Mechanism-data dual-driven correction method for transient effects of aero-engine

Abstract

The application provides a mechanism-data double-driven aero-engine transient effect correction method, which is applied to the technical field of aero-engine health management. The method comprises the following steps: acquiring the rotor speed of the aero-engine at adjacent time points, and determining the direction marker of the current working condition of the aero-engine; acquiring the sensor measurement vector of the aero-engine under the transient working condition, determining the mechanism prediction value corresponding to the sensor measurement vector of the aero-engine and the mechanism residual error corresponding to the sensor measurement vector based on a preset mechanism baseline model; constructing an augmented observable vector according to the direction marker of the current working condition of the aero-engine and the mechanism residual error; predicting the augmented observable vector through a pre-trained augmented Koopman operator to obtain a residual prediction value corresponding to the mechanism residual error; and determining the transient effect correction value of the aero-engine according to the mechanism prediction value corresponding to the sensor measurement vector and the residual prediction value. The method realizes accurate correction of the transient effect.

Description

Technical Field

[0001] This application relates to the field of aero-engine health management technology, and in particular to a method for correcting transient effects in aero-engines based on a mechanism-data dual-drive approach. Background Technology

[0002] The performance diagnosis of aero-engine airflow systems relies on the accurate interpretation of sensor data. Traditional diagnostic methods typically assume the engine is in a steady-state condition, where measurements are only related to current control inputs and health parameters. However, in actual flight missions, engines frequently experience transient processes such as acceleration and deceleration. Under transient conditions, due to factors such as thermal inertia and rotor inertia, sensor measurements can deviate significantly from the steady-state mapping surface, resulting in dynamic deviations of up to 10% to 20% of the steady-state values.

[0003] Existing methods for correcting transient effects in aero-engines mainly fall into two categories. One category is dynamic compensation methods based on classical control theory, which correct the sensor's dynamic response by establishing a simplified first- or second-order transfer function model. However, their compensation accuracy is limited and they are ill-suited for wide-range, multi-variable nonlinear transient processes. The other category is data-driven black-box modeling methods, which use tools such as neural networks or support vector regression to fit transient data. These methods lack physical constraints, have poor extrapolation capabilities, and are prone to producing unreasonable outputs under boundary conditions.

[0004] As can be seen, the existing methods described above result in the transient components in the sensor measurements being coupled with the health degradation signal under transient conditions, making them difficult to separate. This can easily lead to serious deviations in health parameter estimation and system misdiagnosis. Summary of the Invention

[0005] This application provides a mechanism-data dual-driven method for correcting transient effects in aero-engines. This method addresses the shortcomings of existing technologies where transient components in sensor measurements are coupled with health degradation signals, making them difficult to separate. This leads to a significant decrease in the accuracy of gas path performance diagnosis and even system misdiagnosis. The method achieves accurate separation of transient dynamic deviations and health degradation signals in sensor measurements under transient conditions and accurate correction of transient effects.

[0006] This application provides a mechanism-data dual-driven method for correcting transient effects in aero-engines, including: Obtain the rotor speed of the aero-engine at adjacent moments and determine the direction marker of the current operating condition of the aero-engine; The sensor measurement vector of the aero-engine under transient operating conditions is obtained. Based on a preset mechanism baseline model, the mechanism prediction value corresponding to the sensor measurement vector of the aero-engine and the mechanism residual corresponding to the sensor measurement vector are determined. Based on the orientation marker of the current operating condition of the aero-engine and the mechanism residual, an augmented observable vector is constructed; The augmented observable vector is predicted by the pre-trained augmented Koopman operator to obtain the residual prediction value corresponding to the mechanism residual; The transient effect correction value of the aero-engine is determined based on the mechanism prediction value and the residual prediction value corresponding to the sensor measurement vector.

[0007] In one possible implementation, the step of obtaining the rotor speed of the aero-engine at adjacent moments and determining the orientation marker of the current operating condition of the aero-engine includes: obtaining the rotor speed of the aero-engine at adjacent moments, and determining the orientation marker according to the rotor speed at the current moment and the sub-speed at the previous moment using formula (1): ;in, The direction marker is represented by k, which represents the discrete-time index. This indicates that the aircraft engine is in Rotor speed at any given time This indicates that the aircraft engine is in Rotor speed at any given time For a sign function, when hour, This indicates that the current operating condition of the aero-engine is acceleration mode; when hour, This indicates that the current operating condition of the aero-engine is deceleration mode.

[0008] In one possible implementation, the step of constructing the augmented observable vector based on the orientation marker of the current operating condition of the aero-engine and the mechanistic residual includes: determining the augmented observable vector using formula (2) based on the mechanistic residual and the orientation marker: ,in, Denotes the augmented observable vector, Indicates that the sensor measurement vector is in The mechanistic residual corresponding to the time step, This indicates that the aircraft engine is in The direction marker corresponding to the time. This represents the nonlinear interaction term between the mechanistic residual and the direction marker. The norm of the residual of the mechanism is represented.

[0009] In one possible implementation, the pre-training step of the augmented Koopman operator includes: obtaining the augmented observable vector sequence under historical transient conditions, and constructing a snapshot matrix at the current time. and the snapshot matrix at the next time step Based on the flight envelope points corresponding to the current flight envelope parameters. The time constant of the transient response of the mechanistic baseline model is obtained by looking up a table. Set weight hyperparameters To minimize the total loss function For the objective, iteratively solve the augmented Koopman operator. The total loss function that minimizes the total loss is expressed as: , This refers to physical constraint terms, the physical constraint terms We obtain the following from formula (3): ,in, This indicates the augmented Koopman operator. The first in continuous time form 1 eigenvalue, Represents eigenvalues The real part, This represents the total number of eigenvalues.

[0010] In one possible implementation, the physical constraint term Used to constrain the augmented Koopman operator The eigenvalues ​​are consistent with the time constants of the baseline model of the mechanism under different flight envelopes.

[0011] In one possible implementation, the step of predicting the augmented observable vector using a pre-trained augmented Koopman operator includes: the eigenvalue spectrum of the augmented Koopman operator contains a first subset of eigenvalues. Second eigenvalue subset Based on the orientation marker of the current operating condition of the aero-engine, match the corresponding first subset of eigenvalues ​​from the eigenvalue spectrum of the augmented Koopman operator. or the second eigenvalue subset The augmented observable vector is then used to perform residual prediction based on the feature vectors corresponding to the matched subset of feature values.

[0012] In one possible implementation, after determining the transient effect correction value of the aero-engine, the method further includes: determining the health index of the aero-engine based on the sensor measurement vector of the aero-engine under transient operating conditions, the transient effect correction value of the aero-engine, and the nominal steady-state model output value.

[0013] In one possible implementation, the step of acquiring the sensor measurement vector of the aero-engine under transient operating conditions, and determining the mechanistic prediction value and the mechanistic residual corresponding to the sensor measurement vector of the aero-engine based on a preset mechanistic baseline model, includes: acquiring the sensor measurement vector, timing control vector, and flight envelope parameters of the aero-engine under transient operating conditions; mapping the timing control vector and the flight envelope parameters to obtain the mechanistic prediction value corresponding to the sensor measurement vector of the aero-engine through the mechanistic baseline model; and determining the mechanistic residual corresponding to the sensor measurement vector based on the difference between the sensor measurement vector and the corresponding mechanistic prediction value.

[0014] In one possible implementation, the step of obtaining the mechanism prediction value corresponding to the sensor measurement vector of the aero-engine through the mechanism baseline model mapping based on the timing control vector and the flight envelope parameters includes: matching the mechanism baseline model parameters under the corresponding flight envelope parameters according to the flight envelope parameters at the current time through a preset parameter lookup table; wherein, the mechanism baseline model parameters include a time constant. and gain The mechanistic baseline model is a mechanistic baseline model with first-order inertia and delay. The first-order inertia and delay mechanistic baseline model is discretized using a bilinear transformation, and the time constant is... and the gain Transformed into first discrete-time coefficients Second discrete time coefficient According to the first discrete-time coefficient and the second discrete time coefficient Delay steps Timing control vector The mechanism prediction value corresponding to the sensor measurement vector at the current discrete moment is determined by formula (4): ,in, Represents a discrete-time index. Indicates the first Mechanistic prediction values ​​at discrete time points Indicates the first Timing control vectors at discrete moments.

[0015] This application also provides a mechanism-data dual-driven transient effect correction device for aero-engines, including: The operating condition marking module is used to obtain the rotor speed of the aero-engine at adjacent moments and determine the direction marking of the current operating condition of the aero-engine. The mechanism prediction module is used to obtain the sensor measurement vector of the aero-engine under transient operating conditions, and based on the preset mechanism baseline model, determine the mechanism prediction value corresponding to the sensor measurement vector of the aero-engine and the mechanism residual corresponding to the sensor measurement vector. The residual prediction module is used to construct an augmented observable vector based on the orientation marker of the current operating condition of the aero-engine and the mechanism residual; and to predict the augmented observable vector using a pre-trained augmented Koopman operator to obtain the residual prediction value corresponding to the mechanism residual. The transient correction module is used to determine the transient effect correction value of the aero-engine based on the mechanism prediction value and the residual prediction value corresponding to the sensor measurement vector.

[0016] This application also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the mechanism-data dual-drive-based aero-engine transient effect correction method as described above.

