An aero-engine multi-dimensional coupling simulation method based on online active learning

Abstract

The application discloses an aero-engine multi-dimension coupling simulation method based on online active learning, and belongs to the technical field of aero-engine overall performance simulation. The method directly starts from zero-dimension whole machine and three-dimension component model coupling simulation without collecting samples offline, and accumulates initial samples in iteration; after the samples reach the standard, an agent model is constructed and updated online to assist the zero-dimension model in quickly iterating to obtain a predicted convergent solution; the confidence is judged according to the predicted variance at the convergent solution, the confidence is directly outputted if the confidence is high, or three-dimension simulation verification is started if the confidence is low, new samples are stored and the agent model is updated, and the zero-dimension model component scaling factor is corrected. The application adopts online active sampling, focuses the samples on the whole machine matching working line, realizes high-precision local fitting with a small amount of samples, introduces a fast exit mechanism based on variance, reduces the three-dimension simulation times with the increase of samples, greatly improves the calculation efficiency while ensuring the accuracy, and solves the problems of high cost of traditional coupling simulation and difficulty in offline training.

Description

Technical Field

[0002] This invention relates to the field of overall performance simulation technology for aero-engines, specifically to a multi-dimensional coupled simulation method for aero-engines based on online active learning. Background Technology

[0004] Accurate prediction of overall engine performance is a core supporting technology for the development of advanced aero-engines. In particular, the new generation of power plants, represented by adaptive variable cycle engines, have introduced complex variable geometry structures in multiple components such as fans, compressors, turbines, and exhaust systems to achieve optimal performance across the entire flight envelope. The introduction of these variable geometry mechanisms greatly increases the coupling degree of the system. Therefore, establishing a high-precision simulation model of overall engine performance is of vital importance for the design of control laws and the matching of flight and engine performance.

[0005] The current overall performance simulation methods mainly include the following three categories: (1) Zero-dimensional (0D) whole machine simulation: This is the most widely used method in engineering applications. Its core is to use the general characteristic diagram of the component for table lookup interpolation, and to establish the whole machine thermodynamic cycle equation system based on the component matching method for solution; (2) Zero-dimensional / three-dimensional (0D / 3D) coupled simulation: In order to improve the simulation accuracy at the component level, the key components in the whole machine model are replaced with three-dimensional CFD numerical simulation. In the simulation process, the zero-dimensional model provides boundary conditions for the three-dimensional model, and the three-dimensional model feeds back the real flow field characteristic parameters. The two alternately iterate until the whole machine converges; (3) Zero-dimensional / surrogate model (0D / SM) coupled simulation: In order to solve the problem of time consumption of 0D / 3D coupled calculation, a large number of three-dimensional samples are collected in the design space in advance through the design of experiments (DOE) method to train surrogate models such as neural networks or Kriging. In the whole machine simulation, the trained offline surrogate model is used to replace the three-dimensional CFD calculation.

[0006] The aforementioned existing technologies all have significant technical limitations when facing adaptive variable cycle engines with multivariable adjustment characteristics. The specific analysis is as follows: (1) Zero-dimensional simulation has insufficient representation ability on variable geometry components, and the accuracy is limited. The core assumption of zero-dimensional simulation is that the component characteristics can be described by low-dimensional characteristic maps. However, components such as adaptive fans introduce additional variable geometry adjustment degrees of freedom such as guide vane angle and bypass ratio adjustment mechanism, which makes the component characteristics change from two-dimensional curves to high-dimensional "characteristic hypersurfaces". As a result, generating high-dimensional general characteristic maps covering all variable geometry combinations requires a lot of computing resources. In engineering, it can often only be handled by simplification, which directly leads to a significant reduction in the accuracy of overall machine performance prediction; (2) The computational cost of zero-dimensional / three-dimensional direct coupling is too high and the engineering practicality is poor. Although zero-dimensional / three-dimensional coupling solves the accuracy problem, CFD calculation requires a lot of time (single calculation takes several hours). Traditional coupling iteration usually requires dozens of CFD calculations to achieve overall machine balance convergence, which is costly and difficult to support engineering design iteration; (3) The coupling method based on offline proxy model has a contradiction between the number of samples and the model accuracy. Building a high-precision surrogate model requires a large number of training samples, which means that large-scale offline 3D computations must be performed before simulation, resulting in huge upfront costs. Furthermore, as the number of variable geometry adjustment variables increases, the number of samples required to maintain the same model accuracy grows exponentially. With limited computing resources, the average accuracy of the global offline surrogate model is often difficult to improve. This is because the sample space covered by offline sampling is wide and the sample points are scattered. However, in actual system operation, the system's matching operating point is located in a specific local region. Since the global surrogate model has sparse samples near the local matching operating point, its prediction accuracy at the operating point is actually low, failing to meet the requirements of high-precision simulation.

[0007] In summary, existing technologies cannot simultaneously meet the core requirements of "high accuracy," "low computational cost," and "zero offline preparation." Therefore, there is an urgent need for a method that does not require offline training data, but starts directly from 0D / 3D coupling, automatically builds a high-precision local model with iteration, and accelerates convergence. Summary of the Invention

[0009] To address the shortcomings of existing technologies, this invention provides a multi-dimensional coupled simulation method for aero-engines based on online active learning, which solves the problems of low accuracy in whole-engine 0D simulation, large computational load in 0D / 3D coupling, high training cost of 0D / SM offline proxy models, and poor local accuracy in existing technologies.

