A method of assessing in-flight thrust of an aeroengine

By employing a data-driven approach and utilizing neural network models and linear regression calibration, we have achieved a precise quantitative assessment of wing thrust for aero-engines, solving the challenge of thrust assessment in field environments and providing accurate data support.

CN121389818BActive Publication Date: 2026-04-17STATE-OWNED SICHUAN WEST MASCH FACTORY +1
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Patent Information

Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
STATE-OWNED SICHUAN WEST MASCH FACTORY
Filing Date
2025-12-23
Publication Date
2026-04-17

AI Technical Summary

Technical Problem

Existing technologies cannot accurately quantify and assess the on-wing thrust of aero engines in field environments. They mainly rely on subjective perception and lack quantitative data support, making them unsuitable for thrust assessment in complex high-altitude environments.

Method used

Through data acquisition and equivalent conversion, neural network model construction, feature transfer and linear regression calibration, the quantitative assessment of the wing thrust of aero-engines is achieved.

Benefits of technology

It can accurately evaluate the on-wing thrust of aero engines in an outdoor environment without the need for large testing equipment, providing quantitative data to support in-flight performance evaluation and solving the shortcomings of existing technologies that rely on subjective perception.

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Abstract

This invention discloses a method for evaluating the on-wing thrust of an aero-engine, comprising: Step 1, acquiring ground reference data, historical flight monitoring data, and flight monitoring data to be evaluated, and converting them to a standard environment; Step 2, constructing a neural network model, using the state parameters of the converted ground reference data as input, and the converted values ​​of key turbine back parameters and thrust parameters as output; Step 3, selecting the optimal test model through a first feature transfer, i.e., after training multiple instance models, selecting the model with the smallest deviation based on historical flight monitoring data; Step 4, performing thrust evaluation through a second feature transfer, inputting the flight monitoring data to be evaluated into the optimal test model, calculating correction coefficients based on linear regression, calibrating the thrust prediction value, and finally obtaining the engine's physical thrust. This invention can effectively solve the difference between ground and high-altitude operating conditions, and achieve accurate quantitative evaluation of the on-wing thrust of aero-engines.
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Description

Technical Field

[0001] This invention relates to the field of aircraft engine maintenance and support, and in particular to a method for evaluating the on-wing thrust of an aircraft engine. Background Technology

[0002] Aero-engine thrust is a core performance parameter for evaluating fighter jet performance and ensuring mission effectiveness. Its accurate acquisition plays a crucial supporting role in engine operational optimization, dynamic monitoring of performance degradation, and maintenance support decisions. Among them, on-wing thrust specifically refers to the actual thrust generated by the aero-engine when it is mounted on the wing (or fuselage) of the fighter jet and in flight. This is different from the test thrust of the engine on the ground test rig, which is detached from the entire aircraft. It can directly reflect the engine's real working performance in complex high-altitude environments (such as different altitudes, temperatures, and Mach numbers) and in the assembled state of the entire aircraft. It is a core indicator for measuring the fighter jet's air maneuverability and payload carrying capacity.

[0003] Currently, direct measurement of aero-engine thrust can only be achieved in a ground environment: using ground test stands and supporting high-precision sensors and force measuring devices, the thrust of an engine detached from the entire aircraft can be accurately tested, and this technology is relatively mature. However, in practical field applications, obtaining on-wing thrust faces significant bottlenecks: on the one hand, the high-altitude environment presents problems such as drastic temperature fluctuations, large pressure gradient changes, and complex airflow interference, making it difficult to deploy ground test stand-level testing equipment; on the other hand, during fighter jet flight, the engine is deeply coupled with the overall aerodynamic layout, fuel supply system, and avionics control system, making it impossible to obtain thrust data through simple disassembly testing. Therefore, current field assessments of on-wing thrust still mainly rely on pilot subjective perception (such as acceleration response and climb rate), lacking quantitative data support, which severely restricts the accurate evaluation of engine performance status in the air.

[0004] Existing indirect thrust acquisition technologies cannot effectively solve the on-wing thrust assessment problem, and their specific limitations are as follows:

[0005] One approach is the traditional physical modeling method, which requires precise physical modeling of the engine. However, the number of measurement points for the engine in the field is limited, and real-time structural data is lacking, making it difficult to establish a complete model. Chinese patent CN110686813A discloses a method for identifying the thrust of a twin-engine aircraft engine through ground taxiing tests. It uses simplified physical motion equations to solve for the thrust. However, the drawback is that it is only applicable to the taxiing phase and cannot calculate the thrust in the air.

[0006] Secondly, there are data-driven methods. Chinese patent CN112149233A discloses a dynamic thrust estimation method for aero-engines based on echo state networks. A simple artificial intelligence model is established and trained to obtain a thrust estimator. However, its drawback is that it does not consider the influence of different external environments (flight altitude, temperature, Mach number, etc.) on the input parameters, and is only applicable to thrust calculations under the same environment. Chinese patent CN111860791A discloses a thrust estimation method and device for aero-engines based on similarity transformation. This method uses the principle of similarity to convert engine parameters and uses a data-driven model to calculate thrust using the new parameters. Its drawback is that it does not consider the nonlinear offset between different operating conditions; high-altitude environments and ground environments cannot be accurately equivalent based on simple similarity transformations.

[0007] In summary, existing technologies cannot overcome the barriers between ground and high-altitude operating conditions, and cannot achieve accurate quantitative calculation of on-wing thrust of aero engines. Therefore, it is particularly necessary to provide a technical solution that can adapt to the field flight environment and effectively obtain on-wing thrust. Summary of the Invention

[0008] The purpose of this invention is to provide a method for evaluating the on-wing thrust of an aero-engine, which can effectively obtain the on-wing thrust, in order to address the problems mentioned above.

[0009] The technical solution adopted in this invention is as follows:

[0010] A method for evaluating the on-wing thrust of an aero-engine, the method comprising the following steps:

[0011] Step 1: Data Acquisition and Equivalent Conversion: Acquire ground-based reference data, historical flight monitoring data, and flight monitoring data to be evaluated for the aero-engine. The ground-based reference data includes state parameters characterizing the engine's operating status and thrust parameters used as the evaluation target. The historical flight monitoring data and the flight monitoring data to be evaluated include state parameters characterizing the engine's operating status. Convert the ground-based reference data, historical flight monitoring data, and flight monitoring data to be evaluated to standard environmental conditions according to preset rules to obtain the converted ground-based reference data, historical flight monitoring data, and flight monitoring data to be evaluated.

