Training method and device for aero-engine modeling driven by mechanism and data fusion

Abstract

The invention provides a training method for aero-engine modeling driven by mechanism and data fusion, and relates to the technical field of aero-engine modeling simulation, and the method comprises the steps: decomposing a simulation model of an aero-engine into a plurality of assemblies containing to-be-identified unknown parameters, and employing an assembly integration algorithm to associate the plurality of assemblies, an end-to-end differentiable complete simulation model is formed; based on hierarchical division of the simulation model, performing parameter pre-estimation by adopting a top-down layer-by-layer progressive strategy to obtain an initial estimation value of the unknown parameter; the strategy comprises the following steps: firstly, estimating unknown parameters of components in a highest level according to actually measured output data, and generating a training target of a next lower level based on a calculation result of an estimated level so as to complete estimation of unknown parameters of the lower level in sequence; and performing gradient back propagation in the complete simulation model by taking the initial estimation value as a starting point to optimize and update unknown parameters.

Description

Technical Field

[0001] This invention relates to the field of aero-engine modeling and simulation technology, and in particular to a training method and apparatus for aero-engine modeling driven by mechanism and data fusion. Background Technology

[0002] In modern scientific research and engineering design, it is crucial to establish simulation models that can accurately reflect real physical processes. These models have irreplaceable value for system performance analysis, state prediction, and optimized control, especially in high-precision fields such as aero-engines and chemical processes.

[0003] Currently, there are two main technical approaches to modeling aero-engines. The first is mechanistic modeling based on physical laws (white-box modeling), which has the advantage of clear physical meaning and good interpretability. However, when there are unknown or difficult-to-describe physical effects within the system, the model accuracy is often limited. The second is data-driven modeling (black-box modeling), which uses machine learning and other methods to directly learn the input-output relationship of the system from measured data. Although it can approximate complex nonlinear systems with high accuracy, it generally suffers from poor physical interpretability and weak generalization ability. To combine the advantages of both approaches, the "mechanism-data fusion modeling" (grey-box modeling) strategy has emerged, describing the clear parts of the mechanism with a mechanistic model and replacing the ambiguous parts with a data-driven surrogate model, becoming a current research hotspot.

[0004] However, existing mechanism-data fusion models still face a core and pressing challenge in training and optimization: joint optimization is extremely difficult. These fusion models typically deeply couple multiple mechanism components with data-driven components, forming a hierarchical, parameter-dimensional overall model. If end-to-end joint optimization is performed directly using randomly initialized parameters, the loss function of the entire model will exhibit highly non-convex characteristics. Coupled with model uncertainty and measurement errors, the optimization process is highly susceptible to getting trapped in local optima, leading to training failure or model accuracy falling far short of expectations. Therefore, there is an urgent need for a systematic training method that can provide high-quality initial parameter values ​​for such complex fusion models and ensure stable convergence of the global optimization process. Summary of the Invention

[0005] This invention provides a training method and apparatus for aero-engine modeling driven by mechanism and data fusion, which solves the technical problems in the prior art, such as the difficulty of joint optimization and the tendency of the training process to get trapped in local optima due to the complexity of model structure, measurement error and high non-convexity of parameter space. This enables high-precision and high-stability modeling of aero-engines.

[0006] This invention provides a training method for aero-engine modeling driven by mechanism and data fusion, comprising the following steps: (a) The simulation model of the aero-engine is decomposed into multiple components containing unknown parameters to be identified, and the multiple components are associated using a component integration algorithm to form an end-to-end differentiable complete simulation model; the multiple components include a mechanism model component and / or a surrogate model component, wherein the mechanism model component is established based on physical mechanisms, and the surrogate model component is established based on a data-driven method; (b) Based on the hierarchical division of the simulation model, a top-down, progressive strategy is adopted to perform parameter pre-estimation to obtain the initial estimated values ​​of the unknown parameters; the strategy includes: firstly estimating the unknown parameters of the components in the highest level according to the measured output data, and generating the training target of the next lower level based on the calculation results of the estimated level, so as to complete the estimation of the unknown parameters of the lower level in sequence. (c) Starting from the initial estimated value, the unknown parameters are optimized and updated by performing gradient backpropagation in the complete simulation model.

[0007] Optionally, in step (b), generating the training target for the next lower level based on the calculation results of the estimated level includes: using the calculation results of the estimated level as the known output of the estimated level, and back-calculating the model input required to generate the known output based on the simulation model, and then using the model input as the training target for the next lower level.

[0008] Optionally, in step (b), estimating the unknown parameters of the highest-level internal components based on the measured output data includes: adjusting the unknown parameters of the highest-level internal components through system identification or machine learning so that, given the model input of that level, the predicted output of the simulation model matches the measured output data.

[0009] Optionally, before performing step (b), the method further includes: selecting one from multiple physical dependency sequences and determining the hierarchical division of the simulation model according to the reverse order of the selected sequence; the physical dependency sequence includes causal chains, energy transfer paths, or mass transfer paths.

[0010] Optionally, the data-driven method adopted by the proxy model component includes at least one of the following: multinomial regression model, support vector regression model, Gaussian process regression model, or neural network-based model; Machine learning models based on data feature mapping, pre-defined basis function learning, or kernel function learning.

[0011] Optionally, the specific form of the component integration algorithm includes at least one of the following: Define explicit function mappings for data transfer or algebraic operations between components; A numerical solver for solving implicit equations formed by the coupling relationships between components; A machine learning model used to fit transitive relationships between components.

