Aero-engine model Bayesian optimization method for quantizing uncertainty

Abstract

The invention relates to the technical field of simulation model optimization, and discloses an aero-engine model Bayesian optimization method for quantizing uncertainty, and the method comprises the steps: building a probability mapping relation from a component index to an output response through constructing a Bayesian neural network agent model based on a probability weight coefficient; and by taking the difference between the output response and the corresponding complete machine test data as a multi-objective loss function and taking the minimization of the multi-objective loss function as an optimization objective, optimizing the component indexes by adopting a Bayesian optimization method based on a Gaussian process to obtain an optimal component index combination. Not only is a nonlinear relationship between high-dimensional parameters and simulation-test deviation accurately modeled through a neural network, but also efficient search of a parameter space is realized through a Gaussian process. The technical problems that when a traditional optimization method is used for processing the high-dimensional, strong-nonlinearity and multi-parameter coupling complex optimization problem of the aero-engine, the calculation efficiency is low, local optimum is prone to occurring, and result uncertainty cannot be quantified are solved.

Description

TECHNICAL FIELD

[0001] The application relates to the technical field of simulation model optimization, and discloses an aero-engine model Bayesian optimization method for quantifying uncertainty. BACKGROUND

[0002] The matching precision of aero-engine overall performance simulation and test data determines the reliability of performance prediction. Accurate model calibration can provide reliable basis for engine performance evaluation, fault diagnosis and control law design, and is of great significance for high-quality and low-cost design. For a complex system represented by an engine, the coupling effect between parameters is significant, making model calibration a high-dimensional nonlinear optimization problem.

[0003] In the development process of model calibration technology, three typical methods have appeared in succession. In the early stage, the fingerprint map method was widely used, which compared the differences between simulation and test results, relied on experience for parameter adjustment, and was intuitive but inefficient, and difficult to handle the coupling of multiple parameters. The intelligent method such as genetic algorithm developed later realized automatic parameter search, but still needed a large number of simulation calculations when dealing with high-dimensional parameter space, and the convergence speed was slow and easy to fall into local optimum. In recent years, the proxy model method such as the optimization method based on Kriging or polynomial response surface significantly reduces the calculation cost. However, the fitting precision of the strong nonlinearity of the engine is limited, and the uncertainty of the calibration result cannot be quantified.

[0004] At present, although advanced methods such as multi-objective Bayesian optimization have made certain progress in parameter calibration, there are still obvious deficiencies in dealing with the complex calibration task of aero-engine overall level multi-parameters and multi-outputs. Especially in ensuring the reliability and engineering interpretability of the calibration result, the existing method is difficult to meet the actual engineering needs. SUMMARY

[0005] The purpose of the present application is to provide an aero-engine model Bayesian optimization method for quantifying uncertainty, which realizes the overall alignment of simulation model and test data and improves the calibration accuracy.

[0006] In order to achieve the above technical effects, the technical scheme adopted by the present application is: An aero-engine model Bayesian optimization method for quantifying uncertainty, comprising: S1, using a Latin hypercube sampling method to generate initial sample points in the constraint space of aero-engine component indicators; the component indicators include compressor flow, compressor efficiency, combustion chamber total pressure recovery coefficient, turbine flow and turbine efficiency; S2, running the aero-engine overall performance simulation model based on the initial sample points to obtain multi-objective output response indicators, the output response indicators including engine thrust, specific fuel consumption and temperature and pressure of engine measurement section; S3. Construct a Bayesian neural network surrogate model based on probability weight coefficients, and train the Bayesian neural network surrogate model with the component indicators and the corresponding output responses of each initial sample point to establish a probability mapping relationship from component indicators to output responses. S4. Using the difference between the output response and the corresponding whole machine test data as the multi-objective loss function, and minimizing the multi-objective loss function as the optimization objective, the component index is optimized using a Bayesian optimization method based on Gaussian process to obtain the optimal combination of component indexes.

[0007] Furthermore, the method for establishing the probabilistic mapping relationship from component indicators to output response in step S3 includes: A Bayesian neural network surrogate model based on probability weight coefficients is constructed. During the forward propagation process, Monte Carlo sampling is used to train the Bayesian neural network surrogate model using variational inference, with the optimization objective being to minimize the loss function. The corresponding probability weight coefficients are used to establish a probabilistic mapping relationship from component indicators to output response; among which, The negative log-likelihood loss is used to predict the output response of a Bayesian neural network surrogate model. These are the probability weight coefficients, i.e., the learnable parameters of the model; Let the weights be the posterior distribution. Let the weights be the prior distribution. For the weighted posterior distribution and prior distribution Divergence; The regularization coefficient is . ; This represents the initial number of sample points.

