Heat exchanger system multi-actuator fault diagnosis method based on unknown input observer

Abstract

The invention relates to a heat exchanger system multi-actuator fault diagnosis method based on an unknown input observer. The method comprises the following steps: establishing a heat exchanger system model; a heat exchanger system nonlinear state space model with multi-actuator faults is given; rewriting the state space model into a linear variable parameter form by using a parameter Jacobian linearization technology so as to obtain a linear variable parameter model of the heat exchanger system; designing an unknown input observer; designing a diagnosis strategy of fault detection, isolation and estimation according to residual information generated by an unknown input observer; and completing a multi-actuator fault diagnosis task of the heat exchanger system according to the fault diagnosis strategy. The unknown input observer designed by the invention is simple in structure and does not need model state expansion; the designed unknown input observer is high in efficiency, and a fault diagnosis task can be completed on line at different sampling moments by only needing a small amount of computing resources; the designed unknown input observer has high sensitivity to multi-actuator faults; the method has feasibility and effectiveness.

Description

Technical Field

[0001] The present invention belongs to the field of multi-actuator fault diagnosis, and in particular relates to a multi-actuator fault diagnosis method for a heat exchanger system based on an unknown input observer. Background Art

[0002] As the core equipment in the field of industrial chemical industry, heat exchanger has flexible structural design, wide range of material selection, strong adaptability, high temperature and high pressure resistance, etc., so it is widely used in industrial chemical fields such as electricity, chemical industry, food, and pharmaceutical industry, and is a very critical industrial chemical equipment. The stability and efficiency of the operation of the heat exchanger system are directly related to the smoothness of the entire production process and the rational use of energy. However, due to the complexity of the working environment, such as extreme temperature, high pressure, corrosive media, etc., the heat exchanger faces a variety of failure risks, such as decreased heat exchange efficiency, leakage, blockage, etc., which cause the system actuator mechanism to fail and stop working. Not only does it affect production efficiency, it may also cause safety accidents. Therefore, the development of efficient, fast and stable fault diagnosis technology is of great significance to improving the safety, reliability and economy of the heat exchanger system.

[0003] Designing a suitable fault diagnosis method for nonlinear systems such as heat exchangers, which are difficult to establish accurate mathematical models, have complex system structures, and are easily affected by external unknown input disturbances, has become a focus in this field. The unknown input observer shows unique advantages. By designing a specific observer structure, it can effectively identify fault signals without fully understanding all the inputs of the system. Specifically, the unknown input observer can extract fault features from the output signal of the system and maintain sensitivity to fault information even when there are unknown input disturbances in the system. By comparing the difference between the output of the unknown input observer and the actual system output, the residual signal is obtained, which can achieve accurate diagnosis of single or multiple actuator faults, providing key information for timely maintenance measures and avoiding system fault escalation. Summary of the invention

[0004] The present invention provides a multi-actuator fault diagnosis method for a heat exchanger system based on an unknown input observer. An unknown input observer is designed to generate a fault diagnosis signal that is robust to unknown input but sensitive to fault information. It is often used to solve the problem of system fault diagnosis containing model uncertainty or unknown input disturbance. By comparing the residual signal in the designed observer, single or multi-actuator fault diagnosis can be achieved, further solving the safety problem of the heat exchanger system. Its advantage is that it solves the problems of complex structure, low implementation efficiency, high computing resource occupation and weak sensitivity to multiple faults in existing diagnostic methods.

[0005] To achieve the purpose of the present invention, the technical solution is as follows:

[0006] A multi-actuator fault diagnosis method for a heat exchanger system based on an unknown input observer is implemented as follows:

[0007] Step 1: Establish a heat exchanger system model;

[0008] Step 2: Provide a nonlinear state space model of the heat exchanger system with multiple actuator faults;

[0009] Step 3: Use the parameter Jacobian linearization technique to rewrite the state space model into a linear variable parameter form, thereby obtaining a linear variable parameter model of the heat exchanger system;

[0010] Step 4: Design unknown input observer;

[0011] Step 5: Design a fault diagnosis strategy based on the residual information generated by the unknown input observer;

[0012] Step 6: Complete the multi-actuator fault diagnosis task of the heat exchanger system according to the fault diagnosis strategy.

[0013] Furthermore, the heat exchanger system model in step 1 is:

[0014]

[0015] Among them, ρ1, ρ2, ρ p are the fluid density in the tube, shell and wall of the heat exchanger system respectively; C p1 , C p2 , They represent the specific heat capacity of the tube, shell and wall respectively; A represents the heat exchanger area; h1 and h2 represent the heat transfer of the tube and shell respectively; V1, V2, V p They represent the tube volume, shell volume, and wall volume respectively; t represents the time; d represents mathematical differential; Respectively represent the input temperature of the heat exchanger tube and the input temperature of the heat exchanger shell; θ p (t) represent the state variables of the heat exchanger tube, shell and wall at time t respectively; q1(t) and q2(t) represent the cold process flow rate and hot flow rate at time t respectively.