[0017] This application also provides a non-transitory computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the mechanism-data dual-driven aero-engine transient effect correction method as described above.

[0018] This application also provides a computer program product, including a computer program that, when executed by a processor, implements the mechanism-data dual-drive-based aero-engine transient effect correction method as described above.

[0019] The transient effect correction method for aero-engines based on mechanism-data dual-drive provided in this application embodiment determines the orientation marker of the current operating condition of the aero-engine by acquiring the rotor speed of the aero-engine at adjacent time points; acquires the sensor measurement vector of the aero-engine under transient operating conditions, and determines the mechanism prediction value and the mechanism residual corresponding to the sensor measurement vector of the aero-engine based on a preset mechanism baseline model; constructs an augmented observable vector according to the orientation marker of the current operating condition of the aero-engine and the mechanism residual; predicts the augmented observable vector through a pre-trained augmented Koopman operator to obtain the residual prediction value corresponding to the mechanism residual; and determines the transient effect correction value of the aero-engine according to the mechanism prediction value and the residual prediction value corresponding to the sensor measurement vector. By acquiring the rotor speed of the aero-engine at adjacent time points and determining the direction marker, a basis for distinguishing acceleration / deceleration modes is provided for subsequent transient processing, enabling adaptive processing for different transient directions. The sensor measurement vector is decomposed into mechanistic prediction values ​​and mechanistic residuals using a mechanistic baseline model, achieving preliminary decoupling of transient dynamic bias and health degradation signals using physical mechanisms. An augmented observable vector is constructed by nonlinearly fusing the direction marker and mechanistic residual, making this vector simultaneously contain directional information, residual amplitude, and their cross-coupling characteristics, providing a physically discriminative state representation for the linear prediction model. The state evolution prediction of the augmented observable vector in a high-dimensional linear space is performed using a pre-trained augmented Koopman operator, transforming the complex nonlinear transient dynamics prediction problem into a linear prediction problem, significantly reducing computational complexity while maintaining prediction accuracy. Finally, the transient effect correction value is determined by fusing the mechanistic prediction value and the residual prediction value, achieving a balance between physical consistency and data accuracy. This method can simultaneously overcome the modeling difficulties caused by directional inconsistency and time-varying full envelope during the transient process of aero-engines. It can accurately correct transient effects in the full flight envelope and bidirectional transient processes, effectively separate transient components and health degradation signals in sensor measurements, avoid health parameter estimation deviations and system misdiagnosis caused by the coupling of transient components and degradation signals, and provide a reliable data foundation for the performance diagnosis of aero-engine gas path systems. Attached Figure Description

[0020] To more clearly illustrate the technical solutions in this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0021] Figure 1This is a flowchart illustrating the mechanism-data dual-driven method for correcting transient effects in aero-engines provided in this application embodiment. Figure 2 This is a graph showing the analysis results of the transient effect correction method provided in this application embodiment under the high-pressure compressor outlet temperature T30 parameter; Figure 3 This is a graph showing the analysis results of the transient effect correction method provided in this application under the low-pressure turbine outlet temperature T50 parameter; Figure 4 This is a graph showing the analysis results of the transient effect correction method provided in this application under the fan rotor speed Nf parameter; Figure 5 This is a graph showing the analysis results of the transient effect correction method provided in this application under the core machine rotor speed Nc parameter; Figure 6 This is a graph showing the analysis results of the transient effect correction method provided in this application under the low-pressure turbine outlet total pressure P50 parameter; Figure 7 This is a schematic diagram of the structure of the mechanism-data dual-drive aero-engine transient effect correction device provided in the embodiments of this application; Figure 8 This is a schematic diagram of the structure of the electronic device provided in the embodiments of this application. Detailed Implementation

[0022] To make the objectives, technical solutions, and advantages of this application clearer, the technical solutions of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0023] To better understand the embodiments of this application, the prior art will first be described in detail: In actual flight operations of aero-engines, modeling transient effects faces two major challenges: First, directional inconsistency. Due to thermal inertia and rotor inertia, sensor responses during acceleration and deceleration exhibit significantly different dynamic trajectories, forming a hysteresis loop with nonlinear multi-valued mapping. Traditional compensation methods based on symmetric filtering or fixed-order transfer functions struggle to effectively isolate this directionally dependent dynamic bias. Second, achieving both time-varying performance and stability across the entire flight envelope is difficult. At different flight altitudes and Mach numbers, the dramatic changes in air density and heat exchange efficiency cause the system time constant to vary over a wide range. Existing fixed-parameter models cannot adaptively adjust to flight conditions, making it difficult to accurately track the engine's true transient behavior across the entire flight envelope. These bottlenecks further couple transient components in sensor measurements with health degradation signals, severely limiting the accuracy and robustness of gas path performance diagnosis.

[0024] To address the aforementioned technical issues, this application proposes a mechanism-data dual-driven method for correcting transient effects in aero-engines. By acquiring the rotor speed of the aero-engine at adjacent time points and determining the direction marker, a basis for discriminating acceleration / deceleration modes is provided for subsequent transient processing, enabling adaptive processing for different transient directions. The sensor measurement vector is decomposed into mechanism prediction values ​​and mechanism residuals using a mechanism baseline model, achieving preliminary decoupling of transient dynamic deviations and health degradation signals using physical mechanisms. An augmented observable vector is constructed by nonlinearly fusing the direction marker and mechanism residuals, simultaneously containing direction information, residual amplitude, and their cross-coupling characteristics, providing a physically discriminative state representation for the linear prediction model. A pre-trained augmented Koopman operator is used to predict the state evolution of the augmented observable vector in a high-dimensional linear space, transforming the complex nonlinear transient dynamics prediction problem into a linear prediction problem, significantly reducing computational complexity while maintaining prediction accuracy. Finally, the transient effect correction value is determined by fusing the mechanism prediction value and the residual prediction value, achieving a balance between physical consistency and data accuracy. This method can simultaneously overcome the modeling difficulties caused by directional inconsistencies and time-varying full envelope characteristics during the transient process of aero-engines. It achieves accurate correction of transient effects in both the full flight envelope and bidirectional transient processes, effectively separating transient components from health degradation signals in sensor measurements. This avoids health parameter estimation biases and system misdiagnosis caused by the coupling of transient components and degradation signals, providing a reliable data foundation for the performance diagnosis of aero-engine gas path systems.

[0025] It should be noted that the execution subject involved in the embodiments of this application can be a mechanism-data dual-driven aero-engine transient effect correction device, or it can be an electronic device. Optionally, the electronic device includes: a computer, a mobile terminal, an industrial control computer, a data acquisition workstation, an airborne data processing unit, a server, or an embedded controller, etc.

[0026] The following section uses electronic equipment as an example to elaborate on the transient effect correction method for aero-engines based on mechanism-data dual-drive provided in this application: Figure 1 This is a flowchart illustrating the transient effect correction method for aero-engines based on a mechanism-data dual-drive approach provided in this application. Figure 1 As shown, the method includes the following steps 101-105.

[0027] Step 101: Obtain the rotor speed of the aero-engine at adjacent moments and determine the direction marker of the current operating condition of the aero-engine.

[0028] Rotor speed refers to the rotational speed used to characterize the rotor of an aero-engine, usually expressed in revolutions per minute (r / min).

[0029] Optionally, the rotor speed includes the high-voltage rotor speed. and / or low-pressure rotor speed For example, the high-voltage rotor speed can be used. This is because the high-pressure rotor is more sensitive to transient responses and can more promptly reflect the operating condition switching caused by changes in fuel flow; in other embodiments, it can also monitor simultaneously. and This is to ensure the robustness of direction determination.

[0030] The directional markers for the current operating conditions of an aero-engine indicate whether the engine is in acceleration or deceleration mode.

[0031] In step 101, the electronic device acquires the rotor speed of the aero-engine at adjacent moments (e.g., the current moment and the previous moment), and determines whether the directional marker of the current operating condition of the aero-engine is an acceleration mode or a deceleration mode based on the rotational speed of the aero-engine rotor at adjacent moments. This directional marker enables effective differentiation of the asymmetric characteristics of transient responses during acceleration and deceleration in subsequent steps, overcoming the modeling bias caused by inconsistencies in direction in traditional methods.

[0032] Step 102: Obtain the sensor measurement vector of the aero-engine under transient operating conditions. Based on the preset mechanism baseline model, determine the mechanism prediction value corresponding to the sensor measurement vector of the aero-engine and the mechanism residual corresponding to the sensor measurement vector.

[0033] The sensor measurement vector refers to the vector formed by the measurement parameters synchronously collected by multiple sensors in the aero-engine's airflow system under transient operating conditions. This sensor measurement vector is used to characterize the aero-engine's current true output response, i.e., the actual sensor measurement value.

[0034] Optionally, the sensor measurement vector includes, but is not limited to, physical parameters of the aero-engine such as low-pressure rotor speed, high-pressure rotor speed, compressor outlet pressure, turbine outlet temperature, and fuel flow rate.

[0035] The mechanistic baseline model is a mathematical model based on the aero-thermodynamic principles of aero-engines, describing the input-output mapping relationship of the engine under steady-state operating conditions. This mechanistic baseline model takes flight envelope parameters and timing control vectors as inputs and outputs the steady-state expected values ​​of each sensor under healthy conditions.

