A method for fault diagnosis of aero-engine rotor bearing system

Abstract

This invention discloses a fault diagnosis method for aero-engine rotor bearing systems. Based on a rotor mechanism model, a multi-degree-of-freedom event-triggered interval observer is designed. More realistic performance indicators are introduced during the residual interval generation process, transforming it into a convex optimization problem under linear matrix inequality constraints. This gives the novel event-triggered interval observer optimal robustness to unknown disturbances and sensitivity to early misalignment faults. The effectiveness of the proposed method is verified through a rotor-bearing system misalignment experimental platform. Compared to the Luenberger interval observer, the newly proposed event-triggered interval observer has a wider range of applications. When the rotor is fault-free, the residual interval contains zeros; once a rotor misalignment fault occurs, the residual interval does not contain zeros. The introduction of an event-triggered mechanism significantly reduces the number of communication calls and alleviates the pressure on the communication network while ensuring detection effectiveness.

Description

Technical Field

[0001] This invention belongs to the field of intelligent system technology application, and specifically relates to a fault diagnosis method for aero-engine rotor bearing system. Background Technology

[0002] With the rapid development of aero-engines, aircraft are becoming faster, higher, and farther. However, the complexity of aero-engines and their long operating hours increase the frequency of malfunctions, leading to irreversible consequences. Aero-engines are one of the causes of the longest downtime and greatest economic losses for aircraft. Therefore, fault diagnosis for aero-engines is crucial. Currently, an increasing number of research groups are focusing on aero-engine fault diagnosis technologies. How to perform online condition monitoring and rapid, accurate fault detection of rotor-bearing systems has become a research hotspot in intelligent maintenance of rotating machinery.

[0003] In aero-engines, the rotor-bearing transmission system acts as a vital artery, transmitting power and motion. Over long-term operation, its precision declines, leading to frequent failures. Rotor-bearing system misalignment is particularly prone to occur in the initial stages. Rotor-bearing system misalignment refers to a misalignment of the rotor's centerline during operation, even though it should be coaxial. This misalignment causes vibration and wear throughout the aero-engine, affecting normal aircraft operation. Early misalignment faults in the rotor-bearing system evolve more slowly and have lower amplitudes compared to sudden failures. These characteristics make early misalignment detection extremely difficult. Model-based analytical methods, compared to data-driven methods, offer a deeper understanding of the rotor system's internal structure, thus demonstrating significant effectiveness in detecting early misalignment faults and excellent real-time performance. The key to model-based analytical methods lies in the generation of residuals and the setting of thresholds. Summary of the Invention

[0004] To address the technical issues of numerous design constraints in interval observers, which can easily lead to unsolvable situations in rotor systems, and the inaccurate detection results caused by unknown interferences in the rotor system covering early misalignment fault signals, this invention aims to provide a fault diagnosis method for aero-engine rotor bearing systems.

[0005] To achieve the above-mentioned technical objectives, the technical solution of the present invention is: a fault diagnosis method for an aero-engine rotor bearing system, comprising the following steps:

[0006] Step 1: Simplify the faulty rotor-bearing system into a vibration model, and then obtain the dynamic model of the misalignment fault in the rotor-bearing system using Newton's second law; including:

[0007] Step 1.1: Establish the differential equation for misalignment of the rotor-bearing system based on Newton's second law; the following equation is obtained:

[0008]

[0009] in, The second derivative in the x-direction. The first derivative in the x-direction. The second derivative in the y-direction. Let be the first derivative in the y-direction, be the displacement response in the x and y directions, be the first derivative for velocity, be the second derivative for acceleration, be m for the coupling mass, be c for the rotor damping coefficient at the bearing, be k for the stiffness of the elastic shaft, be e for mass eccentricity, be ω for rotational speed, be t for time, and be P. x and P y F represents the frictional forces in the x and y directions at the disk, respectively. xc and F yc , respectively, represent the excitation forces received by the rotor in the x and y directions, and g is the gravitational acceleration;

[0010] Step 1.2: Transform the rotor-bearing system misalignment differential equations into state equations;

[0011]

[0012] in, d represents an unknown interference term, f represents a misalignment fault signal, and Λ represents a constant term. The matrix coefficients of the unknown interference term, The matrix coefficients for misalignment faults, where y(k) is the output signal.