[0012] Step 2: Data-driven model construction: Based on the engine structure, a neural network model is constructed. The state parameters in the converted ground reference data are used as the model input, and the converted values ​​of the turbine back key parameters and thrust parameters in the state parameters are used as the model output.

[0013] Step 3: First Feature Transfer: Based on the converted ground reference data, the training set and validation set are divided. The neural network model is trained in multiple rounds to obtain multiple instance models. The best-performing instance models on the validation set are selected by using a preset loss index. The converted historical flight monitoring data is used as auxiliary domain data input to the selected instance models. The deviation between the converted turbine back key parameter values ​​output by each instance model based on the converted historical flight monitoring data and the measured turbine back key parameter conversion values ​​in the historical flight monitoring data is compared. The instance model with the smallest deviation is selected as the optimal test model.

[0014] Step 4: Secondary Feature Transfer: Input the converted flight monitoring data to be evaluated into the optimal test model to obtain the optimal predicted values ​​of the converted thrust parameters and the optimal predicted values ​​of the converted key parameters behind the turbine output by the optimal test model; Based on the linear regression algorithm, calculate the correction coefficient using the optimal predicted values ​​of the converted key parameters behind the turbine output by the optimal test model and the measured converted values ​​of the converted key parameters behind the turbine in the converted flight monitoring data to be evaluated; calibrate the optimal predicted values ​​of the converted thrust parameters using the correction coefficient to obtain the final predicted value of the converted thrust of the aero-engine on-wing; Based on the thrust conversion formula, convert the final predicted value of the converted thrust of the aero-engine on-wing into the final predicted value of the engine's physical thrust.

[0015] Furthermore, the state parameters mentioned in step 1 include control parameters, gas path cross-section parameters, and variable geometric parameters;

[0016] The control parameters include high-pressure rotor speed N1, low-pressure rotor speed N2, and throttle lever angle PLA;

[0017] The gas path cross-sectional parameters include the total temperature at the fan inlet (T1), the total pressure at the fan inlet (P1), and the total pressure at the compressor outlet (P). 31 Low-pressure turbine after total pressure P6, low-pressure turbine after total temperature T6;

[0018] The variable geometric parameters include fan guide vane angle a1, compressor guide vane angle a2, and engine exhaust nozzle angle D8.

[0019] The thrust parameter is the engine's physical thrust F;

[0020] The key parameters after the turbine are the low-pressure turbine after total pressure P6 or the low-pressure turbine after total temperature T6 in the gas path section parameters.

[0021] Furthermore, according to preset rules, the ground reference data and flight monitoring data are converted to standard environmental conditions, including the high-pressure rotor speed N1, the low-pressure rotor speed N2, and the compressor outlet total pressure P. 31 The specific conversion process for low-pressure turbine after total pressure P6, low-pressure turbine after total temperature T6, and engine physical thrust F is as follows:

[0022] The formula for converting the high-voltage rotor speed is as follows:

[0023] ;

[0024] Where: N 1R X represents the converted high-voltage rotor speed, N1 represents the measured high-voltage rotor speed, and X represents the calculated high-voltage rotor speed. N1 T1 is the high-voltage rotor speed correction factor, 288.15 is the standard ambient reference temperature, T1 is the measured total temperature at the fan inlet, and 273.15 is the temperature conversion factor.

[0025] The formula for converting low-pressure rotor speed is as follows:

[0026] ;

[0027] Where: N 2R X is the converted low-pressure rotor speed, N2 is the measured low-pressure rotor speed, and X is the measured low-pressure rotor speed. N2 T1 is the low-pressure rotor speed correction factor, 288.15 is the standard ambient reference temperature, T1 is the measured total temperature at the fan inlet, and 273.15 is the temperature conversion factor.

[0028] The formula for converting the total pressure at the compressor outlet is as follows:

[0029] ;

[0030] Where: P 31R P is the converted total compressor outlet pressure. 31 P1 represents the measured total pressure at the compressor outlet, 101.325 represents the standard ambient reference pressure, and P1 represents the measured total pressure at the fan inlet.

[0031] The formula for converting total pressure after low-pressure turbine is as follows:

[0032] ;

[0033] Where: P 6R P6 is the converted total pressure after the low-pressure turbine, 101.325 is the standard ambient reference pressure, and P1 is the measured total pressure at the fan inlet.

[0034] The formula for calculating the total temperature after the low-pressure turbine is as follows:

[0035] ;

[0036] Wherein: T 6R T6 represents the converted total temperature after the low-pressure turbine, and X represents the measured total temperature after the low-pressure turbine. T6 273.15 is the total temperature correction factor after the low-pressure turbine, and 273.15 is the temperature conversion factor.

[0037] The formula for converting thrust parameters is as follows:

[0038] ;

[0039] Wherein: F R Here are the converted thrust parameters, where F is the measured physical thrust of the engine, and X is... F P1 is the thrust correction factor, 101.325 is the standard environmental reference pressure, and P1 is the measured total pressure at the fan inlet.

[0040] Furthermore, the neural network model mentioned in step 2 is a long short-term memory neural network model, which includes a parameter input module, a feature extraction module, a feature coupling module, a feature dimensionality reduction module, and a result output module; the specific working process of each module is as follows:

[0041] The parameter input module concatenates l consecutive time series input parameter data into a single input sample, where l is the number of consecutive time series data.

[0042] The feature extraction module extracts features from the input sample and outputs a feature vector of size [l, c1], where c1 is the preset hidden feature dimension.

[0043] The feature coupling module adopts a bidirectional long short-term memory neural network model to perform bidirectional information coupling on the feature vector and outputs a coupled feature vector of length [l, c2], where c2 is the preset hidden feature dimension of the bidirectional long short-term memory neural network model.

[0044] The feature dimensionality reduction module uses a fully connected neural network to flatten and reduce the dimensionality of the coupled feature vectors.