[0036] In step 102, the electronic device first acquires the measurement vectors collected by the sensors in real time under transient conditions. Then, based on a preset mechanistic baseline model, it determines the mechanistic prediction values ​​corresponding to each sensor measurement vector under the current conditions. Finally, based on the mechanistic prediction values ​​corresponding to the sensor measurement vectors and the actual sensor measurements, it determines the mechanistic residuals corresponding to the sensor measurement vectors. These mechanistic residuals characterize the dynamic deviation components in the sensor measurements, excluding the steady-state reference components. These dynamic deviation components include deviations caused by transient effects and possible health degradation signals. Through this step, the sensor measurements can be decomposed into mechanistic prediction values ​​reflecting the health state and residual components reflecting transient dynamic deviations, achieving preliminary decoupling between transient effects and degradation signals.

[0037] Step 103: Construct an augmented observable vector based on the direction markers and mechanism residuals of the current operating conditions of the aero-engine.

[0038] In step 103, the electronic device combines the direction marker determined in step 101 with the mechanistic residual calculated in step 102 to construct an augmented observable vector. This step fuses the direction marker and mechanistic residual in a nonlinear expansion manner to construct the augmented observable vector, ensuring that the vector simultaneously contains transient direction information, residual magnitude information, and cross-coupling information between the two, thus fully preserving the direction dependence and nonlinear characteristics of the transient process. This augmented observable vector provides the augmented Koopman operator with physically discriminative state input, enabling the subsequent linear prediction model to effectively distinguish between acceleration and deceleration trajectories in high-dimensional space, fundamentally solving the technical bottleneck of traditional methods' inability to characterize the direction dependence of transient processes.

[0039] Step 104: Predict the augmented observable vector using the pre-trained augmented Koopman operator to obtain the predicted residual value corresponding to the mechanistic residual.

[0040] The augmented Koopman operator refers to a linear prediction model for the state evolution of a nonlinear dynamic system after it has been elevated to a high-dimensional linear space using Koopman operator theory. This augmented Koopman operator is pre-trained based on historical transient data and is used to predict the augmented observable vector at the next time step based on the augmented observable vector at the current time step, thereby extracting the residual prediction value corresponding to the mechanistic residual.

[0041] In step 104, the electronic device inputs the augmented observable vector constructed in step 103 into a pre-trained augmented Koopman operator. This augmented Koopman operator performs linear state prediction on the augmented observable vector, outputs the predicted value of the augmented observable vector at the next time step, and extracts the predicted residual value corresponding to the mechanistic residual from the predicted value. Through this step, the pre-trained augmented Koopman operator is used to predict the state evolution of the augmented observable vector in a high-dimensional linear space, effectively modeling and compensating for the thermal hysteresis effect during acceleration / deceleration. Furthermore, the originally complex nonlinear transient dynamics prediction problem is transformed into a prediction problem in a linear state space, significantly reducing computational complexity while maintaining prediction accuracy.

[0042] Step 105: Determine the transient effect correction value of the aero-engine based on the mechanism prediction value and residual prediction value corresponding to the sensor measurement vector.

[0043] In step 105, the electronic device superimposes or compensates the mechanism prediction value obtained in step 102 with the residual prediction value obtained in step 104 to obtain the transient effect correction value of the sensor measurement vector under transient conditions. This transient effect correction value is used to characterize the dynamic deviation component in the sensor measurement value caused by the transient process. By correcting the sensor measurement vector with this transient effect correction value, the steady-state equivalent measurement value reflecting the true health state of the engine can be restored, thus providing an accurate data basis for subsequent gas path performance diagnosis.

[0044] Optionally, steps 101 and 102 above can be performed simultaneously or sequentially depending on the actual situation, and this application does not impose specific limitations.

[0045] In the embodiments of this application, the technical solutions described in steps 101-105 above, by acquiring the rotor speed of the aero-engine at adjacent moments and determining the direction marker, provide a basis for the discrimination of acceleration / deceleration modes for subsequent transient processing, enabling adaptive processing for different transient directions; by decomposing the sensor measurement vector into mechanistic prediction values ​​and mechanistic residuals through the mechanistic baseline model, the transient dynamic deviation and health degradation signal are initially decoupled using physical mechanisms; by nonlinearly fusing the direction markers and mechanistic residuals to construct an augmented observable vector, the vector simultaneously contains directional information, residual amplitude, and its cross-coupling characteristics, providing a physically discriminative state representation for the linear prediction model; by using a pre-trained augmented Koopman operator to predict the state evolution of the augmented observable vector in a high-dimensional linear space, the complex nonlinear transient dynamics prediction problem is transformed into a linear prediction problem, significantly reducing computational complexity while ensuring prediction accuracy; finally, by fusing the mechanistic prediction values ​​and residual prediction values ​​to determine the transient effect correction values, the unity of physical consistency and data accuracy is achieved. This method can simultaneously overcome the modeling difficulties caused by directional inconsistency and time-varying full envelope during the transient process of aero-engines. It can accurately correct transient effects in the full flight envelope and bidirectional transient processes, effectively separate transient components and health degradation signals in sensor measurements, avoid health parameter estimation deviations and system misdiagnosis caused by the coupling of transient components and degradation signals, and provide a reliable data foundation for the performance diagnosis of aero-engine gas path systems.

[0046] In some embodiments, the step of the electronic device acquiring the rotor speed of the aero-engine at adjacent moments and determining the orientation marker of the current operating condition of the aero-engine may include: the electronic device acquiring the rotor speed of the aero-engine at adjacent moments, and the electronic device determining the orientation marker according to the rotor speed at the current moment and the sub-speed at the previous moment using formula (1): ;in, This indicates the direction marker, and k represents the discrete-time index. Indicates that the aircraft engine is Rotor speed at any given time Indicates that the aircraft engine is Rotor speed at any given time For a sign function, when hour, This indicates that the current operating condition of the aero-engine is acceleration mode; when hour, This indicates that the current operating condition of the aero-engine is deceleration mode.

[0047] In this embodiment of the application, for example, the electronic device acquires the rotor speed signal of the aircraft engine at a preset sampling period. At the end of each sampling period, the electronic device obtains the rotor speed at the current moment. It also reads the rotor speed recorded in the previous sampling period from the historical data cache. The electronic device calculates the difference between the two and inputs the difference into a sign function to generate a direction marker. (i.e., the calculation process of Formula 1), if the direction mark If the value is positive, the electronic device marks the current sampling period as the acceleration mode; if the direction marker is positive... If the value is negative, the electronic device marks the current sampling period's operating condition as a deceleration mode. After the determination is completed, the electronic device writes the current rotor speed into the data buffer to overwrite the data from the previous period, thus achieving data sliding update. By repeating the above steps in each sampling period, the electronic device can track the directional changes of the aero-engine's transient operating conditions in real time.

[0048] It should be noted that by repeating the above steps in each sampling period, the directional changes of the transient operating conditions of the aero-engine can be tracked in real time and continuously with extremely low computational overhead. This provides accurate and reliable directional marker input for the subsequent differentiation of the asymmetric transient response of the acceleration and deceleration process, fundamentally solving the problem of inconsistent transient modeling direction caused by the inability of traditional methods to determine the operating condition direction in real time.

[0049] In some embodiments, the step of the electronic device constructing an augmented observable vector based on the orientation marker and mechanistic residual of the current operating condition of the aero-engine may include: the electronic device determining the augmented observable vector based on the mechanistic residual and orientation marker using formula (2): ,in, Represents the augmented observable vector. Indicates the sensor measurement vector in The mechanistic residual corresponding to the time step, Indicates that the aircraft engine is The direction marker corresponding to the time. The nonlinear cross term representing the mechanistic residual and the direction label. The norm of the mechanistic residual.

[0050] In this embodiment of the application, for example, the electronic device obtains the direction marker through step 101. Step 102: Computer processing of residuals Then, the augmented observable vector is constructed according to formula (2). Specifically, the electronic device first obtains the current time. Mechanism of residual and the direction marker at the current moment. Subsequently, the electronic device calculates the residual of this mechanism. With this direction mark The product of the two yields the nonlinear cross term between them. The nonlinear cross term This is used to characterize the modulation effect of the orientation marker on the residuals of each sensor, that is, the degree of influence of the acceleration or deceleration process on the transient deviation amplitude; at the same time, the electronic equipment calculates the residual of this mechanism. L2 norm This yields a scalar value reflecting the overall energy magnitude of the transient deviation. After calculating each of the above components, the electronic device will output the mechanism residual. Direction markers Nonlinear cross terms and the norm of the mechanistic residual By combining columns, we can construct the augmented observable vector. .

[0051] It should be noted that by fusing the direction marker and the mechanistic residual in a nonlinear extension manner to construct the augmented observable vector, this augmented observable vector simultaneously contains transient direction information, residual magnitude information, and cross-coupling information between the two. This fully preserves the direction dependence and nonlinear characteristics of the transient process, providing the augmented Koopman operator with physically discriminative state input. This enables the subsequent linear prediction model to effectively distinguish between acceleration and deceleration trajectories in high-dimensional space, fundamentally solving the technical bottleneck of traditional methods being unable to characterize the direction dependence of transient processes.

