A method for obtaining a gas turbine gas path health benchmark based on a Kalman filter

Abstract

The application belongs to the technical field of aero-engines, and particularly relates to a gas turbine gas path health benchmark acquisition method based on a Kalman filterer. The present application aims at the problem that the existing health benchmark relies on a pure simulation model, leading to a large deviation from the real machine and an easy false alarm and missed alarm of fault diagnosis, and proposes the following scheme: firstly, a gas path performance degradation model is constructed by introducing the efficiency and flow fault factors of components such as compressors and turbines; secondly, the steady-state operating condition data in the healthy state are screened, the fault factors are iteratively optimized, the root mean square error between the model output and the measured data is minimized, and the twin matching of the model and the real machine is realized; then, the calibrated model is linearized at the steady state point, and a segmented discrete state space model is established; finally, the Kalman filterer is used to filter out noise and output high-precision gas path health benchmark values. The present application can also generate fault samples through forward simulation of the calibrated model.

Description

Technical Field

[0001] This application belongs to the field of aero-engine technology, and specifically relates to a method for obtaining gas turbine gas path health benchmarks based on Kalman filters. Background Technology

[0002] The foundation of model-based and data-driven gas turbine fault diagnosis methods lies in the deviation analysis between monitored values ​​and baseline values. Baseline values ​​refer to the operating parameter values ​​and component performance parameter values ​​of the gas turbine under optimal conditions within the current operating boundary. Due to the aerodynamic coupling relationship between the various components of the gas turbine, the baseline state of the gas turbine exhibits a strong dependency on the operating boundary conditions, influenced by factors such as the environment, load, and the equipment's own health status. Only after the health baselines of each operating point within the operating domain are correctly determined can gas turbine anomaly detection, fault location, and severity assessment be performed. Therefore, determining the health baseline is the primary technical issue to be addressed in gas turbine health management, and how to scientifically determine the state baseline values ​​has become one of the key technologies that gas turbine fault diagnosis research needs to solve.

[0003] The current health management program uses a linear interpolation table calculated based on a dynamic simulation model of a gas turbine built on component characteristics as the health benchmark for gas path fault diagnosis.

[0004] The existing technical solutions and their specific disadvantages are as follows:

[0005] 1) The current health management solution uses a linear interpolation table calculated by a dynamic simulation model of a gas turbine based on component characteristics as the health benchmark for gas circuit fault diagnosis. The model itself deviates from the actual test conditions of the gas turbine, which may cause misdiagnosis or missed diagnosis of gas circuit faults and increase maintenance costs.

[0006] 2) There is a lack of real fault data for gas turbines. Without sufficient accumulation of fault data, the gas circuit fault diagnosis algorithm cannot fully learn various fault modes and fault characteristics during training. This results in insufficient generalization ability of the established diagnostic model, which leads to misjudgment or omission when facing untrained faults, affecting the fault diagnosis rate and increasing maintenance costs. Summary of the Invention

[0007] To address the aforementioned issues, this application provides a method for obtaining a gas turbine gas path health benchmark based on a Kalman filter, comprising the following steps:

[0008] Step S1: Using the gas turbine simulation model in the design phase as the ideal health benchmark, a gas path performance degradation model including component performance deviations is established by introducing failure factors that characterize the efficiency and flow degradation of the compressor, high-pressure turbine, and power turbine.

[0009] Step S2: Collect actual operating monitoring data of the gas turbine under healthy conditions, filter steady-state operating condition data according to the preset power fluctuation threshold, and use ambient temperature and ambient pressure as boundary conditions, and fuel quantity and load torque as input parameters;

[0010] Step S3: Input the steady-state operating condition data selected in step S2 into the gas path performance degradation model constructed in step S1, define the root mean square error between the model output and the actual operating data as the objective function, and adjust the fault factor iteratively to make the output parameters of the gas path performance degradation model match the selected steady-state operating condition data, thereby obtaining the calibrated gas path twin model.

[0011] Step S4: Based on the calibrated gas path twin model obtained in step S3, the nonlinear model is linearized at the steady-state operating point. The state space matrix is ​​identified by the step-by-step fitting method, a linear state space model corresponding to each steady-state operating point is constructed, and the linear model is discretized.

