Method for estimating health degree of pneumatic actuator

Abstract

The invention discloses a health degree estimation method for a pneumatic actuator. According to the invention, system identification is carried out at a stable working point and a discrete state space model is obtained. And comprehensively considering disturbance and excitation signals and the health condition of the actuator, and constructing a discrete state space expression form suitable for the augmented Kalman filter. The health information is modeled as an unknown input disturbance variable and is taken as part of a state variable. And an augmented Kalman filter is adopted to carry out combined prediction on the system state quantity and the unknown input interference quantity. And maintaining the acquired control input sequence and the unknown input disturbance variable sequence output by the filter by adopting a sliding window mechanism, and obtaining an estimated value of a health matrix of the pneumatic actuator by adopting a least square method for a data sequence in a window. And finally, performing feature extraction and analysis on the health matrix estimation value to realize real-time evaluation and dynamic tracking of the health state of the pneumatic actuator. According to the method, accurate, stable and real-time health degree information can still be provided under the condition that the pneumatic actuator has faults, disturbance or model mismatch, and powerful technical support is provided for fault-tolerant control and predictive maintenance of a complex system.

Description

Technical Field

[0001] The invention belongs to the field of process control and relates to a method for estimating the health status of a pneumatic actuator. Background Art

[0002] In modern industrial systems, pneumatic actuators are widely used in fields such as automation and control, aerospace, rail transit, and process industries. Due to their simple structure, fast response, and low maintenance costs, they have become a crucial component of actuators. However, the health of pneumatic actuators directly impacts system stability and safety. This is particularly true in scenarios with extremely high reliability requirements, such as high-speed rail traction / braking systems and process industry control. Therefore, health monitoring and fault diagnosis are particularly important.

[0003] Over long-term operation, pneumatic actuators are susceptible to factors such as friction, leakage, valve wear, and air source contamination, leading to system performance degradation. For example, aging seals within cylinders can cause gas leaks, resulting in reduced thrust. Valve wear or blockage can affect flow control and reduce system response speed. Furthermore, moisture and impurities in the air source can cause corrosion and carbon deposits, further affecting actuator accuracy. These issues not only reduce production efficiency but can also lead to serious safety hazards, such as train brake failure and unexpected shutdowns of industrial production equipment.

[0004] Existing health monitoring methods for pneumatic actuators primarily include health monitoring based on physical redundancy and health estimation based on mathematical models. Physical redundancy methods improve system reliability by adding additional backup actuators, but this approach is costly and increases system complexity. Mathematical model-based methods, on the other hand, rely on physical or data-driven models of the actuator to assess its health status by measuring input and output signals. These health monitoring methods still have some drawbacks, such as insufficient real-time performance. Under complex operating conditions, such as during high-speed train braking, existing health estimation methods struggle to reflect the deterioration of pneumatic actuators in real time, impacting the system's ability to respond quickly. They also suffer from weak noise immunity. Pneumatic systems inherently have strong nonlinear characteristics and are susceptible to noise interference from factors such as ambient temperature and air source pressure fluctuations, leading to increased health estimation errors. Furthermore, they suffer from slow convergence. When the actuator's health status undergoes a sudden change (such as a sudden leak or valve failure), existing methods converge slowly, resulting in delayed health assessments and impacting the timeliness of fault diagnosis.

[0005] Therefore, in order to address the defects of the existing technology, the present invention proposes an augmented Kalman filter (AKF) based on the excitation signal, the least squares method and the feature extraction to achieve high-precision and high-real-time estimation of the health of the pneumatic actuator. Summary of the Invention

[0006] The purpose of the present invention is to provide a method for estimating the health status of a pneumatic actuator.

[0007] The present invention specifically involves performing system identification at a stable operating point and obtaining a discrete state-space model. By comprehensively considering disturbances, excitation signals, and actuator health, a discrete state-space representation suitable for an augmented Kalman filter is constructed. To improve the accuracy of actuator health parameter identification, excitation signals of different orders but consistent amplitudes are injected into the control input ports to ensure sufficient system excitation across all frequency bands. To prevent excitation signals from interfering with the filter's state estimation, the excitation signals are introduced into the model as known control variables to eliminate their influence and ensure the accuracy of the estimation results. To quantify the health of the pneumatic actuator, health information is modeled as an unknown input disturbance and included as part of the state variable. An augmented Kalman filter is used to jointly predict the system state variable and the unknown input disturbance variable. The relationship between the control input and the unknown input disturbance variable is expanded, and a sliding window mechanism is used to maintain the collected control input sequence and the filter output unknown input disturbance variable sequence, ensuring real-time estimation results and improving the stability and robustness of the health estimation. The least squares method is used on the data sequence within the window to obtain an estimate of the pneumatic actuator health matrix. Finally, by extracting and analyzing the features of the estimated value of the health matrix, real-time evaluation and dynamic tracking of the health status of the pneumatic actuator are achieved, providing a basis for fault warning and maintenance decision-making.

