A Multi-Source Data Fusion and Interpretable Deep Learning-Based Oblique Detonation Initiation Prediction Method

Abstract

This invention discloses a multi-source data fusion and interpretable deep learning method for predicting oblique detonation initiation, belonging to the interdisciplinary field of high-speed propulsion technology and artificial intelligence. The method first constructs a multi-source dataset containing a large amount of simulation data and a small amount of experimental data; it then pre-trains a deep neural network using the simulation data to learn the macroscopic trend of the detonation distance; next, it fine-tunes the model using experimental data through transfer learning to achieve data fusion; then, it extracts an explicit analytical formula from the fused model using symbolic regression; finally, it calculates the predicted detonation distance based on the formula and constructs a detonation criterion by comparing it with the wedge length. This invention achieves high-precision modeling under sparse experimental data conditions, possesses both physical interpretability and generalization ability, and the analytical formula can be directly used for combustion chamber design, fuel evaluation, and envelope analysis, reducing dependence on experimental data.

Description

Technical Field

[0001] This invention relates to the field of high-speed propulsion technology and artificial intelligence, and in particular to a method for predicting oblique detonation initiation using multi-source data fusion and interpretable deep learning. Background Technology

[0002] Sliding detonation engines utilize the oblique shock wave induced by the wedge to generate a detonation wave within the combustion chamber. They offer advantages such as short combustion chamber length, high thermal cycle efficiency, and relatively simple structure, and are considered a crucial power source for future high-speed aircraft. In the organization of sliding detonation combustion, the initiation distance (the length from the starting point of the combustible mixture at the wedge surface to the formation of a stable sliding detonation wave) is a key parameter for evaluating the success of combustion chamber design. This parameter directly determines the minimum required length of the combustion chamber, thus affecting the overall layout and weight of the aircraft.

[0003] Currently, obtaining detonation distance mainly relies on three methods: theoretical analysis, numerical simulation, and wind tunnel experiments. However, theoretical analysis and numerical simulation involve large amounts of data but suffer from systematic biases, making it difficult to accurately describe complex real physical processes. Experimental data is precise but expensive to obtain, and the samples are extremely sparse, making it impossible to independently support the establishment of predictive models with good generalization capabilities. Traditional modeling methods cannot effectively integrate the aforementioned heterogeneous data, and existing deep learning methods suffer from the "black box" problem, lacking physical interpretability and making it difficult to extract intuitive rules to guide design. Summary of the Invention

[0004] The purpose of this invention is to provide a method for predicting oblique detonation initiation using multi-source data fusion and interpretable deep learning, which solves the technical problems of high-precision modeling under sparse experimental data conditions, effective fusion of multi-source heterogeneous data, and lack of physical interpretability of the model.

[0005] To achieve the above objectives, this invention provides a method for predicting oblique detonation initiation using multi-source data fusion and interpretable deep learning, comprising the following steps: Step S1: Construct a multi-source heterogeneous dataset, including a first dataset (source domain data) and a second dataset (target domain data); the first dataset comes from theoretical analysis and numerical simulation, with a large sample size but systematic bias; the second dataset comes from experimental measurements, with a small sample size but high accuracy; the characteristics of the datasets include the incoming Mach number. wedge angle Equivalent ratio Types of gaseous fuels , and derived features built upon physical knowledge; Step S2: Construct a deep neural network as the base model and pre-train it using the first dataset to learn the macroscopic physical trend of the detonation distance changing with the working conditions; Step S3: Use the second dataset to perform transfer learning fine-tuning on the pre-trained model, achieving the fusion of multi-source data at the model level to obtain a fused model. ; Step S4: Employ interpretable machine learning algorithms to fuse the models. For the teacher model, extract the explicit analytical formula for detonation distance. ; Step S5: Calculate the predicted detonation distance based on analytical formulas , and the actual length of the given wedge Comparison, constructing detonation criteria: if The detonation was deemed successful. If it fails, the detonation is deemed a failure.