[0045] The result output module outputs a two-dimensional result. ;

[0046] This includes the predicted value of the low-pressure turbine after total pressure from the model output. and the converted and predicted values ​​of the thrust parameters output by the model. .

[0047] Furthermore, in step 3: the preset loss metric is the loss function value Loss calculated on the validation set. Val Loss function value Val The calculation formula is as follows:

[0048] ;

[0049] Where mse() is the mean squared error calculation function, P 6R,Val To verify the converted value of total pressure after the measured low-pressure turbine, F is the predicted value of the low-pressure turbine after total pressure output by the model. R,Val To verify the converted values ​​of the measured thrust parameters, The predicted values ​​are the converted values ​​of the thrust parameters output by the model.

[0050] Furthermore, in step 3, the training set and validation set are divided based on the converted ground reference data. The neural network model is trained multiple times to obtain multiple instance models. The specific process of selecting the best-performing instance models on the validation set using a preset loss metric is as follows:

[0051] The converted ground reference data is divided into a training set and a validation set. The neural network model is trained for w rounds, generating one instance model in each round, resulting in w instance models. The loss function value (Loss) of the w instance models on the validation set is calculated. Val Select the loss function value Loss Val The smallest m-instance model, where 2 ≤ m < w.

[0052] Furthermore, in step 3, the converted historical flight monitoring data is used as auxiliary domain data input to the filtered instance models. The deviations of the converted turbine back-end key parameters output by each instance model based on the converted historical flight monitoring data are compared with the measured converted turbine back-end key parameters in the historical flight monitoring data. The instance model with the smallest deviation is selected as the optimal test model. The specific process is as follows:

[0053] Input the converted historical flight monitoring data into the above m instance models to obtain the predicted low-pressure turbine afterburner total pressure based on the converted historical flight monitoring data output by each instance model. Calculate its conversion value P with the measured low-pressure turbine total pressure in historical flight monitoring data. 6R,Hist The instance model with the smallest mean squared error among the test models is selected as the optimal test model.

[0054] Furthermore, the specific process of step 4 is as follows:

[0055] Step 4.1: Constructing a linear relationship formula based on the linear regression algorithm: Input the converted flight monitoring data to be evaluated into the optimal test model. Construct a linear relationship formula based on the optimal predicted value of the converted turbine back key parameter output by the optimal test model and the measured converted value of the turbine back key parameter in the converted flight monitoring data to be evaluated. The linear relationship formula is as follows:

[0056] ;

[0057] Among them, P 6R,Real This is the converted value of the total pressure after the low-pressure turbine from the flight monitoring data to be evaluated. The optimal predicted values ​​are the converted values ​​of the key parameters after the turbine output by the optimal test model; h1 and h2 are the correction coefficients to be solved; δ is the error of the linear transformation.

[0058] Step 4.2: Define the matrix and vectors needed to solve for the correction coefficients:

[0059] Let n be the number of flight monitoring data samples to be evaluated used to calculate the correction factor, then:

[0060] Input matrix Z: The converted total pressure P after the measured low-pressure turbine from n flight monitoring data samples to be evaluated. 6R,Real The matrix is ​​composed of two columns, one for the constant 1 and the other for the matrix, and its expression is as follows: ;

[0061] The coefficient vector H consists of the correction coefficients h1 and h2 to be solved, and its vector expression is: ;

[0062] Output vector Y: Consisting of n flight monitoring data samples to be evaluated The structure, expressed as a vector, is as follows: ;

[0063] Error vector δ: Composed of the linear transformation errors of n flight monitoring data samples to be evaluated, the vector expression is as follows. ;

[0064] Step 4.3: Derive the formula for solving the correction coefficients and calculate the coefficient vector H:

[0065] Transform the linear relationship formula in step 4.1 into matrix form Y=ZH+δ;

[0066] To minimize the sum of squares of the error vector δ, the formula for solving the correction coefficient vector H is derived using the least squares method:

[0067] ;

[0068] Among them, Z T The transpose of the input matrix Z is obtained by swapping the rows and columns of the input matrix Z; Z T Z is the transpose matrix Z T The product matrix of the input matrix Z is obtained by calculating according to the matrix multiplication rules; (Z) T Z) −1 The inverse of matrix ZTZ is obtained by matrix inversion.

[0069] Substitute the input matrix Z and output vector Y defined in step 4.2 into the above solution formula to calculate the coefficient vector H;

[0070] Step 4.4: Extract correction coefficients and calibrate the optimal predicted thrust parameter conversion values:

[0071] The coefficient vector calculated from step 4.3 In the above, the first element is extracted as the correction coefficient h1 and the second element is extracted as the correction coefficient h2;

[0072] The converted flight monitoring data of the aero-engine to be evaluated is input into the optimal test model to obtain the converted and predicted thrust parameters output by the optimal test model. ;

[0073] The optimal predicted value of the converted thrust parameter according to the calibration formula After calibration, the final predicted value of the on-wing thrust of the aero-engine is obtained. The calibration formula is:

[0074] ;

[0075] in This is the final predicted value of the on-wing thrust of the aero-engine. The optimal predicted value is the converted value of the thrust parameters output by the optimal test model, and h1 and h2 are correction coefficients.

[0076] The formula for calculating the final predicted value of the engine's physical thrust, based on the thrust parameter conversion formula, is as follows:

[0077] ;

[0078] in: This is the final predicted value of the engine's physical thrust. X represents the final predicted value of the on-wing thrust of the aero-engine. F P1 is the thrust correction factor, 101.325 is the standard ambient reference pressure, and P1 is the total pressure at the fan inlet.

[0079] In summary, due to the adoption of the above technical solution, the beneficial effects of the present invention are:

[0080] This invention first converts ground-based benchmark data, historical flight monitoring data, and flight monitoring data to be evaluated to standard environmental conditions, eliminating the impact of environmental differences on parameters. Then, it uses a first feature transfer algorithm to select the optimal test model adapted to the historical flight monitoring data, resolving the incompatibility between ground-trained neural network models and high-altitude operating conditions. Finally, it uses a second feature transfer algorithm based on linear regression to calculate correction coefficients, calibrating the optimal predicted value of the thrust parameter conversion to compensate for the deviation between the model output and the measured value. Finally, it converts the final predicted value of the on-wing thrust of the aero-engine into the final predicted value of the engine's physical thrust. This invention overcomes the operating condition barriers between ground test environments and high-altitude flight environments, eliminating the need for large-scale test equipment that cannot be deployed in the field. It enables the quantitative evaluation of on-wing thrust of aero-engines through data processing and model optimization, overcoming the shortcomings of existing technologies that can only measure ground thrust and rely on subjective perception, providing accurate data support for engine in-flight performance evaluation. Attached Figure Description

[0081] Figure 1 This is a flowchart of the present invention. Detailed Implementation

[0082] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations.