[0016] Furthermore, the nonlinear state space model of the heat exchanger system in step 2 is:

[0017]

[0018] Among them, x(l), u(l), y(l) represent the state vector, input vector, and output vector respectively; represents the first-order differential of x(l); f(·) and g(·) represent the nonlinear function of the input state and the nonlinear function of the output state, respectively; represents m (1, 2, 3, ···) actuator fault input vectors.

[0019] Furthermore, the parameter Jacobian linearization technique is used to rewrite the state space model into a linear variable parameter form:

[0020]

[0021] Among them, A i , B i , C i , D i 、F i , Δx i , Δy i represents a constant matrix of appropriate dimension; μ i (·) is a weighting function; ζ(l) is a scheduling parameter; Represents the summation function from i=1 to M.

[0022] Furthermore, the system matrix of the linear variable parameter model of the heat exchanger system is given as:

[0023]

[0024] in, They represent the state variables of the ith heat exchanger tube and shell at a certain moment. From the above system matrix, the linear variable parameter model of the heat exchanger system can be obtained.

[0025] Furthermore, the unknown input observer in step 4 is:

[0026]

[0027] Where Φ(l) is the state variable of the unknown input observer;

[0028] represents the first-order differential of Φ(l); K i , These are matrices to be designed to achieve unknown input decoupling; is the gain matrix of the unknown input observer.

[0029] Furthermore, the estimated dynamic error and existence condition of the unknown input observer are as follows:

[0030] Estimated dynamic error:

[0031] Where e(t) is the estimated dynamic error of the unknown input observer; represents the first-order differential of e(t).

[0032] Existence conditions:

[0033] Among them, X, W i is a symmetric positive definite matrix; is the unknown input observer matrix to be determined; α is the gain coefficient to be determined; T represents the transposed sign.

[0034] Furthermore, the fault diagnosis strategy in step 5 is:

[0035]

[0036] in, r(l) is the residual information, is the estimated value of the output vector y(l), |·| is the modulus symbol; r th (l) is the preset threshold.

[0037] (1) Fault detection and isolation

[0038]

[0039] in, represents m (1, 2, 3, ···) fault components; r m represents m (1, 2, 3, ···) residual components.

[0040] (2) Fault estimation

[0041]

[0042] in, is the fault estimation value at time t; y(t) is the output variable of the unknown input observer at time t; is the first-order differential of y(t); Φ(t) is the state variable of the unknown input observer at time t; represents the first-order differential of Φ(t); G1 and G2 are both matrices to be determined.

[0043] Compared with the prior art, the present invention has the following advantages:

[0044] 1) The designed unknown input observer has a simple structure and does not require model state expansion;

[0045] 2) The designed unknown input observer is highly efficient and can complete the fault diagnosis task online with only a small amount of computing resources at different sampling times;

[0046] 3) The designed unknown input observer is highly sensitive to multi-actuator faults;

[0047] 4) The present invention has clear ideas and strong feasibility. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 is a flow chart of the method of the present invention;

[0049] Figure 2 It is the fault detection and isolation of heat exchangers in case of multiple actuator failures;

[0050] Figure 3 is the failure estimate of the heat exchanger under multiple actuator failure conditions. DETAILED DESCRIPTION

[0051] The specific implementation of the present invention is described in detail below in conjunction with the accompanying drawings. The specific implementation of the present invention adopts a heat exchanger system.

[0052] The present invention designs an unknown input observer for a heat exchanger system, solving the problem of multi-actuator fault detection, isolation and estimation in the heat exchanger system. The unknown input observer designed by the present invention has a simple structure and does not require model state expansion; the unknown input observer designed is highly efficient and only requires a small amount of computing resources at different sampling times to complete the fault diagnosis task online; the unknown input observer designed is highly sensitive to multi-actuator faults; and the invented method is feasible and effective.

[0053] like Figure 1 As shown in FIG. 1 , a multi-actuator fault diagnosis method for a heat exchanger system based on an unknown input observer is implemented as follows:

[0054] Step 1: Establish a heat exchanger system model;

[0055] The heat exchanger system model is:

[0056]

[0057] Among them, ρ1, ρ2, ρ p are the fluid density in the tube, shell and wall of the heat exchanger system respectively; C p1 , C p2 , They represent the specific heat capacity of the tube, shell and wall respectively; A represents the heat exchanger area; h1 and h2 represent the heat transfer of the tube and shell respectively; V1, V2, V p They represent the tube volume, shell volume, and wall volume respectively; t represents the time; d represents mathematical differential; Respectively represent the input temperature of the heat exchanger tube and the input temperature of the heat exchanger shell; θ p(t) represent the state variables of the heat exchanger tube, shell and wall at time t respectively; q1(t) and q2(t) represent the cold process flow rate and hot flow rate at time t respectively.

