A method for multiplicative fault detection based on polytope filtering under random bit flips

Abstract

The application discloses a multiplicative fault detection method based on polytope filtering under random bit flip, and belongs to the technical field of networked system fault diagnosis. The method considers the occurrence of multiplicative fault, introduces the theory of fully symmetric polyhedral set member filtering, establishes a measurement output mathematical model containing random bit flip, further deduces a state estimation error dynamic equation and an error polytope recursion evolution law, and designs an interval state observer. Then, the minimum polytope radius in the normal working mode is taken as an optimization index to analytically solve an optimal observer gain matrix, so as to weaken the influence of unknown disturbance and quantization error on state estimation. Finally, a prediction output consistency set and a nominal state evolution interval are respectively constructed, which not only can accurately identify the random bit flip jump in the channel, but also realizes the joint discrimination of the multiplicative fault of the physical system, and effectively guarantees the robustness and reliability of the fault detection of the complex networked system.

Description

Technical Field

[0001] This invention relates to the field of fault diagnosis technology for networked systems, and in particular to a multiplicative fault detection method based on multicell filtering under random bit flipping. Background Technology

[0002] In networked systems, sensors, controllers, and actuators exchange information via a shared communication network. Due to bandwidth limitations, measurement signals typically require quantization and binary encoding before transmission. This process inevitably introduces quantization errors, and under the influence of electromagnetic interference, signal attenuation, and multipath effects, transmitted bits may randomly flip, causing the decoded measurement value at the receiving end to deviate from the true measurement value.

[0003] Existing research mainly focuses on improving the accuracy of state estimation and designing anti-disturbance filters, with insufficient attention paid to fault detection problems caused by quantization errors and random bit flipping coupling. Especially in industrial process systems, system parameters are affected by component aging, actuator performance degradation, and environmental changes, making them prone to multiplicative faults. Traditional detection methods based on fixed threshold residuals are susceptible to communication anomalies and bounded disturbances, posing a risk of false alarms or missed alarms.

[0004] The fully symmetric polytopic set-membership filtering method does not rely on the exact statistical distribution assumptions of external disturbances. Under conditions where process disturbances and measurement noise are unknown but bounded, it can efficiently and compactly provide the set envelope of system states through fully symmetric polytopes. Compared to traditional filtering and general set-membership estimation methods, fully symmetric polytopic set-membership filtering not only exhibits strong robustness to bounded noise but also significantly reduces the computational complexity and conservatism of high-dimensional state estimation due to its unique geometric and algebraic operational properties. Applying this method to fault detection in networked systems, it can directly utilize the dynamic state interval boundaries provided by the fully symmetric polytope, effectively improving the system's resistance to and ability to distinguish between communication anomalies and its own multiplicative faults.

[0005] Therefore, it is crucial to develop an integrated detection method that can uniformly consider the effects of process disturbances, measurement noise, quantization errors, and random bit flips, and achieve both bit flip detection and multiplicative fault discrimination. Summary of the Invention

[0006] In view of the above problems, this invention provides a multiplicative fault detection method based on multicellular filtering under random bit flipping, and studies the cooperative detection problem of multiplicative faults in networked uncertain systems with quantization errors and random bit flipping. By introducing the relevant theory of fully symmetric multicellular set-membership filtering, a feasible set surrounding the true state of the system and the predicted values ​​of the measured output is generated. A class of fully symmetric multicellular state observers is designed, and then the dynamic equation of the state estimation error and the expression of the recursive evolution of the error multicellular body are derived, transforming the anti-interference problem of the system against unknown disturbances and quantization errors into the multicellular body problem. - Radius minimization problem. Based on the above modeling and derivation, the geometric algebraic properties of fully symmetric multicellular structures are utilized... - Radius optimization theory provides a rigorous mathematical proof and guarantee for improving the robustness of state estimation accuracy by analytically solving the optimal observer gain matrix. At the same time, the predicted output set and nominal state evolution interval constructed by this method can effectively distinguish and detect bit flips and system-level multiplicative faults in the communication channel.

[0007] To achieve the above objectives, the technical solution adopted by the present invention is as follows: In a first aspect, the present invention provides a multiplicative fault detection method based on multicell filtering under random bit flipping, comprising the following steps: Step 1: Construct discrete-time linear system models existing under different operating modes, and define the system's state vector. Measurement output vector Given the input vector Unknown but bounded process perturbation vector and measurement noise vector Modeling; Step 2: For networked transmission scenarios, a probabilistic uniform quantizer is introduced to quantize and binary encode the measured output signal, and a mathematical model of the receiver's measurement output, including random bit-flipping interference, is established to obtain the actual measured value at the receiver. ; Step 3: For the system models in Step 1 and Step 2, construct a state observer based on fully symmetric multicellular set-membership filtering, and obtain the estimated value of the system state based on the observer. Solve the dynamic equations of the state estimation errors by combining the system model and the observer model, and derive the set of state estimation errors using the properties of fully symmetric multiple cells. The recursive evolution law is used to obtain the upper and lower bound estimates of the system state; Step 4: Based on multicellular structures - The radius minimization criterion is derived to minimize the estimation error in multiple cells. of - Observer gain matrix with radius minimized in normal operating mode The optimal solution expression is obtained to reduce the impact of unknown disturbances and quantization errors on state estimation; Step 5: Based on the observer, calculate Predicted set of time measurement output By judging the measured value at the receiving end Design bit flip detection logic to determine whether the bit is included in the prediction set; Step Six: Using the open-loop state simulator under normal operating conditions, generate the nominal state boundary for normal system operation. By judging the system state estimate calculated in step three If the nominal state boundary is exceeded, execute the fault detection logic based on state interval consistency to complete the determination of multiplicative faults in the system.