[0012] Optionally, when the component integration algorithm includes a numerical solver for solving implicit equations, the implicit equations include algebraic equations, ordinary differential equations, differential algebraic equations, or partial differential equations.

[0013] Optionally, the optimization and update of the unknown parameters in step (c) includes: When calculating the loss function, an optimization control method is introduced to limit the magnitude of parameter updates. This optimization control method includes introducing a regularization term to constrain the unknown parameters.

[0014] This invention also provides a training device for aero-engine modeling driven by mechanism and data fusion, comprising: The model building module is used to decompose the simulation model of the aero-engine into multiple components containing unknown parameters to be identified, and to associate the multiple components using a component integration algorithm to form an end-to-end differentiable complete simulation model; the multiple components include a mechanism model component and / or a surrogate model component, wherein the mechanism model component is established based on physical mechanisms, and the surrogate model component is established based on a data-driven method; The parameter pre-estimation module is used to perform parameter pre-estimation based on the hierarchical division of the simulation model, using a top-down, progressive strategy to obtain the initial estimated values ​​of the unknown parameters. The strategy includes: first, estimating the unknown parameters in the highest level based on the measured output data, and generating the training target for the next lower level based on the calculation results of the estimated levels, so as to complete the estimation of the unknown parameters in the lower levels in sequence. The parameter fine-tuning module is used to optimize and update the unknown parameters by performing gradient backpropagation in the complete simulation model, starting from the initial estimated value.

[0015] The present invention also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement a training method for aero-engine modeling driven by mechanism and data fusion as described above.

[0016] The present invention also provides a non-transitory computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements a training method for aero-engine modeling driven by mechanism and data fusion as described above.

[0017] The present invention also provides a computer program product, including a computer program that, when executed by a processor, implements a training method for aero-engine modeling driven by mechanism and data fusion as described above.

[0018] The training method and apparatus for aero-engine modeling driven by mechanism and data fusion provided by this invention decomposes the aero-engine into mechanism model components and surrogate model components, and couples them with an end-to-end differentiable component integration algorithm, so that the gradient can smoothly backpropagate throughout the entire model, thereby avoiding gradient vanishing or exploding. Subsequently, based on the inherent causal relationship chain or energy / mass transfer path of the system, it is divided into multiple levels from the output end to the input end, and a top-down, progressive parameter pre-estimation strategy is adopted. First, the highest level parameters are calibrated using measured output data, and then the training target of the next level is generated in reverse based on the estimated level results. High-quality initialization of unknown parameters is completed layer by layer, significantly reducing the non-convexity of the loss function and providing a good starting point for global optimization. Finally, starting from the initial estimate, a unified gradient backpropagation and joint optimization update are performed in the complete simulation model, and regularization or other optimization control methods are introduced into the loss function to limit the parameter update amplitude and ensure stable convergence to the global optimum during the fine-tuning stage, thereby overcoming the extremely difficult problem of joint optimization and realizing high-precision, high-stability, and high-generalization modeling and training of aero-engines. Attached Figure Description

[0019] To more clearly illustrate the technical solutions in this invention 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 invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0020] Figure 1 This is a flowchart illustrating the training method for aero-engine modeling driven by mechanism and data fusion provided by the present invention.

[0021] Figure 2 This is a schematic diagram of the structure of the training device for modeling aero-engines driven by mechanism and data fusion provided by the present invention.

[0022] Figure 3 This is a schematic diagram of the structure of the electronic device provided by the present invention. Detailed Implementation

[0023] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0024] For aero-engines, modeling and simulation are core components of modern scientific research and engineering design. Establishing high-precision simulation models is of irreplaceable value for system performance analysis, state prediction, fault diagnosis, and optimized control.

[0025] In the practice of aero-engine modeling, there are generally two main technical approaches. To better understand the innovativeness of the embodiments of this invention, the characteristics and limitations of these two methods are described in more detail below.

[0026] The first approach is mechanistic modeling, also known as white-box modeling. Its core idea is based on a deep understanding of the system's internal physical laws, such as the laws of conservation of mass, energy, and momentum. It uses a series of mathematical equations (e.g., ordinary differential equations (ODEs), partial differential equations (PDEs), or systems of algebraic equations) to accurately describe the system's dynamic behavior and static characteristics. The key advantage of this method is that the constructed model has clear physical meaning, good interpretability, and, because it is based on universal physical laws, usually has strong extrapolation capabilities, meaning it can make reasonable predictions even outside the training data range. However, for systems with complex structures, multi-field coupling, and unknown or difficult-to-describe physical effects (e.g., complex friction, turbulence effects, material nonlinearities), relying solely on mechanistic modeling often faces significant challenges. Not only is the development cost high, but the simplification or neglect of complex effects often leads to models whose accuracy fails to meet engineering requirements.

[0027] The second approach, in contrast to mechanistic modeling, is data-driven modeling, also known as black-box modeling. This method bypasses the complex physical mechanisms within the system, directly utilizing a large amount of input-output data collected from system experiments or operation. Machine learning algorithms such as neural networks and support vector machines are used to fit the nonlinear mapping relationship from input to output. Its advantage lies in its ability to approximate arbitrarily complex dynamic responses with extremely high accuracy, making it particularly suitable for systems whose internal mechanisms are not yet fully understood. However, its black-box nature also brings significant drawbacks: the model typically lacks physical interpretability, making it difficult to understand its internal decision-making logic; its generalization ability is severely limited by the coverage of the training data, easily leading to overfitting; more importantly, its predictions may violate basic physical constraints (such as energy conservation), severely restricting its use in safety-critical or high-reliability prediction engineering applications.