[0010] To achieve the above objectives, the present invention provides the following technical solution: a multi-dimensional coupled simulation method for aero-engines based on online active learning, comprising the following steps:

[0011] Step S1: At the beginning of the simulation, directly run the coupled simulation of the zero-dimensional whole model and the three-dimensional component model. Through at least two three-dimensional simulation iterations, generate initial samples and store them in the sample library.

[0012] Step S2: When the number of samples in the sample library reaches a preset threshold, a surrogate model is constructed and trained using the sample library data. The surrogate model is used to predict component characteristics and provides the prediction variance.

[0013] Step S3: Embed the trained surrogate model into the zero-dimensional whole model. The zero-dimensional model calls the surrogate model for rapid iteration to obtain the predicted convergent solution that satisfies the convergence condition of the zero-dimensional whole model.

[0014] Step S4: Determine whether the prediction variance of the surrogate model at the predicted converged solution is lower than a preset confidence threshold; if the prediction variance is lower than the preset confidence threshold, determine that the prediction accuracy of the surrogate model meets the requirements, terminate the whole-machine coupled calculation, and output the predicted converged solution as the final simulation result; if the prediction variance is higher than or equal to the preset confidence threshold, determine that the prediction accuracy of the surrogate model does not meet the requirements, and proceed to step S5.

[0015] Step S5: Run a three-dimensional simulation using the predicted converged solution as the boundary condition to obtain the actual component characteristics. Store the operating point in the sample library and update the surrogate model online. Use the three-dimensional simulation results to correct the component characteristic scaling factor in the zero-dimensional whole machine model. Return to step S3 to continue accelerating the prediction using the surrogate model.

[0016] Preferably, in step S1, there is no need to conduct offline sample collection based on experimental design in advance, and all samples are derived from intermediate data in the whole machine coupling iteration process.

[0017] Preferably, the active learning update in step S5 causes the sample points to be automatically concentrated near the matching working line of the actual operation of the aero-engine, and high-precision fitting of the working point region is achieved by using local samples near the working line of the engine.

[0018] Preferably, the fast exit mechanism in step S4 reduces the number of 3D simulations required as the number of samples increases until prediction is performed entirely through a surrogate model.

[0019] The preferred proxy model construction strategy in step S2 is as follows: when the number of samples is lower than a first quantity threshold, the Kriging model is used; when the number of samples is higher than or equal to the first quantity threshold, the model is switched to a neural network model or a Bayesian neural network model.

[0020] Preferably, the components that are coupled with the whole machine for simulation include any one or more combinations of the fan, compressor, combustion chamber, turbine, or tail nozzle.

[0021] Preferably, in step S1, the scaling factor of component characteristics in the zero-dimensional whole machine model is corrected according to the following formula:

[0022] ;

[0023] ;

[0024] ;

[0025] In the formula, These are correction factors for flow rate, pressure ratio, and efficiency; 0D and 3D represent the characteristics of zero-dimensional simulation and three-dimensional simulation, respectively. and Representing different iteration steps; This is a relaxation factor to prevent oscillations during the iteration process and accelerate convergence.

[0026] Preferably, in step S4, in order to eliminate the influence of different physical dimensions, normalized prediction variance is used as the confidence index, and its calculation formula is as follows:

[0027] ;

[0028] in, To normalize the prediction variance, This represents the prediction variance output by the surrogate model at the point of convergence. This is the predicted mean output by the surrogate model at the predicted convergent solution.

[0029] Preferably, when the Bayesian neural network model is used, the dropout variational inference technique is employed to keep the dropout layer on during the prediction phase. By performing multiple random forward propagations on the same input condition, the mean and variance of the multiple output results are statistically analyzed and used as the prediction characteristic value and prediction uncertainty of the surrogate model.

[0030] Preferably, in step S1, the input boundary condition vector passed from the zero-dimensional whole machine model to the three-dimensional component model includes at least the converted rotational speed, total inlet pressure, total inlet temperature, and component pressure ratio; the real performance parameter vector fed back from the three-dimensional component model to the zero-dimensional whole machine model includes at least the physical flow rate, pressure ratio, and adiabatic efficiency.

[0031] This invention provides a multi-dimensional coupled simulation method for aero-engines based on online active learning. It has the following beneficial effects:

[0032] 1. This invention greatly reduces the threshold for engineering applications by eliminating the need for time-consuming DOE offline sampling beforehand and enabling the multi-dimensional coupled simulation task of the whole machine to be started at any time.

[0033] 2. This invention automatically focuses on the matching working point of the actual operation of the whole machine by deriving sample points entirely from the multi-dimensional coupling and iterative process of the whole machine. Compared with the full coverage of traditional proxy models, this method only requires a very small number of samples to achieve high-precision fitting at the working point.

[0034] 3. This invention reduces the number of 3D calculations by more than 80% compared to traditional coupling methods through an evolutionary process of "initial accumulation - proxy assistance - full proxy".

[0035] 4. This invention introduces a variance-based fast exit mechanism and uses a surrogate model to determine the accuracy of component characteristic prediction, thereby avoiding unnecessary over-computation. Attached Figure Description

[0037] Figure 1 This is a simulation diagram illustrating the 0D / SM / 3D multi-dimensional coupling between the adaptive fan component and the whole engine of an adaptive variable cycle engine.

