An engine component performance trend prediction method based on particle filter algorithm

Abstract

The application belongs to the field of engine component design, and particularly relates to an engine component performance trend prediction method based on a particle filtering algorithm. Test data in a stable rotating speed state time period of an engine is obtained, and after interpolation processing, steady state performance identification calculation is performed to obtain a performance correction factor of each component and a decay trajectory of the performance correction factor with test cycles. A health parameter is used to represent the performance decay degree of the engine / component in the decay trajectory to obtain a measurement value of the health parameter at different times, and then an exponential function is estimated by a least square method to establish a state space equation. The state space equation is calculated by a particle filtering algorithm to obtain a component performance parameter result and a probability distribution at a target time. Both the deviation between actual test data points and a regression function and the performance parameter trend change near the current test cycle number are considered, and the performance result and a confidence range thereof at a target cycle number can be effectively predicted.

Description

Technical Field

[0001] This application belongs to the field of engine component design, and specifically relates to a method for predicting the performance trend of engine components based on a particle filter algorithm. Background Technology

[0002] During the entire life cycle of an aero-engine, the overall performance inevitably declines due to factors such as blade contamination, blade erosion, creep, clearance changes, and foreign object damage, while individual components are at risk of failure. These factors have a relatively small impact on the performance of the air intake, combustion chamber, flow path, and nozzle, but a significant impact on the performance of rotating components. Rotating components are the most critical parts of the engine and directly affect its operational safety. Performance trend prediction methods can accurately predict the performance of each engine component at a target time, improving the engine's safety, economy, and reliability.

[0003] Existing technical solutions include model-based methods and data-driven methods, with the data-driven methods including two computational approaches.

[0004] The first method is based on the relationship between component performance parameter values ​​and cycle number across different test runs. It selects a function expression that conforms to the changes in component performance parameters and obtains the component performance result at the target time (cycle number) through extrapolation of the fitted function. The relevant technical solutions are as follows:

[0005] Step 1: Process the test results of steady-state performance parameters of the engine under specified operating conditions for each sustained test run;

[0006] Step 2: Calculate the performance parameters (efficiency and converted flow rate) of each component.

[0007] Step 3: Based on the relationship between performance parameters and the number of cycles, select a suitable function expression, such as fitting using the least squares method;

[0008] Step 4: Extrapolate the fitted function according to time (number of cycles) to calculate the component performance parameter values ​​at the target time.

[0009] First, the least squares method achieves curve fitting for the changing parameters throughout the process by minimizing the sum of squared deviations between all data points and the regression function, assuming that the parameter weights are consistent across all time points from the initial cycle number to the current cycle number. However, it does not focus on the parameter trend changes near the target cycle number, leading to a certain degree of bias in the performance trend extrapolation calculation. Second, while the least squares method can calculate the performance parameter values ​​at the target time (cycle number), it cannot provide the confidence range of the calculated results at the target time (cycle number).

[0010] The second method is a time series prediction method based on a sliding window, and the relevant technical solutions are as follows:

[0011] Step 1: Set up a sliding window, using the actual measured values ​​corresponding to the loop numbers in the sliding window before the current loop number as the feature vector (input variable), and the measured value of the current loop number as the output variable;

[0012] Step 2: Extract the feature vectors and output variables from the trajectory of the component performance correction factor change from the initial loop number to the current loop number, form a training dataset, and complete the training of the time series prediction algorithm;

[0013] Step 3: During multi-step prediction, the historical parameter values ​​within the sliding window are updated to the predicted values ​​corresponding to the current loop number, forming a new feature vector;

[0014] Step 4: Finally, the parameter values ​​between the current cycle number and the target cycle number are predicted sequentially using a time series prediction algorithm.

[0015] Time series-based prediction algorithms involve a large number of hyperparameter settings. Achieving the optimal combination of model parameters requires extensive debugging, comparison, and optimization, and the physical meaning of these parameters is difficult to interpret. Furthermore, this method relies on high-quality training data. Time series-based prediction algorithms use a sliding window approach to extract feature parameters and output parameters from the initial iteration number to the current iteration number. These feature parameters and output parameters are easily affected by noise fluctuations in the experimental data, leading to varying degrees of fluctuation in the prediction results of the trained mathematical model and affecting the prediction accuracy of the measured parameters.

[0016] Therefore, how to more accurately and effectively predict the component performance parameters at the target time (number of cycles) based on continuous test data is a problem that needs to be solved. Summary of the Invention

[0017] To address the aforementioned issues, this application provides a method for predicting the performance trends of engine components based on a particle filter algorithm, thereby resolving the problem of low prediction accuracy of measurement parameters in existing technologies.