[0052] In some embodiments, the pre-training step of the augmented Koopman operator may include: the electronic device acquiring an augmented observable vector sequence under historical transient conditions, and constructing a snapshot matrix at the current time. and the snapshot matrix at the next time step Based on the current flight envelope point The time constant of the transient response of the mechanistic baseline model is obtained by looking up a table. Set weight hyperparameters To minimize the total loss function For the objective, iteratively solve the augmented Koopman operator. The function that minimizes the total loss is expressed as: , Represents physical constraint terms. We obtain the following from formula (3): ,in, Represents the augmented Koopman operator The first in continuous time form 1 eigenvalue, Represents eigenvalues The real part, This represents the total number of eigenvalues.

[0053] The augmented observable vector sequence refers to the time series formed by constructing augmented observable vectors for multiple consecutive sampling times under historical transient operating conditions. This augmented observable vector sequence covers historical operating data of aero-engines under various transient operating conditions and is used for offline training of the augmented Koopman operator.

[0054] A snapshot matrix is ​​a matrix constructed by arranging augmented observable vector sequences in a specific time sequence, used to augment the data-driven identification of the Koopman operator.

[0055] Flight envelope point This refers to the operating point of the flight envelope determined by the flight envelope parameters at each time step in the training data. During the pre-training process of the augmented Koopman operator, data at different times may correspond to different flight envelope points.

[0056] It is understandable that the electronic device obtains the time constant at the current flight envelope point by looking up the flight envelope parameters at the current time through a preset parameter lookup table at each moment. The time constant of the mechanism baseline model in step 102 comes from the same parameter lookup table, thereby ensuring that the physical constraint terms and the dynamic characteristics of the mechanism baseline model are physically consistent.

[0057] Weight hyperparameters It refers to a pre-defined non-negative scalar used to weigh the relative importance of the data fitting term and the physical constraint term in the total loss function.

[0058] In this embodiment of the application, firstly, the electronic device acquires the augmented observable vector sequence under historical transient operating conditions. ,in To determine the time series length of the training data, this augmented observable vector sequence covers transient process data of aero-engines at multiple flight envelope points and various acceleration / deceleration rates. Electronic equipment will... Construct a snapshot matrix for the current time step by arranging the augmented observable vectors column-wise. , will The augmented observable vectors are arranged in columns to construct a snapshot matrix for the next time step. .

[0059] Secondly, the electronic device targets the augmented observable vector at each time step in the training data. Obtain the flight envelope point corresponding to the flight envelope parameters at that moment. and with the flight envelope point Using an index, query a pre-defined parameter lookup table to obtain the time constant corresponding to that moment. .

[0060] Subsequently, the electronic device sets the weight hyperparameters. The initial values ​​are based on the snapshot matrix at the current time. and the snapshot matrix at the next time step The augmented Koopman operator is iteratively solved with the goal of minimizing the total loss function. Specifically, in each iteration, the electronic device computes the current augmented Koopman operator. eigenvalues and eigenvalues real part Substitute into formula (3): Calculate physical constraint terms ,in, This indicates the augmented Koopman operator. The first in continuous time form 1 eigenvalue, Represents eigenvalues The real part, This represents the total number of eigenvalues. Next, the electronic device calculates the total loss function. Electronic devices use optimization algorithms to update the augmented Koopman operator. , so that the total loss function Continuously decrease the value. Repeat the above iterative process until the convergence condition is met, then stop iterating and output the current augmented Koopman operator. As a training result.

[0061] After training, the electronic device will solve for the augmented Koopman operator. The pre-stored augmented Koopman operator is stored in the non-volatile storage medium of the electronic device for online prediction in step 104. During the online prediction phase, the electronic device directly calls the pre-stored augmented Koopman operator. The augmented observable vector at the current moment With augmented Koopman operator By multiplying them, we can obtain the predicted value of the augmented observable vector at the next time step, and extract the predicted value of the residual corresponding to the mechanistic residual from it.

[0062] It is understood that the above optimization algorithm can be gradient descent or alternating direction multiplier method, and the embodiments of this application do not limit it in any way.

[0063] The convergence condition for the above iterative process can be that the change in the total loss function between two consecutive iterations is less than a preset threshold, the number of iterations reaches a preset maximum number of iterations, or both conditions are met simultaneously or either condition is met. The above convergence condition is designed to balance solution accuracy and computational efficiency. This application does not impose any restrictions on the specific form of the convergence condition, and those skilled in the art can flexibly set it according to the actual application scenario.

[0064] It should be noted that, through the above-mentioned offline pre-training process, the electronic equipment, based on the physical information online dynamic mode decomposition framework, trains the augmented Koopman operator by means of data fitting and physical constraint co-optimization. This ensures that the dynamic characteristics of the operator are consistent with the physical response law of the aero-engine while guaranteeing prediction accuracy. The training process is completed offline, and the state prediction can be completed by only one matrix multiplication in the online prediction stage. It takes into account both prediction accuracy and real-time computation, which is suitable for the actual deployment requirements of the aero-engine airborne health management system.

[0065] In some embodiments, physical constraints Used to constrain the augmented Koopman operator The eigenvalues ​​are consistent with the time constants of the mechanistic baseline model under different flight envelopes. Specifically, when the eigenvalues real part The closer When the value of the physical constraint term is smaller, it indicates that the augmented Koopman operator is stronger. The closer the dynamic characteristics of the model are to the physical response characteristics of the baseline mechanistic model, the greater the difference between them; conversely, the larger the deviation between the two, the larger the value of the physical constraint term. The augmented Koopman operator trained using this physical constraint term... While data-driven fitting is used, its dominant dynamic behavior is restricted to a reasonable range determined by the physical time constant of the aero-engine, thereby avoiding non-physical divergent modes that may be generated by pure data-driven methods and improving the extrapolation and generalization ability of the model across the entire flight envelope.

[0066] In some embodiments, the step of an electronic device predicting the augmented observable vector using a pre-trained augmented Koopman operator may include: the eigenvalue spectrum of the pre-trained augmented Koopman operator contains a first subset of eigenvalues. Second eigenvalue subset The electronic equipment matches the corresponding first subset of eigenvalues ​​from the eigenvalue spectrum of the augmented Koopman operator based on the orientation markers of the current operating condition of the aero-engine. or the second eigenvalue subset The electronic device performs residual prediction on the augmented observable vector by using the feature vectors corresponding to the matched subset of feature values.

[0067] The eigenvalue spectrum of the augmented Koopman operator exhibits a splitting property, meaning that the eigenvalue spectrum, composed of all eigenvalues ​​of the augmented Koopman operator, splits into a first subset of eigenvalues ​​corresponding to the acceleration mode, depending on the orientation label of the current operating condition of the aero-engine. The second eigenvalue subset corresponding to the deceleration mode The first eigenvalue subset The eigenvalues ​​in the first subset are used to characterize the transient dynamic characteristics of the aero-engine during acceleration, and the eigenvalues ​​in the second subset are used to characterize the transient dynamic characteristics of the aero-engine during deceleration, so as to mathematically distinguish and reconstruct the different transient trajectory branches of the aero-engine during acceleration and deceleration.

[0068] In this embodiment, the electronic device invokes a pre-trained augmented Koopman operator. The eigenvalue spectrum of this augmented Koopman operator naturally exhibits a splitting characteristic corresponding to the direction labels, i.e., some eigenvalues ​​correspond to acceleration modes, and some eigenvalues ​​correspond to deceleration modes. Based on this splitting characteristic, the electronic device automatically divides all eigenvalues ​​into a first subset corresponding to acceleration modes. and the second eigenvalue subset corresponding to the deceleration mode And store the feature vectors corresponding to each feature value subset respectively.

[0069] Secondly, the electronic device obtains the current direction marker, if If the current operating condition is determined to be acceleration mode, the electronic device selects the first matching subset of eigenvalues ​​from the eigenvalue spectrum. and the corresponding eigenvectors; if If the current operating condition is determined to be a deceleration mode, the electronic equipment selects the matching second subset of feature values. and the corresponding eigenvectors.

[0070] Finally, the electronic device will use the augmented observable vector for the current time step 103 to construct the data. The feature vectors are dynamically projected onto the subspace spanned by the feature vectors corresponding to the matched feature subsets, and then the modalities of this subspace are dynamically reconstructed to output the corresponding residual prediction values.

[0071] It should be noted that by naturally splitting the eigenvalue spectrum of the augmented Koopman operator into acceleration and deceleration subsets, the directional inconsistency of the acceleration and deceleration processes of aero-engines is strictly distinguished mathematically, realizing the independent representation and reconstruction of different transient trajectory branches, and providing a new interpretable analytical perspective for a deeper understanding of transient dynamic characteristics.

[0072] In some embodiments, the step of an electronic device acquiring sensor measurement vectors of an aero-engine under transient operating conditions and determining the mechanistic prediction value and the mechanistic residual corresponding to the sensor measurement vectors of the aero-engine based on a preset mechanistic baseline model may include: the electronic device acquiring sensor measurement vectors, timing control vectors, and flight envelope parameters of the aero-engine under transient operating conditions; the electronic device mapping the timing control vectors and flight envelope parameters to obtain the mechanistic prediction value corresponding to the sensor measurement vectors of the aero-engine through the mechanistic baseline model; and the electronic device determining the mechanistic residual corresponding to the sensor measurement vectors based on the difference between the sensor measurement vectors and the corresponding mechanistic prediction values.

[0073] Among them, the timing control vector refers to the vector formed by the control commands output by the aero-engine control system during the transient process, which is used to characterize the current control input state of the engine.