[0006] Preferably, the derived features in step S1 include the post-shock temperature. Post-shock pressure Combination of reactivity parameters , Damköhler number Combinatorial dimensionless numbers One or more of the following; in, The characteristic chemical reaction time of fuel, For activation energy, is the gas constant.

[0007] Preferably, the deep neural network in step S2 employs a multi-layer feedforward architecture, and the pre-training loss function includes a data fitting term and a physical knowledge-based regularization term: ; in and This is a priori estimate of the detonation distance with respect to Mach number and wedge angle, obtained based on theoretical analysis.

[0008] Preferably, the transfer fine-tuning in step S3 adopts a parameter freezing strategy, preserving the underlying parameters of the pre-trained model unchanged while fine-tuning the higher-level parameters; the fine-tuning loss function includes experimental fitting loss, knowledge distillation loss, and smoothness constraint loss, and the total loss function is in the form of: ; in, The total number of samples in the second dataset. For the fusion model to the first The predicted detonation distance for each experimental sample input. For the first The actual measured detonation distance of each experimental sample; The weighting coefficients for knowledge distillation loss are used to balance experimental fit with the preservation of knowledge from the source domain. The number of subset samples to be extracted from the first dataset for distillation. For the fusion model to the first The predicted detonation distance for each distillation sample input. This refers to the predicted detonation distance of the pre-trained model for the same distillation sample input; The weighting coefficients for the smoothness constraint loss are... The number of sampling points used to calculate the smoothness constraints, To output the fusion model for the first The partial derivatives of each input feature.

[0009] Preferably, the interpretable machine learning algorithm in step S4 employs either genetic programming-based symbolic regression or the SINDy algorithm based on sparse regression; the search objective of symbolic regression is to simultaneously minimize the fitting error and the complexity of the expression. ; in, This is the function space generated by a combination of primitive variables, mathematical operators, and basis functions based on physical knowledge.

[0010] Preferably, the analytical formula extracted in step S4 has the following general form: ; in, For undetermined coefficients, The basis functions found from symbolic regression include: One or more of them.

[0011] Preferably, the fuel type is determined by its chemical kinetic parameters. Continuous representations, rather than inputting as discrete categorical variables, where Characteristic chemical reaction time, For activation energy, It is a pre-exponential factor.

[0012] Preferably, the detonation criterion in step S5 further incorporates a safety factor. The criteria are expanded to a multi-level decision: like It was determined to be "reliable detonation"; like It was determined to be "critical detonation"; like The result was determined to be "detonation failure".

[0013] Preferably, the system implementing the above method includes: a data acquisition and processing module for collecting and processing multi-source heterogeneous data and constructing derived features; a deep neural network pre-training module for pre-training the model using a first dataset; a transfer learning fine-tuning module for fine-tuning the pre-trained model using a second dataset to obtain a fusion model; an interpretable analytical formula extraction module for extracting explicit analytical formulas from the fusion model using a symbolic regression algorithm; and an initiation criterion generation and application module for calculating the predicted initiation distance based on the analytical formula, comparing it with the actual length of the wedge to generate an initiation criterion, and applying it to the combustion chamber design evaluation.

[0014] Preferably, the detonation criterion generation and application module is also used to output the generated detonation criterion to the combustion chamber design unit, fuel adaptability assessment unit, flight envelope analysis unit, or real-time detonation status monitoring unit of the oblique detonation engine, so as to guide the combustion chamber structure design, screen suitable fuels, assess the detonation reliability within the flight envelope, or generate active control commands.

[0015] Therefore, the multi-source data fusion and interpretable deep learning oblique detonation initiation prediction method of the present invention, which adopts the above structure, has the following beneficial effects: (1) This invention uses a transfer learning framework to transfer the physical knowledge contained in a large amount of simulation data to a small sample of experiments, which significantly reduces the dependence on expensive experimental data and requires only a small number of experimental points.