[0028] Before further elaborating on the specific steps of this invention, it should be noted that, in addition to the major drawback of joint optimization mentioned in the background art, existing technologies also generally suffer from other significant problems in the training practice of fusion models: (1) Lack of effective initial parameter estimation. Traditional methods usually use random initialization or empirical values. When the model has a deep hierarchy and a large number of parameter dimensions, the optimization process is difficult to converge.

[0029] (2) The hierarchical structure is not fully utilized. Most existing algorithms do not divide the model into layers according to the causal chain or energy transfer path of the aero-engine, resulting in mutual interference between parameter updates of each layer.

[0030] (3) Lack of targeted constraints in the fine-tuning stage. In the global optimization stage, if no limit is set on the parameter update magnitude, it often leads to parameter drift, loss of physical meaning or overfitting.

[0031] In summary, existing technologies lack a unified modeling and training framework that simultaneously possesses physical interpretability, data adaptability, and efficient trainability, and in particular, lack a systematic training method that can combine hierarchical parameter prediction and global fine-tuning mechanisms.

[0032] To systematically address all the aforementioned problems, this invention proposes a two-stage training framework of "hierarchical parameter pre-estimation – global joint fine-tuning". The hierarchical parameter pre-estimation stage aims to solve the problems of difficult parameter initialization and insufficient utilization of the hierarchical structure, providing an excellent starting point for global optimization; while the global joint fine-tuning stage ensures that the stability and physical rationality of the model are maintained during the fine-tuning of parameters by introducing optimization constraints.

[0033] Before describing the technical solutions of the embodiments of the present invention, the terms and concepts involved in the embodiments of the present invention will be explained illustratively.

[0034] A complete simulation model is a mathematically end-to-end differentiable computational model that connects multiple components representing different parts of an aero-engine through a specific integration algorithm.

[0035] Mechanistic Model Component: A mathematical model is a mathematical model built on explicit first principles of physics (such as the laws of conservation of mass, energy, and momentum), and its structure and parameters have clear physical meaning.

[0036] Surrogate Model Component: A mathematical model built using data-driven methods (such as machine learning) is used to approximate the input-output relationship of a specific part by learning from measured data when the physical mechanism is unclear or too complex.

[0037] Initial Estimate: refers to a set of high-quality, non-random initial values ​​obtained for all unknown parameters in the model through the hierarchical pre-estimation steps of this invention before global joint optimization. Its purpose is to guide the subsequent optimization process to converge more easily to the global optimum.

[0038] Gradient backpropagation is an algorithm for efficiently calculating the gradient of the loss function with respect to all parameters in a differentiable model (such as a neural network or a complete simulation model). It is the foundation for achieving unified optimization and updating of parameters.

[0039] System identification refers to the theory and method of determining the values ​​of unknown parameters in a mathematical model with a pre-defined structure (usually a mechanistic model) based on the system's input and output data.

[0040] Machine learning refers to a class of algorithms that enable computers to automatically learn patterns and rules from data. It is used to build surrogate model components or to learn parameter mapping relationships from data in the parameter estimation step.

[0041] Causal chain / energy transfer path / mass transfer path: refers to the objectively existing, directional sequence of actions or flow routes of matter / energy within an aero-engine. In this invention, these physical laws are used as the scientific basis for dividing the model hierarchy.

[0042] Polynomial Regression Model: A data-driven approach that establishes the input-output relationship by fitting a polynomial function of the input variables.

[0043] Support Vector Regression Model: A data-driven approach that aims to find a function that minimizes the maximum deviation from the sample data points.

[0044] Gaussian Process Regression Model: A non-parametric data-driven method based on Bayesian theory that can provide not only predicted values ​​but also the uncertainty of the predictions.

[0045] Neural Network-based Model: A data-driven approach that mimics the structure of biological neural networks, learning extremely complex input-output mappings through a large number of parameterized nonlinear transformation layers.

[0046] Data feature mapping refers to transforming raw input data into another (usually higher-dimensional) feature space through a certain function, so that it is easier to discover data patterns in the new space.

[0047] Preset Basis Function Learning refers to representing the target function as a linear combination of a set of predefined basis functions (such as Fourier series or polynomials) with known form. The goal of learning is to determine the combination coefficients of each basis function.

[0048] Kernel Function Learning: A machine learning technique that indirectly calculates the inner product of data in a high-dimensional space by defining a kernel function, thereby enabling complex nonlinear modeling without explicit feature mapping.

[0049] Explicit Function Mapping: This refers to the relationship between components that can be expressed by a direct, analytical mathematical formula, such as Y = f(X).

[0050] Numerical Solver: A numerical solver is an iterative algorithm used to solve mathematical equations (especially implicit equations, such as G(X, Y) = 0) for which analytical solutions cannot be obtained directly, such as the Newton-Raphson solver. In this invention, it serves as a component integration algorithm to solve for the coupling balance relationships between components.

[0051] Figure 1 This is one of the flowcharts illustrating the training method for mechanism and data fusion-driven aero-engine modeling provided by the present invention. The method includes: Step 101: Decompose the simulation model of the aero-engine into multiple components containing unknown parameters to be identified, and use a component integration algorithm to associate the multiple components to form an end-to-end differentiable complete simulation model.