[0012] Step S5: Substitute the discretized linear state-space model obtained in step S4 into the Kalman filter algorithm, filter out measurement noise through prediction and correction iteration, and output unbiased estimated gas turbine gas path monitoring parameters, which are used as the gas path health benchmark value under the current operating conditions.

[0013] Preferably, the fault factors mentioned in step S1 specifically include: compressor flow factor, compressor efficiency factor, high-pressure turbine flow factor, high-pressure turbine efficiency factor, power turbine flow factor, and power turbine efficiency factor.

[0014] The efficiency factor is defined as the ratio of the isentropic efficiency under the decay state to the isentropic efficiency under the healthy state, and the flow factor is defined as the ratio of the reduced flow rate under the decay state to the reduced flow rate under the healthy state.

[0015] Preferably, the screening criterion for the steady-state operating condition data in step S2 is:

[0016] Select 1000 consecutive sampling points, i.e., the power generation conversion data within a 20-second time window. If the difference between the maximum and minimum power generation conversion data within the time window is less than 35kW, it is determined to be steady-state operating condition data.

[0017] Preferably, the failure factors of the compressor, high-pressure turbine, and power turbine are calculated and increased or decreased in increments of 0.01.

[0018] Observe whether the changes in exhaust temperature and gas generator speed are changing in the direction of decreasing error;

[0019] When the root mean square error e between the model output value and the actual operating data reaches its minimum value, the iteration stops, and the current fault factor value is output as the initial health status of the component under this operating condition.

[0020] Preferably, the formula for calculating the root mean square error e in step S3 is:

[0021] ;

[0022] Where e is the root mean square error; n is the number of parameters, k n For the nth actual running parameter, g n This is the output value for the nth model.

[0023] Preferably, at the steady-state operating point (x0, u0) determined in step S3, a Taylor expansion is performed on the calibrated gas path twin model obtained in step S3, ignoring higher-order terms, to obtain the following linear state-space equation:

[0024] ;

[0025] Where A, B, C, and D are the system matrix, input matrix, output matrix, and feedforward matrix, respectively.

[0026] Preferably, the step-by-step fitting method in step S4 specifically includes:

[0027] First, perform steady-state fitting on the nonlinear model to ensure that the steady-state response of the state-space model is the same as that of the nonlinear model;

[0028] After meeting the steady-state accuracy requirements, the transient process is then fitted to identify the coefficient matrices A, B, C, and D.

[0029] Preferably, based on the calibrated gas path twin model obtained in step S3, different combinations of fault factors are positively implanted to simulate and generate gas path fault data samples under different fault modes, which are used to expand the gas turbine fault diagnosis dataset.

[0030] Preferably, the maximum relative error of the gas path health baseline value output in step S5 does not exceed 2.2%, and the average relative error does not exceed 0.65%.

[0031] It has the following advantages:

[0032] 1) Accurate gas path health baselines are the foundation for health management status monitoring, health assessment and fault diagnosis. Obtaining accurate gas path health baselines can improve the accuracy of fault early warning and fault diagnosis and reduce the possibility of missed or false alarms.

[0033] 2) Based on accurate gas path health benchmarks, the gas turbine health management system can more accurately predict the maintenance needs of the gas turbine, avoid unnecessary maintenance operations, improve the reliability and availability of the gas turbine, and reduce maintenance costs. Attached Figure Description

[0034] Figure 1 This is the process for establishing a health benchmark model;

[0035] Figure 2 It is the displacement of the operating point and the translation of the characteristic curve of the compressor efficiency characteristics;

[0036] Figure 3 It is a gas path performance degradation model;

[0037] Figure 4 This is a flowchart of the degradation model optimization process;

[0038] Figure 5 It is a comparison of the error before and after the adjustment.

[0039] Figure 6 It is based on the principle of stepwise fitting.