[0013] Step 1.3: Establish a dynamic model of the rotor-bearing system misalignment fault by using the state equations sampled periodically with a zero-order hold;

[0014]

[0015] Where Z(k+1) represents the state at the next time step, and matrices A, D, F, and C are derived from matrices... Obtained through a zero-order hold.

[0016] Step 2: Based on the dynamic model of misalignment faults in the rotor-bearing system, design a novel event-triggered interval observer with multiple design degrees of freedom; including:

[0017] Step 2.1: Establish an event trigger so that the output signal can only be transmitted to the fault detection interval observer under specific conditions;

[0018]

[0019] in, And η>0 are the event triggering parameters, y(k) is the output signal, y T (k) is the output rotor. It is the event trigger threshold;

[0020] Step 2.2: Establish a rotor-bearing system misalignment fault zone observer, as follows:

[0021]

[0022] in

[0023]

[0024]

[0025] Z (k) and These are the lower and upper bounds for the estimation of state Z(k), respectively. ξ (k), y (k), All are intermediate variables, ||y(k)||≤Y(k), Ψ, φ, L , All of these are gain parameters of the interval observer (7). r (k) and These represent the lower and upper bounds of the residuals, respectively. The residuals are the differences between the estimated output and the upper and lower bounds. D is the coefficient of the unknown interference term. and d Represents the upper and lower bounds of interference;

[0026] Step 2.3: By improving the rotor-bearing system misalignment fault range observer, a new event-triggered range observer is obtained. This includes the following steps:

[0027] Step 2.3.1: Based on the dynamic model (3) of the rotor-bearing system misalignment fault and the misalignment fault detection interval observer (5), transform (6) and (7) into the following forms:

[0028]

[0029]

[0030] Define e as the dynamic model of misalignment fault in a rotor-bearing system. Z (k) and As shown below:

[0031] e Z (k)=Z(k)-Z (k) (10)

[0032]

[0033] Step 2.3.2: Based on the misalignment fault detection interval observer (7), e ξ (k), and e Z (k), The relationship between them is as follows:

[0034]

[0035]

[0036] Substituting (12) and (13) into formulas (8) and (9), we obtain the following equations:

[0037]

[0038]

[0039] Step 2.3.3: According to We obtain the following inequality

[0040]

[0041]

[0042] Among them, D + =max{0, D}, D - =D + -D, d(k) position interference term;

[0043] Step 2.3.4: According to the definition of event error ε(k) and the dynamic model (3) of the rotor-bearing system misalignment fault given when no fault occurs, the output boundary is ||y(k)||≤Y(k), where the event triggering parameters are explained as follows:

[0044]

[0045] make

[0046] A new type of event-triggered interval observer is obtained:

[0047]

[0048] in

[0049] Step 3: Introduce a more realistic l1 / H during the residual interval generation process of the new event-triggered interval observer. ∞ Performance metrics are used to verify the robustness of the residual interval to unknown disturbances and the sensitivity to early rotor misalignment faults in the novel event-triggered interval observer. The l1 performance metric represents electromagnetic interference. The effect on the residual r(k), i.e., the robustness of the residual relative to bounded disturbances and measurement noise, H ∞ The performance index represents the effect of misalignment fault f(k) on residual r(k), that is, it is used to represent the sensitivity of the residual to the fault signal;

[0050] Step 4: Prove ΨA- in the novel event-triggered interval observer L C and The nonnegative definiteness of the parameters theoretically verifies the feasibility of a novel event-triggered interval observer.

[0051] Step 5: Based on l1 and H ∞ The optimal solution of the parameters in the observer in step 2 is obtained by optimizing the performance indicators, so that the residual interval has the best interference robustness and fault sensitivity;

[0052] Step 6: Compare whether the residual interval contains a zero point to determine whether a fault has occurred; compare the residual interval with the zero point position. If the residual interval contains a zero point, the rotor-bearing system is fault-free; if the residual interval does not contain a zero point, the rotor-bearing system has a fault and an alarm will be triggered.