[0008] The present invention specifically comprises the following steps:

[0009] Step 1: Collect input and output variables of an industrial process system with multiple inputs and outputs. The output variables include inventory variables and component variables. Each input variable corresponds to a pneumatic actuator, and the input variable represents the key operating flow or energy input regulated by the pneumatic actuator. Before controlling the component variables to achieve the target product quality, it is necessary to control the inventory variables through some input variables to achieve dynamic stability and safe operation of the system and obtain the stable operating point of the system.

[0010] Step 2: Build a pneumatic actuator health estimation model:

[0011] First, at the stable operating point obtained in step 1, the industrial process system is identified to obtain the transfer function model of the remaining input variables and component variables. The transfer function model is converted into a state space model and discretized to obtain the following discrete state space expression:

[0012] where x k ∈R nx Represented as the state vector at the current sampling moment, x k+1It is represented as the state vector at the next sampling moment, which is used to describe the dynamic information that cannot be directly observed, such as internal energy and material distribution in the industrial process; k ∈R ny It is represented as the output vector at the current sampling time, corresponding to the component index that needs to be precisely controlled; u k ∈R nu The control input vector at the current sampling time corresponds to the control action applied by the remaining pneumatic actuators. The matrices A, B, and C represent the state transition matrix, input matrix, and output matrix, respectively, and their dimensions match the number of variables.

[0013] Assume that the health matrix of the pneumatic actuator is F, F = diag(f1,f2,…,f i ,…,f nu ) is a diagonal matrix used to describe the pneumatic actuator fault. i =1 means that the i-th actuator has no obstacles; f i =0 means complete failure; 0 <f i <1 indicates partial failure.

[0014] Then, process noise is introduced Measurement noise v k , construct a pneumatic actuator health estimation model, and obtain the denoised pneumatic actuator health estimation model:

[0015] Where F is the health matrix of the pneumatic actuator, the noise sequence v k They obey the Gaussian distribution with zero mean: Q x is the covariance matrix of the state noise, and R is the covariance matrix of the measurement noise.

[0016] Since the actuator fault described by the pneumatic actuator health matrix F cannot be directly obtained, the unknown input disturbance d is introduced. k Indicates the impact of the actuator health on the input, d k =(F k -I)u k , I is a unit vector with dimension nu; so that BFu k =B(u k +d k ).

[0017] The converted pneumatic actuator health estimation model is obtained:

[0018] Then, due to the lack of effective information of the unknown input interference d, it is modeled as in It obeys a Gaussian distribution with zero mean, that is, where Q . It is represented as the covariance matrix of the unknown input d.

[0019] The pneumatic actuator health estimation model is further converted into:

[0020] Finally, the unknown input disturbance d k With the state vector x k Merge into Get the pneumatic actuator health estimation model:

[0021]

[0022] in It also obeys the Gaussian distribution with zero mean, that is in δ k: is the Kroneckerdelta function.

[0023] Step 3: Based on the pneumatic actuator health estimation model constructed in step 2, the excitation signal is used as the known control variable disturbance s k The model is added to ensure that the state estimation of the filter will not be disturbed by the excitation signal, while retaining the role of the excitation signal in identifying the health of the actuator. The health estimation model of the pneumatic actuator after disturbance compensation is obtained: The model satisfies the observability criterion:

[0024] Preferably, the excitation signal uses a pseudo-random binary sequence excitation signal PRBS, and PRBS excitation signals of different orders but the same amplitude are added to different input ports.

[0025] Step 4: Based on the pneumatic actuator health estimation model constructed in step 4, the Kalman filter is used to calculate the current state vector x k and the unknown input disturbance d k Make a prediction. The prediction process is as follows:

[0026] From step three, we can see Assume that the industrial process system has a posterior state vector estimate value for the previous moment: The error covariance matrix of this posterior state vector estimate is And the output of the controller at the current moment is u k , the observable vector obtained by the observer at the current moment is y k , then the pneumatic actuator health estimation model is used to obtain the prior estimated state vector at the current moment: Represents the estimated value of the state vector, and the error covariance matrix of the estimated value of the state vector is:

[0027] The residual between the estimated observation value obtained according to the prior estimate and the actual observation value To compensate for the prior prediction state, select the optimal Kalman gain K k To minimize the mean square error matrix of the compensated estimate, where the optimal Kalman gain K k : This gives the optimal estimated state vector: Finally, update the error covariance matrix of the optimal posterior estimate at the current moment:

[0028] Extracting unknown input disturbances from the optimal estimated state vector I is a unit vector with dimension nu, is the optimal estimated state vector output by the Kalman filter at the current moment.