[0038] Figure 2 This is the overall flowchart of the whole-machine multi-dimensional coupling method based on online active learning of the present invention;

[0039] Figure 3 This is a flowchart of the technical solution of the present invention;

[0040] Figure 4 This is a comparative diagram showing the number of 3D calculations required for the two methods of 0D / 3D and 0D / SM / 3D in this invention to achieve convergence. Detailed Implementation

[0042] To enable those skilled in the art to better understand the present invention, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0043] This invention proposes a multi-dimensional coupling method for the whole machine based on online active learning and zero-dimensional / surrogate model / three-dimensional (0D / SM / 3D) coupling. Taking the multi-dimensional coupling simulation of the adaptive fan component and the whole machine of a double-bypass adaptive variable cycle engine as an example ( Figure 1 This describes the specific operational steps of a preferred embodiment of the present invention (e.g.) Figure 3 (As shown).

[0044] Step S1: At the initial stage of the simulation task, the sample database is empty. At this time, the system is set to "high-fidelity data accumulation mode".

[0045] 1. Boundary Condition Generation: Based on the given operating conditions, run the zero-dimensional whole machine model to generate the input boundary condition vector for the fan component in the current iteration step. ,in To convert the rotational speed, For the inlet temperature, For the inlet temperature, This refers to the pressure ratio.

[0046] 2. 3D Simulation Execution: Call a 3D CFD solver (such as ANSYS CFX) to... Calculations are performed for the boundary conditions. Flow field residuals are monitored during the calculation, and the true performance parameter vector is output upon convergence. ,in For traffic, For pressure ratio, For efficiency.

[0047] 3. Sample storage: The samples ( Stored in the sample database.

[0048] 4. Scaling Factor Correction: The scaling factor of components in the zero-dimensional model is corrected using the 3D results. This embodiment uses the following correction formula with a relaxation factor:

[0049] ;

[0050] in, The value is set to 0.5 to prevent initial iteration oscillations.

[0051] 5. Loop Check: Repeat the above process until the number of samples in the sample library reaches a certain threshold. Reaching the preset threshold (That is, at least 2 real sample points must be accumulated).

[0052] Step S2: When At this time, the system activates the "Proxy Model Building Module". Based on the current data volume in the sample database, it adaptively selects the modeling algorithm: small sample stage (…). ): Construct a Kriging (Gaussian process regression) model. The Matern5 / 2 kernel function is chosen to capture non-smooth variations in physical properties. The Kriging model can analytically output the predicted mean. and prediction variance Large sample stage ( ): Switch to a Bayesian Neural Network (BNN). Employ Dropout variational inference (MCDropout) to estimate the mean and variance of the prediction distribution by performing multiple random forward propagations (e.g., sampling 50 times) during prediction, thereby improving computational efficiency. Online update: In subsequent steps, whenever new 3D simulation data is generated, it is immediately added to the training set and the model parameters are updated (incremental updates or full retraining are performed for Kriging models).

[0053] Step S3: Embed the trained surrogate model into the iterative loop of the zero-dimensional whole-machine solver. In each internal Newton-Raphson iteration step of the zero-dimensional solver,

[0054] 1. Generate the current working condition using a zero-dimensional solver. ;

[0055] 2. Invoke the surrogate model to predict the characteristics under this operating condition. and confidence index (variance) );

[0056] 3. Zero-dimensional solver utilization Calculate the overall performance residuals until the residuals converge (residual norm). ), and obtain the predicted convergent solution .

[0057] Step S4: Check the predicted convergent solution obtained in step S3. Normalized prediction variance at :

[0058] ;

[0059] Set confidence threshold (i.e., 0.5% uncertainty).

[0060] Scenario A (High Confidence): If If the accuracy of the proxy model in this local area is determined to be sufficient, the whole-machine coupled calculation will be terminated directly. The final component characteristics are output to the zero-dimensional model to complete this simulation task. At this point, the computational cost is only the time (in seconds) required for zero-dimensional computation.

[0061] Scenario B (low confidence): If The current operating condition is determined to be located in a sparse sample region (unknown region), indicating a high risk in the surrogate model's prediction, necessitating 3D correction. Proceed to step S5.

[0062] Step S5: Perform 3D simulation and update the agent model through active learning.

[0063] 1. Perform three-dimensional calculations to predict convergent solutions. Assuming boundary conditions, start the 3D CFD solver to calculate the true values. .

[0064] 2. Sample library update: Add new samples ( Stored in the sample database. Because... It is a convergent solution coupled with the zero-dimensional whole machine and the agent model. This sample point must be located near the working line of the whole machine matching operation, thus realizing precise local densification near the working point.

[0065] 3. Model and Parameter Updates: Based on the updated sample database, the surrogate model is immediately retrained. Simultaneously, utilizing... The scaling factor of the zero-dimensional model is adjusted again (refer to the formula in step S1).

[0066] 4. Closed-loop iteration: Return to step S3 and re-predict the inner loop using the updated, more accurate surrogate model and scaling factor.

[0067] See attached document Figure 2 , Figure 2 A flowchart illustrating a zero-dimensional / proxy model / three-dimensional coupling method based on online active learning according to an embodiment of the present invention is shown.

[0068] In the initial stage of the simulation task startup, corresponding to Figure 2 In step S1, since the sample library is empty at this point, a surrogate model that meets the accuracy requirements cannot be built. Therefore, the method executes a high-fidelity data accumulation process. This process aims to obtain initial real physical field data through the direct coupling of the zero-dimensional whole-machine model and the high-fidelity three-dimensional model, providing cold-start samples for subsequent surrogate model construction. This process specifically includes the following sub-steps:

[0069] Step S101: Initialize the sample library to an empty set and read the preset whole machine simulation task.