[0053] Compared with the prior art, the present invention has the following technical effects:

[0054] This invention establishes an intelligent detection model for rotor-bearing systems based on a self-designed event-triggered interval observer, thereby achieving intelligent detection of rotor-bearing system faults. Compared with traditional fault detection methods, the newly proposed event-triggered interval observer has a wider range of applications than the Luenberger interval observer. When there is no rotor fault, the residual interval includes the origin. Once a rotor misalignment fault occurs, the residual interval does not include the origin. By introducing an event-triggered mechanism, the number of communication attempts is greatly reduced while ensuring detection effectiveness, thus alleviating the pressure on the communication network. Attached Figure Description

[0055] Figure 1 It is the overall flowchart;

[0056] Figure 2 This is a schematic diagram of rotor misalignment. Detailed Implementation

[0057] The specific embodiments of the present invention will be further described below with reference to the accompanying drawings. It should be noted that these descriptions are for the purpose of aiding understanding the present invention, but do not constitute a limitation thereof. Furthermore, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0058] Intelligent detection of misalignment faults in rotor-bearing systems has become an important branch and research hotspot in intelligent maintenance. However, existing methods, particularly interval observers, have many design constraints, easily leading to unsolvable situations in rotor systems. Furthermore, unknown disturbances in the rotor system can overshadow early misalignment fault signals, resulting in inaccurate detection results. Therefore, this invention addresses the problem of numerous constraints in interval observers by designing a novel event-triggered interval observer. Compared to the Luenbegrer interval observer, the novel event-triggered interval observer has more design freedom, increasing its application range (i.e., the interval observer has a solvable gain in more practical rotor-bearing systems).

[0059] This embodiment uses the rotor-bearing system commonly used in aero engines as an example to illustrate the aero engine fault diagnosis method designed in this invention. Figure 1 As shown, the steps are as follows.

[0060] Step 1: Simplify the rotor-bearing system with faults into a vibration model, and then obtain the dynamic model of the misalignment fault of the rotor-bearing system using Newton's second law;

[0061] Step 1.1: Figure 2 In the rotor-bearing model shown, neglecting the vibration of the casing and bearing supports, the misalignment differential equation of the rotor-bearing system is established based on Newton's second law. The following equation is obtained:

[0062]

[0063] in, The second derivative in the x-direction. The first derivative in the x-direction. The second derivative in the y-direction. Let be the first derivative in the y-direction, be the displacement response in the x and y directions, be the first derivative for velocity, be the second derivative for acceleration, be m for the coupling mass, be c for the rotor damping coefficient at the bearing, be k for the stiffness of the elastic shaft, be e for mass eccentricity, be ω for rotational speed, be t for time, and be P. x and P y F represents the frictional forces in the x and y directions at the disk, respectively. xc and F yc denoted as x and y, respectively, represent the excitation forces received by the rotor in the x and y directions, and g is the gravitational acceleration.

[0064] Step 1.2: Transform the rotor-bearing system misalignment differential equation (1) into the following state equation:

[0065]

[0066] in, d represents an unknown interference term, f represents a misalignment fault signal, and Λ represents a constant term. The matrix coefficients of the unknown interference term, The matrix coefficients for misalignment faults, where y(k) is the output signal.

[0067] Step 1.3: Establish a dynamic model of the rotor-bearing system misalignment fault by using the state equations sampled periodically through a zero-order hold.

[0068]

[0069] Where Z(k+1) represents the state at the next time step, and matrices A, D, F, and C are derived from matrices... Obtained through a zero-order hold.

[0070] Step 2: Based on the dynamic model of misalignment fault in the rotor-bearing system, design a novel event-triggered interval observer with multiple design degrees of freedom;

[0071] Step 2.1: Establish an event trigger so that the output signal can only be transmitted to the fault detection interval observer under specific conditions.