[0008] In one embodiment of the present invention, the discrete uncertain system models constructed in step one under different operating modes are shown below: (1) in, This indicates that the system is in different operating modes. At that time, the system was normal, when Other values ​​indicate that a corresponding fault has occurred in the system, assuming that the system may have [faults / problems]. Different working modes Represents positive integers. It is the set of positive integers; Represents the state vector of the system. This represents the system's measurable output vector. Represents the input vector; To satisfy unknown but bounded conditions for process perturbation; This represents measurement noise that satisfies unknown but bounded conditions. All are constant matrices of known dimension for the system under different operating modes; furthermore... Let be the dimension of the system state vector. Let be the dimension of the input vector. The dimension of the measurable output. Let be the dimension of the perturbation of the unknown process. The dimension of the measurement noise is unknown. It is represented as a real number field in Euclidean space; meanwhile, the faults that occur in the system are introduced into the system in the form of multiplicative faults, specifically manifested as different constant parameter matrices in different operating modes of the system. Only when When the system is in normal working mode, it is in normal working mode. In other states, the system is in different fault modes.

[0009] In one embodiment of the present invention, the method assumes an initial state in system equation (1). System process disturbance and measuring noise It is unknown but bounded, and is constrained by the corresponding fully symmetric multicellular structure: (2) in, It is a positive integer. Given the known initial values ​​of the system state, , and Given a matrix of known dimensions, and , and All are known fully symmetrical multicellular organisms.

[0010] In one embodiment of the present invention, step two involves introducing a probability uniform quantizer to quantize and binary encode the measurement output signal, and obtaining the actual measurement value at the receiving end. The specific process is as follows: The probabilistic uniform quantizer discretizes the measured output data, assuming the system output... All elements are within the measurement range Inside, among them, , Given a constant real number, use bits. The binary bitstream data represents the measurement data, then Bit-bit binary stream representation Each discrete value, with different quantized values ​​represented as follows: (3) in, Given a set, The quantized values ​​are uniformly distributed. Therefore, the quantizer will measure the interval Divided into equal parts There are n sub-intervals, each with a length of n. ; For measurement output The element There must exist positive integers. , making If true, the probability uniform quantizer will Quantified as and The probabilities are as follows: (4) in, and , The first measurement output after quantization There are elements, and the quantized measurement output is represented as ; After quantization, a binary encoding mechanism is used to... Encode the data to obtain a binary bit stream. as follows: (5) in, Represents a single bit after encoding. Bit data makes up a binary bit stream. , Determined by the following formula: (6) Define quantization error vector as follows: (7) According to equation (4), the quantization error vector It is bounded and can be multicellular. Surrounded by, among ; Then, the binary bit stream is transmitted through a binary symmetric channel. In actual wireless or wired channel transmission, due to electromagnetic interference, signal attenuation, etc., some bits may randomly jump with a very small probability. The received binary bit stream data is represented as follows: (8) in, This represents the bits after transmission through the channel. Let be a random variable that follows a Bernoulli distribution, and Its physical meaning is: (9) According to equation (8), the actual measurement output vector after decoding at the receiving end is... Represented as: (10).

[0011] In one embodiment of the present invention, step three includes: To mitigate the impact of unknown disturbances on state estimation, the state estimation observer is designed as follows: (11) in, State vector The estimated value, The parameters of the observer to be designed; Define the state estimation error vector as Considering The recursive formula for the dynamic error is as follows: (12) Introducing the theory of fully symmetric multicellular set-membership filtering, assuming The time-state estimation error vector satisfies ,in, for The time step contains the state error vector A fully symmetrical multicellular body Multicellular The center vector, Multicellular Given a generating matrix of known dimension, then in At time t, the state estimation error vector Will be included in multicellular bodies In this context, the recursive formulas for calculating the center vector and the generating matrix are as follows: (13) in, Unknown disturbances in the system A generating matrix of known dimensions. Unknown measurement noise in the system A generating matrix of known dimensions. for Time-generating matrix The matrix after dimensionality reduction operator processing They are respectively The center vector and generating matrix at time t, and also at the initial time. At that time, the observer's initial value was set to Then, from equation (2), we can see that the initial error vector satisfy ; Based on error multicell description System state vector The upper and lower bound estimates are calculated as follows: (14) At this point, the actual system state satisfies ; where vector The Each component is defined as the generating matrix. The sum of the absolute values ​​of the corresponding rows, i.e. ,in To generate the matrix The number of columns, They are respectively Time-state vector The lower and upper bound estimates.

[0012] In one embodiment of the present invention, step four involves making the estimation error multicell... of - Observer gain matrix with radius minimized in normal operating mode The expression is as follows: Define performance metrics ,in, The trace of the matrix is ​​given when the system is in normal operating mode, i.e. At that time, The formula for obtaining the optimal observer gain matrix with the smallest radius is: (15) in, auxiliary matrix and The definition is as follows: (16).