[0016] (2) The dual-stage training strategy designed in this invention can retain the broad spectrum of simulation data while correcting systematic biases through experimental data, so that the model has both high accuracy and good generalization ability. The prediction accuracy at the experimental points is significantly improved compared with training with simulation data alone, and the effective fusion of multi-source heterogeneous data is realized.

[0017] (3) The explicit analytical formula extracted by interpretable machine learning in this invention can not only be used for fast calculation, but also help researchers understand the influence mechanism of the combined effect of various physical parameters on the detonation distance. Each term in the formula has a clear physical meaning.

[0018] (4) The present invention constructs an initiation criterion based on the direct comparison of “wedge length versus initiation distance”, providing engineers with a simple and intuitive evaluation tool that can quickly determine the initiation probability of a given combustion chamber configuration under different operating conditions, supporting scheme screening and optimization design.

[0019] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0020] Figure 1 This is an overall flowchart of the multi-source data fusion and interpretable deep learning oblique detonation initiation prediction method of the present invention; Figure 2 This is a schematic diagram of the transfer learning fine-tuning process in the method of the present invention; Figure 3 This is the Pareto front plot of the symbolic regression extraction analytical formula in the method of this invention; Figure 4 This is a schematic diagram illustrating the application of the detonation criterion in the method of the present invention; Figure 5 This is a schematic diagram illustrating the theoretical calculation of the detonation distance for hydrogen fuel in the method of this invention. Figure 6 This is a schematic diagram illustrating the theoretical calculation of the kinetic limit for hydrogen fuel in the method of this invention. Figure 7 This is a schematic diagram of the detonation distance prediction results in the method of the present invention, where (a), (b), and (c) correspond to the comparison of prediction results under different working conditions, respectively. Figure 8 This is a schematic diagram of the dynamic limit prediction results in the method of the present invention, where (a), (b), and (c) correspond to the comparison of prediction results under different working conditions, respectively. Figure 9 This is a comparison chart of the prediction errors of the method of the present invention and the traditional method at the experimental point. Detailed Implementation

[0021] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0022] Unless otherwise defined, the technical or scientific terms used in this invention shall have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains. The terms "first," "second," and similar terms used in this invention do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Terms such as "comprising" or "including" mean that the element or object preceding the word encompasses the elements or objects listed following the word and their equivalents, without excluding other elements or objects. Terms such as "connected" or "linked" are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. Terms such as "upper," "lower," "left," and "right" are used only to indicate relative positional relationships; when the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0023] Example This invention provides a method for predicting oblique detonation initiation using multi-source data fusion and interpretable deep learning, comprising the following steps: Step S1: Construct a multi-source heterogeneous dataset: Collect and construct datasets from two different sources: a first dataset (source domain data) and a second dataset (target domain data).

[0024] Step S11: Determine the input feature space: The key physical parameters affecting the initiation distance of oblique detonation shock are identified as input features of the model, including: Incoming Mach number ( Dimensionless numbers, typically ranging from 4 to 10. wedge angle (Unit: degrees or radians, generally ranging from 15° to 45°); Equivalent ratio (Dimensionless number, typically ranging from 0.3 to 1.5); Types of gaseous fuels (Categorical variables, including hydrogen) ethylene Acetylene Small molecule gaseous fuels); To convert categorical fuel variables into numerical inputs, a fuel feature vector is constructed. The characteristic chemical reaction time for fuel (based on simplified mechanism calculations). As the global activation energy, This is a pre-exponential factor. In this way, the chemical properties of different fuels can be characterized in a continuous feature space.

[0025] Step S12: Construct derived features based on physical knowledge: Based on combustion theory and gas dynamics analysis, a set of derived features capable of characterizing physical coupling is constructed as candidate basis functions for subsequent interpretable machine learning search: Post-shock temperature Calculated based on the oblique shock wave relation. ; in For the incoming flow to be at a constant temperature, For specific heat ratio, Shock angle (by and pass (Relationship established).

[0026] Post-shock pressure : ; Combination of reactivity parameters The effect of characterizing the rate of chemical reaction.

[0027] The ratio of the flow timescale to the reaction timescale (Damköhler number): ; in For reference length, Flow rate.