[0029] Initial state estimate It is usually assumed to be an all-zero vector of dimension (nx+nu), and the initial error covariance matrix is ​​usually assumed to be an all-zero square matrix of dimension nx.

[0030] Step 5: Predict the unknown input interference and control input data within M sampling moments through step 4, and store the unknown input interference sequence and control input sequence through the sliding window mechanism; calculate the health information matrix F using the least squares method. Specifically:

[0031] Step 5.1: Maintain a sliding window of size M to store the control input vectors at the current moment and the past M sampling moments, forming a control input sequence U = [u kGa u kGa+1 …u k ]; where u k is the sampling value of the control input of the continuous system at time k. The unknown input interference sequence D at M sampling moments is obtained. k-a d kGa+1 …d k ];

[0032] Step 5.2: The relationship between the unknown input disturbance and the control input is d k =(F k -I)u k Expanding, we get: [d kGa d kGa+1 …d k ]=(F k -I)[u kGau kGa+1 …u k ]; simplified to: D = (F k -I)U;

[0033] The dimension of matrix U is nu×M, which is non-singular in most cases and cannot be directly inverted. Therefore, the least squares method is used to estimate the current pneumatic actuator health matrix F. k The goal is to solve the error matrix (D-(F k -I)U)Minimum optimal F k : where |·| e is the Frobenius norm. Taking the derivative of the objective function and setting it to zero, we get the optimal solution: F k =DU T (UU T ) -1 +I, get the current pneumatic actuator health estimation matrix

[0034] Step 5.3: Based on the definition of the pneumatic actuator health matrix f as a diagonal matrix in step 2, the current pneumatic actuator health estimation matrix obtained in step 5.2 is Perform feature extraction so that Get the current pneumatic actuator health matrix F k : where f ki That is, it represents the estimated value of the health status of the i-th actuator at time k.

[0035] This enables real-time estimation of the health status of pneumatic actuators in industrial process systems.

[0036] Beneficial effects of the present invention:

[0037] The present invention integrates state disturbance, observation disturbance, actuator health and excitation signal into the Kalman filter model. By mapping the actuator health into unknown input variables, it can not only achieve high-precision real-time estimation of system state variables and unknown input variables with the help of augmented Kalman filter, but also effectively decouple disturbance, model mismatch and actuator failure at the model level. Using a sliding window mechanism, the unknown input quantity d in the last M moments is dynamically stored. k and control input u kThe data is combined to form a time series data block. By combining the data sequences D and U at these M moments and solving them using the least squares method, an actuator health matrix can be constructed after feature extraction. This matrix can quantitatively reflect the performance changes of the actuator under different operating conditions, thereby achieving an accurate assessment of the actuator health status. During the least squares solution process, the present invention introduces an excitation signal, which effectively overcomes the problem of data correlation in the traditional least squares method, which leads to matrix ill-conditioning or irreversibility. The excitation signal can enhance the excitability of the data and ensure good numerical stability and reversibility during the matrix solution process.

[0038] This invention enables real-time monitoring and dynamic assessment of actuator health during operation. It provides accurate, stable, and real-time health information even in the presence of pneumatic actuator failures, disturbances, or model mismatches. Its robustness and adaptability significantly improve the accuracy and real-time performance of actuator health estimation, providing powerful technical support for fault-tolerant control and predictive maintenance of complex systems, and offering more reliable data support and diagnostic evidence for fault-tolerant control, fault prediction, and health management. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 It is the structural diagram of the distillation tower;

[0040] Figure 2 It is the structural diagram of the control system;

[0041] Figure 3 This is the model building stage of this method;

[0042] Figure 4 This is the data collection stage of this method;

[0043] Figure 5 The data processing of this method is used to obtain the health status of the pneumatic actuator;

[0044] Figure 6 To identify the detection effect of the accurate system;

[0045] Figure 7 Detection effect when identifying inaccurate systems. DETAILED DESCRIPTION

[0046] The present invention will be further described below with reference to the accompanying drawings.