[0013] In one embodiment of the present invention, the bit flip detection logic designed in step five is specifically as follows: Predicted set of time measurement output Represented by a fully symmetrical multicellular structure, i.e. Its center vector and generating matrix It is calculated by the following formula: (17) In addition, a bit flip detection flag is designed. The logic is as follows: (18) When the measured value at the receiving end meets hour, The signal is determined to have not undergone bit flipping during transmission; when hour, The signal is determined to have undergone random bit flipping.

[0014] In one embodiment of the present invention, the execution of fault detection logic based on state interval consistency in step six specifically includes: The system is in normal working mode, that is... An open-loop state simulator is used to generate the nominal state boundaries of the system when no faults occur. : (19) in, They are respectively The estimated values ​​of the state bound and upper bound of the time-limited system in normal operating mode. This is the observer state estimation vector in normal mode. These are the center vector and error range vector of the error multicell in normal mode, respectively; In addition, design fault detection flags. The logic is as follows: (20) When the observer estimates the state, it satisfies hour, The system is determined to be operating without faults; when hour, The system was determined to have a multiplicative fault.

[0015] In a second aspect, the present invention provides a computer-readable storage medium storing computer instructions which are executed by a processor using the method described above.

[0016] Thirdly, the present invention provides a computer program product storing computer instructions, which are executed by a processor using the method described above.

[0017] The beneficial effects achieved by this invention are as follows: 1. In designing the fault detection algorithm, this invention takes into account the random bit flipping phenomenon that may occur during the transmission of the measurement signal in the network channel, which has a positive effect on reducing the false alarm rate of remote fault detection in the control system.

[0018] 2. This invention utilizes the multi-cell set member estimation theory to propose collaborative detection methods for faults and bit flips based on state interval consistency and output consistency, respectively. This has important theoretical guiding significance for improving the physical integrity and information security of industrial control systems.

[0019] 3. This invention optimizes the state estimation error multicell. - The expression for the observer gain is derived from the radius, which not only facilitates the theoretical design of observation parameters, but also provides technical support for improving the accuracy of fault detection.

[0020] In summary, this invention addresses networked systems exhibiting quantization errors and random bit flipping by constructing a fully symmetric multi-cell set-member state observer and utilizing... - The radius minimization filtering method is used to optimize the observer gain design, achieving high-precision estimation of the upper and lower bounds of the system state. At the same time, by using multi-cell filtering theory, the measurement output prediction consistency set and nominal state evolution interval are designed. This not only accurately detects random large-value bit flips and jumps in the channel, but also successfully decouples communication anomalies and multiplicative faults in the physical system and achieves joint discrimination, greatly improving the reliability and robustness of fault diagnosis in complex networked systems. Attached Figure Description

[0021] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the embodiments of the present invention will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the drawings without creative effort.

[0022] Figure 1 This is a flowchart of the multiplicative fault detection method based on multicell filtering under random bit flipping according to the present invention.

[0023] Figure 2 This is a comparison diagram of different states of the networked system of the present invention and their nominal state upper and lower bound estimates.

[0024] Figure 3 This is a comparison diagram of the quantized and decoded measurement output data of the networked system of the present invention.

[0025] Figure 4 This is a timing diagram of the fault detection results of the present invention.

[0026] Figure 5 This is a timing diagram of the bit flip detection results of the present invention. Detailed Implementation

[0027] The embodiments of the technical solution of the present invention will now be described in detail with reference to the accompanying drawings. These embodiments are merely illustrative of the technical solution of the present invention and are therefore intended to limit the scope of protection of the present invention.

[0028] Unless otherwise defined, all technical and scientific terms used in this invention have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains; the terminology used in this invention is for the purpose of describing particular embodiments only and is not intended to limit the invention; the terms “comprising” and “having”, and any variations thereof, in the specification, claims and foregoing description of the drawings are intended to cover non-exclusive inclusion.

[0029] In this invention, the reference to "embodiment" means that a specific feature, structure, or characteristic described in connection with an embodiment may be included in at least some embodiments of the invention. The appearance of this phrase in various places in the specification does not necessarily refer to the same embodiment, nor is it a separate or alternative embodiment mutually exclusive with other embodiments. It will be explicitly and implicitly understood by those skilled in the art that the embodiments described in this invention can be combined with other embodiments.

[0030] Example 1: This embodiment provides a multiplicative fault detection method based on multicell filtering under random bit flipping conditions. See [link to relevant documentation]. Figure 1 ,include: Step 1: Construct discrete-time linear system models existing under different operating modes, and define the system's state vector. Measurement output vector Given the input vector Unknown but bounded process perturbation vector and measurement noise vector Modeling; Step 2: For networked transmission scenarios, a probabilistic uniform quantizer is introduced to quantize and binary encode the measured output signal, and a mathematical model of the receiver's measurement output, including random bit-flipping interference, is established to obtain the actual measured value at the receiver. ; Step 3: For the system models in Step 1 and Step 2, construct a state observer based on fully symmetric multicellular set-membership filtering, and obtain the estimated value of the system state based on the observer. Solve the dynamic equations of the state estimation errors by combining the system model and the observer model, and derive the set of state estimation errors using the properties of fully symmetric multiple cells. The recursive evolution law is used to obtain the upper and lower bound estimates of the system state; Step 4: Based on multicellular structures - The radius minimization criterion is derived to minimize the estimation error in multiple cells. of - Observer gain matrix with radius minimized in normal operating mode The optimal solution expression is obtained to reduce the impact of unknown disturbances and quantization errors on state estimation; Step 5: Based on the observer, calculate Predicted set of time measurement output By judging the measured value at the receiving end Design bit flip detection logic to determine whether the bit is included in the prediction set; Step Six: Using the open-loop state simulator under normal operating conditions, generate the nominal state boundary for normal system operation. By judging the system state estimate calculated in step three If the nominal state boundary is exceeded, execute the fault detection logic based on state interval consistency to complete the determination of multiplicative faults in the system.