[0074] Optionally, the timing control vector includes, but is not limited to: fuel flow rate, adjustable inlet guide vane angle, adjustable stator vane angle, etc.

[0075] Flight envelope parameters are a set of parameters used to characterize the current flight environment state of an aircraft. Flight envelope parameters include at least flight altitude and Mach number.

[0076] In this embodiment, the electronic device synchronously acquires sensor measurement vectors, timing control vectors, and flight envelope parameters under transient operating conditions via the airborne data bus of the aero-engine. The sensor measurement vectors contain real-time readings from multiple sensor channels, the timing control vectors contain control command values ​​such as fuel flow rate within the current sampling period, and the flight envelope parameters contain the current flight altitude and Mach number. The acquisition of these three types of data is synchronized to ensure temporal consistency. Next, the electronic device invokes a pre-established mechanism baseline model based on the aero-engine aerodynamics and thermodynamics principles, inputting the timing control vectors and flight envelope parameters into this model. Through model mapping, the mechanism prediction value corresponding to the aero-engine's sensor measurement vectors is obtained. Finally, after obtaining the mechanism prediction value, the electronic device performs an element-wise difference operation between the synchronously acquired sensor measurement vectors and the aforementioned mechanism prediction value, i.e., obtains the mechanism residual corresponding to the sensor measurement vectors. This mechanism residual has the same dimension as the sensor measurement vectors.

[0077] It should be noted that by using a pre-established mechanistic baseline model based on the aero-thermodynamic principles of aero-engines, combined with synchronously acquired time-series control vectors and flight envelope parameters, the sensor measurement vectors are decomposed in real time into steady-state mechanistic prediction values ​​reflecting the health status and mechanistic residuals containing transient dynamic deviations. This achieves preliminary decoupling between transient effects and health degradation signals, while ensuring that the decomposition results have clear physical meaning and operational condition adaptability across the entire flight envelope. This provides a physically reliable and interpretable data foundation for the subsequent construction of augmented observable vectors.

[0078] In some embodiments, the step of the electronic device obtaining the mechanism prediction value corresponding to the sensor measurement vector of the aero-engine through mechanism baseline model mapping based on the timing control vector and flight envelope parameters may include: the electronic device matching the mechanism baseline model parameters under the corresponding flight envelope parameters according to the flight envelope parameters at the current moment through a preset parameter lookup table; wherein, the mechanism baseline model parameters include a time constant. and gain The mechanistic baseline model is a mechanistic baseline model with first-order inertia plus delay. This electronic device uses a bilinear transformation to discretize the first-order inertia plus delay mechanistic baseline model, and the time constant... and gain Transformed into first discrete-time coefficients Second discrete time coefficient The electronic device is based on the first discrete time coefficient. Second discrete time coefficient Delay steps Timing control vector The mechanism prediction value corresponding to the sensor measurement vector at the current discrete moment is determined by formula (4): ,in, Represents a discrete-time index. Indicates the first Mechanistic prediction values ​​at discrete time points Indicates the first Timing control vectors at discrete moments.

[0079] Among them, the parameter lookup table refers to a pre-established two-dimensional or multi-dimensional data table used to establish the mapping relationship between flight envelope parameters and mechanism baseline model parameters.

[0080] Understandably, the parameter lookup table is pre-stored in the non-volatile storage medium of the electronic device, covering the entire flight envelope of the aero-engine, and the model parameter values ​​at consecutive envelope points are obtained through interpolation between different flight envelope points.

[0081] Optionally, the above interpolation methods include, but are not limited to: linear interpolation, spline interpolation, or interpolation methods based on radial basis functions.

[0082] The mechanistic baseline model with first-order inertia and delay refers to a low-order linear mathematical model used to describe the dynamic characteristics of sensor output response of aero-engines under transient conditions. Based on physical mechanisms, this model can characterize the main dynamic characteristics of aero-engines during transient processes with relatively low computational complexity. In the continuous-time domain, this model describes the dynamic relationship between the input (i.e., the sequential control vector) and the output (i.e., the sensor measurement vector) through the following first-order linear differential equation: , in, Indicates continuous time; express Mechanism prediction values ​​at any given time; express The timing control vector at each moment; Indicates the current flight envelope point The time constant is used to characterize the speed of system response; Gain represents the proportional relationship between the change in input and the steady-state change in output. This represents the delay time, which characterizes the time required for the output to begin producing a response after a change in the input.

[0083] The bilinear transformation is a numerical integration method that converts a continuous-time domain transfer function or differential equation into a discrete-time domain difference equation. In the embodiments of this application, the bilinear transformation is used to convert the aforementioned first-order inertial plus delay continuous-domain differential equation into a discrete-domain difference equation.

[0084] In this embodiment of the application, the electronic device performs the following operations in each sampling period: First, the electronic device acquires the current time. Flight envelope parameters Based on flight envelope parameters Using an index, a pre-defined parameter lookup table is queried to obtain the mechanistic baseline model parameters, i.e., the time constant, at the current envelope point. and gain Secondly, the electronic device, based on the current sampling period and the time constant, and gain The first discrete-time coefficient in the discrete domain is calculated using the bilinear transform formula. Second discrete time coefficient Next, the electronic device reads the delay steps from the delay buffer. Previous timing control vector Finally, the electronic device will use the mechanism prediction value from the previous sampling period. The first discrete time coefficient at the current moment Second discrete time coefficient and the delayed timing control vector Substitute into formula (4): The next time step (i.e.) is calculated. Mechanism prediction value at time) This enables the recursive updating of the mechanistic baseline model in the discrete time domain.

[0085] It should be noted that the above formula (4) The time step represents the predicted value for the next time step calculated in the current recursive step. In actual airborne system implementation, after the electronic equipment completes the calculation in each sampling period, it will... Output the mechanism prediction value at the current moment.

[0086] The aforementioned mechanistic baseline model with first-order inertia and delay is based on the physical dynamic characteristics of aero-engines. Its time constant and gain adaptively vary with the flight envelope, accurately characterizing the changes in system response speed and steady-state gain at different altitudes and Mach numbers. This effectively overcomes the prediction bias caused by parameter mismatch in fixed-parameter models across the entire flight envelope. Furthermore, the low-order model structure with first-order inertia and delay significantly reduces computational complexity, requiring only a small number of multiply-accumulate operations to complete the recursive update for each sampling period. This makes it extremely suitable for the stringent real-time requirements of aero-engine airborne health management systems.

[0087] In some embodiments, after determining the transient effect correction value of the aero-engine, the electronic device further includes: determining the health index of the aero-engine based on the sensor measurement vector of the aero-engine under transient operating conditions, the transient effect correction value of the aero-engine, and the nominal steady-state model output value.

[0088] The nominal steady-state model output value refers to the expected values ​​of each sensor output by the mathematical model that is pre-established based on the aero-thermodynamic principles of aero-engines and describes the input-output mapping relationship of the engine under steady-state conditions in a new or healthy state.

[0089] In this embodiment, after the electronic device determines the transient effect correction value for the current sampling period in step 105, it first acquires the sensor measurement vector at the current moment and the transient effect correction value determined in step 105. The electronic device subtracts the transient effect correction value from the sensor measurement vector to obtain the equivalent steady-state measurement value after transient compensation. Through the above subtraction operation, the dynamic deviation component caused by the transient process in the sensor measurement value is effectively removed, and the equivalent steady-state measurement value approximates the engine's true steady-state response value under the current operating condition (i.e., reflecting the steady-state output under the current healthy state).

[0090] Secondly, the electronic device acquires the timing control vector at the current moment, uses the timing control vector as input, queries or calculates the nominal steady-state model, and obtains the nominal steady-state model output value of a healthy engine under the current control input. This nominal steady-state model output value represents the ideal measurement value that should be output under the same control input conditions and when the engine has not experienced any performance degradation.

[0091] Finally, the electronic equipment fuses the equivalent steady-state measurement value after transient compensation with the nominal steady-state model output value to obtain the health index of the aero-engine. This health index characterizes the deviation between the actual steady-state response and the healthy steady-state benchmark. When the engine is in a healthy state, the actual steady-state response is approximately equal to the healthy steady-state benchmark, and the aero-engine's health index approaches zero. When the engine experiences performance degradation, the actual steady-state response deviates from the healthy steady-state benchmark, and the aero-engine's health index exhibits a continuous positive or negative shift. The magnitude and direction of this shift correspond to the type and degree of component degradation. For example, the formula for calculating the aero-engine's health index is as follows: ： ,in, Indicates the health indicators of an aircraft engine. Indicates the current time The sensor measurement vector, Indicates the current time Transient effect correction value, This represents the equivalent steady-state measurement after transient compensation. This represents the output value of the nominal steady-state model.

[0092] It should be noted that by using transient effect correction values ​​to remove the dynamic deviation components from sensor measurements, and then combining them with the nominal steady-state model output values ​​to construct health indicators, the health indicators directly quantify the deviation between the engine's actual steady-state response and the health benchmark. This achieves effective extraction and accurate characterization of health degradation signals under transient operating conditions, and realizes precise separation between transient dynamic deviations and health degradation signals, providing accurate and reliable quantitative basis for the early detection of aero-engine gas path performance degradation.