[0008] Furthermore, the multi-objective loss function described in step S4 ,in For the Bayesian neural network surrogate model The deviation between the output response and the corresponding experimental data To output the number of response metrics, For the first The variance of each output response.

[0009] Furthermore, the method for optimizing the component indicators using the Bayesian optimization method based on Gaussian processes in step S4 includes: A Gaussian process surrogate model is established, and radial basis functions are used to construct the function values ​​of the multi-objective loss function corresponding to the component indicators and the initial sample points. Mapping; The L-BFGS-B algorithm is selected as the internal solver. The acquisition function is maximized through a multi-start point optimization strategy, and the next candidate point for component index is found from multiple starting points. The Bayesian neural network surrogate model is used to predict the multi-objective output simulation values ​​of candidate points for component indicators. The deviation between the simulation values ​​and the corresponding whole machine test data is calculated, as well as the multi-objective loss function value of the candidate points for component indicators. The calibration is stopped when the preset number of iterations is reached. The optimal combination of component indicators with the minimum multi-objective loss function is recorded, and the optimal combination of component indicators is output.

[0010] Furthermore, after using a Bayesian neural network surrogate model to predict the multi-objective output simulation values ​​of component indicator candidate points, the component indicator candidate points and their multi-objective loss function values ​​are... The Gaussian process proxy model is updated by adding it to historical data samples.

[0011] Furthermore, the radial basis function kernel function takes the form of: ,in For the first Component metrics for each data sample For the first Component metrics for each data sample , The value is taken from the total number of samples in the historical optimization data; The kernel function value is used for measurement. and Similarity between them; Let V be the signal variance of the kernel function, and σ is a hyperparameter of the kernel function; is the length scaling parameter of the kernel function, and is a hyperparameter of the kernel function; for and The Euclidean distance between them; The kernel function is an exponential function, such that its value is always positive and within [0, ... Within the range.

[0012] Furthermore, the expected improvement amount EI is used as the acquisition function combined with a random exploration strategy with a 10% probability to select the next component index.

[0013] Furthermore, the acquisition function is defined as follows:

[0014] in , It is the cumulative distribution function of the standard normal distribution. It is the probability density of the standard normal distribution. This represents the minimum observed multi-objective loss function value. For Gaussian process models in The posterior mean at the location, For Gaussian process models in The posterior standard deviation at the given location, For component index combination, The exploration coefficients of the acquisition function.

[0015] Furthermore, before constructing the Bayesian neural network proxy model based on probability weight coefficients in step S3, the component indices and corresponding output responses of each initial sample point are normalized in advance.

[0016] Compared with existing technologies, the beneficial effects of this invention are as follows: This invention integrates Bayesian neural networks and Gaussian processes into a unified architecture. It accurately models the nonlinear relationship between high-dimensional parameters and simulation-experiment deviations through neural networks, and achieves efficient search of the parameter space through Gaussian processes to obtain the optimal combination of component indicators. This solves the technical problems of low computational efficiency, easy getting trapped in local optima, and inability to quantify the uncertainty of results in traditional optimization methods when dealing with complex optimization problems of high-dimensional, strongly nonlinear, and multi-parameter coupling in aero-engines, as well as the contradiction between accuracy and efficiency in high-dimensional scenarios. This significantly improves the reliability and engineering applicability of the optimization results. Attached Figure Description

[0017] Figure 1 This is a flowchart of the Bayesian optimization method for the aero-engine model in Example 1; Figure 2 This is a flowchart of the Bayesian optimization method for the aero-engine model in Example 2. Detailed Implementation

[0018] The present invention will now be described in further detail with reference to the embodiments and accompanying drawings. However, this should not be construed as limiting the scope of the above-described subject matter of the present invention to the following embodiments; all technologies implemented based on the content of the present invention fall within the scope of the present invention.

[0019] Example 1 See Figure 1 A Bayesian optimization method for quantifying uncertainty in aero-engine models, comprising: S1. Initial sample points are generated within the constraint space of the parameters of various components of the aero-engine using the Latin hypercube sampling method; the component parameters include compressor flow rate, compressor efficiency, combustion chamber total pressure recovery coefficient, turbine flow rate, and turbine efficiency. S2. Based on the initial sample points, run the overall performance simulation model of the aero-engine to obtain multi-objective output response indicators, including engine thrust, fuel consumption rate, and temperature and pressure of the engine measurement section. S3. Construct a Bayesian neural network surrogate model based on probability weight coefficients, and train the Bayesian neural network surrogate model with the component indicators and the corresponding output responses of each initial sample point to establish a probability mapping relationship from component indicators to output responses. S4. Using the difference between the output response and the corresponding whole machine test data as the multi-objective loss function, and minimizing the multi-objective loss function as the optimization objective, the component index is optimized using a Bayesian optimization method based on Gaussian process to obtain the optimal combination of component indexes.