[0018] The technical solution of this application is: a method for predicting the performance trend of engine components based on a particle filter algorithm, comprising:

[0019] The test data during the stable engine speed period is obtained, and after interpolation, steady-state performance identification calculation is performed to obtain the decay trajectory of the performance correction factor of each component with the number of test runs.

[0020] The performance degradation of the engine / component in the degradation trajectory is represented by health parameters. The measured values ​​of the health parameters at different times are obtained. Then, the exponential function is estimated by the least squares method to establish the state-space equation.

[0021] The state-space equations are calculated using a particle filter algorithm to obtain the component performance parameters and probability distribution at the target time.

[0022] Preferably, the method for interpolating the test data is as follows:

[0023] The obtained experimental data are averaged using a moving average method. Defective parameter values ​​are removed from the cross-sectional temperature and pressure parameters. An equal-toroidal or equal-flow averaging method is then performed to obtain the processed steady-state performance parameters for the selected engine condition. The interpolation formula for the processed steady-state performance parameters is as follows:

[0024] ;

[0025] In the formula, Y represents the performance parameter, N1r represents the converted speed of the low-pressure rotor, the subscript start represents the starting speed of the interpolation calculation, end represents the ending speed of the interpolation calculation, and current represents the current interpolation speed.

[0026] Preferably, steady-state performance identification calculations are performed, specifically as follows:

[0027] The specific formula for calculating and analyzing the engine's airflow performance is as follows:

[0028] ;

[0029] In the formula, h represents the functional relationship between the measurement parameters and the component performance correction factors, Z represents the measurement parameter vector calculated from the steady-state performance model, and X represents the performance correction factor vector of each component.

[0030] Let δ represent the degree of parameter variation. Performing a first-order Taylor series expansion of h(x) at a given operating point yields:

[0031] ;

[0032] Ignoring the influence of higher-order terms in the influence coefficient matrix H, the following is obtained through matrix transformation:

[0033] ;

[0034] The nonlinear equations are solved using the Newton-Raphson algorithm to calculate the component performance correction factor for each test, thereby obtaining the trajectory of component performance correction factor changes in different tests during sustained testing.

[0035] Preferably, the state-space equations are established as follows:

[0036] Based on the degree of performance degradation, the health parameters of the engine / component at a specified time are calculated using an identification method, thereby obtaining the degradation function of the engine / component health parameters. ,for:

[0037] ;

[0038] In the formula Represents the model parameter vector. This represents the time value corresponding to the decay curve. Indicates measurement parameter noise. This represents a mathematical model / functional relationship between time and health parameters. A function representing engine / component health parameters that change over time;

[0039] Assume the degradation trend of health parameters follows an exponential function, as follows:

[0040] ;

[0041] Based on the measured values ​​of health parameters at different times, the parameters a, b, and c of the exponential function are estimated using the least squares method, where the health parameters at time k are:

[0042] ;

[0043] The measurement equation is established based on the changing trend of the exponential function:

[0044] ;

[0045] in, ;

[0046] The current state variable parameters As parameters of the state variable in the previous moment The function is such that the state parameters at adjacent time points follow a Gaussian distribution, resulting in the state equation:

[0047] ;

[0048] The measurement equation and the state equation are transformed from exponential functions into state-space equations.

[0049] Preferably, the state-space equation is calculated using a particle filtering algorithm. Specifically, based on the state observation equation and historical test data, the particle filtering algorithm tracks the change process of the test data and extrapolates and predicts the component performance parameters at the target time, thereby calculating the component performance parameter results and probability distribution corresponding to the target number of cycles.

[0050] Preferably, the component performance parameter results and probability distribution corresponding to the target number of cycles are calculated, specifically as follows:

[0051] At time k=0, according to the prior probability distribution generate One sampled particle;

[0052] Then, based on the importance probability distribution at time k, samples were taken. Each particle, and to The importance of each particle is calculated to obtain the importance value of each particle.

[0053] The normalized weight of each particle is calculated based on the importance value of each particle and the total importance value.

[0054] Set a threshold for the number of valid samples, and calculate the number of valid samples based on the normalized weight of each particle. When the number of valid samples When the effective sample size threshold is met, the value and weight of each particle are obtained, and the state parameters are estimated based on the value and weight of each particle; if the threshold is not met, resampling is performed.

[0055] The particle sampling and effective sample count are re-evaluated to predict the state up to the current time step, and calculations are performed. By analyzing the state parameters and measurement parameters at a given time, we can obtain the component performance parameters and probability distribution at the target time.