[0047] In this embodiment, the health status detection of a pneumatic actuator in a distillation tower system is taken as an example to illustrate the specific implementation process of the method of the present invention.

[0048] like Figure 1 As shown, a method for estimating the health status of a pneumatic actuator includes the following steps:

[0049] Step 1: Collect input variables and output variables of an industrial process system with multiple inputs and outputs. Output variables include inventory variables (slow-dynamic variables such as liquid level and pressure) and component variables (fast-dynamic variables such as product composition and purity). Each input variable corresponds to a pneumatic actuator, and the input variable represents the key operating flow or energy input regulated by the pneumatic actuator. Before controlling the component variables to achieve the target product quality, it is necessary to control the inventory variables through some input variables to achieve dynamic stability and safe operation of the system and obtain the stable operating point of the system.

[0050] Step 2: Figure 2 As shown, a pneumatic actuator health estimation model is constructed:

[0051] First, at the stable operating point obtained in step 1, the industrial process system is identified to obtain the transfer function model of the remaining input variables and component variables. The transfer function model is converted into a state space model and discretized to obtain the following discrete state space expression:

[0052] where x k ∈R nx Represented as the state vector at the current sampling moment, x k+1 It is represented as the state vector at the next sampling moment, which is used to describe the dynamic information that cannot be directly observed, such as internal energy and material distribution in the industrial process; k ∈R ny It is represented as the output vector at the current sampling time, corresponding to the component index that needs to be precisely controlled; u k ∈R nu Represented as the control input vector at the current sampling time, corresponding to the control action applied by the remaining pneumatic actuators (such as flow adjustment caused by opening changes). Matrices A, B, and C represent the state transition matrix, input matrix, and output matrix, respectively, and their dimensions match the variable dimensions.

[0053] Assume that the health matrix of the pneumatic actuator is F, F = diag(f1,f2,…,f i ,…,f nu ) is a diagonal matrix used to describe the pneumatic actuator fault. i =1 means that the i-th actuator has no obstacles; f i =0 means complete failure; 0 <f i <1 indicates partial failure.

[0054] Then, process noise is introduced Measurement noise v k , construct a pneumatic actuator health estimation model, and obtain the denoised pneumatic actuator health estimation model:

[0055] Where F is the health matrix of the pneumatic actuator, the noise sequence v k They obey the Gaussian distribution with zero mean: v k ~N(0,R)), Q x is the covariance matrix of the state noise, and R is the covariance matrix of the measurement noise.

[0056] Since the actuator fault described by the pneumatic actuator health matrix F cannot be directly obtained, the unknown input disturbance d is introduced. k Indicates the impact of the actuator health on the input, d k =(F k -I)u k , I is a unit vector with dimension nu; so that BFu k =B(u k +d k ).

[0057] The converted pneumatic actuator health estimation model is obtained:

[0058] Then, due to the lack of effective information of the unknown input interference d, it is modeled as in It obeys a Gaussian distribution with zero mean, that is, where Q d It is represented as the covariance matrix of the unknown input d.

[0059] The pneumatic actuator health estimation model is further converted into:

[0060] Finally, the unknown input disturbance d k With the state vector x k Merge into Get the pneumatic actuator health estimation model:

[0061]

[0062] in It also obeys the Gaussian distribution with zero mean, that is in δ k: is the Kroneckerdelta function.

[0063] Step 3: In order to avoid the influence of the excitation signal on the Kalman filter state estimation, based on the pneumatic actuator health estimation model constructed in step 2, the excitation signal is used as a known control variable interference sk The model is added to ensure that the state estimation of the filter will not be disturbed by the excitation signal, while retaining the role of the excitation signal in identifying the health of the actuator. The health estimation model of the pneumatic actuator after disturbance compensation is obtained: The model satisfies the observability criterion: That is, the rank of the augmented observability matrix is ​​equal to the extended state dimension, which ensures that the output y can be obtained from the measurement k The system state vector x is uniquely determined in k and the input interference vector d k , providing feasibility guarantee for constructing extended state Kalman filter.

[0064] Specifically, an excitation signal is added to the input. In this embodiment, a PRBS (Pseudo-Random Binary Sequence) excitation signal is used. The PRBS excitation signal is generated by a shift register (such as a linear feedback shift register (LFSR)) and consists of a string of binary digits, where "1" and "0" appear in a pseudo-random pattern. A PRBS signal is determined by the order (i.e., the number of shift registers), the tap (which specifies the register data bits for the logical operation), and the seed (the initial value of the shift register).