[0083] Therefore, the following detailed description of the embodiments of the invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the invention without inventive effort are within the scope of protection of the invention.

[0084] It should be noted that, unless otherwise specified, the embodiments and features described in this invention can be combined with each other.

[0085] It should be noted that similar labels and letters in the following figures indicate similar items. Therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures.

[0086] In the description of this invention, it should be noted that the terms "center," "upper," "lower," "left," "right," "vertical," "horizontal," "inner," and "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings, or the orientation or positional relationship commonly used when the product of this invention is in use, or the orientation or positional relationship commonly understood by those skilled in the art. They are only used for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of this invention. In addition, the terms "first," "second," etc., are only used to distinguish descriptions and should not be construed as indicating or implying relative importance.

[0087] In the description of this invention, it should also be noted that, unless otherwise explicitly specified and limited, the terms "set," "install," "connect," and "link" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0088] like Figure 1 As shown, this invention discloses a method for evaluating the on-wing thrust of an aero-engine, the method comprising the following steps:

[0089] Step 1: Data Acquisition and Equivalent Conversion: Acquire ground-based reference data, historical flight monitoring data, and flight monitoring data to be evaluated for the aero-engine. The ground-based reference data includes state parameters characterizing the engine's operating status and thrust parameters used as the evaluation target. The historical flight monitoring data and the flight monitoring data to be evaluated include state parameters characterizing the engine's operating status. Convert the ground-based reference data, historical flight monitoring data, and flight monitoring data to be evaluated to standard environmental conditions according to preset rules to obtain the converted ground-based reference data, historical flight monitoring data, and flight monitoring data to be evaluated.

[0090] Step 2: Data-driven model construction: Based on the engine structure, a neural network model is constructed. The state parameters in the converted ground reference data are used as the model input, and the converted values ​​of the turbine back key parameters and thrust parameters in the state parameters are used as the model output.

[0091] Step 3: First Feature Transfer: Based on the converted ground reference data, the training set and validation set are divided. The neural network model is trained in multiple rounds to obtain multiple instance models. The best-performing instance models on the validation set are selected by using a preset loss index. The converted historical flight monitoring data is used as auxiliary domain data input to the selected instance models. The deviation between the converted turbine back key parameter values ​​output by each instance model based on the converted historical flight monitoring data and the measured turbine back key parameter conversion values ​​in the historical flight monitoring data is compared. The instance model with the smallest deviation is selected as the optimal test model.

[0092] Step 4: Secondary Feature Transfer: Input the converted flight monitoring data to be evaluated into the optimal test model to obtain the optimal predicted values ​​of the converted thrust parameters and the optimal predicted values ​​of the converted key parameters behind the turbine output by the optimal test model; Based on the linear regression algorithm, calculate the correction coefficient using the optimal predicted values ​​of the converted key parameters behind the turbine output by the optimal test model and the measured converted values ​​of the converted key parameters behind the turbine in the converted flight monitoring data to be evaluated; calibrate the optimal predicted values ​​of the converted thrust parameters using the correction coefficient to obtain the final predicted value of the converted thrust of the aero-engine on-wing; Based on the thrust conversion formula, convert the final predicted value of the converted thrust of the aero-engine on-wing into the final predicted value of the engine's physical thrust.

[0093] This invention first converts ground-based benchmark data, historical flight monitoring data, and flight monitoring data to be evaluated to standard environmental conditions, eliminating the impact of environmental differences on parameters. Then, it uses a first feature transfer algorithm to select the optimal test model adapted to the historical flight monitoring data, resolving the incompatibility between ground-trained neural network models and high-altitude operating conditions. Finally, it uses a second feature transfer algorithm based on linear regression to calculate correction coefficients, calibrating the optimal predicted value of the thrust parameter conversion to compensate for the deviation between the model output and the measured value. Finally, it converts the final predicted value of the on-wing thrust of the aero-engine into the final predicted value of the engine's physical thrust. This invention overcomes the operating condition barriers between ground test environments and high-altitude flight environments, eliminating the need for large-scale test equipment that cannot be deployed in the field. It enables the quantitative evaluation of on-wing thrust of aero-engines through data processing and model optimization, overcoming the shortcomings of existing technologies that can only measure ground thrust and rely on subjective perception, providing accurate data support for engine in-flight performance evaluation.

[0094] Furthermore, the state parameters mentioned in step 1 include control parameters, gas path cross-section parameters, and variable geometric parameters;

[0095] The control parameters include high-pressure rotor speed N1, low-pressure rotor speed N2, and throttle lever angle PLA;

[0096] The gas path cross-sectional parameters include the total temperature at the fan inlet (T1), the total pressure at the fan inlet (P1), and the total pressure at the compressor outlet (P). 31Low-pressure turbine after total pressure P6, low-pressure turbine after total temperature T6;

[0097] The variable geometric parameters include fan guide vane angle a1, compressor guide vane angle a2, and engine exhaust nozzle angle D8.

[0098] The thrust parameter is the engine's physical thrust F;

[0099] The key parameters after the turbine are the low-pressure turbine after total pressure P6 or the low-pressure turbine after total temperature T6 in the gas path section parameters.

[0100] Furthermore, according to preset rules, the ground reference data and flight monitoring data are converted to standard environmental conditions, including the high-pressure rotor speed N1, the low-pressure rotor speed N2, and the compressor outlet total pressure P. 31 The specific conversion process for low-pressure turbine after total pressure P6, low-pressure turbine after total temperature T6, and engine physical thrust F is as follows:

[0101] The formula for converting the high-voltage rotor speed is as follows:

[0102] ;

[0103] Where: N 1R X represents the converted high-voltage rotor speed, N1 represents the measured high-voltage rotor speed, and X represents the calculated high-voltage rotor speed. N1 T1 is the high-voltage rotor speed correction factor, 288.15 is the standard ambient reference temperature, T1 is the measured total temperature at the fan inlet, and 273.15 is the temperature conversion factor.