[0072]

[0073] in, And η>0 are the event triggering parameters, y(k) is the output signal, y T (k) is the output rotor. It is the event trigger threshold.

[0074] Step 2.2: Establish a rotor-bearing system misalignment fault zone observer, as follows:

[0075]

[0076] in

[0077]

[0078]

[0079] Z(k) and These are the lower and upper bounds for the estimation of state Z(k), respectively. ξ (k), y (k), All are intermediate variables, Ψ, φ, L , All of these are gain parameters of the interval observer (7). r (k) and These represent the lower and upper bounds of the residuals, respectively. The residuals are the differences between the estimated output and the upper and lower bounds. D is the coefficient of the unknown interference term. and d This represents the upper and lower bounds of interference.

[0080] Step 2.3: Improve the rotor-bearing system misalignment fault zone observer through the following steps to obtain a new event-triggered zone observer;

[0081] Step 2.3.1: Based on the dynamic model (3) of the rotor-bearing system misalignment fault and the misalignment fault detection interval observer (5), transform (6) and (7) into the following forms:

[0082]

[0083]

[0084] Define a dynamic model for misalignment faults in a rotor-bearing system. e Z (k) and As shown below:

[0085] e Z (k)=Z(k)- Z (k) (10)

[0086]

[0087] Step 2.3.2: Based on the misalignment fault detection interval observer (7), e ξ (k), and e Z (k), The relationship between them is as follows:

[0088]

[0089]

[0090] Substituting (12) and (13) into formulas (8) and (9), we obtain the following equations:

[0091]

[0092]

[0093] Step 2.3.3: According to We obtain the following inequality

[0094]

[0095]

[0096] Among them, D + =max{0, D}, D - =D + -D, d(k) position interference term;

[0097] Step 2.3.4: According to the definition of event error ε(k) and the dynamic model (3) of the rotor-bearing system misalignment fault given when no fault occurs, the output boundary is ||y(k)||≤Y(k), where the event triggering parameters are explained as follows:

[0098]

[0099] make

[0100] A new type of event-triggered interval observer is obtained:

[0101]

[0102] in

[0103] Step 3: Introduce a more realistic l1 / H during the residual interval generation process of the new event-triggered interval observer. ∞ Performance metrics are used to verify the robustness of the residual interval to unknown disturbances and the sensitivity to early rotor misalignment faults in the novel event-triggered interval observer designed in step 2. The l1 performance metric represents electromagnetic interference. The effect on the residual r(k), i.e., the robustness of the residual relative to bounded disturbances and measurement noise, H ∞ The performance index represents the effect of misalignment fault f(k) on residual r(k), that is, it is used to represent the sensitivity of the residual to the fault signal;

[0104] Step 3.1: For the residual l1 / H ∞ The performance metrics are introduced as follows:

[0105] 1) Electromagnetic interference The effect on the residual r(k) is represented by the l1 performance index, which is used to represent the robustness of the residual relative to bounded disturbances and measurement noise, as follows:

[0106]

[0107] in

[0108] 2) The effect of misalignment fault f(k) on residual r(k) is expressed by H. ∞ The performance metric, which represents the sensitivity of the residual to the fault signal, is expressed as follows:

[0109]

[0110] Where 0 ≠ f(k) ∈ l2, It is a weighted matrix.

[0111] Step 3.2: Divide system (19) into two subsystems, namely:

[0112] When there is no fault (f(k)=0)

[0113]

[0114] When there is no electromagnetic interference

[0115]

[0116] Among them, the residual r is divided into r d and r f residual r d Only includes the effects of unknown disturbances, residual r f It only includes the effects of misalignment faults.

[0117] Step 3.3: Obtain the robustness condition for unknown interference during misalignment fault detection.

[0118] The Lyapunov function is given below:

[0119]

[0120] When the following inequalities are satisfied, the system (22) is stable and satisfies the performance index given in (20).

[0121]

[0122]

[0123] Where 0 < σ < 1, ε > 0, η > 0.