[0093] Optionally, in some embodiments, the electronic device inputs health indicators into the cumulative sum control chart for detection; when the cumulative sum statistic of the cumulative sum control chart exceeds a preset control limit threshold, the electronic device determines that the aircraft engine has experienced performance degradation and triggers an early warning signal; when the cumulative sum statistic does not exceed the control limit threshold, the electronic device determines that the aircraft engine has not experienced performance degradation and continues to monitor the health indicators in subsequent sampling periods.

[0094] The Cumulative Sum Control Chart (CUSUM) is a statistical process control tool based on the sequential probability ratio test principle, used to detect small, persistent deviations in aero-engine health indicators. This CUSUM amplifies weak degradation signals by recursively summing the cumulative deviations of health indicators, thereby improving the sensitivity of detecting early performance degradation in aero-engines.

[0095] The control limit threshold is a pre-set numerical limit used to compare with the cumulative sum of CUSUM statistics to determine whether the health indicators of the aircraft engine have experienced a significant and persistent deviation.

[0096] Optionally, the control limit threshold is preset based on the false alarm rate and missed detection rate required for the diagnostic testing of the aero-engine's gas path performance, using Monte Carlo simulation or historical fault data statistics. In this embodiment, the range of the control limit threshold is... ,in This represents the standard deviation of health indicators under engine health conditions. The specific value can be determined through simulation or experimental verification based on the actual engine model and application scenario.

[0097] In this embodiment, the electronic device inputs the calculated health indicators of the aero-engine into a pre-established CUSUM for real-time monitoring. Within the CUSUM, the electronic device calculates the cumulative sum and statistics relative to a health baseline value for each component of the health indicator. When the cumulative sum and statistics exceed a preset control threshold, the electronic device determines that the aero-engine is experiencing performance degradation and triggers a warning signal. When the cumulative sum and statistics do not exceed the preset control threshold, the electronic device does not trigger a warning signal and stores the current cumulative sum and statistics in a cache for recursive updates of the cumulative sum and statistics at the next time step, thereby maintaining the long-term monitoring capability for small, persistent deviations in the health indicators.

[0098] Optionally, in some embodiments, the electronic device may also employ an exponentially weighted moving average control chart instead of CUSUM to detect small, persistent shifts in health indicators. The exponentially weighted moving average control chart, by assigning higher weights to recent data, is more sensitive to recent trends in engine performance.

[0099] It should be noted that, based on the completion of transient effect correction, the corrected and restored steady-state equivalent measurement value is used for the accurate calculation of health indicators. Combined with the cumulative sum control chart, the small and persistent deviations of health indicators are detected in real time with high sensitivity. This can effectively avoid the estimation bias of health parameters and system misdiagnosis caused by the coupling of transient components and degradation signals, and realize high-precision and high-sensitivity early diagnosis of the performance degradation of the aero-engine gas path under transient conditions.

[0100] To better understand the embodiments of this application, the following describes an online correction and diagnostic experiment of the mechanism-data dual-driven aero-engine transient effect correction method (hereinafter referred to as the transient effect correction method) provided in the embodiments of this application, and the experimental results are described in detail: A mechanism- and data-driven method for correcting transient effects in aero-engines is employed to perform online transient correction of the original sensor measurement residuals under transient operating conditions. For example, Figure 2 This is a graph showing the analysis results of the transient effect correction method provided in this application under the parameter T30 at the outlet temperature of the high-pressure compressor. Figure 2 The dataset comprises four sets of graphs. The first set compares the raw data with baseline calculations. This set compares the changes over time of the raw sensor measurements of the turbine outlet temperature T30 of the aero-engine (the gray curve) with the output value of the mechanistic baseline model based on steady-state aero-thermodynamics (the blue curve) over more than 800,000 discrete time steps. The first set of graphs clearly shows that the gray curve exhibits severe upward and downward pulses and systematic deviations across the entire time axis due to frequent engine acceleration and deceleration, with amplitude fluctuations far exceeding those of the blue curve. This first set of graphs clearly reflects the overall degree of deviation and the presence of strong nonlinear transient bias components from a physical perspective, demonstrating the technical defect of strong transient effects coupled with health signals in the raw sensor measurements.

[0101] The second set of figures shows the prediction trend of the corrected residuals. This set of figures illustrates the evolution trend of the predicted residuals (i.e., the red curves) as a function of time steps after linear state-space prediction of the constructed augmented observable vector using the augmented Koopman operator pre-trained in this application. The amplitude fluctuations of the predicted residuals are mainly concentrated between -0.25 and 0.10, and exhibit highly characteristic asymmetric pulse sequences (e.g., negative spikes corresponding to deceleration modes). This indicates that the model can accurately capture and linearly reconstruct the direction-dependent dynamic thermal hysteresis effect of the sensor caused by thermal inertia and rotor inertia in a high dimension, which can be used to quantitatively evaluate the high-precision fitting effect of the transient effect correction model on the nonlinear dynamic error sequence.

[0102] The third set of figures compares the corrected results with the original data. This set of figures overlays the equivalent steady-state measurement curve (i.e., the green curve) obtained after transient effect correction using the transient effect correction method proposed in this application with the gray curve corresponding to the original sensor measurement value on the same time axis. It can be clearly observed from the third set of figures that the green curve, while fully covering the original operating condition response range, extremely accurately eliminates dynamic spikes, glitches, and low-frequency drift components caused by the transient process, and perfectly preserves the reasonable physical dynamic response characteristics of the aero-engine during wide-range switching. This third set of figures allows technicians to intuitively judge that the transient effect correction method proposed in this application effectively removes transient interference components throughout the entire flight envelope and during bidirectional transient processes, restoring the equivalent steady-state response that reflects the true health state of the engine.

[0103] The fourth set of figures is a comparison of error distributions. This set of figures quantitatively compares the probability density and root mean square error (RMSE) distribution of the deviations between the outputs of each method and the original measurements before and after correction within the error interval. The uncorrected original baseline error (the blue histogram) exhibits a loose distribution over an extremely wide range of -6 to +6, with an RMSE as high as 2.836. In contrast, the corrected error after transient bias compensation using the transient effect correction method proposed in this application (the green histogram) is extremely compressed and highly converged to the 0-mean central axis, forming a very narrow green peak, with the RMSE plummeting to 0.002. This fourth set of figures quantitatively reflects the disruptive improvement in sensor measurement accuracy and diagnostic benchmarks brought about by the transient effect correction method proposed in this application, verifying the significant technological advancements in accuracy and robustness of the mechanism-data dual-drive architecture.

[0104] Furthermore, as can be seen from the corrected curve (green curve) in the third set of figures, this curve is decoupled from the transient peak shape of the original measured value (gray curve), while still maintaining a reasonable dynamic response rate of the engine components. In the steady-state segment of the time series, the difference between the corrected curve and the actual measured value is compressed to a very small range, indicating that the system reference deviation caused by model mismatch or low-frequency sensor drift has been effectively decoupled. As a comparison, Figure 2The first set of figures also shows the steady-state mapping curve (i.e., the blue curve corresponding to the output value of the mechanistic baseline model) as a control group. Although this steady-state mapping curve is relatively close to the measured value in the steady-state operation of the engine, it deviates significantly from the actual measurement during the transient process of frequent acceleration and deceleration, and completely fails to reflect the dynamic overshoot and response hysteresis caused by sensor thermal inertia and rotor mechanical inertia. This technically demonstrates that simply relying on traditional steady-state empirical models or steady-state mappings is insufficient for the task of transient effect correction under severe transient conditions across the entire flight envelope and wide envelope. In contrast, the transient effect correction method proposed in this application, by learning the nonlinear dynamic mode of the measurement residual online and applying steady-state or transient physical boundary constraints in the state space evolution, successfully removes the unmodeled dynamics and low-frequency systematic offsets in the transient process, making the corrected equivalent data closer to a stationary sequence with zero mean. This provides a highly reliable observation input benchmark for subsequent filtering estimation of health parameters, condition monitoring, and condition-based maintenance.

[0105] Furthermore, to verify the versatility and adaptability of the method provided in this application embodiment on different types of sensors and multiple core gas path parameters of aero-engines, this application also conducted online transient correction experiments on low-pressure turbine outlet temperature T50, fan rotor speed Nf, core engine rotor speed Nc, and low-pressure turbine outlet total pressure P50 respectively: Figure 3 This is a graph showing the analysis results of the transient effect correction method provided in this application under the low-pressure turbine outlet temperature T50 parameter. (See figure) Figure 3 As shown, the low-pressure turbine outlet temperature T50 is at the end of the gas expansion and work process. Due to its strong thermal inertia, the gray curve corresponding to the original sensor measurement value and the blue curve corresponding to the output value of the mechanism baseline model exhibit significant time-domain deviation and asymmetric hysteresis under frequently switching transient conditions. After online correction using the transient effect correction method provided in this application embodiment, the amplitude fluctuation range of the red curve corresponding to the residual prediction value is mainly concentrated between -0.30 and 0.10, and a specific negative thermal hysteresis peak is accurately captured. The superimposed comparison of the equivalent steady-state measurement value curve (i.e., the green curve) obtained after correction and the gray curve corresponding to the original sensor measurement value shows that while perfectly preserving the macroscopic step trend of the component itself, the dynamic delay deviation is accurately eliminated. From the quantitative statistical results of the fourth set of figures, the uncorrected original baseline error (i.e., the blue histogram) shows a wide-ranging, loosely distributed pattern, with a root mean square error (RMSE) as high as 2.879. In contrast, the error distribution after correction by the transient effect correction method proposed in this application (i.e., the green histogram) converges significantly towards the 0 axis, and the RMSE drops sharply to 0.002. This fully verifies the extreme correction accuracy of the transient effect correction method proposed in this application on the thermal inertia temperature parameter.