[0065] To improve the accuracy of actuator health estimation, PRBS excitation signals of different orders but the same amplitude are added to different input ports. The signal amplitude can be adjusted for different targets, for example, the signal output can vary between "1" and "-1", thereby fully stimulating the system. While maintaining model estimation accuracy, it effectively solves the problem of ill-conditioned or irreversible matrices caused by data correlation during the least squares method used in step 5 to estimate actuator health.

[0066] Step 4: Based on the pneumatic actuator health estimation model constructed in step 4, the Kalman filter is used to calculate the current state vector x k and the unknown input disturbance d k Make predictions, such as Figure 3 As shown, the prediction process is as follows:

[0067] From step three, we can see Assume that the industrial process system has a posterior state vector estimate value for the previous moment: (The subscript k-1|k-1 indicates that the estimated value is the posterior estimated value at the previous moment). The error covariance matrix of the posterior state vector estimate is And the output of the controller at the current moment is u k , the observable vector obtained by the observer at the current moment is y k, then the pneumatic actuator health estimation model is used to obtain the prior estimated state vector at the current moment: (The subscript k|k-1 indicates that the estimated value is the prior estimate at time k). Represents the estimated value of the state vector, and the error covariance matrix of the estimated value of the state vector is:

[0068] The residual between the estimated observation value obtained according to the prior estimate and the actual observation value To compensate for the prior prediction state, select the optimal Kalman gain K k To minimize the mean square error matrix of the compensated estimate, where the optimal Kalman gain K k : This gives the optimal estimated state vector: Finally, update the error covariance matrix of the optimal posterior estimate at the current moment:

[0069] Extracting unknown input disturbances from the optimal estimated state vector I is a unit vector with dimension nu, is the optimal estimated state vector output by the Kalman filter at the current moment.

[0070] Initial state estimate The initial error covariance matrix is ​​typically assumed to be an all-zero vector of dimension (nx + nu). The initial error covariance matrix is ​​typically assumed to be an all-zero square matrix of dimension nx. The noise covariance matrix Q is determined through experimentation and statistical analysis, while the measurement noise covariance matrix R is determined by sensor characteristics (such as measurement accuracy).

[0071] Step 5: Predict the unknown input interference and control input data within M sampling moments through step 4, and store the unknown input interference sequence and control input sequence through the sliding window mechanism; calculate the health information matrix F using the least squares method. Figure 4 As shown, specifically:

[0072] Step 5.1: Maintain a sliding window of size M to store the control input vectors at the current moment and the past M sampling moments, forming a control input sequence U = [u kGa u kGa+1 …u k ]; where u k is the sampling value of the control input of the continuous system at time k. The unknown input interference sequence D at M sampling moments is obtained. k-a d kGa+1 …d k ];

[0073] Step 5.2: The relationship between the unknown input disturbance and the control input is dk =(F k -I)u k Expanding, we get: [d kGa d kGa+1 …d k ]=(F k -I)[u kGa u kGa+1 …u k ]; simplified to: D = (F k -I)U;

[0074] The dimension of matrix U is nu×M, which is non-singular in most cases and cannot be directly inverted. Therefore, the least squares method is used to estimate the current pneumatic actuator health matrix F. k The goal is to solve the error matrix (D-(F k -I)U)Minimum optimal F k : where |·| e is the Frobenius norm. Taking the derivative of the objective function and setting it to zero, we get the optimal solution: F k =DU T (UU T ) -1 +I, get the current pneumatic actuator health estimation matrix

[0075] To ensure that UU T Reversible,In step 4, a PRBS excitation signal is applied to the control input,which effectively improves the excitation of the data, thereby ensuring the full rank of the matrix and achieving reversibility.

[0076] Step 5.3: Based on the definition of the pneumatic actuator health matrix F as a diagonal matrix in step 2, the current pneumatic actuator health estimation matrix obtained in step 5.2 is Perform feature extraction so that Get the current pneumatic actuator health matrix F k : where f ki That is, it represents the estimated value of the health status of the i-th actuator at time k.

[0077] This enables real-time estimation of the health status of pneumatic actuators in industrial process systems.

[0078] In this implementation, Figure 5 The embodiment of the present invention is described by taking the distillation tower shown as an example.