[0056] Preferably, based on the prior probability distribution generate The sampled particles are:

[0057] ;

[0058] Importance probability distribution is ;

[0059] The importance value for each particle is:

[0060] ;

[0061] The normalized weight for each particle is:

[0062] ;

[0063] Number of valid samples for:

[0064] ;

[0065] The state parameters are estimated based on the value and weight of each particle, as follows:

[0066] ;

[0067] ;

[0068] ;

[0069] The state parameters at time t are:

[0070] ;

[0071] The measurement parameters for time are:

[0072] .

[0073] The engine component performance trend prediction method based on particle filter algorithm in this application has the following advantages:

[0074] By identifying the decay trajectory of performance correction factors for each engine component through sustained test run data of a single engine, and selecting a function expression that closely approximates the performance decay trajectory, the method tracks and predicts component performance changes using state equations and particle filtering algorithms. This method considers both the deviation between actual test data points and the regression function, as well as the trend changes of performance parameters near the current test cycle number, and can effectively predict the performance results and their confidence range for the target cycle number.

[0075] Compared with time series prediction algorithms that use sliding windows, the particle filter algorithm based on performance decay trajectories involves model parameters that are easier to understand, has better prediction accuracy than time series-based prediction algorithms, can describe the uncertainty of the prediction result at the target time through confidence intervals, and can interpret the physical meaning of the prediction result. Attached Figure Description

[0076] Figure 1 This is a schematic diagram illustrating the prediction of engine health parameters in this application;

[0077] Figure 2 This is a schematic diagram of the performance degradation trajectory of the component in this application (high-pressure compressor efficiency correction factor);

[0078] Figure 3 This is a schematic diagram of the particle filter algorithm calculation process in this application;

[0079] Figure 4 This is a schematic diagram of the component performance trend prediction results (high-pressure compressor efficiency correction factor) of this application. Detailed Implementation

[0080] 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 inventive 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.

[0081] The first aspect of this application provides a method for predicting the performance trend of engine components based on a particle filter algorithm, comprising the following steps:

[0082] Step S100: Obtain test data within the engine's stable speed period and process it to obtain the engine steady-state performance parameter test results for each test during the sustained test.

[0083] The obtained test data were averaged using a moving average method. Bad parameter values ​​of the cross-sectional temperature and pressure parameters were removed, and equal-flow or equal-circuit averages were performed to obtain the steady-state performance parameters of the selected engine state. The interpolation calculation of the steady-state performance parameter test results is shown in equation (1).

[0084] (1)

[0085] In formula (1), Y represents the performance parameter, N1r represents the converted speed of the low-pressure rotor, the subscript start represents the starting speed of the interpolation calculation, end represents the ending speed of the interpolation calculation, and current represents the current interpolation speed.

[0086] Step S200: Based on the steady-state performance test results of the current test run, identify and calculate the performance correction factors and attenuation trajectory of each component.

[0087] Specifically:

[0088] The specific formula for calculating and analyzing the engine's airflow performance is as follows:

[0089] (2)

[0090] In formula (2), h represents the functional relationship between the measurement parameters and the component performance correction factor, Z represents the measurement parameter vector calculated by the steady-state performance model, and X represents the performance correction factor vector of each component.

[0091] If the performance of a component changes, δ represents the degree of parameter change. A first-order Taylor series expansion of h(x) at a given operating point yields:

[0092] (3)

[0093] The influence coefficient matrix H is obtained, and its mathematical expression is:

[0094] (4)

[0095] Ignoring the influence of higher-order terms in the influence coefficient matrix H, we obtain:

[0096] (5)

[0097] The following was obtained through matrix transformation:

[0098] (6)

[0099] The nonlinear equations are solved using the Newton-Raphson algorithm to obtain the calculated values ​​of the performance correction factors for each component that meet the accuracy requirements of the objective function measurement parameters.

[0100] Using the above identification and calculation method, the component performance correction factor corresponding to each test can be calculated, thereby obtaining the trajectory of component performance correction factor changes in different test cycles during sustained testing.

[0101] Step S300: The degree of performance degradation of the engine / component in the degradation trajectory is represented by health parameters, such as... Figure 1 As shown, the measured values ​​of health parameters at different times are obtained, and then the exponential function is estimated by the least squares method to establish the state-space equation.

[0102] By obtaining the aforementioned performance degradation level, the health parameters of the engine / component at a specified time can be calculated using an identification method. This allows for the acquisition of the degradation trend of the engine / component health parameters at different times, ultimately leading to the determination of the degradation function of the engine / component health parameters. . Figure 1 In this context, RUL represents the remaining engine life, and PDF represents the probability density function of the prediction result.