[0052] The components include a mechanistic model component and / or a proxy model component, wherein the mechanistic model component is established based on physical mechanisms and the proxy model component is established based on a data-driven method.

[0053] In step 101, the overall simulation model of the gas turbine system is first decomposed into multiple components with clear input-output relationships and physical meanings, based on the physical structure and working principle of the gas turbine system. In this embodiment, the system is decomposed into three main components: the compressor assembly, the combustion chamber assembly, and the turbine assembly.

[0054] (1) Compressor assembly (mechanism model assembly).

[0055] This component simulates the pressure and temperature rise of air as it flows through a compressor. It employs a mechanistic modeling method based on the laws of thermodynamics, with the compressor characteristic curve, specifically the compressor's pressure ratio π, as its core element. c and efficiency η c It's about converting the rotational speed n. cor and converted flow rate m cor The compressor outlet temperature is a function of the compressor. It can be calculated using the thermodynamic formula: T out_c = T in_c (1 +(πc ((k-1) / k) - 1 / η c To characterize performance deviations caused by manufacturing tolerances, component aging, and other factors, a flow correction factor p1 and an efficiency correction factor p2 are introduced as the first type of unknown parameters to be identified. The corrected converted flow rate and efficiency are m' and m', respectively. cor = p1 m cor and η' c = p2 η c .

[0056] (2) Combustion chamber components (mixing mechanism / surrogate model components).

[0057] This component simulates the process of fuel mixing and burning with high-pressure air in the combustion chamber, resulting in a rapid temperature rise. A hybrid modeling strategy is employed: for pressure changes, the mechanistic component is used, where the total pressure at the combustion chamber outlet is multiplied by the total pressure at the inlet by a pressure recovery coefficient σ to be identified. b We obtain, i.e., P out_b = σ b P in_b For outlet temperature, the key influencing factor is combustion efficiency η. b Due to the extreme complexity of the mechanism, it is difficult to establish an accurate analytical model. Therefore, a surrogate model is used for fitting. This surrogate model is specifically a neural network NN_b, whose input is the fuel flow rate m. f Airflow m a Isostatic variables, output as combustion efficiency η b Therefore, the unknown parameters of this component include σ in the mechanistic part. b And the neural network weights and biases w in the surrogate model part b .

[0058] (3) Turbine assembly (mechanism model assembly).

[0059] This component simulates the process of high-temperature, high-pressure gas flowing through a turbine and expanding to do work. Its modeling method is similar to that of a compressor, employing mechanistic modeling based on turbine characteristic diagrams. The turbine's equivalent flow rate is m. cor_t and efficiency η t It's about the turbine expansion ratio π. t And converted speed n cor_t The function of turbine outlet temperature T. out_t It can be calculated using the following formula: T out_t = T in_t (1 - η t (1 - π t-(k-1) / k )).

[0060] Similarly, flow correction coefficient p3 and efficiency correction coefficient p4 are introduced as the first type of unknown parameters to be identified in order to correct the deviation between the theoretical model and the actual performance.

[0061] After defining the components, this step uses a component integration algorithm to associate the three components together, forming a complete gas turbine system simulation model. The association between components includes not only explicit data transfer (such as the compressor outlet acting as the combustion chamber inlet), but more importantly, it requires solving for the core physical coupling relationships within the system. In this embodiment, this coupling relationship is embodied in the power balance equation: the power consumed by the compressor, W... c It must be related to the power W generated by the turbine. t Balance is achieved on the same rotor (with the same rotational speed n).

[0062] The power balance equation W c (π c , η c , ...) = W t (π t , η t The equations {p1, p2, σ} constitute a nonlinear algebraic equation, i.e., an implicit equation. Therefore, the component integration algorithm in this embodiment is specifically a numerical solver for solving the implicit equation, such as a Newton-Raphson method or a Broyden method solver. To achieve end-to-end differentiability of the entire model, the iterative process of this numerical solver itself also needs to be differentiable. This is accomplished by implementing the solver algorithm in a computational framework that supports automatic differentiation (such as PyTorch, JAX), so that the gradient of the solution output by the solver (i.e., the system operating point) with respect to any parameters inside the model can be automatically calculated through gradient backpropagation. In this way, a system is constructed that ranges from system-level inputs (such as fuel flow) to system-level outputs (such as engine speed), containing unknown parameters to be identified {p1, p2, σ}. b , w b The complete simulation model is end-to-end differentiable for p3, p4}. In this embodiment, the component integration algorithm itself does not include the second type of unknown parameters to be identified, but in other more complex systems, the algorithm may include such parameters.

[0063] Step 102: Based on the hierarchical division of the simulation model, a top-down, progressive strategy is adopted to pre-estimate the parameters and obtain the initial estimated values ​​of the unknown parameters. The strategy includes: first, estimating the unknown parameters of the components in the highest level based on the measured output data, and generating the training target of the next lower level based on the calculation results of the estimated level, so as to complete the estimation of the unknown parameters of the lower level in sequence.

[0064] After constructing a complete, end-to-end differentiable simulation model, step 102 aims to provide a set of high-quality initial estimates for the unknown parameters to be identified in the model, in order to overcome the problem of easily getting trapped in local optima when directly performing end-to-end optimization. The core of this step is to adopt a top-down, layer-by-layer parameter pre-estimation strategy.