[0070] Step S102: Run the zero-dimensional whole-machine model to obtain the component input boundary conditions for the current iteration step. The zero-dimensional whole-machine model is based on the component method or state variable model. According to the control law and flight environment at the current moment, the inlet thermodynamic parameters and operating state parameters of the fan component are calculated by solving the mass, momentum and energy conservation equations. The calculated converted speed, inlet total pressure, inlet total temperature and the pressure ratio target value requested by the zero-dimensional model are extracted and assembled into the input boundary condition vector.

[0071] Step S103: Using the input boundary condition vector as the boundary conditions, call the high-fidelity physics solver to perform three-dimensional simulation calculations. Specifically, the total inlet pressure and total inlet temperature are applied to the inlet boundary of the three-dimensional computational domain, the converted rotational speed is converted to the physical rotational speed and applied to the rotational domain, and the target pressure ratio is converted to the corresponding static pressure and applied to the outlet boundary. The solver is started to perform iterative flow field calculations, and the flow field residuals are monitored in real time during the calculation process. For the discrete solution of the Navier-Stokes equations (NS equations), the selection of the turbulence model, and the mesh generation technique, conventional computational fluid dynamics algorithms in this field can be used. After the flow field calculation converges, the three-dimensional flow field results are post-processed and integrated to output the physical flow rate, actual pressure ratio, and adiabatic efficiency under this condition, and these parameters are assembled into a vector of true performance parameters.

[0072] Step S104: Combine the input boundary condition vector generated in step S102 with the real performance parameter vector obtained in step S103 to form a sample pair and store it in the sample library.

[0073] Step S105: Correct the component scaling factor in the zero-dimensional model using the 3D simulation results. The component scaling factor is used to linearly scale the flow rate or efficiency values ​​read from the component characteristic maps in the zero-dimensional model to compensate for the error between the zero-dimensional and 3D models. To prevent numerical oscillations due to drastic changes in the flow field during the initial coupling phase, this invention uses a dynamic correction formula with a relaxation factor to update the scaling factor:

[0074] ;

[0075] in, Indicates the updated scaling factor; Indicates the scaling factor used in the current iteration step; This represents the three-dimensional true performance parameters calculated in step S103; This represents the original calculated value of the zero-dimensional model before correction; This represents the relaxation factor. In this embodiment, the relaxation factor is set to 0.5. This value ensures that the new scaling factor is mainly determined by the factor value at the previous time step, while incorporating a portion of the current error correction. This smooths the parameter change trajectory and suppresses the instability of numerical calculations while ensuring the correct correction direction.

[0076] Step S106: Determine whether the number of samples in the sample library has reached the preset minimum sample threshold. In this embodiment, the minimum sample threshold is set to 2, meaning that at least 2 real discrete sample points need to be accumulated. If the threshold is not reached, return to step S102 to continue execution; if the threshold is reached or exceeded, the high-fidelity data accumulation stage is determined to be complete, and the process proceeds to the subsequent surrogate model construction stage.

[0077] See attached document Figure 2 When the number of samples in the sample library meets the preset minimum sample threshold, the method enters the adaptive proxy model construction phase. Figure 2 Step S2. This stage dynamically selects a modeling algorithm whose computational complexity matches its predictive power based on the current accumulated sample size, in order to optimize computational efficiency while ensuring accuracy. Specifically, it includes the following sub-steps:

[0078] Step S201: Obtain the total number of samples in the current sample library and compare it with a preset algorithm switching threshold. In this embodiment, the algorithm switching threshold is set to 50. If the total number of samples is less than the algorithm switching threshold, it is determined that the current stage is small sample stage, and step S202 is executed; if the total number of samples is greater than or equal to the algorithm switching threshold, it is determined that the current stage is large sample stage, and step S203 is executed.

[0079] Step S202: Construct a surrogate model based on Gaussian process regression. Considering the non-smooth variations in the characteristics of aero-engine components under certain operating conditions, this embodiment selects the Matern5 / 2 kernel function as the covariance function. Compared to the conventional Gaussian kernel function (RBF), this kernel function is more sensitive to capturing local abrupt changes and roughness in physical characteristics, and is suitable for nonlinear fitting when samples are sparse. The hyperparameters of the Gaussian process regression model (including feature length scale and signal variance) are optimized using maximum likelihood estimation, a well-known technique in this field. Based on the trained Gaussian process regression model, for any given input condition, the model can analytically calculate the predicted mean and predicted variance based on the properties of the joint Gaussian distribution. This predicted variance quantifies the model's cognitive uncertainty about the current prediction point and is directly used as a confidence metric in subsequent steps.

[0080] Step S203: Construct a Bayesian neural network model based on Monte Carlo Dropout (MCDropout). This model employs a multi-layer feedforward neural network architecture. In this embodiment, it is specifically configured to include an input layer, two hidden layers each containing 64 neurons, and an output layer, with a dropout layer following the hidden layers. The activation function is a modified linear unit (MLU). Variational inference techniques are introduced during model training and prediction. Specifically, the dropout layer is kept on during the inference phase, meaning that connections of some neurons are randomly blocked with a fixed probability during each forward propagation. To capture the uncertainty of the prediction results, multiple repetitions of the forward propagation calculation are performed on the same input condition (e.g., 50 times). Due to the randomness of the dropout layer, each forward propagation produces different predicted output values. Based on the results of multiple random samplings, the arithmetic mean of all predicted output values ​​is calculated as the final performance prediction result. Simultaneously, the statistical variance of all predicted output values ​​is calculated, and this statistical variance is added to the reciprocal of the model accuracy (representing observation noise) to obtain the total prediction variance. The total prediction variance comprehensively reflects the uncertainty of model parameters and the noise level of the data itself, thus serving as a confidence metric for large sample sizes. Using a Bayesian neural network can keep the computational complexity linear under large sample conditions, avoiding the cubic computational bottleneck that occurs in Gaussian process regression as the sample size increases.