[0104] The formula for converting low-pressure rotor speed is as follows:

[0105] ;

[0106] Where: N 2R X is the converted low-pressure rotor speed, N2 is the measured low-pressure rotor speed, and X is the measured low-pressure rotor speed. N2 T1 is the low-pressure rotor speed correction factor, 288.15 is the standard ambient reference temperature, T1 is the measured total temperature at the fan inlet, and 273.15 is the temperature conversion factor.

[0107] The formula for converting the total pressure at the compressor outlet is as follows:

[0108] ;

[0109] Where: P 31R P is the converted total compressor outlet pressure. 31 P1 represents the measured total pressure at the compressor outlet, 101.325 represents the standard ambient reference pressure, and P1 represents the measured total pressure at the fan inlet.

[0110] The formula for converting total pressure after low-pressure turbine is as follows:

[0111] ;

[0112] Where: P 6R P6 is the converted total pressure after the low-pressure turbine, 101.325 is the standard ambient reference pressure, and P1 is the measured total pressure at the fan inlet.

[0113] The formula for calculating the total temperature after the low-pressure turbine is as follows:

[0114] ;

[0115] Wherein: T 6R T6 represents the converted total temperature after the low-pressure turbine, and X represents the measured total temperature after the low-pressure turbine. T6 273.15 is the total temperature correction factor after the low-pressure turbine, and 273.15 is the temperature conversion factor.

[0116] The formula for converting thrust parameters is as follows:

[0117] ;

[0118] Wherein: F R Here are the converted thrust parameters, where F is the measured physical thrust of the engine, and X is... F P1 is the thrust correction factor, 101.325 is the standard environmental reference pressure, and P1 is the measured total pressure at the fan inlet.

[0119] This invention provides specific conversion formulas for core parameters such as high-pressure rotor speed, low-pressure turbine back pressure, and thrust, by introducing a model-adaptive correction coefficient (X). N1 X N2 X T6 By using ground reference data (288.15K, 101.325kPa) and standard environmental reference values ​​(288.15K, 101.325kPa), the measured parameters under different environments are accurately converted to a unified standard environment, eliminating the interference of environmental factors such as temperature and pressure on the parameters. This achieves "environmental normalization" between ground reference data and flight monitoring data, avoiding data deviations caused by uncorrected environmental parameters in existing technologies. It provides parameters of a unified dimension for subsequent model training (based on ground data) and flight data adaptation (first-time migration), ensuring the applicability of the model in cross-environment scenarios and improving the accuracy of basic data for on-wing thrust assessment.

[0120] Furthermore, the neural network model mentioned in step 2 is a long short-term memory neural network model, which includes a parameter input module, a feature extraction module, a feature coupling module, a feature dimensionality reduction module, and a result output module; the specific working process of each module is as follows:

[0121] The parameter input module concatenates l consecutive time series input parameter data into a single input sample, where l is the number of consecutive time series data.

[0122] The feature extraction module extracts features from the input sample and outputs a feature vector of size [l, c1], where c1 is the preset hidden feature dimension.

[0123] The feature coupling module adopts a bidirectional long short-term memory neural network model to perform bidirectional information coupling on the feature vector and outputs a coupled feature vector of length [l, c2], where c2 is the preset hidden feature dimension of the bidirectional long short-term memory neural network model.

[0124] The feature dimensionality reduction module uses a fully connected neural network to flatten and reduce the dimensionality of the coupled feature vectors.

[0125] The result output module outputs a two-dimensional result. ;

[0126] This includes the predicted value of the low-pressure turbine after total pressure from the model output. and the converted and predicted values ​​of the thrust parameters output by the model. .

[0127] In specific implementation, the number of consecutive time-series data entries l in the parameter input module is set to 6, that is, 6 consecutive time-series input parameter data are concatenated to form a single input sample; the preset hidden feature dimension c1 of the feature extraction module is set to 4, and after feature extraction of the input sample, a feature vector of size [6,4] is output. The preset hidden feature dimension c1=4 is a manually set hyperparameter; the feature coupling module uses a bidirectional long short-term memory neural network, and its preset hidden feature dimension c2 is set to 32; when processing the feature vector, this module considers both the information passed forward and the information passed backward between samples. The hidden feature is output once in each of the forward and backward propagation processes, so the final output is a coupled feature vector of length [6,64] (64=2×32); the feature dimensionality reduction module flattens the coupled feature vector of length [6,64] and inputs it into the regression module composed of a fully connected neural network to complete the dimensionality reduction; after dimensionality reduction, the result output module outputs a two-dimensional result. .

[0128] This invention addresses the problems of existing data-driven models neglecting temporal characteristics and lacking dynamic fitting capabilities. By coupling temporal information through bidirectional LSTM and collaborating with multiple modules, it improves the model's accuracy in depicting the dynamic operating state of the engine.

[0129] Furthermore, in step 3: the preset loss metric is the loss function value Loss calculated on the validation set. ValLoss function value Val The calculation formula is as follows:

[0130] ;

[0131] Where mse() is the mean squared error calculation function, P 6R,Val To verify the converted value of total pressure after the measured low-pressure turbine, F is the predicted value of the low-pressure turbine after total pressure output by the model. R,Val To verify the converted values ​​of the measured thrust parameters, The predicted values ​​are the converted values ​​of the thrust parameters output by the model.

[0132] This invention simultaneously measures the predicted value of the low-pressure turbine after total pressure output by the model using mean square error. Predicted values ​​converted from thrust parameters The deviation, focusing on F which is directly related to the wing thrust. R,Val It also incorporates measurable P 6R,Val As a verification measure, this avoids misjudgments of model performance caused by measuring a single parameter, and provides a clear quantitative standard for model selection in a feature transfer process. It addresses the subjective nature of model performance judgment in existing technologies, ensuring that the "optimal performing models" selected from w instance models are suitable for thrust prediction and also align with measured P values. 6R,Val Small deviation; quantified loss metric (Loss) Val This improves the objectivity and reliability of model selection, laying a high-quality candidate foundation for "selecting the optimal test model by combining historical flight monitoring data" in the subsequent feature transfer, and indirectly ensuring the accuracy of on-wing thrust assessment.