[0040] Figure 7 It is a comparison between the estimation results of the gas turbine health benchmark model and the actual operating data. Detailed Implementation

[0041] To make the objectives, technical solutions, and advantages of this application clearer, the technical solutions in the embodiments of this application will be described in more detail below with reference to the accompanying drawings. In the drawings, the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The described embodiments are only some, not all, of the embodiments of this application. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain this application, and should not be construed as limiting this application. All other embodiments obtained by those skilled in the art based on the embodiments of this application without creative effort are within the scope of protection of this application. The embodiments of this application will be described in detail below with reference to the accompanying drawings. Figure 1

[0042] A gas turbine health baseline model represents the health status of the gas turbine and serves as the criterion for analyzing gas path performance degradation, detecting and diagnosing faults, and assessing gas path health. By setting reasonable thresholds through the health baseline model, fault boundaries are determined, and fault modes are identified to complete model-based research on gas turbine performance monitoring and fault diagnosis. The health baseline is the foundation for gas turbine gas path fault diagnosis, and its specific technical solutions are as follows:

[0043] Gas path health baseline model acquisition based on Kalman filter: Based on the dynamic simulation model of gas turbine components, this study investigated the gas turbine health baseline modeling method, established a state-space model, and designed a Kalman filter to estimate the stable operating conditions of the gas turbine above idle speed. The gas path health baseline model acquisition process based on Kalman filter is as follows: Figure 1 As shown, the specific steps are as follows:

[0044] Step 1: Construction of Gas Turbine Gas Path Performance Degradation Model: The gas turbine model in the design phase is taken as the desired ideal state. Therefore, the gas turbine simulation model in the design phase is defined as an "ideal gas turbine" or ideal machine baseline state model, serving as the absolute evaluation benchmark for this type of turbine.

[0045] When a component of a gas turbine fails, the resulting change in component performance comprises two parts. One part is the shift in the characteristic curve directly caused by the failure; this is an independent quantity, only related to the failure. The other part is the change in parameters caused by the re-matching of components due to a change in the common operating point. For other components that have not failed, their parameters will also change, but their characteristic curves will not shift; their operating points will only move along the characteristic curve due to matching with other components. For example... Figure 1 As shown, this characterizes the displacement of the compressor efficiency characteristic line at the operating point and the translation of the characteristic line under fault conditions.

[0046] It can be seen that the normal common operating point on the compressor efficiency characteristic curve is point A, and the operating point during a fault is point C. The change in performance parameters caused by the fault can be divided into two parts: one part is BC, which is directly caused by the fault, and the other part is the change AB, which is caused by the re-matching of other gas turbine components, resulting in a shift in the characteristic curve. BC is obtained by measuring the parameters, which represents the change in the corresponding performance parameters. As for the characteristic parameters of other components, their operating points will also change, but only by moving along the characteristic curve; the characteristic curve will not shift. Therefore, the fault state of each component can only be characterized by changes in its own characteristics.

[0047] In this study, the dynamic model of the gas turbine in the design phase was modified to add fault factors characterizing the efficiency and flow degradation of gas circuit components such as compressor, high-pressure turbine, and power turbine, and a performance degradation model was established.

[0048] Compressor failure factors:

[0049] (1)

[0050] (2)

[0051] (3)

[0052] (4)

[0053] in, Compressor flow failure factor; This is the equivalent flow rate when compressor performance deteriorates; The flow rate is the equivalent flow rate when the compressor is in good condition; This is a compressor efficiency failure factor; The isentropic efficiency when compressor performance deteriorates; The isentropic efficiency when the compressor is healthy.

[0054] Turbine failure factors:

[0055] (5)

[0056] (6)

[0057] (7)

[0058] (8)

[0059] in, Turbine flow failure factor; This refers to the reduced flow rate when turbine performance deteriorates. The deducted flow rate is calculated when the turbine is healthy. Turbine efficiency failure factor; The isentropic efficiency when turbine performance degrades; The isentropic efficiency when the turbine is healthy.

[0060] When the failure factor is 1, it indicates that the gas turbine's gas path is at an absolutely healthy baseline. This model can be used to characterize the degree of deviation between the actual gas turbine and the design stage.