[0081] Step S204: Perform online update. During subsequent system-wide coupling iterations, the model update mechanism is triggered immediately whenever the 3D solver generates new real samples and stores them in the sample library. If the current stage is a small sample phase, the Gaussian process regression model is incrementally updated or fully retrained; if the current stage is a large sample phase, the Bayesian neural network is updated using gradient descent with the new samples, adjusting the network weights and biases. The updated model will be used for zero-dimensional system-wide iterative prediction in the next time step.

[0082] See attached document Figure 2 After the surrogate model is built or updated, the trained surrogate model is embedded into the iterative loop of the zero-dimensional whole-machine solver. Figure 2 Step S3 in the process. This step aims to replace traditional 3D calculations or static map lookups with the fast predictive capabilities of the surrogate model, providing real-time feedback on component characteristics during the numerical iteration process of the zero-dimensional solver. This process specifically includes the following sub-steps:

[0083] Step S301: Initiate the equilibrium equation solving process of the zero-dimensional engine solver. The zero-dimensional engine solver is based on the Newton-Raphson iteration method or the Broden rank-one correction method, aiming to make the mass flow rate residual, power balance residual, and pressure balance residual of each section of the engine approach zero by adjusting independent variables. In each internal iteration step, the solver generates the currently attempted component operating conditions based on the Jacobian matrix or gradient direction.

[0084] Step S302: Construct the input vector required for the surrogate model. Extract the thermodynamic and control parameters related to the fan components from the current iterative state variables of the zero-dimensional solver. Specifically, combine the currently attempted converted speed, inlet total pressure, inlet total temperature, and pressure ratio target value into an input operating condition vector. To eliminate the influence of the order-of-magnitude difference between different physical dimensions on the neural network or Gaussian process regression, standardize the physical quantities in the input operating condition vector using the mean and variance of the training set data, ensuring that their numerical distribution is consistent with the sample space used when training the surrogate model.

[0085] Step S303: Invoke the surrogate model for synchronous prediction. The standardized input condition vector generated in step S302 is passed to the trained surrogate model. At this point, the surrogate model acts as a virtual component in the zero-dimensional whole-machine model, simultaneously outputting two sets of data in a single forward calculation: the first set is a vector of predicted characteristic values, containing the predicted mean values ​​of flow rate, pressure ratio, and efficiency, used for participating in the whole-machine thermodynamic cycle calculation; the second set is a confidence index, i.e., the prediction variance corresponding to the above predicted values. It should be noted that although the prediction variance does not directly participate in the residual calculation of the equilibrium equations of the zero-dimensional solver, it is cached by the system and used as a basis for subsequent judgments on whether the operating point is in a sparse sample region.

[0086] Step S304: Calculate the overall engine performance residuals and determine convergence. The zero-dimensional solver uses the characteristic predictions output by the surrogate model, combined with the continuity equations upstream and downstream of the engine flow path, to calculate the current mass imbalance and energy imbalance. The norm of the residual vector is calculated and compared with a preset convergence tolerance (e.g., 10). −4 The independent variables are compared. If the residual norm is greater than the convergence tolerance, the independent variables are corrected using Newton's method, and the process returns to step S302 for the next iteration; if the residual norm is less than or equal to the convergence tolerance, the zero-dimensional solver is determined to be converged.

[0087] Step S305: Output the predicted convergent solution. When the zero-dimensional solver meets the convergence condition, the current input condition vector is determined as the predicted convergent solution. Simultaneously, the prediction variance and prediction mean corresponding to this predicted convergent solution are extracted and passed to the subsequent active learning decision module to evaluate the credibility of the current simulation results. In this way, the present invention achieves rapid simulation while retaining the ability to quantitatively track the uncertainty of the calculation results.

[0088] See attached document Figure 2 After obtaining the predicted convergent solution from the zero-dimensional whole-machine solver, the system enters the uncertainty-based active learning decision-making stage. Figure 2 Step S4 in the simulation. This stage utilizes the statistical information output by the surrogate model to quantitatively assess the reliability of the current prediction results and generate control instructions to determine the subsequent simulation path. This process specifically includes the following sub-steps:

[0089] Step S401: Calculate the normalized prediction variance at the converged solution. Considering that the engine performance parameter vector includes multiple parameters with different physical dimensions such as flow rate, pressure ratio, and efficiency, in order to uniformly measure the prediction uncertainty of the model, it is necessary to calculate the normalized prediction variance for each performance parameter corresponding to the converged solution. This invention constructs the following formula for calculating the normalized prediction variance:

[0090] ;

[0091] in, This represents the normalized prediction variance; This represents the prediction variance output by the surrogate model at the predicted convergent solution in step S3. This represents the mean prediction output by the surrogate model at the convergent solution in step S3. After calculating the normalized prediction variance corresponding to each performance parameter, the maximum value is selected as the comprehensive confidence evaluation index for the current operating condition.