[0133] Furthermore, in step 3, the training set and validation set are divided based on the converted ground reference data. The neural network model is trained multiple times to obtain multiple instance models. The specific process of selecting the best-performing instance models on the validation set using a preset loss metric is as follows:

[0134] The converted ground reference data is divided into a training set and a validation set. The neural network model is trained for w rounds, generating one instance model in each round, resulting in w instance models. The loss function value (Loss) of the w instance models on the validation set is calculated. Val Select the loss function value Loss Val The smallest m-instance model, where 2 ≤ m < w.

[0135] Multiple rounds of training cover model states with different initial parameters and data batches, reducing the random bias of single-round models; retaining m optimal models instead of 1 not only selects high-performance long short-term memory neural network instance models, but also maintains model diversity, providing sufficient candidates for further adaptation with flight monitoring data, and solving the problems of insufficient generalization ability and weak anti-interference of single models in existing technologies; setting m candidate models ensures that there are enough high-performance models to choose from during a feature transfer, avoiding failure of high-altitude scenarios due to poor adaptability of a single model, improving the model's adaptability to flight data, and providing a guarantee for selecting the optimal test model that is truly adapted to high-altitude working conditions.

[0136] Furthermore, in step 3, the converted historical flight monitoring data is used as auxiliary domain data input to the filtered instance models. The deviations of the converted turbine back-end key parameters output by each instance model based on the converted historical flight monitoring data are compared with the measured converted turbine back-end key parameters in the historical flight monitoring data. The instance model with the smallest deviation is selected as the optimal test model. The specific process is as follows:

[0137] Input the converted historical flight monitoring data into the above m instance models to obtain the predicted low-pressure turbine afterburner total pressure based on the converted historical flight monitoring data output by each instance model. Calculate its conversion value P with the measured low-pressure turbine total pressure in historical flight monitoring data. 6R,Hist The instance model with the smallest mean squared error among the samples is taken as the optimal test model, i.e. .

[0138] Furthermore, the specific process of step 4 is as follows:

[0139] Step 4.1: Constructing a linear relationship formula based on the linear regression algorithm: Input the converted flight monitoring data to be evaluated into the optimal test model. Construct a linear relationship formula based on the optimal predicted value of the converted turbine back key parameter output by the optimal test model and the measured converted value of the turbine back key parameter in the converted flight monitoring data to be evaluated. The linear relationship formula is as follows:

[0140] ;

[0141] Among them, P 6R,Real This is the converted value of the total pressure after the low-pressure turbine from the flight monitoring data to be evaluated. The optimal predicted values ​​are the converted values ​​of the key parameters after the turbine output by the optimal test model; h1 and h2 are the correction coefficients to be solved; δ is the error of the linear transformation.

[0142] Step 4.2: Define the matrix and vectors needed to solve for the correction coefficients:

[0143] Let n be the number of flight monitoring data samples to be evaluated used to calculate the correction factor, then:

[0144] Input matrix Z: The converted total pressure P after the measured low-pressure turbine from n flight monitoring data samples to be evaluated. 6R,Real The matrix is ​​composed of two columns, one for the constant 1 and the other for the matrix, and its expression is as follows: ;

[0145] The coefficient vector H consists of the correction coefficients h1 and h2 to be solved, and its vector expression is: ;

[0146] Output vector Y: Consisting of n flight monitoring data samples to be evaluated The structure, expressed as a vector, is as follows: ;

[0147] Error vector δ: Composed of the linear transformation errors of n flight monitoring data samples to be evaluated, the vector expression is as follows. ;

[0148] Step 4.3: Derive the formula for solving the correction coefficients and calculate the coefficient vector H: Transform the linear relationship formula in Step 4.1 into matrix form Y=ZH+δ;

[0149] To minimize the sum of squares of the error vector δ, the formula for solving the correction coefficient vector H is derived using the least squares method:

[0150] ;

[0151] Among them, Z T The transpose of the input matrix Z is obtained by swapping the rows and columns of the input matrix Z; Z T Z is the transpose matrix Z T The product matrix of the input matrix Z is obtained by calculating according to the matrix multiplication rules; (Z) T Z) −1 The inverse of matrix ZTZ is obtained by matrix inversion.

[0152] Substitute the input matrix Z and output vector Y defined in step 4.2 into the above solution formula to calculate the coefficient vector H;

[0153] Step 4.4: Extract correction coefficients and calibrate the optimal predicted thrust parameter conversion values:

[0154] The coefficient vector calculated from step 4.3 In the above, the first element is extracted as the correction coefficient h1 and the second element is extracted as the correction coefficient h2;

[0155] The converted flight monitoring data of the aero-engine to be evaluated is input into the optimal test model to obtain the converted and predicted thrust parameters output by the optimal test model. ;

[0156] The optimal predicted value of the converted thrust parameter according to the calibration formula After calibration, the final predicted value of the on-wing thrust of the aero-engine is obtained. The calibration formula is:

[0157] ;

[0158] in This is the final predicted value of the on-wing thrust of the aero-engine. The optimal predicted value is the converted value of the thrust parameters output by the optimal test model, and h1 and h2 are correction coefficients.

[0159] The formula for calculating the final predicted value of the engine's physical thrust, based on the thrust parameter conversion formula, is as follows:

[0160] ;

[0161] in: This is the final predicted value of the engine's physical thrust. X represents the final predicted value of the on-wing thrust of the aero-engine. F P1 is the thrust correction factor, 101.325 is the standard ambient reference pressure, and P1 is the total pressure at the fan inlet.