[0031] Example 2: The definitions, properties, and related lemmas involved in this invention are as follows: Definition 1: Fully symmetrical multicellular structure It is a hypercube exist Void space The mapping on is denoted as: (twenty one) in, Multicellular The center vector, Multicellular The generating matrix. To represent polytopes more concisely, polytopes... Also recorded as .

[0032] Property 1: Two fully symmetrical multicellular bodies and Minkowski and With linear mapping It can be expressed by the following equation: (twenty two) (twenty three) Property 2: Given a Fully symmetrical multicellular structures , ,exist: (twenty four) in, Represents the generating matrix The Line 1 Column elements, Multicellular The center vector.

[0033] Property 3: If it exists ,in If we are a known constant, then Can be multicellular Included, among which , .

[0034] Definition 2: For fully symmetric multicellular organisms ,That - The radius is defined as follows: (25) in, Denotes the Frobenius norm of a matrix. Represents the trace operation of a matrix.

[0035] Lemma 1: Fully Symmetric Multicellular Structures It can be formed by the smallest interval box Includes: (26) in, , It is a diagonal matrix, and its diagonal elements are: , , indicating the generation matrix The absolute values ​​of each row of elements in the matrix are summed to obtain the generating matrix of the interval boxes. .

[0036] Lemma 2: Consider m-order fully symmetric multicells and integers The dimensionality reduction operation is defined as follows: (1) Generate the matrix Arranged in descending order of Euclidean norm, the matrix is ​​obtained. : (27) in, ; (2) When At that time, fully symmetrical multicellular bodies No dimensionality reduction calculation is needed, when hour, Can be a maximum of A fully symmetrical multicellular structure of a dimension includes: (28) in, The matrix after dimensionality reduction.

[0037] To obtain according to Lemma 1 The interval envelope, i.e.: (29) Definition 3: (Matrix Trace Operation) Given a matrix of suitable dimension , , and Then the following operations hold true: (30) This embodiment provides a multiplicative fault detection method based on multicell filtering under random bit flipping conditions. See [link to relevant documentation]. Figure 1 The method includes: Step 1: Establish a class of discrete-time uncertain system models with different operating modes, as shown below: Consider a class of discrete-time linear uncertain systems with unknown but bounded noise and different operating modes: (31) In actual industrial systems, component damage, sudden changes, or environmental factors may cause parameter drift and gain changes; this invention is designed to detect this type of multiplicative fault.

[0038] in, This indicates that the system is in different operating modes. At that time, the system was normal, when Other values ​​indicate that a corresponding fault has occurred in the system. It is a positive integer.

[0039] Assumption 1: The initial state in system equation (31) System process disturbance and measuring noise It is unknown but bounded, and is constrained by the corresponding fully symmetric multicellular structure: (32) in, It is a positive integer. Given the known initial values ​​of the system state, , and Given a matrix of known dimensions, and , and All are known fully symmetrical multicellular organisms.