[0092] Step S402: Set a confidence threshold and perform logical judgment. A confidence threshold is preset based on the specific accuracy requirements of the simulation task. In this embodiment, the confidence threshold is set to 0.005. The comprehensive confidence evaluation index (i.e., the maximum normalized prediction variance) determined in step S401 is compared with the confidence threshold. If the normalized prediction variance is less than the confidence threshold, the current operating condition is determined to be a high-confidence situation, and step S403 is executed; if the normalized prediction variance is greater than or equal to the confidence threshold, the current operating condition is determined to be a low-confidence situation, and step S404 is executed.

[0093] Step S403: Execute the high-confidence termination strategy. When a high-confidence condition is identified, it indicates that the current predicted convergent solution is located in a densely covered region of the sample library, and the prediction accuracy of the surrogate model meets the requirements of the whole-machine coupled simulation. At this time, the method flow does not trigger the 3D solver, directly adopts the predicted mean output by the surrogate model as the final component characteristic data, and passes it to the zero-dimensional whole-machine model to complete the calculation of this iteration step. The simulation calculation cost at this time depends only on the time consumed by the zero-dimensional iteration and the inference of the surrogate model.

[0094] Step S404: Execute the low-confidence correction strategy. When a low-confidence situation is identified, it indicates that the current predicted convergent solution is located in a sparse region or extrapolation region of the sample library. The surrogate model lacks sufficient understanding of the physical laws in this region, and directly using the prediction results may introduce significant simulation errors. At this time, the system suspends the current zero-dimensional whole-machine computation task, activates the active learning correction mechanism, generates a new 3D simulation task based on the current predicted convergent solution, and proceeds to the subsequent 3D simulation and model update process (corresponding to step S5). This judgment mechanism ensures that high-fidelity computing resources are only called when the model prediction uncertainty is high, thereby realizing on-demand allocation of computing resources.

[0095] See attached document Figure 2 When the current operating condition is determined to be a low-confidence situation, the method performs the corresponding 3D correction and model update process. Figure 2 Step S5 in the process. This procedure uses the predicted convergent solution as a guide to acquire high-fidelity data in regions with high prediction uncertainty and update the surrogate model. This process specifically includes the following sub-steps:

[0096] Step S501: Start the fixed-point high-fidelity simulation calculation. Using the physical quantities in the predicted convergent solution output by the zero-dimensional whole-machine solver in step S3 as input parameters, set the boundary conditions of the three-dimensional computational fluid dynamics solver. Specifically, the target values ​​of converted rotational speed, inlet total pressure, inlet total temperature, and pressure ratio contained in the predicted convergent solution are mapped to the rotational speed, inlet boundary conditions, and outlet back pressure boundary conditions of the three-dimensional flow field calculation domain, respectively. Start the solver calculation until the flow field converges, and obtain the true performance parameter vector under this condition through post-processing integration. The true performance parameter vector includes at least the physical flow rate, actual pressure ratio, and adiabatic efficiency.

[0097] Step S502: Perform a physical constraint-based sample library update. Combine the predicted convergent solution with the actual performance parameter vector obtained in step S501 to form a new sample pair and store it in the sample library. Since the predicted convergent solution is the equilibrium solution calculated by the zero-dimensional engine model under the constraints of the equations for mass conservation, energy conservation, and momentum conservation, the newly added sample points are naturally distributed in physical space along the engine's steady-state operating line or dynamic operating trajectory. This sampling method uses the physical constraint equations of the engine model to replace the traditional space-filling algorithm, realizing sample supplementation only within the parameter space where the engine may actually operate.

[0098] Step S503: Perform online update of the surrogate model. Based on the sample library after the new samples are added, the update process of the surrogate model is immediately triggered. If a Gaussian process regression model is currently used, the covariance vector between the new samples and the existing samples is calculated, and the covariance matrix and its inverse matrix are updated using the block matrix inversion lemma or direct reconstruction method, and the hyperparameters are re-optimized; if a Bayesian neural network model is currently used, the new samples are added to the current training dataset, and gradient descent iterations are performed on the network for a preset number of rounds. The weight matrix and bias vector of the network are adjusted through the backpropagation algorithm to minimize the prediction residual of the model at the new sample points.

[0099] Step S504: Correct the scaling factor of the zero-dimensional model components. To ensure that the zero-dimensional model remains consistent with the latest three-dimensional calculation results in the next iteration, the scaling factor of the zero-dimensional model components is corrected again using the actual performance parameter vector. The correction formula with a relaxation factor is as follows:

[0100] ;

[0101] in, Indicates the updated scaling factor; This indicates the scaling factor used at the current moment; This represents the actual performance parameter values ​​calculated in step S501; This represents the original calculated value of the zero-dimensional model before correction; This represents the relaxation factor. This step, by introducing a relaxation factor, eliminates the current operating point baseline error while suppressing numerical iteration oscillations caused by excessive correction magnitude.

[0102] Step S505: Perform closed-loop recalculation. After updating the surrogate model parameters and correcting the scaling factor, the method returns to step S3. Using the updated surrogate model with reduced variance and the corrected zero-dimensional model, restart the zero-dimensional whole-machine solution process for the current time step. At this point, since the surrogate model has been calibrated with real samples in the current local region, the normalized prediction variance in the recalculation process will meet the confidence threshold requirement, thus outputting the final simulation result.