[0061] Step 2: Gas Turbine Steady-State Operating Data Screening: Select monitoring data from a specific time period under healthy gas turbine conditions, and screen the steady-state operating data to obtain the operating data under steady-state conditions. The selection criterion for steady-state operating conditions is that the difference between the maximum and minimum converted power generation power within 1000 sampling points (20 seconds) is less than 35 kW;

[0062] Step 3: Acquisition of gas turbine health baseline data: Select ambient temperature and ambient pressure as boundary conditions, and parameters such as fuel quantity and load torque as input quantities. Calculate the parameters of each section through the gas turbine dynamic simulation model as the gas turbine health baseline data.

[0063] Establishment of a benchmark model for gas turbine evaluation: Based on the gas turbine simulation model, a gas path performance degradation model is established. Through forward calculation and the incorporation of fault factors, gas path fault data samples can be obtained, addressing the problem of scarce gas turbine fault samples. When the gas turbine model deviates significantly from the actual gas turbine being evaluated, the component characteristics of the gas path performance degradation model need to be optimized and adjusted before obtaining fault data samples from the simulation evaluation machine to ensure consistency with the operating data of the gas turbine being evaluated.

[0064] Therefore, this study uses a trial-and-error method to optimize and match component parameters. The specific process is as follows:

[0065] 1) Based on steps one, two, and three, obtain the current model output value;

[0066] 2) Match the model output values ​​with the actual gas turbine data for calculation:

[0067] (9)

[0068] Where e is the root mean square error (objective function); k is the actual operating parameter; g is the model output value; and n is the number of parameters;

[0069] 3) Observe whether the root mean square error of the calculation results of the gas turbine gas path performance degradation model and the operating data meets the root mean square error requirements;

[0070] 4) If the error requirement is not met, the failure factors of the compressor and turbine are calculated by increasing / decreasing in step size of 0.01 using the trial and error method, and the direction of change of exhaust temperature and gas generator speed is observed to see if they change in the direction of reducing error.

[0071] 5) When the root mean square error e is minimized, the matching ends; otherwise, return to 3) to continue the solution.

[0072] 6) Output the fault factor values ​​that match the experimental data with the model.

[0073] In this study, taking operating condition 1.0 as an example, the default initial values ​​of the fault factors were both 1 before and after adjustment, and the deviations of fuel flow and compressor outlet pressure from the experimental data were greater than 5%. Through optimization, the initial values ​​of the fault factors for compressor efficiency and flow were 1; the initial value of the fault factor for high-pressure turbine efficiency was 1.08, and the initial value of the fault factor for flow was 1.02; the initial value of the fault factor for power turbine efficiency was 0.99, and the initial value of the fault factor for flow was 1.02. A comparison of the model calculation results with the operational data before and after adjustment is shown below. Figure 5 It can be seen that the calculation results of the adjusted gas path attenuation model under normal conditions are consistent with the operating data of the evaluation machine.

[0074] The gas path performance degradation model was optimized and adjusted using experimental data, achieving a matching twin between the model and the baseline data. The optimized component performance parameters are shown in the table.

[0075] Table 1 Initial values ​​of failure factors of major components under different operating conditions

[0076] Operating conditions Compressor flow factor Compressor efficiency factor Power Turbine Flow Factor Power Turbine Efficiency Factor High-pressure turbine flow factor High-pressure turbine efficiency factor Root mean square error 1.0 1.00 1.00 1.02 0.99 1.02 1.08 0.0126 0.9 1.06 0.98 1.00 1.04 1.01 1.04 0.0056 0.8 1.05 0.98 1.01 1.04 1.01 1.04 0.0071 0.6 1.05 0.99 1.00 1.03 1.03 1.02 0.0160 0.5 1.01 1.00 1.00 1.06 1.01 1.00 0.0237 0.3 1.02 0.94 1.00 1.01 1.00 1.04 0.0345

[0077] Further, the gas path performance degradation model can be used as a twin model of a gas turbine. By reverse-calculating the fault factor, the matching between the operating data and the simulation data of the gas path performance degradation model can be achieved.

[0078] Step 4: Obtaining the linear state-space model of the gas turbine: Add a small disturbance of +0.5% to the fuel quantity, linearize the evaluation benchmark model, and obtain the linear state-space model of each steady-state operating point by using the step-by-step fitting method or the subspace modeling method.