[0079] The distillation tower system is used to separate components with different boiling points in the feed. The feed is introduced in the middle of the tower. A condenser and a reflux system are provided at the top of the tower, and a reboiler system and a top / bottom product collection system are provided at the bottom of the tower. The valves in the system control the gas-liquid flow rate through pneumatic actuators. The working process is as follows: the raw material enters the distillation tower from the middle. A reboiler is provided at the bottom of the tower, which vaporizes part of the bottom liquid into steam by providing heat. The flow rate of the steam is V. After the steam rises, it contacts the descending liquid through the tower plate for heat and mass exchange to achieve the separation of light and heavy components. The steam at the top of the tower is introduced into the condenser. After condensation, it is divided into two parts, one part is the condensation reflux with a flow rate of L, which returns to the top of the tower to enhance the separation efficiency, and the other part is the top product of the distillation tower output distillation tower system, the top product discharge flow is D, and the molar fraction of the top product is y t The heavy components are collected at the bottom of the tower to form the bottom product. The discharge flow rate of the bottom product of the distillation tower is B, and the molar fraction of the bottom product is y u .

[0080] Before control, adjust the distillation tower top product discharge flow rate D, distillation tower bottom product discharge flow rate B, tower top gas phase flow rate V T Make the system reach a stable working state. Under this state, the liquid retention volume M of the condenser t , liquid holdup of reboiler M u , the pressure P in the tower remains dynamically stable. At this stable operating point, the distillation tower control system uses two control inputs u = [LV u ](where L is the condensation reflux flow rate, V u is the reboiled steam flow rate, both inputs are flow rates, both are controlled by pneumatic actuators) to control the two outputs y = [y D y u ](where y t is the molar fraction of the top product, y u is the molar fraction of the bottom product) to achieve product quality control.

[0081] The condensation reflux flow rate L and the reboiled steam flow rate V u is the input variable, the molar fraction of the top product y t and the molar fraction of the bottom product y u The transfer function model of the output system The system transfer function model is converted into a state space model and discretized to obtain a discrete state space model: where x k ∈R nx Represented as the state vector at the current sampling moment, Expressed as the mole fraction of the top product and the mole fraction of the bottom product at the current sampling moment, Expressed as the condensation reflux flow L and reboiled steam flow V at the current sampling timeu The matrices A, B, and C represent the state transition matrix, input matrix, and output matrix, respectively, and their dimensions match the dimensions of the variables.

[0082] Process noise and measurement noise are introduced to consider system uncertainty, and the actuator health is modeled and converted into unknown input disturbance d k , the unknown input disturbance variable is used to indirectly characterize the health of the actuator and is incorporated into the model as an extended state variable. . The condensate reflux flow rate L and the reboiled steam flow rate V are introduced as deterministic control inputs. u At the end, the interference of the excitation signal on the state estimation channel is eliminated through the feedforward compensation mechanism, ensuring the accuracy of the filter core estimation function. It also effectively solves the problem of matrix ill-conditioning or irreversibility caused by data correlation in the process of estimating the health of the actuator using the least squares method, and obtains the pneumatic actuator health estimation model after disturbance compensation:

[0083]

[0084] The current state vector x is filtered by the augmented Kalman filter (AKF) k and the unknown input disturbance d k Combining the real-time state estimation of the Kalman filter with the estimation of unknown input disturbances, the system can dynamically adjust the prediction and correction process in a dynamic environment to ensure the stability and robustness of the system under different working conditions. The Kalman filter plays a key role in this process. By using its optimal estimation characteristics, it effectively reduces the impact of noise on the system state estimation, thereby providing a more accurate system state quantity x k and the unknown input disturbance d k .

[0085] The sliding window mechanism is used to store the data sequence (the unknown input interference d of the control input sequence and the augmented Kalman filter output) k sequence), combined with the least squares method to estimate the health matrix, and finally realize the real-time evaluation of the health status of the pneumatic actuator through feature extraction. According to the evaluation results, the pneumatic actuator health status controller can make adjustments to ensure the stability of product quality.

[0086] Through the sliding window mechanism, the system can continuously collect, update and manage historical data, providing efficient and accurate support for subsequent fault detection and data analysis.

[0087] To demonstrate the effectiveness of the above method, the excitation signal generators at the two input ends are set to generate a seventh-order PRBS signal and a ninth-order PRBS signal with the same amplitude. The following experiment is performed:

[0088] Experiment 1:

[0089] The input variables to be identified are the condensate reflux flow rate L and the reboiled steam flow rate V u , the output is the molar fraction y of the top product t and the molar fraction of the bottom product y u The system transfer function model is The model can better reflect the condensation reflux flow rate L and the reboiled steam flow rate V u The output is the molar fraction y of the top product D and the molar fraction of the bottom product y u impact.