[0103] (7)

[0104] In the formula Represents the model parameter vector. This represents the time value corresponding to the decay curve. Indicates measurement parameter noise. This represents a mathematical model / functional relationship between time and health parameters. A function representing engine / component health parameters that change over time.

[0105] In order to apply the recursive Bayesian method to estimate the parameters of a dynamic system, the performance degradation model / function in Equation 7 needs to be rewritten in the form of a state-space equation. The performance degradation function can be... Treating it as an observation equation, the function parameters at different times The change is regarded as a state equation, and the specific equation expression is shown in Equations 8 and 9.

[0106] By combining particle filtering methods, the parameters of nonlinear models at different times can be predicted, thereby predicting future performance changes. It is generally assumed that the state parameters at adjacent times follow a Gaussian distribution.

[0107] (8)

[0108] (9)

[0109] In the formula This represents the parameter vector of the decay model. This represents the health parameters at time k. Let the health parameter random variable be a Gaussian distribution. Let represent a state variable parameter random variable that follows a Gaussian distribution.

[0110] Assume the degradation trend of health parameters conforms to the exponential function trend of Equation 10 (see...) Figure 2 Based on the measured health parameters at different times, the parameters a, b, and c of the exponential function are estimated using the least squares method. The calculation method for the health parameters at time k is shown in Equation 11. .

[0111] (10)

[0112] (11)

[0113] To enable computational estimation using the particle filter algorithm, the posterior probability from the previous step is used as the prior probability for the current iteration. The measurement equation can be rewritten as Equation 12; where .

[0114] (12)

[0115] The current state variable parameters As parameters of the state variable in the previous moment The state is a function of the state. It is generally assumed that the state parameters at adjacent time points follow a Gaussian distribution. The state equation is shown in Equation 13.

[0116] (13)

[0117] Therefore, the exponential function can be transformed into a state-space equation using equations (12) and (13) and then calculated and estimated using the particle filter algorithm.

[0118] Step S400, the particle filter calculation method is as follows: Based on the state observation equation and historical test data, the particle filter algorithm tracks the change process of the test data, and extrapolates and predicts the component performance parameters at the target time, calculating the component performance parameter results and probability distribution corresponding to the target cycle number. See [link to detailed calculation process] for details. Figure 3 .

[0119] The specific design is as follows:

[0120] Step 1: Particle set initialization

[0121] At time k=0, according to the prior probability distribution generate One sampled particle.

[0122] (14)

[0123] Step 2: Importance Sampling

[0124] Based on the importance probability distribution at time k Sampling One particle.

[0125] Step 3: Calculate the weights

[0126] According to Equation 15 The importance of each particle is calculated to obtain the importance value of each particle.

[0127] (15)

[0128] Step 4: Normalize weights

[0129] The normalized weight of each particle is calculated based on its importance value and the total importance value. The total importance value is obtained by summing, as shown below:

[0130] (16)

[0131] Step 5: Resampling

[0132] The number of valid samples is calculated according to Equation 17. If ,but , Otherwise, it depends on the importance weight. Resampling : , , This represents the threshold for the number of valid samples.

[0133] (17)

[0134] Step 6: State Estimation

[0135] State parameters are estimated based on equations 18 to 20.

[0136] (18)

[0137] (19)

[0138] (20)

[0139] Step 7: Repeat steps 2 through 6 to predict the state up to the current moment.

[0140] Step 8: Performance Trend Prediction

[0141] Calculated using Equation 21 The state parameters at time t are calculated using Equation 22. Measurement parameters at time. Calculation results and interpretation. Figure 4 .

[0142] (twenty one)

[0143] (twenty two)

[0144] In summary, this application has the following advantages:

[0145] By identifying the decay trajectory of performance correction factors for each engine component through sustained test run data of a single engine, and selecting a function expression that closely approximates the performance decay trajectory, the method tracks and predicts component performance changes using state equations and particle filtering algorithms. This method considers both the deviation between actual test data points and the regression function, as well as the trend changes of performance parameters near the current test cycle number, and can effectively predict the performance results and their confidence range for the target cycle number.

[0146] Compared with time series prediction algorithms that use sliding windows, the particle filter algorithm based on performance decay trajectories involves model parameters that are easier to understand, has better prediction accuracy than time series-based prediction algorithms, can describe the uncertainty of the prediction result at the target time through confidence intervals, and can interpret the physical meaning of the prediction result.