[0106] Figure 4 This is a graph showing the analysis results of the transient effect correction method provided in this application under the fan rotor speed Nf parameter. Figure 4 As shown, the fan rotor speed Nf, a core parameter characterizing the mechanical inertia of the engine's low-pressure rotor, is as high as 1.0 × 10⁻⁶. 6 The system oscillates violently within the range of 1100 to 1450 rpm during multiple transient cycles in discrete time steps. In the first set of figures, due to the large absolute magnitude of the speed baseline, the transient dynamic deviation caused by the mechanical rotational inertia easily interferes with subsequent diagnosis. The corresponding uncorrected root mean square error (RMSE) of the original baseline is as high as 45.896, and the blue histogram deviates from the 0-center axis. After calling the pre-trained augmented Koopman operator to perform state projection prediction on the augmented observable vector, the red curve corresponding to the residual prediction value in the second set of figures accurately depicts the bidirectional dynamic energy release characteristics corresponding to the acceleration or deceleration modes. Finally, the corrected equivalent steady-state measurement curve (i.e., the green curve) in the third set of figures effectively removes the transient components superimposed on the mechanical speed. The corrected RMSE is dramatically reduced from 45.896 to 0.164, and the error distribution forms an extremely high and narrow absolute convergence peak at 0.

[0107] Figure 5 This is a graph showing the analysis results of the transient effect correction method provided in this application under the core machine rotor speed Nc parameter. (See figure) Figure 5 As shown, the core engine rotor speed Nc, as a key indicator characterizing the dynamic behavior of the high-pressure rotor, is extremely sensitive to transient changes in timing control inputs such as engine fuel flow. The first set of figures clearly shows that the gray curve corresponding to the original sensor measurement values ​​fluctuates wildly during the transient process, exhibiting severe nonlinear dynamic misalignment with the blue curve corresponding to the mechanistic baseline model due to the inertia of the high-pressure rotor. This results in an uncorrected root mean square error (RMSE) of 72.742 for the original baseline. After transient bias compensation using the transient effect correction method proposed in this application, the red curve corresponding to the residual prediction value in the second set of figures effectively reproduces this highly dynamic mechanical process. The equivalent steady-state measurement curve (i.e., the green curve) obtained after correction in the third set of figures eliminates transient spikes while retaining the physical step within the full envelope. Statistical comparison in the fourth set of figures shows that the correction error (i.e., the green histogram) is highly converged, and the RMSE is significantly reduced to 0.391, strongly demonstrating the superior ability of the transient effect correction method proposed in this application to capture the high dynamic response of high-pressure core engine components.

[0108] Figure 6 This is a graph showing the analysis results of the transient effect correction method provided in this application under the low-pressure turbine outlet total pressure P50 parameter. (See figure) Figure 6As shown, the total pressure P50 at the low-pressure turbine outlet, as a high-dynamic aerodynamic pressure parameter in the gas path, has the physical characteristics of fast transmission speed and huge absolute magnitude fluctuation with operating conditions. As can be seen from the first set of figures, within a wide range of fluctuations from 7400 to 8600 Pa, the gray curve corresponding to the original sensor measurement value deviates drastically from the blue curve corresponding to the output value of the mechanistic baseline model, resulting in an uncorrected root mean square error (RMSE) of up to 150.099. This is highly likely to cause false alarms and misdiagnosis of degradation in traditional health management systems. The transient effect correction method proposed in this application adopts an adaptive adjustment through a dual-driven architecture of mechanism and data. The second set of figures accurately predicts the nonlinear evolution trajectory of the pressure residual; the third set of figures shows the accurate equivalent steady-state restoration of the high-frequency fluctuations of the gray curve by the corrected green curve; the statistical distribution of the fourth set of figures shows that the correction error (i.e., the green histogram) exhibits perfect zero-mean white noise characteristics, and the RMSE is reduced from 150.099 to 0.546, achieving a reduction in error across orders of magnitude.

[0109] In summary, the transient effect correction method provided in this application can accurately isolate transient components across the entire time axis and flight envelope when dealing with multiple physical fields and various types of air path sensor parameters such as temperature (i.e., T30, T50), rotational speed (i.e., Nf, Nc), and pressure (i.e., P50). Its statistical error exhibits high consistency, alignment, and strong convergence, fundamentally overcoming the industry problem of strong transient effects and health degradation signals being coupled together in the prior art. This provides a highly reliable and accurate steady-state equivalent data foundation for the air path diagnosis of aero-engines.

[0110] The transient effect correction device for aero-engines based on mechanism-data dual-drive provided in the embodiments of this application is described below. The transient effect correction device for aero-engines based on mechanism-data dual-drive described below can be referred to in correspondence with the transient effect correction method for aero-engines based on mechanism-data dual-drive described above.

[0111] Figure 7 This is a schematic diagram of the structure of the transient effect correction device for aero-engines based on mechanism-data dual-drive provided in an embodiment of this application. Figure 7 As shown, the device includes: a working condition marking module 701, a mechanism prediction module 702, a residual prediction module 703, and a transient correction module 704.

[0112] The operating condition marking module 701 is used to obtain the rotor speed of the aero-engine at adjacent moments and determine the direction marking of the current operating condition of the aero-engine.

[0113] The mechanism prediction module 702 is used to acquire the sensor measurement vector of the aero-engine under transient operating conditions, and based on the preset mechanism baseline model, determine the mechanism prediction value corresponding to the sensor measurement vector of the aero-engine and the mechanism residual corresponding to the sensor measurement vector.

[0114] The residual prediction module 703 is used to construct an augmented observable vector based on the orientation marker of the current operating condition of the aero-engine and the mechanism residual; and to predict the augmented observable vector using a pre-trained augmented Koopman operator to obtain the residual prediction value corresponding to the mechanism residual.

[0115] The transient correction module 704 is used to determine the transient effect correction value of the aero-engine based on the mechanism prediction value and the residual prediction value corresponding to the sensor measurement vector.

[0116] Optionally, the operating condition marking module 701 is also used to obtain the rotor speed of the aero-engine at adjacent moments, and to determine the direction mark according to the rotor speed at the current moment and the sub-speed at the previous moment using formula (1): ;in, This indicates the direction marker, and k represents the discrete-time index. This indicates that the aircraft engine is in Rotor speed at any given time This indicates that the aircraft engine is in Rotor speed at any given time For a sign function, when hour, This indicates that the current operating condition of the aero-engine is acceleration mode; when hour, This indicates that the current operating condition of the aero-engine is deceleration mode.

[0117] Optionally, the mechanism prediction module 702 is further configured to acquire the sensor measurement vector, timing control vector, and flight envelope parameters of the aero-engine under transient operating conditions; based on the timing control vector and the flight envelope parameters, obtain the mechanism prediction value corresponding to the sensor measurement vector of the aero-engine through the mechanism baseline model mapping; and determine the mechanism residual corresponding to the sensor measurement vector based on the difference between the sensor measurement vector and the corresponding mechanism prediction value.

[0118] Optionally, the mechanism prediction module 702 is further configured to, based on the flight envelope parameters at the current moment, match and obtain the mechanism baseline model parameters under the corresponding flight envelope parameters through a preset parameter lookup table; wherein, the mechanism baseline model parameters include a time constant. and gain The mechanistic baseline model is a mechanistic baseline model with first-order inertia and delay. This first-order inertia and delay mechanistic baseline model is discretized using a bilinear transformation, and the time constant is... and the gain Transformed into first discrete-time coefficients Second discrete time coefficient According to the first discrete-time coefficient and the second discrete-time coefficient Delay steps Timing control vector The mechanism prediction value corresponding to the sensor measurement vector at the current discrete moment is determined by formula (4): ,in, Represents a discrete-time index. Indicates the first Mechanistic prediction values ​​at discrete time points Indicates the first Timing control vectors at discrete moments.

[0119] Optionally, the residual prediction module 703 is also used to determine the augmented observable vector according to the mechanism residual and the direction marker by formula (2): ,in, This represents the augmented observable vector. This indicates that the sensor's measurement vector is in The mechanistic residual corresponding to the time step, This indicates that the aircraft engine is in The direction marker corresponding to the time. This represents the nonlinear interaction term between the residual of this mechanism and the direction marker. This represents the norm of the residuals of the mechanism.

[0120] Optionally, the residual prediction module 703 is also used to acquire the augmented observable vector sequence under historical transient conditions and construct a snapshot matrix at the current moment. and the snapshot matrix at the next time step Based on the flight envelope points corresponding to the current flight envelope parameters. The time constant of the transient response of the mechanistic baseline model is obtained by looking up a table. Set weight hyperparameters To minimize the total loss function For the objective, iteratively solve the augmented Koopman operator. The function that minimizes the total loss is expressed as: , This represents a physical constraint term. We obtain the following from formula (3): ,in, This indicates the augmented Koopman operator The first in continuous time form 1 eigenvalue, Represents eigenvalues The real part, This represents the total number of eigenvalues.