[0040] Step 2: Model potential quantization errors and random bit flips in networked systems: In networked systems, measurement and control data need to be transmitted via a shared communication network. Due to bandwidth limitations, the transmitted data needs to be quantized and encoded before transmission. A probabilistic uniform quantizer is used to discretize the sensor measurement output. Assuming the system output... All elements are within the measurement range In, among them, , Given a constant real number, use bits. The binary bitstream data represents the measurement data, then A bit-bit binary stream can represent A discrete value, and different quantized values ​​can be represented as follows: (33) in, Given a set, The quantized values ​​are uniformly distributed. Therefore, the quantizer will measure the interval Divided into equal parts There are n sub-intervals, each with a length of n. ; For measurement output The element There must exist positive integers. , making If true, the probability uniform quantizer will Quantified as and The probabilities are as follows: (34) in, and , The first measurement output after quantization There are elements, and the quantized measurement output can be represented as ; After quantization, a binary encoding mechanism is used to... Encode the data to obtain a binary bit stream. as follows: (35) in, Represents a single bit after encoding. Bit data makes up a binary bit stream. , It can be determined by the following formula: (36) Note 1: Rational numbers Indicates the measurement output signal The element In the Each interval is quantized to the right boundary. The probability when measuring the output signal Approaching the right boundary At that time, its left boundary As the distance increases, the rational number... Size increases, Quantified as The probability increases, and vice versa; Define quantization error vector as follows: (37) for From the probability quantization principle (34), we know that: (38) According to equation (37), the error vector Each component Therefore, the error vector From property 3, we know that the quantization error vector It is bounded and can be multicellular. Surrounded by, among ; Then, the binary bit stream is transmitted through a binary symmetric channel. In actual wireless or wired channel transmission, due to electromagnetic interference, signal attenuation, and other factors, some bits may randomly change with a very small probability. The received binary bitstream data can then be represented as follows: (39) in, This represents the bits after transmission through the channel. Let be a random variable that follows a Bernoulli distribution, and Its physical meaning is: (40) According to equation (8), the actual measurement output vector after decoding at the receiving end is... It can be represented as: (41) Step 3: Introduce the theory of fully symmetric multicellular set-membership filtering, establish a state estimation observer, and obtain the upper and lower bounds of the state estimation: To mitigate the impact of unknown disturbances on state estimation, the state estimation observer is designed as follows: (42) in, State vector The estimated value, The parameters of the observer to be designed; Define the state estimation error vector as Considering The recursive formula for the dynamic error is as follows: (43) Using the theory of fully symmetric multicell set-membership filtering, it is assumed that The time-state estimation error vector satisfies ,in, for The time step contains the state error vector A fully symmetrical multicellular body Multicellular The center vector, Multicellular Given the known dimension of the generating matrix, according to equation (43), the state estimation error vector is... yes The linear transformation of and the superposition of several bounded perturbation terms, then in Time, including multicellular The following can be calculated: (44) To ensure that the number of columns in the generated matrix does not increase too rapidly over time, it is necessary to optimize the multicellular matrix. Dimensionality reduction is performed, according to Lemma 2. ,in, Given the dimensionality-reduced generating matrix, the center vector can be obtained from equation (44) using property 1. and generating matrix The recurrence relation is as follows: (45) in, Unknown disturbances in the system A generating matrix of known dimensions. Unknown measurement noise in the system A generating matrix of known dimensions. for Time-generating matrix The matrix after dimensionality reduction operator processing, and also at the initial time... At that time, the observer's initial value was set to Then, from equation (32), we can see that the initial error vector satisfy ; Based on the description of error multicells Property 2, for any point in the multicellular body , its first Each component The upper and lower bounds are determined by the first central vector. Each component and the generating matrix The 1-norm of a row element determines that, ,Right now: (46) make ,in To generate the matrix If the number of columns is given, then equation (46) can be expressed as: (47) According to equation (47), each component of the state error vector Both have upper and lower bounds, and are represented as follows: (48) Combination Then the system state vector The upper and lower bound estimates are calculated as follows: (49) At this point, the actual system state satisfies ;in, They are respectively Time-state vector The lower and upper bound estimates.

[0041] Step 4: Include the state error vector multicellular At every moment -Minimum radius: When the system is running in normal working mode, that is When, define The time step contains the state error vector multicellular of - radius is Using the definition 3 of matrix trace operation, The calculation is as follows: (50) Define auxiliary matrix , , Then equation (50) is calculated as follows: (51) To make the designed state estimation observer as robust as possible to process disturbances and measurement noise, the multicellular... At every moment - The radius needs to be minimized, that is, the objective function needs to be minimized. Let the objective function be... The partial derivatives are zero: (52) The calculation of formula (52) yields: (53) in, Due to the measurement noise generation matrix and quantization error generation matrix It is full rank, and It is a symmetric positive definite matrix, therefore It is also positive definite and invertible, then the observer gain matrix obtained by equation (53) It is a criterion function The only stationary point, and also the only minimum point; Note 2: Step 4 provides a method based on fully symmetric multicellular structures. - The optimal observer design scheme based on the radius minimization criterion can effectively reduce the impact of unknown disturbances on state estimation, improve the accuracy and robustness of state estimation, and use Equation (49) to easily obtain the upper and lower bound estimates of the system state, providing a basis for subsequent fault detection.

[0042] Step 5: Bit Flip Detection and Fault Detection Step 5.1: Bit Flip Detection Mechanism: Since bit flips are instantaneous and involve large value jumps, the measurement data usually deviates significantly from the dynamic prediction range of the system when they occur. Real-time detection of bit flips can be achieved by determining whether the received measurement output is included in the predicted output set. use The state estimation vector output by the time-matter observer is used to construct the prediction set of the measurement output: When the system does not experience bit flipping, the received measurement value Equal to the quantified true measurement value Based on the system equation (31) and the definition of quantization error (37), the following can be calculated: (54) According to the definition of the state error vector Substituting into equation (54), we get: (55) Assumption The state estimation error at time t satisfies Then the predicted output set The following can be calculated using equation (55): (56) The predicted output set can be calculated using property 1. center vector and generating matrix as follows: (57) Based on the above discussion, the bit flip detection logic is defined as follows: (58) When the measured value at the receiving end meets hour, The signal is determined to have not undergone bit flipping during transmission; when hour, The signal is determined to have undergone random bit flipping.

[0043] Step 5.2: Fault Detection Mechanism: Using the nominal state interval of the system in normal working mode as a benchmark, the detection of multiplicative faults is achieved by comparing the estimated state generated by the observer formula (42) with the inclusion relationship of the nominal interval; The system is in normal working mode, that is... An open-loop state simulator is used to generate the nominal state boundaries of the system when no faults occur. : (59) in, They are respectively The estimated values ​​of the state bound and upper bound of the time-limited system in normal operating mode. This is the observer state estimation vector in normal mode. These are the center vector and error range vector of the error multicell in normal mode, respectively; In addition, design fault detection flags. The logic is as follows: (60) When the observer estimates the state, it satisfies hour, The system is determined to be operating without faults; when hour, The system was determined to have a multiplicative fault.