[0079] Suppose that the nonlinear thermodynamic model of the gas turbine is expressed in the following form:

[0080] (10)

[0081] in These are state variables, representing the rotational inertia and volumetric inertia of the gas turbine; For control variables; These are environmental condition parameters; These are output variables. It is assumed that the environmental conditions of the gas turbine remain constant, i.e., environmental condition parameters are not considered. At this time, the control variable The only factor determining the operating state of the gas turbine is the nonlinear model, which can be simplified to:

[0082] (11)

[0083] At a certain steady-state operating point Taylor expansion yields:

[0084] (12)

[0085] In the formula, The higher-order terms after Taylor expansion are omitted. (12) The higher-order derivatives above the second order are:

[0086] (13)

[0087] in, , .

[0088] make , , , Then equation (13) can be expressed as:

[0089] (14)

[0090] The coefficient matrix ABCD is identified using a step-by-step fitting method.

[0091] The steady-state and transient processes are fitted separately. The transient process is then fitted while ensuring that the steady-state response of the state-space model and the nonlinear model is identical. The steady-state and transient step-by-step fitting method directly fits the linear equation system, thus maintaining high computational speed while fully utilizing nonlinear data. The state-space model of a split-shaft gas turbine is essentially a system of linear differential equations. The system's inputs, state variables, derivatives of the state variables, and output variables are linearly related; therefore, fitting can be performed based on this linear relationship.

[0092] Figure 6 The flowchart shows the step-by-step fitting method. The first step is the steady-state fitting of the nonlinear model. After the steady-state model is fitted to meet the requirements, the transient fitting begins. If the requirements are met, the coefficient matrix can be solved.

[0093] Thus, a state-space model of the gas turbine was established. However, due to the unavoidable noise during the operation of the gas turbine, the obtained monitoring parameters are not optimal.

[0094] Step 5: Obtaining the Gas Path Health Benchmark Model Based on Kalman Filter. For the gas turbine's spectral operating conditions, a piecewise linear model is established as the health benchmark model for gas path performance monitoring and fault diagnosis. Since the linear state-space model can only represent the dynamic characteristics within a narrow range of operating points, a Kalman filter is designed to reduce the uncertainty of measurement parameters and improve estimation accuracy by utilizing past measurement parameter information. The linear state-space model needs to be discretized.

[0095] (15)

[0096] Based on this form of equation, and assuming initial conditions The Gaussian mean is Covariance is State estimation equation and error covariance prediction:

[0097] (16)

[0098] Corrected equation:

[0099] (17)

[0100] In the formula, For measured values, The Kalman filter estimate is... This is the filtering residual.

[0101] initial state variables Initial error covariance Measurement of noise covariance and system noise covariance This will affect the performance of the Kalman filter. The initial state variable is generally chosen as the initial measurement value. The initial error covariance affects the convergence speed of the covariance matrix and the Kalman filter gain; it is generally chosen as an arbitrary non-zero matrix. Measurement noise. It is closely related to the accuracy of the sensor. The covariance of the process noise is used to obtain the filtered monitoring parameters, thus obtaining the linear reference model of the gas turbine under healthy conditions.

[0102] Comparison between experimental data and model estimated parameters Figure 5 As shown, the blue line represents the actual operating data, and the orange line represents the model estimated data. The operating data of the spectrum condition were estimated. The baseline model estimate is consistent with the operating parameters of the gas turbine spectrum condition. The maximum relative error is 2.167%, and the average relative error is 0.649%, which meets the model accuracy requirements.

[0103] The above research yielded a baseline model for the health of the gas turbine's gas path, laying the foundation for subsequent health management of the gas turbine.