[0028] Combinatorial dimensionless number This comprehensively reflects the influence of shock wave intensity and fuel concentration. Step S13: Collect the first dataset (source domain data): The first dataset was obtained through theoretical analysis and high-precision numerical simulation. ,in For the input feature vector, These are the detonation distance values ​​(in meters) obtained through numerical simulation. The first dataset has the following characteristics: Large sample size: Usually in to Magnitude; Wide operating condition coverage: Uniform sampling is performed within the input space using experimental design methods (such as Latin hypercube sampling); There is a systematic bias: due to the simplification of the numerical model, There is an unknown systematic error between the true value and the actual value. .

[0029] Step S14: Collect the second dataset (target domain data): The second dataset was obtained through high-speed wind tunnel experiments. ,in This represents the actual detonation distance measured in the experiment. The second dataset has the following characteristics: Small sample size: Usually in to The scale is limited by experimental costs; High accuracy: Experimental measurements reflect the real physical process and can be used as a reference true value; Sparse operating conditions: It can only cover some key operating conditions.

[0030] Step S2: Construct a pre-trained model for transfer learning based on physical information: A deep neural network is constructed as the base model and pre-trained using the first dataset to learn the macroscopic physical trend of the detonation distance changing with the working conditions.

[0031] Step S21: Design the deep neural network architecture: Construct a multi-layer feedforward neural network with the following structure: Input layer: The number of nodes equals the dimension of the input features; ; Hidden layers: Use 4-6 fully connected layers, with the number of nodes in each layer decreasing progressively, such as [128, 64, 32, 16, 8]; Output layer: Single node, outputs predicted detonation distance ; Calculations for each layer: ; in These are the weight matrix and the bias vector, respectively. The activation function is (ReLU or Swish for the hidden layer, and linear activation for the output layer).

[0032] Step S22: Define the pre-training loss function: Mean squared error is used as the pre-training loss function: ; To enhance the stability of model training and incorporate physical constraints, a physics-based regularization term is introduced: ; in and This is a priori estimate of the detonation distance with respect to Mach number and wedge angle, obtained based on theoretical analysis (e.g., according to dimensional analysis, the detonation distance should decrease exponentially with increasing Mach number). The total pre-training loss function is: ; Step S23: Perform pre-training: Use the Adam optimizer to train the neural network using mini-batch stochastic gradient descent until the loss function converges. After pre-training, obtain the model parameters. .

[0033] Step S3: Model fine-tuning and multi-source fusion based on sparse experimental data: By using the second dataset to perform transfer fine-tuning on the pre-trained model, the organic fusion of multi-source data at the model level is achieved.

[0034] Step S31: Design transfer learning strategy: A transfer learning strategy based on parameter freezing and fine-tuning is adopted: Freeze the parameters of the bottom layer: retain the weights of the first k layers (usually 2-3 layers). As always, these layers learn general representations of features (such as shock wave relationships, combustion characteristics, and other fundamental physics). Fine-tuning high-level network parameters: parameters of the remaining layers Make fine adjustments to adapt it to the target domain data distribution.

[0035] Step S32: Define the fine-tuning loss function: The fine-tuning process not only needs to fit the experimental data but also needs to prevent deviations from the physical laws of the source domain from becoming too far off. Therefore, a composite loss function is designed: ; in: Experimental fit loss: measures the deviation between the model output and the experimental values; ; Knowledge distillation loss: measures the deviation between the fine-tuned model output and the pre-trained model output, preventing excessive deviation from the physical trends of the source domain; ; in The Latin hypercube sampling method is used to select from the input space range of the first dataset. Several points are used to ensure effective coverage of the entire input space.

[0036] Smoothness constraint loss: ensures that the model output changes smoothly in the input space, conforming to physical continuity; .

[0037] Step S33: Perform fine-tuning: Use a smaller learning rate (e.g.) (and early stopping strategies, performed on the second dataset) Fine-tuning the training. Selecting hyperparameters through cross-validation. The optimal value.