[0058] Step 2: Provide a nonlinear state space model of the heat exchanger system with multiple actuator faults;

[0059] The nonlinear state space model of the heat exchanger system with multiple actuator failures is:

[0060]

[0061] Among them, x(l), u(l), y(l) represent the state vector, input vector, and output vector respectively; represents the first-order differential of x(l); f(·) and g(·) represent the nonlinear function of the input state and the nonlinear function of the output state, respectively; represents m (1, 2, 3, ···) actuator fault input vectors.

[0062] Step 3: Use the parameter Jacobian linearization technique to rewrite the state space model into a linear variable parameter form, thereby obtaining a linear variable parameter model of the heat exchanger system;

[0063] Through formula (1), using the parameter Jacobian linearization technique, formula (2) can be rewritten into a linear variable parameter form:

[0064]

[0065] Among them, A i , B i , C i , D i 、F i , Δx i , Δy i represents a constant matrix of appropriate dimension; μ i (·) is a weighting function; ζ(l) is a scheduling parameter; Represents the summation function from i=1 to M.

[0066] The matrix in formula (3) is explained item by item as follows:

[0067]

[0068] in, They represent the state variables of the ith heat exchanger tube and shell at a certain moment. From formula (4), the linear variable parameter model of the heat exchanger system can be obtained.

[0069] Step 4: Design unknown input observer;

[0070] The unknown input observer is:

[0071]

[0072] Where Φ(l) is the state variable of the unknown input observer; represents the first-order differential of Φ(l); K i , These are matrices to be designed to achieve unknown input decoupling; is the gain matrix of the unknown input observer.

[0073] The estimated dynamic error and existence conditions of the unknown input observer are given as follows:

[0074]

[0075] Where e(t) is the estimated dynamic error of the unknown input observer; represents the first-order differential of e(t).

[0076]

[0077] Among them, X, W i is a symmetric positive definite matrix; is the unknown input observer matrix to be determined; α is the gain coefficient to be determined; T represents the transposed sign.

[0078] The proof of formula (7) is as follows:

[0079] V(t)=e(t) T Xe(t) (8)

[0080] Among them, V(t) is the Lyapunov function.

[0081] To ensure the exponential convergence of the estimated dynamic error, there exists:

[0082]

[0083] Derivative of formula (8):

[0084]

[0085] Among them, ζ(t) is the scheduling parameter at time t; is the first-order derivative of the Lyapunov function V(t).

[0086] Substituting formula (8) and (10) into formula (9), we can obtain:

[0087]

[0088] From formula (11), we can see that the estimated dynamic error is exponentially convergent, so formula (7) is proved.

[0089] Step 5: Design a fault diagnosis strategy based on the residual information generated by the unknown input observer;

[0090] The fault diagnosis logic is:

[0091]

[0092] in, r(l) is the residual information, is the estimated value of the output vector y(l), |·| is the modulus symbol; r th (l) is the preset threshold.

[0093] The fault detection and isolation strategy is:

[0094]

[0095] in, represents m (1, 2, 3, ···) fault components; r m represents m (1, 2, 3, ···) residual components.

[0096] The fault estimation strategy is:

[0097]

[0098] in, is the fault estimation value at time t; y(t) is the output variable of the unknown input observer at time t; is the first-order differential of y(t); Φ(t) is the state variable of the unknown input observer at time t; represents the first-order differential of Φ(t); G1 and G2 are both matrices to be determined.

[0099] Step 6: Complete the multi-actuator fault diagnosis task of the heat exchanger system according to the fault diagnosis strategy.

[0100] Example 1

[0101] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the specific implementation cases of the method of the present invention are as follows:

[0102] In order to evaluate the performance and effectiveness of the proposed fault diagnosis method, numerical simulations are performed:

[0103] 1) The cycle time is 8h and the sampling period is 3s

[0104] 2) Initial conditions

[0105] 3)

[0106] 4) Consider the following faults:

[0107]

[0108] Figure 2 It is the fault detection and isolation in case of multiple actuator failures, Figure 3 It is the fault estimation under the condition of multiple actuator failures. From the analysis of the figure, it can be seen that when different types of faults occur in the heat exchanger system in different time periods, the method of the present invention can quickly detect and isolate the faults and accurately estimate the fault information, with high diagnostic accuracy, which lays the foundation for the subsequent fault-tolerant control research.

[0109] The method of the present invention provides a new solution to the problem of heat exchanger system failure. In short, the invention has a clear idea, a simple structure, is easy to implement in engineering, and ensures the safety and reliability of the heat exchanger system.