[0044] The multiplicative fault detection method based on multicell filtering under random bit flipping proposed in this invention, considering the quantization error and random bit flipping, as well as bounded disturbances and multiplicative faults in the information transmission process, the designed detection logic formulas (58) and (60) can accurately detect bit flipping and multiplicative faults. The specific implementation method is as follows: To verify the effectiveness and engineering applicability of the fault detection method proposed in this invention, this embodiment uses the classic DTS200 three-tank control system as the verification platform. The three-tank system is a recognized standard benchmark test model in the field of industrial process control and fault diagnosis, which can well simulate the liquid level and flow control process in actual industrial scenarios such as chemical, pharmaceutical and water treatment.

[0045] The system mainly consists of three water tanks connected in series via pipes, and two water pumps providing control inputs to the system. In the physical modeling, the real-time liquid levels of the three water tanks are used as the system's state variables and the sensor's measurement outputs (i.e., the measured analog signals), while the inflow rates of the two water pumps are used as the system's known control inputs. During normal operation, the flow coefficient of the connecting pipes between the water tanks remains constant; however, if the pipes become blocked or leak, it will directly cause changes in the parameter matrix of the system model. This abrupt change in physical parameters is perfectly equivalent to the multiplicative fault of the system targeted by this invention. Its dynamic model can be described as follows: (61) in, These represent the liquid level heights of the three water tanks. The cross-sectional area of ​​the water tank. This refers to the cross-sectional area of ​​the pipes connecting the water tank. Here are the flow coefficients for the three pipes. This represents gravitational acceleration. Table 1 provides the relevant parameters for the three-tank system. Here, we assume that when a system malfunctions, the flow coefficient of the pipes will change, specifically... This can affect the dynamic characteristics of the system.

[0046] Table 1. Parameters of DTS200 Three-Tank System

[0047] System (61) at the open-loop operating point Stable operation, the calculated pump flow rates are as follows: Set the sampling time to The DTS200 system is discretized using a zero-order hold, resulting in a discrete-time state-space model: (62) Among them, control input State vector Measurement output . This indicates that the system is in different operating modes, when At this time, the system is in normal working mode. When a fault occurs, it indicates that a corresponding fault has occurred in the system. The specific parameter matrix is ​​as follows:

[0048] Here we assume the initial state of the system. Process disturbance and measuring noise All are contained in the following multicellular bodies: (63) Furthermore, in networked control scenarios, the continuous analog signals acquired by the level sensor must be digitized and encoded into a binary bit stream by a quantizer before being transmitted to a remote observer / controller via a communication channel. During this process, the transmission of water tank level data is highly susceptible to channel attenuation or electromagnetic interference, resulting in random bit flips and quantization errors.

[0049] Assume the boundary of the measured output signal is The number of bits in the binary code is The corresponding quantization interval is Quantization error Can be multicellular Included. The bit flip probability is set to... The total simulation duration was set to 3000 sampling periods. During the first 1500 sampling periods, the system was in normal operating mode; during the 1501st to 3000th sampling periods, the system experienced a fault and entered fault mode.

[0050] Using MATLAB, we model and analyze equation (31) of a linear discrete-time uncertain system with random bit flips and multiplicative faults. At each time step, we calculate the optimal observer gain according to equation (53). This ensures that the state estimate is robust to unknown but bounded perturbations and quantization errors. The received measurements... Bit flip detection is performed by comparing the predicted output set without bit flips with the set of predicted outputs without bit flips, according to equation (58); the upper and lower bounds of the nominal state estimate are calculated, and the actual state estimate is compared with the nominal state estimate, according to equation (60) for fault detection. Finally, the data required for this embodiment can be obtained, and the specific simulation graphics are as follows. Figures 2 to 5 As shown.

[0051] Multicell filtering theory and multiplicative fault detection technology are applied to a three-tank water system. By setting unknown but bounded process disturbances and measurement noise, and introducing quantization errors and random bit flip signals into the networked system, detection is performed under different operating and fault modes. The results are as follows: Figures 2 to 5 As shown. Figure 2 The figure shows a comparison of different states of a networked system and their nominal state upper and lower bound estimates. Figure 3 This represents a comparison between the quantized data and the received, decoded measurement output data from the networked system. Figure 4 A timing diagram representing the fault detection results. Figure 5 A timing diagram representing the bit flip detection results.

[0052] Considering multiplicative faults occurring in a three-tank system, this study also incorporates quantization errors and potential random bit flips during information transmission. In practical applications, multiplicative faults have a smaller impact on the dynamic evolution of the system compared to other additive fault types, making accurate fault detection inherently difficult. Furthermore, the measurement signal transmission is accompanied by more severe data jump interference such as quantization errors and random bit flips, further increasing the difficulty of fault isolation and detection. However, the simulation results still allow for timely and accurate decoupling and detection of bit flips and multiplicative faults, further confirming the feasibility and applicability of the fully symmetric multicellular state observer constructed in this embodiment. This is precisely because the generator matrix is ​​introduced into the observer design. The radius minimization optimization strategy fully considers the geometric constraints of the multicell radius, resulting in a fault detection observer with strong anti-interference ability and good robustness under the combined effects of unknown but bounded perturbations and complex network anomalies. The simulation study in this embodiment also fully demonstrates the effectiveness of the proposed method for multiplicative fault detection under random bit flipping.