[0104] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A method for obtaining a gas turbine gas path health benchmark based on a Kalman filter, characterized in that, Includes the following steps: Step S1: Using the gas turbine simulation model in the design phase as the ideal health benchmark, a gas path performance degradation model including component performance deviations is established by introducing failure factors that characterize the efficiency and flow degradation of the compressor, high-pressure turbine, and power turbine. Step S2: Collect actual operating monitoring data of the gas turbine under healthy conditions, filter steady-state operating condition data according to the preset power fluctuation threshold, and use ambient temperature and ambient pressure as boundary conditions, and fuel quantity and load torque as input parameters; Step S3: Input the steady-state operating condition data selected in step S2 into the gas path performance degradation model constructed in step S1, define the root mean square error between the model output and the actual operating data as the objective function, and adjust the fault factor iteratively to make the output parameters of the gas path performance degradation model match the selected steady-state operating condition data, thereby obtaining the calibrated gas path twin model. Step S4: Based on the calibrated gas path twin model obtained in step S3, the nonlinear model is linearized at the steady-state operating point. The state space matrix is ​​identified by the step-by-step fitting method, a linear state space model corresponding to each steady-state operating point is constructed, and the linear model is discretized. Step S5: Substitute the discretized linear state-space model obtained in step S4 into the Kalman filter algorithm, filter out measurement noise through prediction and correction iteration, and output unbiased estimated gas turbine gas path monitoring parameters, which are used as the gas path health benchmark value under the current operating conditions.

2. The method for obtaining gas turbine gas path health benchmarks based on Kalman filters as described in claim 1, characterized in that, The fault factors mentioned in step S1 specifically include: compressor flow factor, compressor efficiency factor, high-pressure turbine flow factor, high-pressure turbine efficiency factor, power turbine flow factor, and power turbine efficiency factor. The efficiency factor is defined as the ratio of the isentropic efficiency under the decay state to the isentropic efficiency under the healthy state, and the flow factor is defined as the ratio of the reduced flow rate under the decay state to the reduced flow rate under the healthy state.

3. The method for obtaining gas turbine gas path health benchmarks based on Kalman filters as described in claim 1, characterized in that, The screening criteria for the steady-state operating condition data in step S2 are as follows: Select 1000 consecutive sampling points, i.e., the power generation conversion data within a 20-second time window. If the difference between the maximum and minimum power generation conversion data within the time window is less than 35kW, it is determined to be steady-state operating condition data.

4. The method for obtaining gas turbine gas path health benchmarks based on Kalman filters as described in claim 1, characterized in that, The failure factors of the compressor, high-pressure turbine, and power turbine are calculated and increased or decreased in increments of 0.

01. Observe whether the changes in exhaust temperature and gas generator speed are changing in the direction of decreasing error; When the root mean square error e between the model output value and the actual operating data reaches its minimum value, the iteration stops, and the current fault factor value is output as the initial health status of the component under this operating condition.

5. The method for obtaining gas turbine gas path health benchmarks based on Kalman filters as described in claim 4, characterized in that, The formula for calculating the root mean square error e in step S3 is as follows: ； Where e is the root mean square error; n is the number of parameters, k n For the nth actual running parameter, g n This is the output value for the nth model.

6. The method for obtaining gas turbine gas path health benchmarks based on Kalman filters as described in claim 1, characterized in that, At the steady-state operating point (x0, u0) determined in step S3, a Taylor expansion is performed on the calibrated gas path twin model obtained in step S3. Ignoring higher-order terms, the following linear state-space equation is obtained: ； Where A, B, C, and D are the system matrix, input matrix, output matrix, and feedforward matrix, respectively.

7. The method for obtaining gas turbine gas path health benchmarks based on Kalman filters as described in claim 6, characterized in that, The step-by-step fitting method described in step S4 specifically includes: First, perform steady-state fitting on the nonlinear model to ensure that the steady-state response of the state-space model is the same as that of the nonlinear model; After meeting the steady-state accuracy requirements, the transient process is then fitted to identify the coefficient matrices A, B, C, and D.

8. The method for obtaining gas turbine gas path health benchmarks based on Kalman filters as described in claim 1, characterized in that, Based on the calibrated gas path twin model obtained in step S3, different combinations of fault factors are positively implanted to simulate and generate gas path fault data samples under different fault modes, which are used to expand the gas turbine fault diagnosis dataset.

9. The method for obtaining gas turbine gas path health benchmarks based on Kalman filters as described in claim 1, characterized in that, The maximum relative error of the gas path health baseline value output in step S5 shall not exceed 2.2%, and the average relative error shall not exceed 0.65%.

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