[0020] In this embodiment, a Bayesian neural network surrogate model based on probability weight coefficients is constructed. This surrogate model is trained using the component indices and corresponding output responses at each initial sample point, establishing a probabilistic mapping relationship from component indices to output responses. The difference between the output response and the corresponding whole-engine test data is used as a multi-objective loss function, with minimizing this loss function as the optimization objective. A Gaussian optimization method based on Gaussian processes is employed to optimize the component indices, yielding the optimal combination of component indices. This embodiment integrates a Bayesian neural network and a Gaussian process architecture. It accurately models the nonlinear relationship between high-dimensional parameters and simulation-experiment deviations through neural networks, while simultaneously achieving efficient parameter space search through Gaussian processes. This resolves the accuracy-efficiency contradiction of traditional calibration methods in high-dimensional scenarios. It also addresses the technical challenges of traditional optimization methods in handling complex optimization problems involving high dimensions, strong nonlinearity, and multi-parameter coupling in aero-engines, such as low computational efficiency, susceptibility to local optima, and inability to quantify result uncertainties. This significantly improves the reliability and engineering applicability of the optimization results.

[0021] Example 2 See Figure 2 A Bayesian optimization method for quantifying uncertainty in aero-engine models, comprising: S1. Initial sample points are generated within the constraint space of the indicators of various components of the aero-engine using the Latin hypercube sampling method to form the experimental dataset. , The number of sampling points (i.e., the initial number of sample points); the component indicators include compressor flow rate, compressor efficiency, combustion chamber total pressure recovery coefficient, turbine flow rate, and turbine efficiency; In this embodiment, Indicates the first A sample set of component indicators for an initial sample point. , Indicates the first The first component index of the component index sample set of the initial sample points, and so on. The parameter dimensions for component indicators.

[0022] S2. Based on the initial sample points, run the overall performance simulation model of the aero-engine to obtain multi-objective output response indicators, including engine thrust, fuel consumption rate, and temperature and pressure of the engine measurement section. In this embodiment, the overall performance simulation model of the aero-engine is run using each initial sample point to obtain the target output response index dataset for the corresponding initial sample point. , Indicates the first The first output response index corresponding to each initial sample point. Indicates the first The first initial sample point corresponding to the th... One output response metric, and so on. This refers to the dimensions of the output response metrics.

[0023] S3. Construct a Bayesian neural network surrogate model based on probability weight coefficients, and train the Bayesian neural network surrogate model with the component indicators and the corresponding output responses of each initial sample point to establish a probability mapping relationship from component indicators to output responses. In this embodiment, a Bayesian neural network surrogate model based on probability weight coefficients is constructed. During the forward propagation process, Monte Carlo sampling is used to train the Bayesian neural network surrogate model using variational inference, with the optimization objective being to minimize the loss function. The corresponding probability weight coefficients are used to establish a probabilistic mapping relationship from component indicators to output response; among which, The negative log-likelihood loss is used to measure the accuracy of the surrogate model in predicting the output response. These are the probability weight coefficients, i.e., the learnable parameters of the model; Let the weights be the posterior distribution. Let the weights be the prior distribution. For the weighted posterior distribution and prior distribution Divergence, used to measure and The differences between them promote the generalization of the model; The regularization coefficient is . It is used to balance the likelihood loss term and the regularization term to prevent the model from overfitting. This represents the initial number of sample points.

[0024] S4. Using the difference between the output response and the corresponding whole-machine test data as the multi-objective loss function, and minimizing the multi-objective loss function as the optimization objective, a Bayesian optimization method based on Gaussian processes is used to optimize the component indicators to obtain the optimal combination of component indicators; the specific process includes: S401. Design a multi-objective loss function to make the deviations of all output responses from their corresponding experimental data close to zero. The loss function is in the form of: ,in For the Bayesian neural network surrogate model The deviation between the output response and the corresponding experimental data To output the number of response metrics, For the first The variance of each output response is considered. This multi-objective loss function simultaneously considers the sum of the absolute values ​​of all deviations, the maximum deviation penalty, and the variance constraint (i.e., output balance), striving to make the deviations of all output responses from the experimental data approach zero, thus achieving the calibration objective. This embodiment's multi-dimensional deviation fusion calibration loss function takes into account overall deviation, extreme deviations, and balance, achieving comprehensive alignment between the simulation model and experimental data, and improving calibration accuracy.