[0053] In summary, the simulation results show that, in the event of random bit flips and physical multiplicative faults in a networked system, the fully symmetric multicellular state observer and joint detection logic designed in this invention can effectively detect bit flips and faults. In actual system operation, the state estimation error multicellular structure employed in this invention... The radius minimization optimization mechanism effectively mitigates the impact of unknown but bounded process disturbances, measurement noise, and quantization errors on state interval estimation, significantly enhancing the robustness of fault detection. Therefore, the detection strategy based on fully symmetric multicellular set-membership filtering can effectively address the complex situation of coexisting network communication anomalies and system multiplicative faults, fully demonstrating the effectiveness of the multiplicative fault detection method and observer design proposed in this invention.

[0054] In some embodiments, the present invention provides a computer-readable storage medium storing computer instructions that are executed by a processor as described in any of the above embodiments, a multiplicative fault detection method based on multicell filtering under random bit flipping.

[0055] Computer-readable storage media can take the form of any combination of one or more readable media. A readable medium can be a readable signal medium or a readable storage medium. A readable storage medium can be, for example, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination thereof. More specific examples of readable storage media (not an exhaustive list) may include: electrical connections having one or more wires, portable disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fibers, portable compact disk read-only memory (CD). ROM), optical storage devices, magnetic storage devices, or any suitable combination thereof.

[0056] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, as well as combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0057] Embodiments of the present invention may also be computer program products, comprising computer program instructions that, when executed by a processor, cause the processor to perform the steps in a multiplicative fault detection method based on multicell filtering under random bit flipping according to various embodiments of the present invention, as described in the "Exemplary Methods" section above.

[0058] The steps of the method of the present invention are not limited to the specific order described above, unless otherwise specifically stated. Furthermore, in some embodiments, the invention may also be implemented as a program recorded on a recording medium, the program comprising machine-readable instructions for implementing the method according to the invention. Therefore, the invention also covers recording media storing programs for performing the method according to the invention.

[0059] Although the invention has been described with reference to preferred embodiments, various modifications can be made and components can be replaced with equivalents without departing from the scope of the invention. In particular, the technical features mentioned in the various embodiments can be combined in any manner as long as there is no structural conflict. The invention is not limited to the specific embodiments disclosed herein, but includes all technical solutions falling within the scope of the claims.

Claims

1. A multiplicative fault detection method based on multicell filtering under random bit flipping, characterized in that, Includes the following steps: Step 1: Construct discrete-time linear system models existing under different operating modes, and define the system's state vector. Measurement output vector Given the input vector Unknown but bounded process perturbation vector and measurement noise vector Modeling; Step 2: For networked transmission scenarios, a probabilistic uniform quantizer is introduced to quantize and binary encode the measured output signal, and a mathematical model of the receiver's measurement output, including random bit-flipping interference, is established to obtain the actual measured value at the receiver. ; Step 3: For the system models in Step 1 and Step 2, construct a state observer based on fully symmetric multicellular set-membership filtering, and obtain the estimated value of the system state based on the observer. ; Solve the dynamic equations of the state estimation error by combining the system model and the observer model, and derive the set of state estimation errors using the properties of fully symmetric polytopes. The recursive evolution law is used to obtain the upper and lower bound estimates of the system state; Step 4: Based on multicellular structures - The radius minimization criterion is derived to minimize the estimation error in multiple cells. of - Observer gain matrix with radius minimized in normal operating mode The optimal solution expression is obtained to reduce the impact of unknown disturbances and quantization errors on state estimation; Step 5: Based on the observer, calculate Predicted set of time measurement output By judging the measured value at the receiving end Design bit flip detection logic to determine whether the bit is included in the prediction set; Step Six: Using the open-loop state simulator under normal operating conditions, generate the nominal state boundary for normal system operation. By judging the system state estimate calculated in step three If the nominal state boundary is exceeded, execute the fault detection logic based on state interval consistency to complete the determination of multiplicative faults in the system.

2. The multiplicative fault detection method based on multicell filtering under random bit flipping according to claim 1, characterized in that, The discrete-case linear uncertain system model constructed in step one is shown below: (1) in, This indicates that the system is in different operating modes. At that time, the system was normal, when Other values ​​indicate that a corresponding fault has occurred in the system. A positive integer, representing the total number of possible failure modes of the system; Represents the state vector of the system. This represents the system's measurable output vector. Represents the input vector; To satisfy the unknown but bounded process perturbation; This represents measurement noise that satisfies the condition of being unknown but bounded. All are constant matrices of known dimension under different modes; furthermore... Let be the dimension of the system state vector. Let be the dimension of the input vector. The dimension of the measurable output. Let be the dimension of the perturbation of the unknown process. The dimension of the measurement noise is unknown. It is represented as a real number field in Euclidean space; meanwhile, the faults that occur in the system are introduced into the system in the form of multiplicative faults, specifically manifested as different constant parameter matrices in different operating modes of the system. Only when When the system is in normal working mode, it is in normal working mode. In other states, the system is in different fault modes.