[0147] 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 predicting the performance trend of engine components based on particle filter algorithm, characterized in that, include: The test data during the stable engine speed period is obtained, and after interpolation, steady-state performance identification calculation is performed to obtain the decay trajectory of the performance correction factor of each component with the number of test runs. The performance degradation of the engine / component in the degradation trajectory is represented by health parameters. The measured values ​​of the health parameters at different times are obtained. Then, the exponential function is estimated by the least squares method to establish the state-space equation. The state-space equations are calculated using a particle filter algorithm to obtain the component performance parameters and probability distribution at the target time.

2. The method for predicting engine component performance trends based on particle filter algorithm as described in claim 1, characterized in that, The method for interpolating the experimental data is as follows: The obtained test data are averaged using a moving average method. Defective parameter values ​​are removed from the cross-sectional temperature and pressure parameters. An equal-toroidal or equal-flow averaging method is then performed to obtain the processed steady-state performance parameters for the selected engine condition. The interpolation formula for the processed steady-state performance parameters is as follows: ； In the formula, Y represents the performance parameter, N1r represents the converted speed of the low-pressure rotor, the subscript start represents the starting speed of the interpolation calculation, end represents the ending speed of the interpolation calculation, and current represents the current interpolation speed.

3. The method for predicting engine component performance trends based on particle filter algorithm as described in claim 1, characterized in that, Steady-state performance identification calculations are performed, specifically as follows: The specific formula for calculating and analyzing the engine's airflow performance is as follows: ； In the formula, h represents the functional relationship between the measurement parameters and the component performance correction factors, Z represents the measurement parameter vector calculated from the steady-state performance model, and X represents the performance correction factor vector of each component. Let δ represent the degree of parameter variation. Performing a first-order Taylor series expansion of h(x) at a given operating point yields: ； Ignoring the influence of higher-order terms in the influence coefficient matrix H, the following is obtained through matrix transformation: ； The nonlinear equations are solved using the Newton-Raphson algorithm to calculate the component performance correction factor for each test, thereby obtaining the trajectory of component performance correction factor changes in different tests during sustained testing.

4. The method for predicting engine component performance trends based on particle filter algorithm as described in claim 1, characterized in that, The state-space equations are established as follows: Based on the degree of performance degradation, the health parameters of the engine / component at a specified time are calculated using an identification method, thereby obtaining the degradation function of the engine / component health parameters. ,for: ； In the formula Represents the model parameter vector. This represents the time value corresponding to the decay curve. Indicates measurement parameter noise. This represents a mathematical model / functional relationship between time and health parameters. A function representing engine / component health parameters that change over time; Assume the degradation trend of health parameters follows an exponential function, as follows: ； Based on the measured values ​​of health parameters at different times, the parameters a, b, and c of the exponential function are estimated using the least squares method, where the health parameters at time k are: ； The measurement equation is established based on the changing trend of the exponential function: ； in, ; The current state variable parameters As parameters of the state variable in the previous moment The function is such that the state parameters at adjacent time points follow a Gaussian distribution, resulting in the state equation: ； The measurement equation and the state equation are transformed from exponential functions into state-space equations.

5. The method for predicting engine component performance trends based on particle filter algorithm as described in claim 1, characterized in that, The state-space equations are calculated using a particle filtering algorithm. Specifically, based on the state observation equations and historical experimental data, the particle filtering algorithm tracks the changes in the experimental data and extrapolates and predicts the component performance parameters at the target time. The component performance parameter results and probability distribution corresponding to the target number of cycles are then calculated.

6. The method for predicting engine component performance trends based on particle filter algorithm as described in claim 5, characterized in that, The component performance parameters and probability distribution corresponding to the target number of cycles were calculated as follows: At time k=0, according to the prior probability distribution generate One sampled particle; Then, based on the importance probability distribution at time k, samples were taken. Each particle, and to The importance of each particle is calculated to obtain the importance value of each particle. The normalized weight of each particle is calculated based on the importance value of each particle and the total importance value. Set a threshold for the number of valid samples, and calculate the number of valid samples based on the normalized weight of each particle. When the number of valid samples When the effective sample size threshold is met, the value and weight of each particle are obtained, and the state parameters are estimated based on the value and weight of each particle; if the threshold is not met, resampling is performed. The particle sampling and effective sample count are re-evaluated to predict the state up to the current time step, and calculations are performed. By analyzing the state parameters and measurement parameters at a given time, we can obtain the component performance parameters and probability distribution at the target time.

7. The method for predicting engine component performance trends based on particle filter algorithm as described in claim 6, characterized in that, According to the prior probability distribution generate The sampled particles are: ； Importance probability distribution is ; The importance value for each particle is: ； The normalized weight for each particle is: ; Number of valid samples for: ； The state parameters are estimated based on the value and weight of each particle, as follows: ； ； ； The state parameters at time t are: ； The measurement parameters for time are: 。

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