[0110] The above examples are merely examples for clearly illustrating the present invention, rather than limitations on the implementation modes of the present invention. For ordinary technicians in the relevant field, other different forms of changes or modifications can be made on the basis of the above description to facilitate the understanding and implementation of the invention.

Claims

1. A multi-actuator fault diagnosis method for a heat exchanger system based on an unknown input observer, characterized in that: The steps include: Step 1: Establish a heat exchanger system model; Step 2: Provide a nonlinear state space model of the heat exchanger system with multiple actuator faults; Step 3: Use the parameter Jacobian linearization technique to rewrite the state space model into a linear variable parameter form, thereby obtaining a linear variable parameter model of the heat exchanger system; Step 4: Design unknown input observer; Step 5: Design a fault diagnosis strategy based on the residual information generated by the unknown input observer; Step 6: Complete the multi-actuator fault diagnosis task of the heat exchanger system according to the fault diagnosis strategy.

2. The method for multi-actuator fault diagnosis of a heat exchanger system based on an unknown input observer according to claim 1, characterized in that: The heat exchanger system model in step 1 is: Among them, ρ1, ρ2, ρ p are the fluid density in the tube, shell and wall of the heat exchanger system respectively; C p1 , C p2 , They represent the specific heat capacity of the tube, shell and wall respectively; A represents the heat exchanger area; h1 and h2 represent the heat transfer of the tube and shell respectively; V1, V2, V p They represent the tube volume, shell volume, and wall volume respectively; t represents the time; d represents mathematical differential; Respectively represent the input temperature of the heat exchanger tube and the input temperature of the heat exchanger shell; θ p (t) represent the state variables of the heat exchanger tube, shell and wall at time t respectively; q1(t) and q2(t) represent the cold process flow rate and hot flow rate at time t respectively.

3. The method for multi-actuator fault diagnosis of a heat exchanger system based on an unknown input observer according to claim 2, characterized in that: The nonlinear state space model of the heat exchanger system with multiple actuator failures in step 2 is: Among them, x(l), u(l), and y(l) represent the state vector, input vector, and output vector respectively; represents the first-order differential of x(l); f(·) and g(·) represent the nonlinear function of the input state and the nonlinear function of the output state, respectively; represents m (1, 2, 3, ···) actuator fault input vectors.

4. The method for multi-actuator fault diagnosis of a heat exchanger system based on an unknown input observer according to claim 3, characterized in that: Using the parametric Jacobian linearization technique, the state space model is rewritten into a linear variable parameter form: Among them, A i , B i , C i , D i 、F i , Δx i , Δy i represents a constant matrix of appropriate dimension; μ i (·) is a weighting function; ζ(l) is a scheduling parameter; Represents the summation function from i=1 to M.

5. The method for multi-actuator fault diagnosis of a heat exchanger system based on an unknown input observer according to claim 4, characterized in that: The system matrix of the linear variable parameter model of the heat exchanger system is: in, They respectively represent the state variables of the i-th heat exchanger tube and shell at a certain moment. From the above system matrix, the linear variable parameter model of the heat exchanger system can be obtained.

6. The method for multi-actuator fault diagnosis of a heat exchanger system based on an unknown input observer according to claim 5, characterized in that: The unknown input observer in step 4 is: Where Φ(l) is the state variable of the unknown input observer; represents the first-order differential of Φ(l); K i , These are matrices to be designed to achieve unknown input decoupling; is the gain matrix of the unknown input observer.

7. The method for multi-actuator fault diagnosis of a heat exchanger system based on an unknown input observer according to claim 6, characterized in that: The estimated dynamic error and existence conditions of the unknown input observer are as follows: Estimated dynamic error: Where e(t) is the estimated dynamic error of the unknown input observer; represents the first-order differential of e(t); Existence conditions: Among them, X, W i is a symmetric positive definite matrix; is the unknown input observer matrix to be determined; α is the gain coefficient to be determined; T represents the transposed sign.

8. The method for multi-actuator fault diagnosis of a heat exchanger system based on an unknown input observer according to claim 7, characterized in that: The fault diagnosis strategy in step 5 is: in, r(l) is the residual information, is the estimated value of the output vector y(l), |·| is the modulus symbol; r th (l) is the preset threshold; (1) Fault detection and isolation in, represents m (1, 2, 3, ···) fault components; r m represents m (1, 2, 3, ···) residual components; (2) Fault estimation in, is the fault estimation value at time t; y(t) is the output variable of the unknown input observer at time t; is the first-order differential of y(t); Φ(t) is the state variable of the unknown input observer at time t; represents the first-order differential of Φ(t); G1 and G2 are both matrices to be determined.

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