[0038] After fine-tuning, the fusion model is obtained. The model has the following characteristics: Near the experimental point, the predicted values ​​converged to the actual experimental values, correcting the systematic bias in the simulation data; In the unexperimented region, the predicted values ​​maintain the physical trends supported by a large amount of simulation data and have good generalization ability; Step S4: Mining analytical formulas based on interpretable machine learning: The trained fusion model It is regarded as a "teacher model" and uses an interpretable machine learning algorithm to extract explicit analytical formulas.

[0039] Step S41: Construct a symbolic regression search framework: A symbolic regression algorithm based on genetic programming is employed to search for a concise expression that best fits the behavior in a function space containing the original input and its nonlinear combinations. This is due to the fusion model... It has already integrated simulation and experimental data and is continuous and smooth in the input space, so as to perform symbolic regression for teachers, which can avoid the interference of experimental data sparsity and noise on the symbolic regression process.

[0040] Define function space Generated from the following elements: Primitive variables: ; Mathematical operators: +, -, ×, ÷, exp, log, sin, tan ; constant: ; Combinatorial basis functions based on physical knowledge: wait; Step S42: Generate training data for symbolic regression: Dense sampling is performed within the input space to generate a set of query points. (generally exist to (Scale). For each query point, through the fusion model... Calculate the corresponding predicted detonation distance. The training set for symbolic regression is obtained. .

[0041] Step S43: Perform symbolic regression search: A multi-objective optimization strategy is adopted to simultaneously optimize fitting accuracy and expression complexity: ; in: Mean square error: ; Complexity metric: Defined as the total number of nodes in the expression tree, or a weighted sum based on the number of operators; The search is performed using a genetic programming algorithm: P1. Initialization: Randomly generate the initial population. ; P2. Fitness assessment: Calculate the multi-objective fitness of each individual; P3. Selection: Select the best individuals using either tournament selection or Pareto sorting; P4. Genetic operations: New individuals are generated through crossover (exchanging subtrees) and mutation (replacing subtrees); P5. Iteration: Repeat steps P2-P4 until the maximum algebra or convergence condition is reached.

[0042] Step S44: Select the final analytical formula: Expressions on the Pareto front are selected from the final population; these are candidate formulas that have the minimum MSE for a given complexity. A manual screening process, incorporating physical plausibility, selects expressions that are concise, physically intuitive, and have high fitting accuracy as the final analytical formulas.

[0043] The general form of the final analytical formula can be expressed as: ; in For basis functions found from symbolic regression (such as wait), These are coefficients to be determined.

[0044] For example, for hydrogen fuel, the analytical formula that might be obtained is: ; For ethylene fuel, the possible forms are: ; Step S5: Construct and apply the detonation criterion: Detonation criteria are constructed based on the obtained analytical formula and used for engineering design and performance evaluation.

[0045] Step S51: Calculate the predicted detonation distance: For a given target working condition Select the corresponding analytical formula or general formula based on the fuel type, substitute the parameters, and calculate the predicted detonation distance. .

[0046] Step S52: Obtain the actual length of the wedge surface: Obtain the actual length of the wedge in the combustion chamber design (Unit: meters).

[0047] Step S53: Generate detonation criteria: Based on the comparison between the wedge length and the detonation distance, a detonation criterion is constructed: like The determination is "successful detonation": the length provided by the wedge is sufficient to support the formation and stabilization of the detonation wave; like The result was determined to be "detonation failure": the wedge length was insufficient to form a stable oblique detonation.

[0048] Step S54, applied to combustion chamber design optimization: Integrate the detonation criteria into the combustion chamber design process: Preliminary design: Determine the target detonation distance and the minimum wedge length required for reverse thrust based on flight conditions; Scheme evaluation: For a given combustion chamber design scheme, calculate the probability of successful detonation under different operating conditions; Parameter sensitivity analysis: Analyze the influence of each parameter on the detonation distance using analytical formulas to identify key design parameters; Multi-objective optimization: Combining detonation criteria with performance indicators such as total pressure loss and combustion efficiency, multi-objective optimization design is carried out.