[0025] S402. Establish a Gaussian process surrogate model, and use radial basis functions to construct the function values ​​of the multi-objective loss function corresponding to the component indicators and the initial sample points. The mapping, the kernel function is in the form of ,in For the first Component metrics from a historical optimized data sample. For the first Component metrics from a historical optimized data sample. , The value is taken from the total number of samples in the historical optimization data; The kernel function value is used for measurement. and The similarity between them constitutes the covariance matrix of the Gaussian process model; is the signal variance of the kernel function, which is a hyperparameter of the kernel function used to control the confidence range of the output response in the Gaussian process surrogate model; is the length scale parameter of the kernel function, which is a hyperparameter of the kernel function and determines the rate of similarity decay; for and The Euclidean distance between them facilitates distance-based similarity modeling; It is an exponential function, ensuring that the kernel function value is always positive and within [0, ... Within the range.

[0026] S403. Using the Expected Improvement (EI) as the acquisition function, combined with a 10% probability random exploration strategy, the next component metric is selected; the acquisition function is defined as:

[0027] in , It is the cumulative distribution function of the standard normal distribution. It is the probability density of the standard normal distribution. This represents the minimum observed multi-objective loss function value. For Gaussian process models in The posterior mean at the location, For Gaussian process models in The posterior standard deviation at the given location, For component index combination, This is the exploration coefficient of the acquisition function, which increases the exploration intensity to a certain extent and prevents the algorithm from reaching local optima. It can balance local optimization and global exploration, avoiding getting trapped in local optima.

[0028] S404. Select the L-BFGS-B algorithm as the internal solver, maximize the EI acquisition function through a multi-start point optimization strategy, and find the next candidate point for component index from multiple starting points. S405. Use a Bayesian neural network surrogate model to predict the multi-objective output simulation values ​​of candidate points for component indicators, calculate the deviation between the simulation values ​​and the corresponding whole machine test data, and quantify the uncertainty of the calibration effect by sampling the mean and variance of the output deviation through weights. S406. Calculate the multi-objective loss function value of the component indicator candidate points, and combine the component indicator candidate points with the multi-objective loss function value of the component indicator candidate points. By incorporating historical optimization data samples, the Gaussian process surrogate model is fully updated to avoid extensive simulation calculations, improve optimization efficiency, and enhance the accuracy of subsequent parameter searches. Calibration stops when the preset number of iterations is reached, and the optimal component index combination corresponding to the minimum multi-objective loss function is recorded. The optimal component index combination and the corresponding multi-dimensional deviation prediction results are output. The deviation prediction variance is calculated based on the sampling output of the Bayesian neural network, and a calibration report containing the total deviation, maximum deviation, and uncertainty index is generated to verify the consistency between the simulation model and the experimental data.

[0029] This embodiment can realize a full-link uncertainty quantification mechanism, providing quantifiable confidence intervals from parameter search to deviation prediction, providing a reliable basis for the engineering application of calibration results, thereby reducing the decision-making risk caused by model errors.

[0030] When the Bayesian optimization method for aero-engine models in this embodiment was applied to the optimization of an overall engine model, the initial state of the overall engine model showed a mean square error (MSE) of 0.00317 between the deviations of 20 output performance indicators and experimental data, with the largest single deviation reaching 15.92%. After optimizing 43 model parameters, the MSE of the deviations of the 20 output performance indicators from the experimental data was reduced to 0.00073, a reduction of 76.97%. The largest single deviation was reduced to 8.78%, and the sum of the absolute values ​​of all deviations was reduced by 46.08%, achieving full alignment between the simulation model and experimental data and improving calibration accuracy.

[0031] In some other embodiments, in order to eliminate the influence of different dimensions and orders of magnitude on subsequent model training, before constructing the Bayesian neural network surrogate model based on probability weight coefficients in step S3, the component indices and corresponding output responses of each initial sample point are normalized in advance, and the component indices and corresponding output responses of each initial sample point are mapped to the [0,1] interval, which can improve the training efficiency and prediction accuracy of the Bayesian neural network surrogate model.