3. The multiplicative fault detection method based on multicell filtering under random bit flipping according to claim 2, characterized in that, The method assumes that the initial state in system equation (1) System process disturbance and measuring noise It is unknown but bounded, and is constrained by the corresponding fully symmetric multicellular structure: (2) in, It is a positive integer. Given the known initial values ​​of the system state, , and Given a matrix of known dimensions, and , and All are known fully symmetrical multicellular organisms.

4. The multiplicative fault detection method based on multicell filtering under random bit flipping according to claim 3, characterized in that, Step two introduces a probability uniform quantizer to quantize and binary encode the measured output signal, and obtains the actual measured value at the receiving end. The specific process is as follows: The probabilistic uniform quantizer discretizes the measured output data, assuming the system output... All elements are within the measurement range Inside, among them, , Given a constant real number, use bits. The binary bitstream data represents the measurement data, then Bit-bit binary stream representation Each discrete value, with different quantized values ​​represented as follows: (3) in, Given a set, The quantized values ​​are uniformly distributed. Therefore, the quantizer will measure the interval Divided into equal parts There are n sub-intervals, each with a length of n. ; For measurement output The element There must exist positive integers. , making If true, the probability uniform quantizer will Quantified as and The probabilities are as follows: (4) in, and , The first measurement output after quantization There are elements, and the quantized measurement output is represented as ; After quantization, a binary encoding mechanism is used to... Encode the data to obtain a binary bit stream. as follows: (5) in, Represents a single bit after encoding. Bit data makes up a binary bit stream. , Determined by the following formula: (6) Define quantization error vector as follows: (7) According to equation (4), the quantization error vector It is bounded and can be multicellular. Surrounded by, among ; Then, the binary bit stream is transmitted through a binary symmetric channel. In actual wireless or wired channel transmission, due to electromagnetic interference, signal attenuation, etc., some bits may randomly jump with a very small probability. The received binary bit stream data is represented as follows: (8) in, This represents the bits after transmission through the channel. Let be a random variable that follows a Bernoulli distribution, and Its physical meaning is: (9) According to equation (8), the actual measurement output vector after decoding at the receiving end is... Represented as: (10)。 5. The multiplicative fault detection method based on multicell filtering under random bit flipping according to claim 4, characterized in that, Step three includes: To mitigate the impact of unknown disturbances on state estimation, the state estimation observer is designed as follows: (11) in, State vector The estimated value, The parameters of the observer to be designed; Define the state estimation error vector as Considering The recursive formula for the dynamic error is as follows: (12) Introducing the theory of fully symmetric multicellular set-membership filtering, assuming The time-state estimation error vector satisfies ,in, for The time step contains the state error vector A fully symmetrical multicellular body Multicellular The center vector, Multicellular Given a generating matrix of known dimension, then in At time t, the state estimation error vector Will be included in multicellular bodies In this context, the recursive formulas for calculating the center vector and the generating matrix are as follows: (13) in, Unknown disturbances in the system A generating matrix of known dimensions. Unknown measurement noise in the system A generating matrix of known dimensions. for Time-generating matrix The matrix after dimensionality reduction operator processing They are respectively The center vector and generating matrix at time t, and also at the initial time. At that time, the observer's initial value was set to Then, from equation (2), we can see that the initial error vector satisfy ; Based on error multicell description System state vector The upper and lower bound estimates are calculated as follows: (14) At this point, the actual system state satisfies ; where vector The Each component is defined as the generating matrix. The sum of the absolute values ​​of the corresponding rows, i.e. ,in To generate the matrix The number of columns, They are respectively Time-state vector The lower and upper bound estimates.

6. The multiplicative fault detection method based on multicell filtering under random bit flipping according to claim 5, characterized in that, In step four, the estimation error is made into a multi-cell... of - Observer gain matrix with radius minimized in normal operating mode The expression is as follows: Define performance metrics ,in, The trace of the matrix is ​​given when the system is in normal operating mode, i.e. At that time, The formula for obtaining the optimal observer gain matrix with the smallest radius is: (15) in, auxiliary matrix and The definition is as follows: (16)。 7. The multiplicative fault detection method based on multicell filtering under random bit flipping according to claim 6, characterized in that, The bit flip detection logic designed in step five is specifically as follows: Predicted set of time measurement output Represented by a fully symmetrical multicellular structure, i.e. Its center vector and generating matrix It is calculated by the following formula: (17) In addition, a bit flip detection flag is designed. The logic is as follows: (18) When the measured value at the receiving end meets hour, The signal is determined to have not undergone bit flipping during transmission; when hour, The signal is determined to have undergone random bit flipping.

8. The multiplicative fault detection method based on multicell filtering under random bit flipping according to claim 7, characterized in that, The specific steps for executing the fault detection logic based on state interval consistency in step six are as follows: The system is in normal working mode, that is... An open-loop state simulator is used to generate the nominal state boundaries of the system when no faults occur. : (19) in, They are respectively The estimated values ​​of the state bound and upper bound of the time-limited system in normal operating mode. This is the observer state estimation vector in normal mode. These are the center vector and error range vector of the error multicell in normal mode, respectively; In addition, design fault detection flags. The logic is as follows: (20) When the observer estimates the state, it satisfies hour, The system is determined to be operating without faults; when hour, The system was determined to have a multiplicative fault.

9. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores computer instructions that are executed by a processor according to any one of claims 1 to 8.

10. A computer program product, characterized in that, The computer program product stores computer instructions that are executed by a processor using the method as described in any one of claims 1 to 8.

Images