[0049] Preferred technical solution Preferred Scheme 1: The derived features constructed in steps S1-2 also include flow characteristic parameters such as shock wave uncoating distance and boundary layer thickness, so as to more comprehensively characterize the influence of near-wall flow on the detonation process.

[0050] Preferred Option 2: The deep neural network in step S2-1 adopts a physical information-based architecture design, embedding the oblique shock wave relation as a prior layer in the network to ensure that the model output strictly satisfies the basic laws of gas dynamics.

[0051] Preferred Option 3: The knowledge distillation loss in step S3-2 is weighted, with lower weights assigned to distillation samples closer to the experimental point and higher weights assigned to samples farther from the experimental point, in order to better balance experimental fit and physical preservation.

[0052] Preferred Option 4: The symbolic regression algorithm in step S4-3 adopts an alternative method based on sparse regression (such as the SINDy algorithm). By constructing a dictionary containing a large number of candidate basis functions, the analytical expression is obtained by solving the sparse linear regression problem. ; in, Let be the candidate basis function matrix. This is the coefficient vector.

[0053] Preferred Option 5: The detonation criterion in step S5 further considers the safety margin and introduces a safety factor. The criterion is amended as follows: like It was determined to be "reliable detonation"; like It was determined to be "critical detonation"; like The result was determined to be "detonation failure".

[0054] Taking the prediction of the detonation distance of hydrogen fuel as an example, the details are as follows: like Figure 1 As shown, step S1, data preparation: For hydrogen fuel, collect data from multiple sources: First dataset (simulation data): 2000 sets of operating conditions were calculated through numerical simulation to determine the Mach number of the incoming flow. Value range 5-9, wedge angle Range of values Equivalent ratio Range of values The Latin hypercube sampling method was used to uniformly sample within the design space, obtaining 2000 sets of input parameter combinations. The detonation distance under various operating conditions was calculated through high-precision numerical simulation (using a detailed hydrogen mechanism involving 9 components and 19 steps), yielding simulated values. There are systematic biases in the simulation data; the calculated detonation distance for some simulation data is as follows: Figure 5 As shown, the main issue is that the detonation distance is underestimated in the low Mach number region and overestimated in the high Mach number region.

[0055] The second dataset (experimental data): Through shock tunnel experiments, 36 of the most representative operating conditions were selected (using D-optimal design selection), and the true values ​​of the detonation distance were measured. The experimental measurement uncertainty was controlled within ±5%.

[0056] Step S2: Construct derived features: Based on steps S1-S2, calculate the derived features for each sample: Post-shock temperature : coming from static temperature Based on this, calculations are performed according to the oblique shock wave relation.

[0057] Characteristic reaction time of hydrogen Based on a simplified mechanism Seconds, Damköhler number The corresponding dynamic limit theory calculation results are as follows: Figure 6 As shown.

[0058] Step S3: Pre-training deep neural network: Building deep neural networks: Input layer: 6 nodes ; in, ; Hidden layers: 4 layers, with 128, 64, 32, and 16 nodes respectively; Output layer: 1 node; The Adam optimizer is used, with an initial learning rate of 1. Batch size 64, training for 200 epochs. Physical regularization coefficient. After pre-training, the model's MSE on the simulation test set was 0.0025. .

[0059] Step S4, Migration Fine-tuning: The parameters of the first two layers of the network are frozen, and the parameters of the last two layers are fine-tuned. A schematic diagram of this fine-tuning strategy is shown below. Figure 2 As shown. The fine-tuning learning rate is set to... Knowledge distillation weights; Smoothing constraint weights The training was performed for 50 epochs across 36 experimental sites, employing an early stopping strategy to prevent overfitting.