[0090] The control effect of the condensation reflux flow signal L on the corresponding pneumatic actuator 1 is reduced to 70% at the 100th sampling moment, and the reboiled steam flow signal V u The control effect on actuator 2 drops to 80% at the 150th sampling moment. The actuator health estimated by the above method is different from the actual actuator health. Figure 6 As shown, in the case of a sudden change in the health of the actuator, the method of the present invention can accurately estimate the health of the actuator at about 15 sampling moments, and when the health of both actuators changes, the health of both actuators can still be accurately determined.

[0091] Experiment 2:

[0092] The input variables to be identified are the condensate reflux flow rate L and the reboiled steam flow rate V u , the output is the molar fraction y of the top product t and the molar fraction of the bottom product y u The system transfer function model is The model cannot well reflect the condensation reflux flow rate L and the reboiled steam flow rate V u The output is the molar fraction y of the top product t and the molar fraction of the bottom product y u impact.

[0093] like Figure 7 As shown in the figure, the health of the actuator decays linearly in this experiment. Although there are some deviations in the values ​​due to model mismatch, the actual actuator health change curve is nearly parallel to the pneumatic actuator health change curve estimated by the method of the present invention, and can still provide a relatively accurate judgment on the actuator health.

[0094] It can be seen from the experimental results that the method described in this application can effectively improve the real-time judgment of the health of the actuator, and can accurately distinguish it from the judgment of the changes in the health of each actuator when multiple actuators attenuate. In the presence of interference and model mismatch, it can still provide results with reference value.

Claims

1. A method for estimating the health of a pneumatic actuator, characterized by: Specifically: Perform system identification at the stable operating point and obtain a discrete state space model; comprehensively consider the disturbance, excitation signal and the health status of the actuator, and construct a discrete state space expression suitable for the augmented Kalman filter; to improve the identification accuracy of the actuator health parameters, excitation signals of different orders but consistent amplitudes are injected into the control input port to ensure that the system is fully excited in each frequency band; to avoid the excitation signal interfering with the state estimation of the filter, the excitation signal is introduced into the model as a known control quantity to eliminate its influence and ensure the accuracy of the estimation result; to quantify the health of the pneumatic actuator, the health information is modeled as an unknown input interference quantity, and the It is used as part of the state quantity; an augmented Kalman filter is used to jointly predict the system state quantity and the unknown input interference quantity; the relationship between the control input quantity and the unknown input interference quantity is expanded, and a sliding window mechanism is used to maintain the collected control input sequence and the unknown input interference quantity sequence output by the filter, which ensures the real-time performance of the estimation result and improves the stability and robustness of the health estimation; the least squares method is used for the data sequence within the window to obtain the estimated value of the pneumatic actuator health matrix; finally, by extracting and analyzing the features of the health matrix estimate, the real-time evaluation and dynamic tracking of the pneumatic actuator health status are realized.

