An event-triggered fault detection method for chemical mixing tank system based on iterative interval estimation

Abstract

The present invention discloses a method for event-triggered fault detection of a chemical mixing tank system based on iterative interval estimation. The method first uses linearization technology to establish a discrete dynamic model of the chemical mixing tank system, then uses the system output at the triggering moment to design an iterative observer method, and designs a dynamic output trigger mechanism consisting of the system output and error-dependent trigger parameters to reduce the communication transmission frequency, and then designs a controller that makes the chemical mixing tank system asymptotically stable. Finally, Zonotope technology is used to use data from the normal operation of the system to generate the safety threshold required for fault detection. Compared with the traditional one-step-based estimation method, this method is a new interval estimation method. When applied to a chemical mixing tank system, this method produces a tighter safety threshold interval, which improves the sensitivity and timeliness of fault detection.

Description

Technical Field

[0001] The invention relates to a fault detection method for a chemical mixing tank system, and in particular to an event-triggered fault detection method for a chemical mixing tank system based on iterative interval estimation. Background Art

[0002] Due to the complexity of the usage scenarios of chemical mixing tank systems, it is usually difficult to detect measurement faults masked by noise and interference, which may lead to a decline in system performance. Fault detection, as an important part of fault diagnosis, is crucial to improving the safety and reliability of the system. The main idea of ​​fault detection is to compare the size of the residual signal with the safety threshold. When the amplitude of the residual signal exceeds the safety threshold, the system is deemed to have failed. Based on this idea, researchers have conducted extensive research on the design of trigger conditions and achieved a series of results.

[0003] In addition, chemical mixing tank systems usually use network control that is easy to install and has strong scalability. However, due to limited network bandwidth, data packets inevitably have problems such as delay, packet loss, and timing disorder during network transmission. How to reduce the frequency of communication transmission without sacrificing ideal stability and performance, event-triggered control is particularly important. In an event-triggered control environment, communication transmission will only be carried out when the preset conditions are violated.

[0004] However, the above research works mainly focus on the one-step safety threshold design for chemical mixing tank systems, which leads to low detection sensitivity. Therefore, it is necessary to adopt a k-step iterative method to generate a tighter safety threshold interval to improve the sensitivity and timeliness of fault detection. Summary of the invention

[0005] The purpose of the present invention is to propose an event-triggered fault detection method for a chemical mixing tank system based on iterative interval estimation, which can effectively improve the fault detection sensitivity and timeliness of the chemical mixing tank system under bandwidth-limited conditions.

[0006] The specific technical solution of the present invention is as follows: An event-triggered fault detection method for a chemical mixing tank system based on iterative interval estimation comprises the following steps:

[0007] Using linearization techniques, the discrete dynamics model of the chemical mixing tank system is established as follows:

[0008]

[0009]

[0010] In the formula, x(k)=[δc3(k), δq3(k), δc5(k), δq5(k)]T represents the system state, u(k)=[δq1(k),δq4(k)] T represents the system input, y(k) represents the system output, q i represents the flow rate, c i Indicates the concentration of the chemical, Indicates the target value of flow rate, represents the target value of the concentration of the chemical, V1 and V2 represent the volume of the liquid, q2 and c2 are known constants, i∈{1,…,5} represents the number of the inlet and outlet pipes, and k represents the discrete sampling time;

[0011] An iterative observer method is designed to reconstruct the system state, and the estimated value is continuously corrected in multiple iterations to improve the estimation accuracy. The specific steps are as follows:

[0012] Iteration 0:

[0013]

[0014] Iteration i:

[0015]

[0016] In the formula, and They represent the estimated values ​​of the 0th and i-th system states respectively, and denote the estimated values ​​of the 0th and i-th disturbances respectively;

[0017] Furthermore, a dynamic output trigger mechanism consisting of system output and error-dependent trigger parameters is designed. The specific steps are as follows:

[0018] k s+1 =inf{k>k s ,

[0019] In the formula, e y (k) = y(k s )-y(k) represents the measurement error, k s Indicates the last trigger time, k s+1 represents the next triggering time, Ψ represents the weight matrix, σ(k) represents the triggering parameter and is updated by the following formula:

[0020]

[0021] In the formula, and σ They represent the upper and lower bounds of the trigger parameter, and α represents the weight parameter;

[0022] Furthermore, an event-triggered control scheme for the chemical mixing tank system involved in the present invention is established, and the specific steps are as follows:

[0023]

[0024] Where K is a positive definite feedback gain matrix; this algorithm can ensure the asymptotic stability of the system, and the proof process is as follows:

[0025] C001: Select a composite energy function of the following form:

[0026]

[0027] C002: represents the state observation error of the system, represents the estimated error of the disturbance, P represents the Lyapunov variable matrix;

[0028] C003: Calculate the V between the k+1th sampling time and the kth sampling time [i] (k) and consider H ∞ Performance, including:

[0029]

[0030] C004: In the formula, γ represents H ∞ Performance level indicators;

[0031] C005: Further consideration According to C003, the following formula can be obtained:

[0032]

[0033]

[0034] C006: Therefore, from C004, we can get that when Θ<0, we have:

[0035]

[0036] C007: According to C006, the chemical mixing tank system is asymptotically stable under the event-triggered control scheme designed by the present invention;

[0037] Furthermore, Zonotope technology is used to generate the safety threshold required for fault detection using the data of the normal operation of the system. The specific steps are as follows: the normal operation data of the chemical mixing tank system under the event-triggered control scheme designed by the present invention is obtained, and the reachable set of the observed error signal of each iterative batch is analyzed based on the Zonotope technology:

[0038]

[0039] In the formula, e [i] (k) and Respectively represent the upper and lower bounds of the observation error, Ω [i] (0) represents the reachable set of the initial value of the observation error, Box(·) represents the interval boundary, represents the Minkowski sum;

[0040] Further, the average residual signal interval is calculated to generate the interval of the state of the chemical mixing tank system during normal operation;

[0041]

[0042] In the formula, x [i] (k) and They represent the upper and lower bounds that the chemical mixing tank system can reach respectively;

[0043] Therefore, the safety threshold required for fault detection can be obtained from the upper and lower bounds of state reachability. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 is a flow chart of a method according to an embodiment of the present invention;

[0045] Figure 2 The response diagram of δc3(k) and the obtained state interval when the method proposed in the present invention is used in the embodiment without fault;

[0046] Figure 3 The response diagram of δq3(k) and the obtained state interval of the method proposed in the present invention in the case of no fault are shown in the embodiment;

[0047] Figure 4 The response diagram of δc5(k) and the obtained state interval when the method proposed in the present invention is used in the embodiment without fault;

[0048] Figure 5 The response diagram of δq5(k) and the obtained state interval when the method proposed in the present invention is used in the embodiment without fault;

[0049] Figure 6 The reachable set analysis diagram of the observed errors of δc3(k) and δq3(k) in the embodiment using the method proposed in the present invention under the condition of no fault;

[0050] Figure 7 The reachable set analysis diagram of the observed errors of δc5(k) and δq5(k) in the embodiment using the method proposed in the present invention under the condition of no fault;

[0051] Figure 8 This is a fault detection diagram of δc3(k) in a fault situation using the method proposed in the present invention; DETAILED DESCRIPTION

[0052] The present invention is further explained below in conjunction with specific embodiments. It should be understood that these embodiments are only used to illustrate the present invention and are not used to limit the scope of the present invention. After reading the present invention, various equivalent forms of modifications to the present invention by those skilled in the art all fall within the scope defined by the claims attached to this application.

[0053] like Figure 1 As shown, an event-triggered fault detection method for a chemical mixing tank system based on iterative interval estimation comprises the following steps:

[0054] Step 1: Set the initial values ​​of various parameters;

[0055] Step 2: Update the threshold parameter σ(k);

[0056] Step 3: Use the threshold parameter σ(k) to verify the event-triggered measurement and update the trigger output y(k s );

[0057] Step 4: Use the trigger output y(k s ), update the system state estimate and disturbance estimation

[0058] Step 5: Using state estimation Generate control input u(k) in real time;

[0059] Step 6: Update the algorithm parameters according to the observation error generated by the control input u(k);

[0060] Step 7: Repeat steps 3, 4, 5, and 6 until the current iteration ends and enters the next cycle;

[0061] Step 8: Use Zonotope technology to analyze the reachable set of the error signal observed in each iterative batch;

[0062] Step nine: Calculate the average observation error interval to obtain the interval of the chemical mixing tank system state during normal operation; obtain the safety threshold required for fault detection based on the interval of the state.