[0065] In this embodiment, the strategy first requires dividing the simulation model into multiple sequential levels from the output to the input, based on the system's internal physical laws. Then, the estimation process is strictly performed sequentially from the highest level to the lowest. Specifically, firstly, the unknown parameters within the highest level are identified using available measured system output data. After estimating the parameters of one level, this method uses the calibrated model of that level to generate a set of high-quality, physically meaningful virtual training targets for the next lower level immediately upstream through a back-calculation method. This process is repeated layer by layer until all levels containing unknown parameters have been estimated.

[0066] Finally, the output of step 102 is a complete set of initial estimates for all unknown parameters in the model. Because these initial values ​​are obtained by making full use of the model's physical structure and local data information, they place the starting point for parameter search in a region far superior to random guessing, providing a solid foundation for the rapid and stable convergence of the subsequent global joint fine-tuning steps.

[0067] Step 103: Starting from the initial estimated value, optimize and update the unknown parameters by performing gradient backpropagation in the complete simulation model.

[0068] Step 103 aims to use this excellent initial value as a starting point and complete system measurement data to make unified and refined adjustments to the unknown parameters in the model in order to maximize the overall prediction accuracy of the model.

[0069] The core of this step lies in calculating the global loss function between the model's predicted output and the measured output within a complete end-to-end differentiable model. Then, using gradient backpropagation, the gradient of this loss function with respect to unknown parameters in the model is calculated, leading to a unified and joint optimization update of these parameters. This process is iterated until the model converges, ultimately yielding a fully optimized final parameter set, resulting in a high-precision simulation model that accurately reflects the system's true physical processes.

[0070] The mechanism- and data-driven training method for aero-engine modeling provided in this invention decomposes the aero-engine into mechanism model components and surrogate model components, and couples them with an end-to-end differentiable component integration algorithm. This allows gradients to propagate smoothly back through the entire model, thus avoiding gradient vanishing or exploding. Subsequently, based on the inherent causal chain or energy / mass transfer path of the system, the model is divided into multiple levels from the output end to the input end. A top-down, progressive parameter pre-estimation strategy is adopted. First, the highest-level parameters are calibrated using measured output data. Then, the training target for the next level is generated back-propagated based on the estimated level results. This completes the high-quality initialization of unknown parameters layer by layer, significantly reducing the non-convexity of the loss function and providing a good starting point for global optimization. Finally, starting from this initial estimate, a unified gradient backpropagation and joint optimization update are performed in the complete simulation model. Regularization or other optimization control methods are introduced into the loss function to limit the parameter update amplitude and ensure stable convergence to the global optimum during the fine-tuning stage. This overcomes the extremely difficult problem of joint optimization and achieves high-precision, high-stability, and high-generalization modeling and training of aero-engines.

[0071] Furthermore, after constructing a complete, end-to-end differentiable simulation model, step 102 aims to provide a set of high-quality initial estimates for the unknown parameters to be identified in the model, in order to overcome the problem of easily getting trapped in local optima when directly performing end-to-end optimization. This step first needs to determine the hierarchical structure of the model, and then adopt a top-down, layer-by-layer progressive strategy to systematically estimate the unknown parameters within each level.

[0072] Specifically, before performing parameter pre-estimation, this method first determines the hierarchical division of the model based on the inherent logic of the aero-engine. This is not an arbitrary process, but rather involves selecting one of several physical dependency sequences as the division criterion and determining the hierarchy based on the reverse order of the selected sequence. In this embodiment, the "energy transfer path" is selected as the division criterion. For a gas turbine system, energy flows from the compressor to the combustion chamber and is finally transferred to the turbine. Therefore, the hierarchy is divided in reverse order, defining the turbine assembly at the end of the energy transfer path as the highest level (level 2), while the compressor and combustion chamber assemblies located upstream together constitute a lower level (level 1).

[0073] After the hierarchical division is determined, parameter prediction strictly begins from the highest level. First, the unknown parameters within the highest level (turbine assembly) are estimated based on the measured output data of the system. This process continuously adjusts the unknown parameters of the components within the highest level (i.e., the turbine flow rate and efficiency correction coefficients p3 and p4) by employing system identification methods (such as nonlinear least squares). The goal is to ensure that, given the model input for this level, the predicted output of the component model matches the measured output data (e.g., measured turbine outlet temperature and speed) as closely as possible.

[0074] Once the parameters of the highest level are initially estimated, the core step of this method is to generate the necessary training targets for the next lower level based on the calculation results of the estimated levels. In this embodiment, this means using a pre-calibrated turbine model to back-calculate the model inputs necessary to generate a given, physically accurate model output (e.g., the power required to drive the compressor). This back-calculated turbine inlet gas state is then used as the output training target for the next lower level (compressor and combustion chamber series). Subsequently, a similar approach is used again to adjust the unknown parameters (p1, p2, σ) within this lower level using a machine learning optimizer. b , w b (This continues) until its model's predicted output matches this newly generated "virtual" training objective.

[0075] By sequentially estimating all levels, this step ultimately obtains a complete set of initial estimates for all unknown parameters in the entire simulation model, located in a favorable region of the parameter space, laying a solid foundation for subsequent global joint fine-tuning steps.

[0076] In implementing this invention, the selection of a specific data-driven method for the proxy model components is highly flexible, primarily depending on the complexity of the physical process to be modeled, the quantity and quality of available data, and the requirements for model interpretability and predictive uncertainty. Several feasible implementation methods will be described below.

