded, provable interval estimation of state variables.

[0059] The point estimation results for fault 1 are as follows Figure 6 As shown, Figure 6 The comparison between the actual fault and the observer's fault estimate is shown in the figure, demonstrating that the fault estimator of the present invention can quickly and accurately reconstruct the fault signal, providing support for subsequent determination of fault size and occurrence time.

[0060] Figure 7 To assess the fault detection performance using the state point estimation over-boundary criterion. Figure 7 The time when the estimated state point exceeds the interval boundary corresponds to the actual time of the fault occurrence, indicating that state out-of-bounds detection can effectively warn of slow drift faults and can be used as an auxiliary criterion to improve detection sensitivity and advance warning.

[0061] The residual detection results for fault 1 are as follows: Figure 8 As shown, Figure 8 The system displays the real-time residual value and the normal operating residual range. When a fault occurs, the residual exceeds the boundary of the normal range, enabling accurate fault identification and verifying that the residual range criterion is highly sensitive to sudden faults.

[0062] The residual detection results for fault 2 are as follows: Figure 9 As shown, Figure 9 The data shows that the residual error significantly deviates from the normal fluctuation range after the fault occurs, indicating that the residual detection method of the present invention has a stable and reliable detection capability for different types of faults, reducing false alarms and false negatives.

[0063] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any way. Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make some modifications or alterations to the above-disclosed technical content to create equivalent embodiments without departing from the scope of the present invention. Any simple modifications, equivalent substitutions, and improvements made to the above embodiments without departing from the scope of the present invention, based on the technical essence of the present invention and within the spirit and principles of the present invention, shall still fall within the protection scope of the present invention.

Claims

1. A method for fault detection in wastewater treatment biological processes based on interval estimation, characterized in that, include: Step 1: Based on the kinetic characteristics of the wastewater treatment biological process, establish a TS fuzzy model to describe the nonlinear dynamics of the system; Step 2: Determine the range of variation of the channel coefficients based on the channel fading characteristics of the wireless sensor network; Step 3: Based on the TS fuzzy model and the range of variation of the channel coefficients, design... Robust observers are used to obtain state estimates and residuals; Step 4: Based on the state estimate and the residual, calculate the state interval and residual interval using the Zonotope ensemble propagation algorithm; Step 5: Based on the comparison results between the residual interval and the preset threshold, and the inclusion relationship between the state estimate and the state interval, jointly output the fault category, fault size, and fault occurrence time.

2. The wastewater treatment biological process fault detection method based on interval estimation according to claim 1, characterized in that, Step 1 specifically includes: Based on engineering experience, the upper and lower bounds of variables are defined, including microbial growth rate, activated sludge biomass, returned activated sludge biomass, and organic substrate concentration. Each variable is divided into two intervals, high and low, to obtain multiple premise regions, where each premise region corresponds to a set of TS linear subsystems. Based on the local linearization results within each premise region, construct the corresponding TS linear subsystem; The weights of each fuzzy subsystem are calculated based on the piecewise linear membership function, and the global TS fuzzy model is obtained by weighted averaging. .

3. The wastewater treatment biological process fault detection method based on interval estimation according to claim 1, characterized in that, Step 2 specifically includes: Establish an observer and define the error, receive measurement signals from wireless sensors, substitute the actual system model and the observer into the defined error, and obtain the error dynamics. Introducing in error dynamics Performance constraints, establish Performance metrics determine the range of variation of the channel coefficients.

4. The wastewater treatment biological process fault detection method based on interval estimation according to claim 1, characterized in that, Step 3 specifically includes: Nonlinearity in the system As an interval uncertainty parameter, a Lyapunov function is constructed to analyze the stability of the error system; the channel fading effect is transformed into a matrix inequality form based on the convexity principle of the channel coefficient interval; and the matrix inequality is transformed into a standard linear matrix inequality that can be solved numerically through the variable substitution method and Schur complement lemma. Solve the linear matrix inequalities to obtain the observer gain matrix and the fault estimator gain matrix; calculate the state estimate online based on the observer gain matrix, and extract fault feature information based on the fault estimator gain matrix.

5. The wastewater treatment biological process fault detection method based on interval estimation according to claim 1, characterized in that, Step 4 specifically includes: Construct an initial error zonotope set based on the initial state uncertainty. ; The set of zonotope generators is obtained by iteratively calculating the shape matrix of the initial error zonotope set using the dynamic expression of the error. ; By reducing the order of the shape matrix of the initial error zonotope set, we obtain a zonotope set containing all possible values ​​of the error. ; Using zonotope generator sets and zonotope set Calculate the set of true states to obtain the final state interval and residual interval.

6. The wastewater treatment biological process fault detection method based on interval estimation according to claim 1, characterized in that, Step 5 specifically includes: The residual is determined by the intersection of the residual interval and the normal operating threshold interval to detect whether the residual exceeds the limit; Detect whether the state estimate is out of bounds based on whether the state estimate is contained within the state interval; Based on the joint logical judgment of the residual out-of-bounds and the state estimation out-of-bounds, determine whether a fault has occurred, the fault type, and the time of fault occurrence.

7. The wastewater treatment biological process fault detection method based on interval estimation according to claim 6, characterized in that, The joint logic judgment includes: when the residual exceeds the limit and the state estimate exceeds the limit at the same time, it is determined to be a confirmed fault state; When only the residual exceeds the limit or only the state estimate exceeds the limit, it is judged as a suspected fault state and a delayed confirmation mechanism is triggered. When neither the residual nor the state estimate exceeds the limit, it is determined to be in normal operating condition.

8. A wastewater treatment biological process fault detection system based on interval estimation, applied to the wastewater treatment biological process fault detection method based on interval estimation as described in any one of claims 1-7, characterized in that, include: The modeling module, based on the activated sludge dynamics model, performs interval processing on nonlinear terms, constructs a TS fuzzy model, and outputs a unified set of linear subsystem matrices. The channel processing module receives wireless measurement signals, models and characterizes channel coefficients, and determines their intervals. Robust observer design provides robust conditions to adapt to the channel fading characteristics of wireless sensor networks. The observer design and operation module is used to design the observer gain, in order to The indicators limit the impact of disturbances, calculate the state estimate and residuals online, and extract fault information; The interval propagation module uses zonotope to represent the set of uncertainties, iteratively updates and reduces the order of the correlation matrix, and outputs the state interval and residual interval. The fault detection decision module uses a combination of residual interval out-of-bounds and state point estimation out-of-bounds criteria to make a joint judgment, and outputs the fault category, fault size and fault occurrence time to achieve fault detection with low false alarms.

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