[0063] An embodiment of the present invention is described below:

[0064] Considering the event-triggered fault detection problem of the chemical mixing tank system, the corresponding dynamic model is:

[0065]

[0066]

[0067] The system parameters are: c1 = 4 mol / L, c2 = 2 mol / L, c4 = 1 mol / L,

[0068] Figure 1 is a flow chart of the method of the embodiment of the present invention; applying the proposed method, the state response diagram under no fault condition and the obtained state interval are as follows Figure 2-5 As shown in the figure, the observation error can reach the set analysis diagram in the case of no fault. Figure 6 and Figure 7 As shown, it can be seen that in the iterative process, as the number of iterations increases, the reachable set of the observation error becomes smaller and smaller, indicating that the system performance is getting better and better with the number of iterations;

[0069] According to the obtained state interval, it is assumed that the fault starts to appear from k=100, and the value is 0.02rand(1) to test the effectiveness of the fault detection technology of the present invention. Figure 8 The fault detection diagram of δc3(k) of the proposed method under fault conditions is shown. It can be seen from the figure that the proposed method has a tighter safety threshold due to iterative optimization and can also detect faults faster, which shows that the proposed fault detection method has high sensitivity and timeliness.

[0070] References

[0071] [1] WJLin, Y.He, CKZhang, L.Wang, M.Wu. Event-triggered fault detection filter design for discrete-time memristive neural networks with timedelays. IEEE Transactions on Cybernetics, vol.52, pp. 3359-3369, 2022.

[0072] [2]ZHZhang, GHYang.Event-triggered fault detection for a class ofdiscrete-time linear systems using interval observers.ISA transactions, vol.68, pp.160-169, 2017.

Claims

1. An event-triggered fault detection method for a chemical mixing tank system based on iterative interval estimation, characterized in that: The following steps are involved: Using linearization technology, a discrete dynamic model of the chemical mixing tank system is established. The specific steps are as follows: In the formula, x(k)=[δc3(k), δq3(k), δc5(k), δq5(k)] T represents the system state, u(k)=[δq1(k),δq4(k)] T represents the system input, y(k) represents the system output, q i represents the flow rate, c i Indicates the concentration of the chemical, Indicates the target value of flow rate, represents the target value of the concentration of the chemical, i∈{1,…,5} represents the number of the inlet and outlet pipes, and k represents the discrete sampling time; An iterative observer method is designed using the system output at the trigger time, and then the control input is updated through the reconstructed state. The specific steps are as follows: Iteration 0: Iteration m: In the formula, and denote the estimated values ​​of the 0th and mth system states respectively, and They represent the estimated values ​​of the 0th and mth disturbances respectively; Design a dynamic output trigger mechanism consisting of system output and error-dependent trigger parameters to reduce the communication transmission frequency. The specific steps are as follows: In the formula, e y (k) = y(k s )-y(k) represents the measurement error, k s Indicates the last trigger time, k s+1 represents the next triggering time, Ψ represents the weight matrix, σ(k) represents the triggering parameter and is updated by the following formula: In the formula, and σ represent the upper and lower bounds of the trigger parameter, respectively, and α represents the weight parameter; Controlling a chemical mixing tank system using an event-based controller; With Zonotope technology, data from normal system operation is used to generate safety thresholds required for fault detection.

2. The event-triggered fault detection method for a chemical mixing tank system based on iterative interval estimation according to claim 1 is characterized in that: To use an event-based controller to control a chemical mixing tank system, follow these steps: An event-triggered control scheme for the chemical mixing tank system involved was established as follows: Where K is a positive definite feedback gain matrix; this algorithm can ensure the asymptotic stability of the system.

3. The event-triggered fault detection method for a chemical mixing tank system based on iterative interval estimation according to claim 1 is characterized in that: Using Zonotope technology, data from normal system operation is used to generate the safety threshold required for fault detection. The specific steps are as follows: Obtain the normal operation data of the chemical mixing tank system under the designed event-triggered control scheme, and analyze the reachable set of the residual signal of each iterative batch based on the Zonotope technology: In the formula, e [m] (k) and Respectively represent the upper and lower bounds of the observation error, Ω [m] (0) represents the reachable set of the initial value of the observation error, Box(·) represents the interval boundary, represents the Minkowski sum; Further, the average residual signal interval is calculated to generate the interval of the state of the chemical mixing tank system during normal operation; In the formula, x [m] (k) and They represent the upper and lower bounds of the state of the chemical mixing tank system; therefore, the safety threshold required for fault detection can be obtained from the upper and lower bounds of the state.

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