[0077] In this embodiment, for combustion efficiency η b For modeling, a neural network-based model is preferred. This is a data-driven method that mimics the structure of biological neural networks. Through its deep, multi-layered nonlinear transformation structure containing a large number of adjustable parameters, it becomes a powerful and universal function approximator. Given that combustion is a complex process involving multiple variables and high nonlinearity, neural networks can effectively capture the complex coupling and interaction between fuel flow, air flow, inlet pressure, and temperature, thereby fitting the variation law of combustion efficiency with high accuracy.

[0078] In other situations, other data-driven methods can be employed. For example, if the physical relationship to be modeled is relatively simple, a multinomial regression model can be used. This method establishes the input-output relationship by fitting a multinomial function of the input variables, resulting in a simple and easily interpretable model. If it is necessary to quantify the uncertainty of the model while making predictions, a Gaussian process regression model is an ideal choice; it is a non-parametric method based on Bayesian theory that not only provides predicted values ​​but also confidence intervals for those predictions, which is extremely valuable in risk assessment of safety-critical systems. For scenarios with high input dimensionality and limited sample size, support vector regression models exhibit good generalization ability and robustness. It aims to find a function that minimizes the maximum deviation from all sample data points.

[0079] The effectiveness of the aforementioned models can be understood from their deeper methodological principles. For example, many machine learning models implicitly or explicitly rely on data feature mapping, that is, transforming the original input data into a new feature space through a function, so that it is easier to discover and learn data patterns in it. Pre-defined basis function learning is a specific approach to achieving this goal. Its core is to represent complex unknown functions as a linear combination of a set of pre-defined basis functions with known forms (such as Fourier series or polynomials), and the learning objective is only to determine the combination coefficients of each basis function. The polynomial regression model is a direct application of this methodology.

[0080] In contrast, kernel function learning offers a more ingenious and efficient approach to nonlinear modeling. The core of this technique lies in allowing algorithms to perform inner product operations in a high-dimensional feature space equivalently, without explicit high-dimensional data feature mapping, by defining a computationally inexpensive kernel function. This enables the model to efficiently learn complex nonlinear relationships. Support vector regression and Gaussian process regression models effectively utilize this powerful kernel function learning technique.

[0081] The framework of this invention is open to the specific implementation of the proxy model components, allowing modelers to flexibly select the most suitable data-driven technology according to the specific problem, so as to achieve the best balance between model accuracy, computational efficiency and interpretability.

[0082] In the method of this invention embodiment, connecting independent components into a complete model that can simulate the overall behavior of the system is achieved through a component integration algorithm. The form of this algorithm can be flexibly selected according to the complexity of the relationships between components, and its core task is to realize information exchange and coupled solution between components.

[0083] The simplest form of integration is explicit function mapping. This approach is suitable when the output of one component can be directly used as the input of another component. For example, in the gas turbine system of this embodiment, the outlet pressure and temperature of the compressor assembly are directly used as the inlet pressure and temperature of the combustion chamber assembly. This direct data transfer or simple algebraic relationship is an example of explicit function mapping.

[0084] However, in more complex cases, physical coupling and feedback loops exist between components, and their relationships cannot be expressed by simple explicit functions, instead forming implicit equations. In this case, the component integration algorithm needs to be a numerical solver for solving these implicit equations. In the gas turbine system of this embodiment, the core implicit equation is an algebraic equation composed of power balance conditions: at the steady-state operating point, the power W consumed by the compressor... c It must be related to the power W generated by the turbine. t Equal. Numerical solvers (such as Newton-Raphson solvers) iteratively calculate to find a unique set of solutions (i.e., the operating point of the system) that simultaneously satisfies all the internal equations of the components and the power balance equation. To ensure that the entire model is end-to-end differentiable, the numerical solver itself must also be differentiable.

[0085] Furthermore, when simulating the dynamic response of a system rather than its steady-state operating point, the coupling relationships are described by ordinary differential equations (ODEs). For example, the rate of change of rotor speed depends on the power difference between the turbine and compressor, which is an ODE. In this case, the component integration algorithm manifests as an ODE numerical integrator (such as the Runge-Kutta method). Further, when both dynamic equations and algebraic constraints exist in the system, a system of differential algebraic equations (DAEs) is formed. For physical fields that need to be considered in terms of spatial distribution, such as simulating the spanwise temperature distribution inside turbine blades, partial differential equations (PDEs) are involved. In these cases, the corresponding DAE solver or PDE solver (such as the finite element method) acts as the component integration algorithm.

[0086] Finally, in certain scenarios, the component integration algorithm itself can also be a machine learning model used to fit the transfer relationships between components. For example, if there is a heat transfer or vibration transfer relationship between two physically separate components that is difficult to describe precisely by mechanism, a neural network can be specifically trained to fit this complex transfer relationship. The input of this neural network is the state of the source component, and the output is its influence on the target component, thus building a data-driven bridge between the two components.

[0087] The method of this invention can flexibly adopt different forms of component integration algorithms, from simple explicit functions to complex numerical solvers and even machine learning models, to adapt to the modeling needs of various aero-engines, from static to dynamic and from lumped parameters to distributed parameters.