[0124] To solve (25), we introduce a slack variable H and obtain the following linear matrix inequality:

[0125]

[0126] To solve (26), we introduce a slack variable H and obtain the following linear matrix inequality:

[0127]

[0128] In this context, * represents a symmetric matrix that is omitted.

[0129] In summary, the electromagnetic interference robustness condition is met, and the system (23) is stable.

[0130] Step 3.4: Obtain the sensitivity conditions for unbalanced faults in the rotor-bearing system.

[0131] Based on system (28), the following Lyapunov function is given.

[0132]

[0133] When the following inequalities are satisfied, the system (24) is stable and satisfies the performance index given in (22).

[0134]

[0135] in η > 0.

[0136] To solve (30), we introduce a slack variable H and obtain the following linear matrix inequality:

[0137]

[0138] In summary, the fault sensitivity condition (21) of the rotor-bearing system is obtained and the system (23) is stable.

[0139] Step 4: Prove the ΨA-LC and ΨA-LC in the novel event-triggered interval observer The nonnegative definiteness of the parameters theoretically verifies the feasibility of a novel event-triggered interval observer.

[0140] Obtain ΨA-LC and The condition for a matrix to be nonnegative is given.

[0141] The non-negativity conditions are as follows:

[0142]

[0143]

[0144] Where i,j=1,2.

[0145] Matrix ΨA-LC and Through slack variables and The following equation is obtained.

[0146]

[0147]

[0148] O, K, R, and S are unknown variables.

[0149] According to (32)-(35), the following inequalities are obtained.

[0150] O i,j a i,j -R i c j ≥0 (36)

[0151] K i,j a i,j -S i c j ≥0 (37)

[0152] Where i,j=1,2,O i,j =O T K i,j =K T R i =R T S i =S T .

[0153] Inequalities (36) and (37) are for ΨA- in system (19) L C and The non-negativity condition of the matrix.

[0154] Step 5: Based on l1 and H ∞ The optimal solution of parameters in the observer in step two is obtained by optimizing the performance indicators, so that the residual interval has the best interference robustness and fault sensitivity.

[0155] The gain parameters of the interval observer are obtained by solving the following optimization problem.

[0156]

[0157] Among them, ι1>0, ι2>0, ι3>0 and ι4>0 are weighting factors, which should be given in advance.

[0158] Step 6: Compare whether the residual interval contains a zero point to determine whether a fault has occurred. Compare the residual interval with the zero point position. If the residual interval contains a zero point, the rotor-bearing system is fault-free; if the residual interval does not contain a zero point, the rotor-bearing system has a fault and an alarm will be triggered.

[0159] Once the residual interval does not include the origin. Then an misalignment fault alarm will be issued.

[0160] In summary, this invention designs a novel event-triggered interval observer, which has a wider range of applications. Furthermore, the introduction of an event-triggered strategy reduces communication pressure and saves computational resources. It also introduces a more practical L1 / H... ∞ Performance metrics are used to increase the robustness of the residual range to unknown disturbances and the sensitivity to early rotor misalignment faults.

Claims

1. An aeroengine rotor bearing system fault diagnosis method, characterized in that: The method comprises the following steps: Step 1: simplifying the rotor-bearing system containing faults into a vibration model, and then obtaining a dynamic model of the misalignment fault of the rotor-bearing system through Newton's second law; Step 2: designing a new event-triggered interval observer with multiple design freedoms according to the dynamic model of the misalignment fault of the rotor-bearing system; Step 3: Introduce more realistic performance index in the residual interval generation process of the novel event-triggered interval observer to verify the unknown disturbance robustness and the rotor early misalignment fault sensitivity of the residual interval in the novel event-triggered interval observer performance index, to verify the unknown disturbance robustness and the rotor early misalignment fault sensitivity of the residual interval in the novel event-triggered interval observer Step 4: Prove the non-negativity of and to theoretically verify the feasibility of the novel event-triggered interval observer. Step 5: According to and The optimal solution of the parameters in the observer of step 2 is obtained by optimization calculation of performance indicators, so that the residual interval has the best disturbance robustness and fault sensitivity. Step 6: comparing the residual interval and the origin position to detect whether the fault of the rotor-bearing system occurs online.