[0103] Specific application examples:

[0104] See attached document Figure 4 , Figure 4 A comparison chart of the convergence process of overall aircraft performance parameters under typical flight conditions is shown. The horizontal axis represents the cumulative number of 3D CFD calculations, and the vertical axis represents the normalized overall aircraft performance parameters (such as thrust or fuel consumption rate). The curves marked with squares (0D / 3D) represent the traditional direct coupling method between zero-dimensional and three-dimensional systems, while the curves marked with triangles (0D / SM / 3D) represent the coupling method proposed in this invention, which incorporates a surrogate model and an active learning strategy.

[0105] This embodiment selects a certain type of dual-bypass adaptive variable cycle engine as the object to simulate its overall matching calculation process under the conditions of a flight altitude of 9km and a flight Mach number of 0.8. Under this condition, the engine is in a high-altitude cruise state, and the aerodynamic parameters are quite sensitive to changes in boundary conditions. The specific convergence execution process is described as follows:

[0106] In the initial stage of calculation (corresponding to) Figure 4 (In the x-axis interval 1-2), since the sample library has not yet been established, effective surrogate model prediction results cannot be generated, so the method executes a high-fidelity data accumulation mode. In the first and second whole-machine iteration steps, the boundary conditions generated by the zero-dimensional model are directly passed to the three-dimensional CFD solver, and two complete three-dimensional flow field calculations are performed. The system stores these two sets of real input-output data pairs into the sample library and constructs an initial Kriging surrogate model based on these two nearest sample points. At this point, the convergence curve coincides with the traditional method.

[0107] In the intermediate stage of calculation (corresponding to) Figure 4 (In the x-axis interval 3-4), the zero-dimensional solver begins to call the Kriging surrogate model. In the third system iteration, the zero-dimensional solver quickly calculates an intermediate solution using the surrogate model. At this point, the active learning decision module calculates the normalized prediction variance (CV) at this solution and finds that its value is greater than the preset confidence threshold (Tvar=0.005), determining that the current prediction result is located in a sparse sample region and the confidence is insufficient. The system then triggers the three-dimensional correction mechanism, using this intermediate solution as the boundary condition to start the third three-dimensional CFD calculation. After the calculation is completed, the new samples are incorporated into the database and the surrogate model is updated. The fourth iteration repeats the above process, performing the fourth three-dimensional CFD calculation and updating the model again. In this stage, such as Figure 3 As shown, the slope of the performance parameter curve of the method of the present invention is significantly greater than that of the traditional method, indicating that the surrogate model guides the zero-dimensional solver to approach the real physical equilibrium point more quickly.

[0108] During the convergence phase (corresponding to) Figure 4(From the horizontal axis 5 onwards), the system enters its 5th overall iteration. The zero-dimensional solver calls the surrogate model, which has undergone the first two rounds of local encryption updates, and outputs the predicted convergent solution again. At this point, the calculated normalized prediction variance has significantly decreased and is less than the confidence threshold (CV < 0.005). This indicates that the surrogate model has sufficiently high accuracy in the neighborhood of the current working point and can replace the 3D solver. The system determines that the high confidence condition is met, no longer triggers 3D CFD calculations, and directly outputs the predicted value of the surrogate model as the final result. At this point, the cumulative number of 3D calculations is fixed at 5, and the overall computation is declared converged. In contrast, the traditional 0D / 3D method is still in a slow relaxation convergence process at the 5th iteration, and is still far from the stable value.

[0109] To further verify the advantages of this invention in terms of numerical accuracy and efficiency, the table below lists the detailed monitoring data of this embodiment during the iteration process.

[0110] Table 1. Data Recording of the Whole Machine Coupling Convergence Process under Flight Conditions (H=9km, Ma=0.8)

[0111] Number of iterations Traditional 0D / 3D methods Normalized values ​​of performance parameters Traditional methods residual norm Method of the present invention Normalized values ​​of performance parameters Method of the present invention Normalized prediction variance (CV) Total number of 3D calculations (This invention) 1 0.2014 1.54E-01 0.2014 - 1 2 0.3892 8.92E-02 0.3892 - 2 3 0.5231 5.66E-02 0.7418 0.0423 (High) 3 4 0.6105 3.84E-02 0.8895 0.0187 (High) 4 5 0.6788 2.51E-02 0.9482 0.0064 (High) 5 6 0.7324 1.78E-02 0.9501 0.0032 (Low) 5 7 0.7719 1.25E-02 0.9503 0.0028 (Low) 5 ... ... ... ... ... ... 20 0.9412 4.50E-04 0.9504 0.0015 (Low) 5 22 0.9498 9.80E-05 - - -

[0112] Based on the data records in Table 1 and Figure 4 The curve trend shows that the coupling method proposed in this invention has significant technical advantages in dealing with complex engine matching problems.

[0113] In terms of computational efficiency, traditional 0D / 3D coupling methods, relying solely on relaxation factors for numerical transfer, exhibit a slow and asymptotic convergence process. Data shows that the traditional method only reaches a performance parameter of 0.9498 and residual convergence in the 22nd iteration, meaning it requires 22 expensive 3D CFD calculations. In contrast, the method of this invention stabilizes at a performance parameter of 0.9501 in the 6th iteration, and at this point, the normalized prediction variance drops to 0.0032 (below the threshold of 0.005), triggering the circuit breaker mechanism for 3D computation. The entire process consumes only 5 3D CFD computations. For example, if a single 3D CFD calculation takes 2 hours, the traditional method takes approximately 44 hours, while the method of this invention only takes about 10 hours, improving computational efficiency by over 77%.