[0121] Optionally, this physical constraint term Used to constrain the augmented Koopman operator The eigenvalues ​​are consistent with the time constants of the baseline model of this mechanism under different flight envelopes.

[0122] Optionally, the residual prediction module 703 is further configured to match a corresponding first subset of eigenvalues ​​from the eigenvalue spectrum of the augmented Koopman operator based on the orientation marker of the current operating condition of the aero-engine. or the second eigenvalue subset The augmented observable vector is then used to perform residual prediction by using the feature vectors corresponding to the matched subset of feature values.

[0123] Optionally, the transient correction module 704 is also used to determine the health indicators of the aero-engine based on the sensor measurement vector of the aero-engine under transient operating conditions, the transient effect correction value of the aero-engine, and the nominal steady-state model output value.

[0124] Figure 8 This is a schematic diagram of the structure of the electronic device provided in an embodiment of this application. For example... Figure 8 As shown, the electronic device may include a processor 810, a communications interface 820, a memory 830, and a communication bus 840. The processor 810, communications interface 820, and memory 830 communicate with each other via the communication bus 840. The processor 810 can call logical instructions from the memory 830 to execute a mechanism-data dual-driven transient effect correction method for aero-engines.

[0125] Furthermore, the logical instructions in the aforementioned memory 830 can be implemented as software functional units and, when sold or used as independent products, can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this application. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0126] On the other hand, this application also provides a computer program product, which includes a computer program that can be stored on a non-transitory computer-readable storage medium. When the computer program is executed by a processor, the computer can execute the mechanism-data dual-drive aero-engine transient effect correction method provided by the above methods.

[0127] In another aspect, embodiments of this application also provide a non-transitory computer-readable storage medium storing a computer program thereon, which, when executed by a processor, is implemented to perform the mechanism-data dual-driven aero-engine transient effect correction method provided by the above methods.

[0128] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs. Those skilled in the art can understand and implement this without any creative effort.

[0129] Through the above description of the embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus necessary general-purpose hardware platforms, and of course, it can also be implemented by hardware. Based on this understanding, the above technical solutions, in essence or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in the various embodiments or some parts of the embodiments.

[0130] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application.

Claims

1. A method for correcting transient effects in aero-engines based on a mechanism-data dual-drive approach, characterized in that, include: Obtain the rotor speed of the aero-engine at adjacent moments and determine the direction marker of the current operating condition of the aero-engine; The sensor measurement vector of the aero-engine under transient operating conditions is obtained. Based on a preset mechanism baseline model, the mechanism prediction value corresponding to the sensor measurement vector of the aero-engine and the mechanism residual corresponding to the sensor measurement vector are determined. Based on the orientation marker of the current operating condition of the aero-engine and the mechanism residual, an augmented observable vector is constructed; The augmented observable vector is predicted by the pre-trained augmented Koopman operator to obtain the residual prediction value corresponding to the mechanism residual; The transient effect correction value of the aero-engine is determined based on the mechanism prediction value and the residual prediction value corresponding to the sensor measurement vector.

2. The method for correcting transient effects in aero-engines based on mechanism-data dual-drive as described in claim 1, characterized in that, The step of obtaining the rotor speed of the aero-engine at adjacent moments and determining the direction marker of the current operating condition of the aero-engine includes: Obtain the rotor speed of the aero-engine at adjacent moments, and determine the direction mark according to the rotor speed at the current moment and the sub-speed at the previous moment using formula (1): ； in, The direction marker is represented by k, which represents the discrete-time index. This indicates that the aircraft engine is in Rotor speed at any given time This indicates that the aircraft engine is in Rotor speed at any given time For a sign function, when hour, This indicates that the current operating condition of the aero-engine is acceleration mode; when hour, This indicates that the current operating condition of the aero-engine is deceleration mode.

3. The method for correcting transient effects in aero-engines based on mechanism-data dual-drive as described in claim 1, characterized in that, The step of constructing the augmented observable vector based on the orientation marker of the current operating condition of the aero-engine and the mechanism residual includes: Based on the mechanistic residual and the direction marker, the augmented observable vector is determined using formula (2): ， in, Denotes the augmented observable vector, Indicates that the sensor measurement vector is in The mechanistic residual corresponding to the time step, This indicates that the aircraft engine is in The direction marker corresponding to the time. This represents the nonlinear interaction term between the mechanistic residual and the direction marker. The norm of the residual of the mechanism is represented.

4. The method for correcting transient effects in aero-engines based on mechanism-data dual-drive as described in claim 1, characterized in that, The pre-training steps for the augmented Koopman operator include: Obtain the augmented observable vector sequence under historical transient conditions, and construct the snapshot matrix at the current moment. and the snapshot matrix at the next time step ; Based on the flight envelope points corresponding to the current flight envelope parameters The time constant of the transient response of the mechanistic baseline model is obtained by looking up a table. ; Setting weight hyperparameters To minimize the total loss function For the objective, iteratively solve the augmented Koopman operator. The total loss function that minimizes the total loss is expressed as: , This refers to physical constraint terms, the physical constraint terms We obtain the following from formula (3): ， in, This indicates the augmented Koopman operator. The first in continuous time form 1 eigenvalue, Represents eigenvalues The real part, This represents the total number of eigenvalues.

5. The method for correcting transient effects in aero-engines based on mechanism-data dual-drive as described in claim 4, characterized in that, The physical constraints Used to constrain the augmented Koopman operator The eigenvalues ​​are consistent with the time constants of the baseline model of the mechanism under different flight envelopes.

6. The method for correcting transient effects in aero-engines based on mechanism-data dual-drive as described in claim 1, characterized in that, The step of predicting the augmented observable vector using a pre-trained augmented Koopman operator includes: The eigenvalue spectrum of the augmented Koopman operator contains a first subset of eigenvalues. Second eigenvalue subset ; Based on the orientation marker of the current operating condition of the aero-engine, the corresponding first subset of eigenvalues ​​is matched from the eigenvalue spectrum of the augmented Koopman operator. or the second eigenvalue subset The augmented observable vector is then used to perform residual prediction based on the feature vectors corresponding to the matched subset of feature values.

7. The method for correcting transient effects in aero-engines based on mechanism-data dual-drive as described in claim 1, characterized in that, After determining the transient effect correction value of the aero-engine, the method further includes: The health indicators of the aero-engine are determined based on the sensor measurement vectors of the aero-engine under transient operating conditions, the transient effect correction value of the aero-engine, and the nominal steady-state model output value.

8. The method for correcting transient effects in aero-engines based on mechanism-data dual-drive as described in claim 1, characterized in that, The steps of acquiring the sensor measurement vector of the aero-engine under transient operating conditions, and determining the mechanism prediction value corresponding to the sensor measurement vector and the mechanism residual corresponding to the sensor measurement vector based on a preset mechanism baseline model, include: Acquire the sensor measurement vector, timing control vector, and flight envelope parameters of the aero-engine under transient operating conditions; Based on the timing control vector and the flight envelope parameters, the mechanism prediction value corresponding to the sensor measurement vector of the aero-engine is obtained by mapping through the mechanism baseline model; The mechanism residual corresponding to the sensor measurement vector is determined based on the difference between the sensor measurement vector and the corresponding mechanism prediction value.

9. The method for correcting transient effects in aero-engines based on mechanism-data dual-drive as described in claim 8, characterized in that, The step of obtaining the mechanism prediction value corresponding to the sensor measurement vector of the aero-engine through the mechanism baseline model mapping based on the timing control vector and the flight envelope parameters includes: Based on the flight envelope parameters at the current moment, the mechanistic baseline model parameters under the corresponding flight envelope parameters are obtained by matching them through a preset parameter lookup table; wherein, the mechanistic baseline model parameters include a time constant. and gain ; The mechanistic baseline model is a mechanistic baseline model with first-order inertia and delay. The first-order inertia and delay mechanistic baseline model is discretized using a bilinear transformation, and the time constant is... and the gain Transformed into first discrete-time coefficients Second discrete time coefficient ; According to the first discrete time coefficient and the second discrete time coefficient Delay steps Timing control vector The mechanism prediction value corresponding to the sensor measurement vector at the current discrete moment is determined by formula (4): ， in, Represents a discrete-time index. Indicates the first Mechanistic prediction values ​​at discrete time points Indicates the first Timing control vectors at discrete moments.

10. A mechanism-data dual-driven transient effect correction device for aero-engines, characterized in that, The device is used to implement the mechanism-data dual-drive method for correcting transient effects in aero-engines as described in any one of claims 1-9, comprising: The operating condition marking module is used to obtain the rotor speed of the aero-engine at adjacent moments and determine the direction marking of the current operating condition of the aero-engine. The mechanism prediction module is used to obtain the sensor measurement vector of the aero-engine under transient operating conditions, and based on the preset mechanism baseline model, determine the mechanism prediction value corresponding to the sensor measurement vector of the aero-engine and the mechanism residual corresponding to the sensor measurement vector. The residual prediction module is used to construct an augmented observable vector based on the orientation marker of the current operating condition of the aero-engine and the mechanism residual; and to predict the augmented observable vector using a pre-trained augmented Koopman operator to obtain the residual prediction value corresponding to the mechanism residual. The transient correction module is used to determine the transient effect correction value of the aero-engine based on the mechanism prediction value and the residual prediction value corresponding to the sensor measurement vector.

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