[0162] Step 4 considers the similarity in generation mechanisms between ground reference data, historical flight monitoring data, and the flight monitoring data to be evaluated. That is, the three types of data have similar characteristic distributions but exhibit scaling and offset. Correction coefficients h1 and h2 are calculated based on the optimal predicted value of the turbine back-end key parameter conversion output by the optimal test model and the measured turbine back-end key parameter conversion value in the flight monitoring data to be evaluated. Since the turbine back-end key parameter conversion value is strongly correlated with the engine thrust parameter conversion value, h1 and h2 can be used to correct the optimal predicted value of the thrust parameter conversion value output by the optimal test model. The entire process requires no additional hardware; deviation compensation can be achieved solely through data and algorithms, solving the problem of large deviations between thrust results and actual high-altitude values ​​in existing technologies. Finally, the calibrated on-wing thrust conversion value of the aero-engine is converted into the final predicted value of the engine's physical thrust, achieving accurate quantitative evaluation of the on-wing thrust of the aero-engine.

[0163] Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for evaluating the on-wing thrust of an aero-engine, characterized in that: The method includes the following steps: Step 1: Data Acquisition and Equivalent Conversion: Acquire ground-based reference data, historical flight monitoring data, and flight monitoring data to be evaluated for the aero-engine. The ground-based reference data includes state parameters characterizing the engine's operating status and thrust parameters used as the evaluation target. The historical flight monitoring data and the flight monitoring data to be evaluated include state parameters characterizing the engine's operating status. Convert the ground-based reference data, historical flight monitoring data, and flight monitoring data to be evaluated to standard environmental conditions according to preset rules to obtain the converted ground-based reference data, historical flight monitoring data, and flight monitoring data to be evaluated. Step 2: Data-driven model construction: Based on the engine structure, a neural network model is constructed. The state parameters in the converted ground reference data are used as the model input, and the converted values ​​of the turbine back key parameters and thrust parameters in the state parameters are used as the model output. Step 3: First Feature Transfer: Based on the converted ground reference data, the training set and validation set are divided. The neural network model is trained in multiple rounds to obtain multiple instance models. The best-performing instance models on the validation set are selected by using a preset loss index. The converted historical flight monitoring data is used as auxiliary domain data input to the selected instance models. The deviation between the converted turbine back key parameter values ​​output by each instance model based on the converted historical flight monitoring data and the measured turbine back key parameter conversion values ​​in the historical flight monitoring data is compared. The instance model with the smallest deviation is selected as the optimal test model. Step 4: Secondary Feature Transfer: Input the converted flight monitoring data to be evaluated into the optimal test model to obtain the optimal predicted values ​​of the converted thrust parameters and the optimal predicted values ​​of the converted key parameters behind the turbine output by the optimal test model; Based on the linear regression algorithm, calculate the correction coefficient using the optimal predicted values ​​of the converted key parameters behind the turbine output by the optimal test model and the measured converted values ​​of the converted key parameters behind the turbine in the converted flight monitoring data to be evaluated; calibrate the optimal predicted values ​​of the converted thrust parameters using the correction coefficient to obtain the final predicted value of the converted thrust of the aero-engine on-wing; Based on the thrust conversion formula, convert the final predicted value of the converted thrust of the aero-engine on-wing into the final predicted value of the engine's physical thrust.

2. The on-wing thrust evaluation method for aero-engines according to claim 1, characterized in that: The state parameters mentioned in step 1 include control parameters, gas path cross-section parameters, and variable geometric parameters; The control parameters include high-pressure rotor speed N1, low-pressure rotor speed N2, and throttle lever angle PLA; The gas path cross-sectional parameters include the total temperature at the fan inlet (T1), the total pressure at the fan inlet (P1), and the total pressure at the compressor outlet (P). 31 Low-pressure turbine after total pressure P6, low-pressure turbine after total temperature T6; The variable geometric parameters include fan guide vane angle a1, compressor guide vane angle a2, and engine exhaust nozzle angle D8. The thrust parameter is the engine's physical thrust F; The key parameters after the turbine are the low-pressure turbine after total pressure P6 or the low-pressure turbine after total temperature T6 in the gas path section parameters.

3. The on-wing thrust evaluation method for aero-engines according to claim 2, characterized in that: According to preset rules, ground reference data and flight monitoring data are converted to standard environmental conditions, including high-pressure rotor speed N1, low-pressure rotor speed N2, and compressor outlet total pressure P. 31 The specific conversion process for low-pressure turbine after total pressure P6, low-pressure turbine after total temperature T6, and engine physical thrust F is as follows: The formula for converting the high-voltage rotor speed is as follows: ; Where: N 1R X represents the converted high-voltage rotor speed, N1 represents the measured high-voltage rotor speed, and X represents the calculated high-voltage rotor speed. N1 T1 is the high-voltage rotor speed correction factor, 288.15 is the standard ambient reference temperature, T1 is the measured total temperature at the fan inlet, and 273.15 is the temperature conversion factor. The formula for converting low-pressure rotor speed is as follows: ; Where: N 2R X is the converted low-pressure rotor speed, N2 is the measured low-pressure rotor speed, and X is the measured low-pressure rotor speed. N2 T1 is the low-pressure rotor speed correction factor, 288.15 is the standard ambient reference temperature, T1 is the measured total temperature at the fan inlet, and 273.15 is the temperature conversion factor. The formula for converting the total pressure at the compressor outlet is as follows: ; Where: P 31R P is the converted total compressor outlet pressure. 31 P1 represents the measured total pressure at the compressor outlet, 101.325 represents the standard ambient reference pressure, and P1 represents the measured total pressure at the fan inlet. The formula for converting total pressure after low-pressure turbine is as follows: ; Where: P 6R P6 represents the measured total pressure after the low-pressure turbine, 101.325 is the standard ambient reference pressure, and P1 is the measured total pressure at the fan inlet. The formula for converting the total temperature after the low-pressure turbine is as follows: ; Wherein: T 6R T6 represents the converted total temperature after the low-pressure turbine, and X represents the measured total temperature after the low-pressure turbine. T6 273.15 is the total temperature correction factor after the low-pressure turbine, and 273.15 is the temperature conversion factor. The formula for converting thrust parameters is as follows: ; Wherein: F R Here are the converted thrust parameters, where F is the measured physical thrust of the engine, and X is... F P1 is the thrust correction factor, 101.325 is the standard environmental reference pressure, and P1 is the measured total pressure at the fan inlet.