2. The method for estimating the health of a pneumatic actuator according to claim 1, wherein: The specific steps include: Step 1: Collect input and output variables of an industrial process system with multiple inputs and outputs. Output variables include inventory variables and component variables. Each input variable corresponds to a pneumatic actuator and represents the critical operating flow or energy input regulated by the pneumatic actuator. Before controlling the component variables to achieve target product quality, it is necessary to control the inventory variables through some of the input variables to achieve dynamic stability and safe operation of the system and obtain the system's stable operating point. Step 2: Build a pneumatic actuator health estimation model: First, at the stable operating point obtained in step 1, the industrial process system is identified to obtain the transfer function model of the remaining input variables and component variables. The transfer function model is converted into a state space model and discretized to obtain the following discrete state space expression: where x k ∈R nx Represented as the state vector at the current sampling moment, x k+1 It is represented as the state vector at the next sampling moment, which is used to describe the dynamic information that cannot be directly observed, such as internal energy and material distribution in the industrial process; k ∈R ny It is represented as the output vector at the current sampling time, corresponding to the component index that needs to be precisely controlled; u k ∈R nu It is represented as the control input vector at the current sampling time, corresponding to the control action applied by the remaining pneumatic actuators; matrices A, B, and C represent the state transfer matrix, input matrix, and output matrix, respectively, and their dimensions match the dimension of the variables; Assume that the health matrix of the pneumatic actuator is F, F = diag(f1,f2,…,f i ,…,f nu ) is a diagonal matrix used to describe the pneumatic actuator fault; f i =1 means that the i-th actuator has no obstacles; f i =0 means complete failure; 0 <f i <1 indicates partial failure; Then, process noise is introduced Measurement noise v k , construct a pneumatic actuator health estimation model, and obtain the denoised pneumatic actuator health estimation model: Where F is the health matrix of the pneumatic actuator, the noise sequence v k They obey the Gaussian distribution with zero mean: Q x is the covariance matrix of state noise, R is the covariance matrix of measurement noise; Since the actuator fault described by the pneumatic actuator health matrix F cannot be directly obtained, the unknown input disturbance d is introduced. k Indicates the impact of the actuator health on the input, d k =(F k -I)u k , i is a unit vector with dimension nu; so that BFu k =B(u k +d k ); The converted pneumatic actuator health estimation model is obtained: Then, due to the lack of effective information of the unknown input interference d, it is modeled as in It obeys a Gaussian distribution with zero mean, that is, where Q . Represented as the covariance matrix of the unknown input d; The pneumatic actuator health estimation model is further converted into: Finally, the unknown input disturbance d k With the state vector x k Merge into Get the pneumatic actuator health estimation model: in It also obeys the Gaussian distribution with zero mean, that is in δ k: is the Kronecker delta function; Step 3: Based on the pneumatic actuator health estimation model constructed in step 2, the excitation signal is used as the known control variable disturbance s k The model is added to ensure that the state estimation of the filter will not be disturbed by the excitation signal, while retaining the role of the excitation signal in identifying the health of the actuator. The health estimation model of the pneumatic actuator after disturbance compensation is obtained: The model satisfies the observability criterion: Step 4: Based on the pneumatic actuator health estimation model constructed in step 4, the Kalman filter is used to calculate the current state vector x k and the unknown input disturbance d k Make a prediction. The prediction process is as follows: From step three, we can see Assume that the industrial process system has a posterior state vector estimate value for the previous moment: The error covariance matrix of this posterior state vector estimate is And the output of the controller at the current moment is u k , the observable vector obtained by the observer at the current moment is y k , then the pneumatic actuator health estimation model is used to obtain the prior estimated state vector at the current moment: Represents the estimated value of the state vector, and the error covariance matrix of the estimated value of the state vector is: The residual between the estimated observation value obtained according to the prior estimate and the actual observation value To compensate for the prior prediction state, select the optimal Kalman gain K k To minimize the mean square error matrix of the compensated estimate, where the optimal Kalman gain K k : This gives the optimal estimated state vector: Finally, update the error covariance matrix of the optimal posterior estimate at the current moment: Extracting unknown input disturbances from the optimal estimated state vector I is a unit vector with dimension nu, is the optimal estimated state vector output by the Kalman filter at the current moment; Initial state estimate It is usually assumed to be an all-zero vector of dimension (nx+nu), and the initial error covariance matrix is ​​usually assumed to be an all-zero square matrix of dimension nx; Step 5: Predict the unknown input interference and control input data within M sampling moments through step 4, and store the unknown input interference sequence and control input sequence through the sliding window mechanism; calculate the health information matrix F using the least squares method; specifically: Step 5.1: Maintain a sliding window of size M to store the control input vectors at the current moment and the past M sampling moments, forming a control input sequence U = [u kGa u kGa+1 …u k ]; where u k is the sampling value of the control input of the continuous system at time k; the unknown input interference sequence D at M sampling moments is obtained = [d k-a d kGa+1 …d k ]; Step 5.2: The relationship between the unknown input disturbance and the control input is d k =(F k -I)u k Expanding, we get: [d kGa d kGa+1 …d k ]=(F k -I)[u kGa u kGa+1 …u k ]; simplified to: D = (F k -I)U; The dimension of matrix U is nu×M, which is non-singular in most cases and cannot be directly inverted. Therefore, the least squares method is used to estimate the current pneumatic actuator health matrix F. k The goal is to solve the error matrix (D-(F k -I)U)Minimum optimal F k : where |·| e is the Frobenius norm; taking the derivative of the objective function and setting it to zero, we get the optimal solution: F k =DU U (UU U ) -1 +I, get the current pneumatic actuator health estimation matrix Step 5.3: Based on the definition of the pneumatic actuator health matrix F as a diagonal matrix in step 2, the current pneumatic actuator health estimation matrix obtained in step 5.2 is Perform feature extraction so that Get the current pneumatic actuator health matrix F k : (a≠i); where f ki That is, it represents the estimated value of the health status of the i-th actuator at time k; This enables real-time estimation of the health status of pneumatic actuators in industrial process systems.

3. The method for estimating the health of a pneumatic actuator according to claim 1, wherein: The excitation signal uses a pseudo-random binary sequence excitation signal PRBS, and PRBS excitation signals of different orders but the same amplitude are added to different input ports.

Images