[0060] After fine-tuning, the MSE of the fusion model at the experimental points was 0.0018 m. 2 Compared to the pre-trained model, the MSE at the experimental points is 0.0032 m. 2 The detonation distance prediction results under different operating conditions were reduced by 43.8%. Figure 7 As shown. Among them, Figure 7 (a) The operating condition corresponding to the incoming Mach number Ma=6 and the wedge angle θ=25°. Figure 7 (b) For the working condition Ma=7, θ=30° Figure 7 (c) Corresponding to the working condition of Ma=8, θ=35°. From Figure 7 It can be seen that the pre-trained model (blue curve) has a generally correct trend but exhibits deviations at experimental points, while the fusion model (green curve) closely matches the true values ​​at experimental points (red dots) while maintaining the physical trend in non-experimental regions. A comparison of the experimental point prediction errors of this method and traditional methods is shown below. Figure 9 As shown.

[0061] Furthermore, the prediction results of this method for the kinetic limit (i.e., the detonation boundary) are as follows: Figure 8 As shown, it also has high precision. Figure 8 (a) Different equivalent ratios under the Ma=6 working condition A comparison of the detonation limits Figure 8 (b) Corresponding to the Ma=7 working condition. Figure 8 (c) Corresponding to Ma=8. In the figure, the solid red line represents the limit boundary predicted by this method, the dashed blue line represents the predicted value of the pure simulation model, and the black dots represent the experimental measurement value. The results show that the fusion model can more accurately capture the experimentally measured detonation limit, especially in the low equivalence ratio region, significantly correcting the systematic bias of the simulation data.

[0062] Step S5, Formula Mining: 50,000 points are uniformly sampled in the input space, and the corresponding detonation distance prediction value is obtained through the fusion model to construct a symbolic regression training set.

[0063] A symbolic regression algorithm based on genetic programming (PySR library) was used for the search, with a population size of 500 and 100 generations. The optimal expression on the Pareto front obtained is: ; The complexity of this expression is 2^8 (number of nodes), which is 2^8 on the test set. Maximum relative error Pareto frontier of symbolic regression, such as Figure 3 As shown.

[0064] Step S6, Application of detonation criteria: Design of a certain inclined detonation combustion chamber, wedge length For design point conditions Substitute into the analytical formula to calculate: ; because If the detonation is deemed successful, then... Figure 4 As shown.

[0065] Industrial applicability: The method and system provided by this invention can be applied to the following scenarios: (1) Design of the combustion chamber of the oblique detonation engine: In the preliminary design stage, quickly evaluate the detonation performance of different combustion chamber configurations (wedge length, wedge angle) under different flight conditions, reduce the design space, and reduce the number of expensive CFD calculations and wind tunnel experiments.

[0066] (2) Fuel adaptability assessment: For different fuels (hydrogen, ethylene, acetylene, etc.), the initiation characteristics are quickly compared using analytical formulas to provide a basis for fuel selection and combustion chamber adaptability.

[0067] (3) Flight envelope analysis: Combined with the flight trajectory, analyze the detonation reliability of the aircraft within the entire flight envelope and identify the risk areas that may fail.

[0068] (4) Real-time monitoring and control: The analytical formula is embedded in the airborne computer to predict the detonation state based on the real-time incoming flow parameters, providing a decision basis for active control (such as jet detonation assistance).

[0069] 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 preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A multi-source data fusion and interpretable deep learning oblique detonation initiation prediction method, characterized in that, Includes the following steps: Step S1: Construct a multi-source heterogeneous dataset, including a first dataset and a second dataset; the first dataset comes from theoretical analysis and numerical simulation, with a large sample size but systematic bias; the second dataset comes from experimental measurement, with a small sample size but high accuracy; Features of the dataset include incoming Mach number , wedge angle , equivalence ratio , gas fuel type , and derived features constructed based on physical knowledge; Step S2: Construct a deep neural network as the base model and pre-train it using the first dataset to learn the macroscopic physical trend of the detonation distance changing with the working conditions; Step S3: transfer fine-tuning of the pre-trained model using the second data set, realize multi-source data fusion at the model level, and obtain a fusion model ; Step S4: using an interpretable machine learning algorithm to fuse the models to the teacher model, extracting explicit break-out distance analytical formulas ; Step S5: Calculate the predicted initiation distance based on the analytical formula , and the actual length of the given wedge face , and the actual length of the given wedge face , and the actual length of the given wedge face , and the actual length of the given wedge face 2. The method for predicting oblique detonation initiation using multi-source data fusion and interpretable deep learning as described in claim 1, characterized in that, The derived characteristics in step S1 include one or more of:• Shock wave temperature • Shock wave pressure • Reactivity parameter combination • Damköhler number • Combined dimensionless number wherein, is the characteristic chemical reaction time of the fuel, is the activation energy, is the gas constant.