[0088] In the final stage of the method of this invention, namely step 103, the unknown parameters of the entire simulation model are uniformly and jointly optimized and updated, starting from the initial estimated values ​​obtained by hierarchical pre-estimation. However, there is a potential risk in this global joint optimization stage: in order to fit the measured data perfectly, the optimization algorithm may update some parameters to physically unreasonable ranges, or cause overfitting in the data-driven surrogate model part. To solve this problem, this method introduces an optimization control method to limit the parameter update magnitude when calculating the final loss function.

[0089] One of the most common and effective optimization control methods is to introduce a regularization term that constrains the unknown parameters. Specifically, this means not only minimizing the error (e.g., mean squared error) between the model's predicted and measured outputs, but also adding an additional penalty term to the loss function. The magnitude of this penalty term is positively correlated with the magnitude of the unknown parameters in the model. For example, the L2 regularization term penalizes the sum of squares of the parameters.

[0090] In this embodiment, this regularization term can adjust the unknown parameters to be optimized (including the correction coefficients p1, p2, etc. of the mechanistic components and the neural network weights w of the surrogate model components). b The parameter approaches zero or its initial estimate. This brings two significant benefits: First, it effectively prevents any single parameter from becoming too large during optimization, thus maintaining the physical reasonableness of the parameters and avoiding parameter drift; second, for surrogate model components, it reduces the complexity of the model, effectively suppresses the model's overlearning of noise in the training data, thereby improving the model's generalization ability and mitigating overfitting.

[0091] Besides regularization, other optimization control methods can also be employed. For example, a learning rate decay strategy can be used, which involves using a large learning rate for rapid exploration in the initial stage of optimization, and gradually reducing the learning rate as training progresses, resulting in smaller and smaller parameter update steps, thereby achieving fine-tuning. Another method is gradient pruning, which sets an upper limit on the gradient of the parameters. When the gradient calculated by backpropagation exceeds this upper limit, it is forcibly truncated. This effectively prevents drastic parameter updates caused by individual outlier data points, ensuring the stability of the training process.

[0092] By introducing regularization terms or other optimization control methods during the global fine-tuning stage, this invention ensures that while further improving the model accuracy using measured data, it can effectively maintain the physical consistency and predictive robustness of the model, ultimately obtaining an aero-engine simulation model that is both accurate and reliable.

[0093] The training device for mechanism and data fusion-driven aero-engine modeling provided in the embodiments of the present invention will be described below. The training device for mechanism and data fusion-driven aero-engine modeling described below can be referred to in correspondence with the training method for mechanism and data fusion-driven aero-engine modeling described above.

[0094] This invention provides a training device for aero-engine modeling driven by mechanism and data fusion, see [link to documentation]. Figure 2 ,include: The model building module 210 is used to decompose the simulation model of the aero-engine into multiple components containing unknown parameters to be identified, and to associate the multiple components using a component integration algorithm to form an end-to-end differentiable complete simulation model; the multiple components include a mechanism model component and / or a proxy model component, wherein the mechanism model component is established based on physical mechanisms, and the proxy model component is established based on a data-driven method; The parameter pre-estimation module 220 is used to perform parameter pre-estimation based on the hierarchical division of the simulation model, using a top-down, progressive strategy to obtain the initial estimated values ​​of the unknown parameters. The strategy includes: first, estimating the unknown parameters in the highest level based on the measured output data, and generating the training target for the next lower level based on the calculation results of the estimated levels, so as to complete the estimation of the unknown parameters in the lower levels in sequence. The parameter fine-tuning module 230 is used to optimize and update the unknown parameters by performing gradient backpropagation in the complete simulation model, starting from the initial estimated value.

[0095] Figure 3 An example is a schematic diagram of the physical structure of an electronic device, such as... Figure 3As shown, the electronic device may include: a processor 810, a communications interface 820, a memory 830, and a communications bus 840, wherein the processor 810, the communications interface 820, and the memory 830 communicate with each other through the communications bus 840. The processor 810 can call logic instructions in the memory 830 to execute a training method for aero-engine modeling driven by mechanism and data fusion. This method includes: decomposing the aero-engine simulation model into multiple components containing unknown parameters to be identified, and using a component integration algorithm to associate the multiple components to form an end-to-end differentiable complete simulation model; the multiple components include a mechanism model component and / or a surrogate model component, wherein the mechanism model component is established based on physical mechanisms, and the surrogate model component is established based on a data-driven method; based on the hierarchical division of the simulation model, a top-down, progressively layered strategy is used to pre-estimate the parameters to obtain initial estimates of the unknown parameters; the strategy includes: first, estimating the unknown parameters of the components in the highest level based on measured output data, and generating training targets for the next lower level based on the calculation results of the estimated levels, so as to sequentially complete the estimation of unknown parameters at lower levels; starting from the initial estimates, optimizing and updating the unknown parameters through gradient backpropagation in the complete simulation model.

[0096] 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 the present invention, 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 the present invention. 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.

[0097] On the other hand, the present invention 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 training method for mechanism and data fusion-driven aero-engine modeling provided by the above methods. This method includes: decomposing the aero-engine simulation model into multiple components containing unknown parameters to be identified, and using a component integration algorithm to associate the multiple components to form an end-to-end differentiable complete simulation model; the multiple components include mechanism model components and / or proxy model components. The theoretical model component is established based on physical mechanisms, while the surrogate model component is established based on a data-driven method. Based on the hierarchical division of the simulation model, a top-down, layer-by-layer progressive strategy is adopted to pre-estimate the parameters and obtain initial estimates of the unknown parameters. The strategy includes: first, estimating the unknown parameters of the components in the highest level based on the measured output data, and generating the training target for the next lower level based on the calculation results of the estimated level, so as to complete the estimation of the unknown parameters of the lower levels in sequence; starting from the initial estimates, the unknown parameters are optimized and updated by performing gradient backpropagation in the complete simulation model.