[0032] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A Bayesian optimization method for quantifying uncertainty in aero-engine models, characterized in that, include: S1. The Latin hypercube sampling method is used to generate initial sample points within the constraint space of the indicators of various components of the aero-engine. The component specifications include compressor flow rate, compressor efficiency, combustion chamber total pressure recovery coefficient, turbine flow rate, and turbine efficiency; S2. Based on the initial sample points, run the overall performance simulation model of the aero-engine to obtain multi-objective output response indicators, including engine thrust, fuel consumption rate, and temperature and pressure of the engine measurement section. S3. Construct a Bayesian neural network surrogate model based on probability weight coefficients, and train the Bayesian neural network surrogate model with the component index and the corresponding output response of each initial sample point to establish a probability mapping relationship from component index to output response. S4. Using the difference between the output response and the corresponding whole machine test data as the multi-objective loss function, and minimizing the multi-objective loss function as the optimization objective, the component index is optimized using a Bayesian optimization method based on Gaussian process to obtain the optimal combination of component indexes.

2. The Bayesian optimization method for aero-engine models according to claim 1, characterized in that, The method for establishing the probabilistic mapping relationship from component indicators to output response in step S3 includes: A Bayesian neural network surrogate model based on probability weight coefficients is constructed. During the forward propagation process, Monte Carlo sampling is used to train the Bayesian neural network surrogate model using variational inference, with the optimization objective being to minimize the loss function. The corresponding probability weight coefficients are used to establish a probabilistic mapping relationship from component indicators to output response; among which, The negative log-likelihood loss is used to predict the output response of a Bayesian neural network surrogate model. These are the probability weight coefficients, i.e., the learnable parameters of the model; Let the weights be the posterior distribution. Let the weights be the prior distribution. For the weighted posterior distribution and prior distribution Divergence; The regularization coefficient is . ; This represents the initial number of sample points.

3. The Bayesian optimization method for aero-engine models according to claim 1, characterized in that, The multi-objective loss function mentioned in step S4 ,in For the Bayesian neural network surrogate model The deviation between the output response and the corresponding experimental data To output the number of response metrics, For the first The variance of each output response.

4. The Bayesian optimization method for aero-engine models according to claim 3, characterized in that, The method for optimizing the component indicators using the Bayesian optimization method based on Gaussian processes in step S4 includes: A Gaussian process surrogate model is established, and radial basis functions are used to construct the function values ​​of the multi-objective loss function corresponding to the component indicators and the initial sample points. Mapping; The L-BFGS-B algorithm is selected as the internal solver. The acquisition function is maximized through a multi-start point optimization strategy, and the next candidate point for component index is found from multiple starting points. The Bayesian neural network surrogate model is used to predict the multi-objective output simulation values ​​of candidate points for component indicators. The deviation between the simulation values ​​and the corresponding whole machine test data is calculated, as well as the multi-objective loss function value of the candidate points for component indicators. The calibration is stopped when the preset number of iterations is reached. The optimal combination of component indicators with the minimum multi-objective loss function is recorded, and the optimal combination of component indicators is output.

5. The Bayesian optimization method for aero-engine models according to claim 4, characterized in that, After using a Bayesian neural network surrogate model to predict the multi-objective output simulation values ​​of component indicator candidate points, the component indicator candidate points and the function values ​​of the multi-objective loss function of the component indicator candidate points are... The Gaussian process proxy model is updated by adding it to historical data samples.

6. The Bayesian optimization method for aero-engine models according to claim 5, characterized in that, The radial basis function kernel function is in the form of ,in For the first Component metrics for each data sample For the first Component metrics for each data sample , The value is taken from the total number of samples in the historical optimization data; The kernel function value is used for measurement. and Similarity between them; Let V be the signal variance of the kernel function, and σ is a hyperparameter of the kernel function; is the length scaling parameter of the kernel function, and is a hyperparameter of the kernel function; for and The Euclidean distance between them; The kernel function is an exponential function, such that its value is always positive and within [0, ... Within the range.

7. The Bayesian optimization method for aero-engine models according to claim 4, characterized in that, The next component metric is selected by using the expected improvement value EI as the acquisition function combined with a random exploration strategy with a 10% probability.

8. The Bayesian optimization method for aero-engine models according to claim 7, characterized in that, The acquisition function is defined as follows: in , It is the cumulative distribution function of the standard normal distribution. It is the probability density of the standard normal distribution. This represents the minimum observed multi-objective loss function value. For Gaussian process models in The posterior mean at the location, For Gaussian process models in The posterior standard deviation at the given location, For component index combination, The exploration coefficients of the acquisition function.

9. The Bayesian optimization method for aero-engine models according to any one of claims 1-8, characterized in that, Before constructing the Bayesian neural network surrogate model based on probability weight coefficients in step S3, the component indices and corresponding output responses of each initial sample point are normalized in advance.

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