2. The failure diagnosis method according to claim 1, characterized by: In the step 1, the step 1 comprises the following steps: Step 1.1: establishing a misalignment differential equation of the rotor-bearing system according to Newton's second law; the following formula is obtained: (1) where is the x-direction second derivative, is the x-direction first derivative, is the y-direction second derivative, is the y-direction first derivative, the displacement response in x and y directions, the first derivative is velocity, and the second derivative is acceleration, is the coupling mass, is the rotor's damping coefficient at the bearing, is the stiffness of the flexible shaft, is the mass eccentricity, is the rotational speed, and t is time, and are the rub-impact forces in the direction and direction at the disc, respectively, and are the exciting forces received by the rotor in the direction and direction, respectively, is the gravitational acceleration; Step 1.2: converting the misalignment differential equation of the rotor-bearing system into a state equation; (2) wherein , , is an unknown interference term, is a misalignment fault signal, is a constant term, matrix coefficients of the unknown interference term, matrix coefficients of the misalignment fault, is an output signal, ; Step 1.3: establishing a dynamic model of the misalignment fault of the rotor-bearing system through a zero-order holder for the periodically sampled state equation; (3) wherein is the state at the next time instant, the matrix , , , is obtained by the zero-order hold from the matrix , , , .

3. The failure diagnosis method according to claim 1, characterized by: In the step 2, the step 2 comprises the following steps: Step 2.1: establishing an event triggerer, so that the measured output signal can be transmitted to the fault detection interval observer only when a specific condition is met; (4) wherein and is an event trigger parameter, is an output signal, is an output rotor, is an event trigger threshold; Step 2.2: establishing a misalignment fault interval observer of the rotor-bearing system as follows: (5) Wherein (6) (7) and are lower and upper bounds of the state respectively, , , , , , are intermediate variables, , , , are gain parameters of the interval observer (7), and are lower and upper bounds of the residual, which is the difference between the estimated output and the upper and lower bounds, D is the unknown disturbance term coefficient, and represent the upper and lower bounds of the disturbance; Step 2.3: obtaining a new event-triggered interval observer by improving the misalignment fault interval observer of the rotor-bearing system.

4. The failure diagnosis method according to claim 3, characterized by: In the step 2.3, the step 2.3 comprises the following steps: Step 2.3.1: according to the dynamic model (3) of the misalignment fault of the rotor-bearing system and the misalignment fault detection interval observer (5), converting (6) and (7) into the following form: (8) (9) The definition of the dynamic model (3) of the misalignment fault of the rotor-bearing system is as follows: and as follows: (10) (11) Step 2.3.2: The misalignment fault detection interval observer (5) is observed in relation to the misalignment fault detection interval (6) as shown below: ​​​​ (12) (13) Bringing (12) and (13) into the formula (8) and (9) to obtain the following equations: (14) (15) Step 2.3.3: According to the following inequality is obtained (16) (17) wherein = max{0, }, = max{0, - , location interference term; Step 2.3.4: Definition of the event error and the dynamic model of the misalignment fault of the rotor-bearing system (3) given at the time of no fault occurrence, the output boundary is The event trigger parameters are described as follows: (18) Let , , , A new event-triggered interval observer is obtained: (19) wherein , , , , , , .

5. The failure diagnosis method according to claim 1, characterized by: The performance indicator of step 3, The performance indicator represents the electromagnetic interference The influence on the residual error, i.e. the robustness of the residual error with respect to bounded disturbances and measurement noise, The performance indicator represents the misalignment failure The influence on the residual error, i.e. the sensitivity of the residual error with respect to the failure signal.

6. The failure diagnosis method according to claim 1, characterized by: In the step 6, whether the residual interval contains zero is compared to determine whether the fault occurs; if the residual interval contains zero, the rotor-bearing system is fault-free; if the residual interval does not contain zero, the rotor-bearing system is faulty and an alarm is given.

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