[0098] In another aspect, the present invention also provides a non-transitory computer-readable storage medium storing a computer program thereon. When executed by a processor, the computer program implements a training method for mechanism and data fusion-driven aero-engine modeling provided by the methods described above. This method includes: decomposing an aero-engine simulation model into multiple components containing unknown parameters to be identified, and using a component integration algorithm to associate the multiple components to form an end-to-end differentiable complete simulation model; the multiple components include a mechanism model component and / or a surrogate model component, wherein the mechanism model component is established based on physical mechanisms, and the surrogate model component is established based on a data-driven method; based on the hierarchical division of the simulation model, a top-down, progressively layered strategy is used to pre-estimate the parameters to obtain initial estimates of the unknown parameters; the strategy includes: first, estimating the unknown parameters of the components within the highest level based on measured output data, and generating training targets for the next lower level based on the calculation results of the estimated levels, thereby sequentially estimating the unknown parameters at lower levels; starting from the initial estimates, optimizing and updating the unknown parameters through gradient backpropagation in the complete simulation model.

[0099] 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.

[0100] 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.

[0101] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention 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; and these 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 the present invention.

Claims

1. A training method for aero-engine modeling driven by mechanism and data fusion, characterized in that, Includes the following steps: (a) The simulation model of the aero-engine is decomposed into multiple components containing unknown parameters to be identified, and the multiple components are associated using a component integration algorithm to form an end-to-end differentiable complete simulation model; the multiple components include a mechanism model component and / or a surrogate model component, wherein the mechanism model component is established based on physical mechanisms, and the surrogate model component is established based on a data-driven method; (b) Based on the hierarchical division of the simulation model, a top-down, progressive strategy is adopted to perform parameter pre-estimation to obtain the initial estimated values ​​of the unknown parameters; the strategy includes: firstly estimating the unknown parameters of the components in the highest level according to the measured output data, and generating the training target of the next lower level based on the calculation results of the estimated level, so as to complete the estimation of the unknown parameters of the lower level in sequence. (c) Starting from the initial estimated value, the unknown parameters are optimized and updated by performing gradient backpropagation in the complete simulation model.

2. The method according to claim 1, characterized in that, In step (b), generating the training target for the next lower level based on the calculation results of the estimated level includes: The calculation result of the estimated level is used as the known output of the estimated level, and the model input required to generate the known output is calculated in reverse according to the simulation model. The model input is then used as the training target of the next lower level.

3. The method according to claim 1, characterized in that, In step (b), the unknown parameters of the highest-level components are estimated based on the measured output data, including: By using system identification or machine learning, the unknown parameters of the components within the highest level are adjusted so that, given the model input at that level, the predicted output of the simulation model matches the measured output data.

4. The method according to claim 1, characterized in that, Before performing step (b), the method further includes: The simulation model is hierarchically divided into several physical dependency sequences, including causal chains, energy transfer paths, and mass transfer paths, by selecting one of the multiple physical dependency sequences and determining the hierarchical division of the selected sequence in reverse order.

5. The method according to claim 1, characterized in that, The data-driven approach used by the proxy model component includes at least one of the following: Multinomial regression model, support vector regression model, Gaussian process regression model, or neural network-based model; Machine learning models based on data feature mapping, pre-defined basis function learning, or kernel function learning.

6. The method as described in claim 1, characterized in that, The specific form of the component integration algorithm includes at least one of the following: Define explicit function mappings for data transfer or algebraic operations between components; A numerical solver for solving implicit equations formed by the coupling relationships between components; A machine learning model used to fit transitive relationships between components.

7. The method as described in claim 6, characterized in that, When the component integration algorithm includes a numerical solver for solving implicit equations, the implicit equations include algebraic equations, ordinary differential equations, differential-algebraic equations, or partial differential equations.

8. The method as described in claim 1, characterized in that, The optimization and update of the unknown parameters in step (c) includes: When calculating the loss function, an optimization control method is introduced to limit the magnitude of parameter updates. This optimization control method includes introducing a regularization term to constrain the unknown parameters.

9. A training device for aero-engine modeling driven by mechanism and data fusion, characterized in that, include: The model building module is used to decompose the simulation model of the aero-engine into multiple components containing unknown parameters to be identified, and to associate the multiple components using a component integration algorithm to form an end-to-end differentiable complete simulation model; the multiple components include a mechanism model component and / or a surrogate model component, wherein the mechanism model component is established based on physical mechanisms, and the surrogate model component is established based on a data-driven method; The parameter pre-estimation module is used to perform parameter pre-estimation based on the hierarchical division of the simulation model, using a top-down, progressive strategy to obtain the initial estimated values ​​of the unknown parameters. The strategy includes: first, estimating the unknown parameters in the highest level based on the measured output data, and generating the training target for the next lower level based on the calculation results of the estimated levels, so as to complete the estimation of the unknown parameters in the lower levels in sequence. The parameter fine-tuning module is used to optimize and update the unknown parameters by performing gradient backpropagation in the complete simulation model, starting from the initial estimated value.

10. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the training method for aero-engine modeling driven by mechanism and data fusion as described in any one of claims 1-8.

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