4. The on-wing thrust evaluation method for aero-engines according to claim 1, characterized in that: The neural network model mentioned in step 2 is a long short-term memory neural network model, which includes a parameter input module, a feature extraction module, a feature coupling module, a feature dimensionality reduction module, and a result output module; the specific working process of each module is as follows: The parameter input module concatenates l consecutive time series input parameter data into a single input sample, where l is the number of consecutive time series data. The feature extraction module extracts features from the input sample and outputs a feature vector of size [l, c1], where c1 is the preset hidden feature dimension. The feature coupling module adopts a bidirectional long short-term memory neural network model to perform bidirectional information coupling on the feature vector and outputs a coupled feature vector of length [l, c2], where c2 is the preset hidden feature dimension of the bidirectional long short-term memory neural network model. The feature dimensionality reduction module uses a fully connected neural network to flatten and reduce the dimensionality of the coupled feature vectors. The result output module outputs a two-dimensional result. ; This includes the predicted value of the low-pressure turbine after total pressure from the model output. and the converted and predicted values ​​of the thrust parameters output by the model. .

5. The on-wing thrust evaluation method for aero-engines according to claim 1, characterized in that: In step 3: the preset loss metric is the loss function value Loss calculated on the validation set. Val Loss function value Val The calculation formula is as follows: ; Where mse() is the mean squared error calculation function, P 6R,Val To verify the converted value of total pressure after the measured low-pressure turbine, F is the predicted value of the low-pressure turbine after total pressure output by the model. R,Val To verify the converted values ​​of the measured thrust parameters, The predicted values ​​are the converted values ​​of the thrust parameters output by the model.

6. The on-wing thrust evaluation method for aero-engines according to claim 5, characterized in that: In step 3, the training set and validation set are divided based on the converted ground reference data. The neural network model is trained multiple times to obtain multiple instance models. The specific process of selecting the best-performing instance models on the validation set using a preset loss metric is as follows: The converted ground reference data is divided into a training set and a validation set. The neural network model is trained for w rounds, generating one instance model in each round, resulting in w instance models. The loss function value (Loss) of the w instance models on the validation set is calculated. Val Select the loss function value Loss Val The smallest m-instance model, where 2 ≤ m < w.

7. The on-wing thrust evaluation method for aero-engines according to claim 6, characterized in that: In step 3, the converted historical flight monitoring data is used as auxiliary domain data input to the filtered instance models. The deviations of the converted turbine back-end key parameters output by each instance model based on the converted historical flight monitoring data are compared with the measured converted turbine back-end key parameters in the historical flight monitoring data. The instance model with the smallest deviation is selected as the optimal test model. The specific process is as follows: Input the converted historical flight monitoring data into the above m instance models to obtain the predicted low-pressure turbine afterburner total pressure output by each instance model based on the converted historical flight monitoring data. Calculate its conversion value P with the measured low-pressure turbine total pressure in historical flight monitoring data. 6R,Hist The instance model with the smallest mean squared error among the test models is selected as the optimal test model.

8. The on-wing thrust evaluation method for aero-engines according to claim 1, characterized in that: The specific process of step 4 is as follows: Step 4.1: Construct a linear relationship formula based on the linear regression algorithm: The converted flight monitoring data to be evaluated is input into the optimal test model. A linear relationship formula is constructed based on the optimal predicted value of the converted turbine back key parameter output by the optimal test model and the measured converted value of the turbine back key parameter in the converted flight monitoring data to be evaluated. The linear relationship formula is as follows: ; Among them, P 6R,Real This is the converted value of the total pressure after the low-pressure turbine from the flight monitoring data to be evaluated. The optimal predicted values ​​are the converted values ​​of the key parameters after the turbine output by the optimal test model; h1 and h2 are the correction coefficients to be solved; δ is the error of the linear transformation. Step 4.2: Define the matrix and vectors needed to solve for the correction coefficients: Let n be the number of flight monitoring data samples to be evaluated used to calculate the correction factor, then: Input matrix Z: Calculated low-pressure turbine back pressure P from n flight monitoring data samples to be evaluated. 6R,Real The matrix is ​​composed of two columns, one for the constant 1 and the other for the matrix, and its expression is as follows: ; The coefficient vector H consists of the correction coefficients h1 and h2 to be solved, and its vector expression is as follows: ; Output vector Y: Consisting of n flight monitoring data samples to be evaluated The structure, expressed as a vector, is as follows: ; Error vector δ: Composed of the linear transformation errors of n flight monitoring data samples to be evaluated, the vector expression is as follows. ; Step 4.3: Derive the formula for solving the correction coefficients and calculate the coefficient vector H: Transform the linear relationship formula in step 4.1 into matrix form Y=ZH+δ; To minimize the sum of squares of the error vector δ, the formula for solving the correction coefficient vector H is derived using the least squares method: ; Among them, Z T The transpose of the input matrix Z is obtained by swapping the rows and columns of the input matrix Z; Z T Z is the transpose matrix Z T The product matrix of the input matrix Z is obtained by calculating according to the matrix multiplication rules; (Z) T Z) −1 For matrix Z T The inverse matrix of Z is obtained by matrix inversion operation; Substitute the input matrix Z and output vector Y defined in step 4.2 into the above solution formula to calculate the coefficient vector H; Step 4.4: Extract correction coefficients and calibrate the optimal predicted thrust parameter conversion values: The coefficient vector calculated from step 4.3 In the above, the first element is extracted as the correction coefficient h1 and the second element is extracted as the correction coefficient h2; The converted flight monitoring data of the aero-engine to be evaluated is input into the optimal test model to obtain the converted and predicted thrust parameters output by the optimal test model. ; The optimal predicted value of the converted thrust parameter according to the calibration formula After calibration, the final predicted value of the on-wing thrust of the aero-engine is obtained. The calibration formula is: ; in This is the final predicted value of the on-wing thrust of the aero-engine. The optimal predicted value is the converted value of the thrust parameters output by the optimal test model, and h1 and h2 are correction coefficients. The formula for calculating the final predicted value of the engine's physical thrust, based on the thrust parameter conversion formula, is as follows: ; in: This is the final predicted value of the engine's physical thrust. X represents the final predicted value of the on-wing thrust of the aero-engine. F P1 is the thrust correction factor, 101.325 is the standard ambient reference pressure, and P1 is the total pressure at the fan inlet.

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