[0114] Regarding computational accuracy and stability, the data from steps 5 to 7 in Table 1 show that the performance parameters (0.9482 to 0.9503) output by the method of this invention, after locking the number of 3D calculations, maintain extremely high stability, and the relative error with the final convergence value (0.9498) of the traditional method is less than 0.1%. This confirms that the local encryption strategy based on active learning effectively captures the physical laws near the working point. By forcibly introducing real physical field data in the high CV region (i.e., steps 3, 4, and 5 in Table 1), the surrogate model quickly corrects its prediction deviation under the current working condition; while in the low CV region (after step 6), the high-precision prediction capability of the surrogate model ensures that the whole solver can still maintain the correct evolution direction without 3D intervention, thus solving the technical problem of balancing simulation accuracy and speed under limited computing resources.

Claims

1. A multi-dimensional coupled simulation method for aero-engines based on online active learning, characterized in that, Includes the following steps: Step S1: At the beginning of the simulation, directly run the coupled simulation of the zero-dimensional whole model and the three-dimensional component model. Through at least two three-dimensional simulation iterations, generate initial samples and store them in the sample library. Step S2: When the number of samples in the sample library reaches a preset threshold, a surrogate model is constructed and trained using the sample library data. The surrogate model is used to predict component characteristics and provides the prediction variance. Step S3: Embed the trained surrogate model into the zero-dimensional whole model. The zero-dimensional model calls the surrogate model for rapid iteration to obtain the predicted convergent solution that satisfies the convergence condition of the zero-dimensional whole model. Step S4: Determine whether the prediction variance of the surrogate model at the predicted converged solution is lower than a preset confidence threshold; if the prediction variance is lower than the preset confidence threshold, determine that the prediction accuracy of the surrogate model meets the requirements, terminate the whole-machine coupled calculation, and output the predicted converged solution as the final simulation result; if the prediction variance is higher than or equal to the preset confidence threshold, determine that the prediction accuracy of the surrogate model does not meet the requirements, and proceed to step S5. Step S5: Run a three-dimensional simulation using the predicted converged solution as the boundary condition to obtain the actual component characteristics. Store the operating point in the sample library and update the surrogate model online. Use the three-dimensional simulation results to correct the component characteristic scaling factor in the zero-dimensional whole machine model. Return to step S3 to continue accelerating the prediction using the surrogate model.

2. The multi-dimensional coupled simulation method for aero-engines based on online active learning according to claim 1, characterized in that, In step S1, there is no need to conduct offline sample collection based on experimental design in advance; all samples are derived from intermediate data during the whole machine coupling iteration process.

3. The multi-dimensional coupled simulation method for aero-engines based on online active learning according to claim 1, characterized in that, The active learning update in step S5 enables the sample points to be automatically concentrated near the matching working line of the actual operation of the aero-engine, and high-precision fitting of the working point region is achieved by using local samples near the working line of the engine.

4. The multi-dimensional coupled simulation method for aero-engines based on online active learning according to claim 1, characterized in that, The fast exit mechanism in step S4 reduces the number of 3D simulations required as the number of samples increases until prediction is performed entirely through a surrogate model.

5. The multi-dimensional coupled simulation method for aero-engines based on online active learning according to claim 1, characterized in that, The proxy model construction strategy in step S2 is as follows: when the number of samples is lower than the first quantity threshold, the Kriging model is used; when the number of samples is higher than or equal to the first quantity threshold, the model is switched to a neural network model or a Bayesian neural network model.

6. The multi-dimensional coupled simulation method for aero-engines based on online active learning according to claim 1, characterized in that, Components that are coupled with the whole machine for simulation include any one or more combinations of fans, compressors, combustion chambers, turbines, or exhaust nozzles.

7. The multi-dimensional coupled simulation method for aero-engines based on online active learning according to claim 1, characterized in that, In step S1, the scaling factor of component characteristics in the zero-dimensional whole machine model is corrected according to the following formula: ； ； ； In the formula, These are correction factors for flow rate, pressure ratio, and efficiency. 0D and 3D represent the characteristics of zero-dimensional simulation and three-dimensional simulation, respectively. and Representing different iteration steps; This is a relaxation factor to prevent oscillations during the iteration process and accelerate convergence.

8. The multi-dimensional coupled simulation method for aero-engines based on online active learning according to claim 1, characterized in that, In step S4, to eliminate the influence of different physical dimensions, normalized prediction variance is used as the confidence index, and its calculation formula is as follows: ； in, To normalize the prediction variance, This represents the prediction variance output by the surrogate model at the point of convergence. This is the predicted mean output by the surrogate model at the predicted convergent solution.

9. The multi-dimensional coupled simulation method for aero-engines based on online active learning according to claim 5, characterized in that, When the Bayesian neural network model is used, the dropout variational inference technique is employed. During the prediction phase, the dropout layer is kept on. By performing multiple random forward propagations on the same input condition, the mean and variance of the multiple output results are statistically analyzed and used as the prediction characteristic value and prediction uncertainty of the surrogate model.

10. The multi-dimensional coupled simulation method for aero-engines based on online active learning according to claim 1, characterized in that, In step S1, the input boundary condition vector passed from the zero-dimensional whole machine model to the three-dimensional component model includes at least the converted rotational speed, total inlet pressure, total inlet temperature, and component pressure ratio; the real performance parameter vector fed back from the three-dimensional component model to the zero-dimensional whole machine model includes at least the physical flow rate, pressure ratio, and adiabatic efficiency.

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