3. The multi-source data fusion and interpretable deep learning oblique detonation initiation prediction method according to claim 1, characterized in that, The deep neural network in step S2 employs a multi-layer feedforward architecture, and the pre-training loss function includes a data fitting term and a physics-based regularization term: ； wherein and are a priori estimates of the derivative of the initiation distance with respect to the Mach number and the wedge angle, obtained on the basis of theoretical analysis.

4. The multi-source data fusion and interpretable deep learning oblique detonation initiation prediction method according to claim 1, characterized in that, In step S3, the transfer fine-tuning employs a parameter freezing strategy, preserving the underlying parameters of the pre-trained model while fine-tuning the higher-level parameters. The fine-tuning loss function includes experimental fitting loss, knowledge distillation loss, and smoothness constraint loss, with the total loss function taking the form: ； wherein, is the total number of samples in the second data set, is the predicted initiation distance of the fusion model input with the is the actual measured initiation distance of the is the actual measured initiation distance of the is the actual measured initiation distance of the is the weight coefficient of the knowledge distillation loss, used to balance the experimental fitting and the preservation of the source domain knowledge, is the number of subset samples extracted from the first data set for distillation, is the predicted initiation distance of the fusion model input with the is the predicted initiation distance of the fusion model input with the is the predicted initiation distance of the pre-trained model input with the same distillation sample; is the weight coefficient of the smoothness constraint loss, is the number of sampling points used to calculate the smoothness constraint, is the partial derivative of the fusion model output with respect to the is the partial derivative of the fusion model output with respect to the 5. The method for predicting oblique detonation initiation using multi-source data fusion and interpretable deep learning as described in claim 1, characterized in that, The interpretable machine learning algorithm in step S4 employs either genetic programming-based symbolic regression or the SINDy algorithm based on sparse regression; the search objective of symbolic regression is to simultaneously minimize the fitting error and the complexity of the expression. ； in, This is the function space generated by a combination of primitive variables, mathematical operators, and basis functions based on physical knowledge.

6. The method for predicting oblique detonation initiation using multi-source data fusion and interpretable deep learning as described in claim 1, characterized in that, The analytical formula extracted in step S4 has the following general form: ； in, For undetermined coefficients, The basis functions found from symbolic regression include: One or more of them.

7. The method for predicting oblique detonation initiation using multi-source data fusion and interpretable deep learning as described in claim 1, characterized in that, Gaseous fuels include one or more of hydrogen, ethylene, and acetylene; fuel types are identified by their chemical kinetic parameters. Continuous representations, rather than inputs as discrete categorical variables, where Characteristic chemical reaction time, For activation energy, It is a pre-exponential factor.

8. The method for predicting oblique detonation initiation using multi-source data fusion and interpretable deep learning as described in claim 1, characterized in that, The detonation criterion in step S5 further incorporates a safety factor. The criteria are expanded to a multi-level decision: like It was determined to be "reliable detonation"; like It was determined to be "critical detonation"; like The result was determined to be "detonation failure".

9. The method for predicting oblique detonation initiation using multi-source data fusion and interpretable deep learning as described in claim 1, characterized in that, The system implementing the above method includes: a data acquisition and processing module for collecting and processing multi-source heterogeneous data and constructing derived features; a deep neural network pre-training module for pre-training the model using the first dataset; a transfer learning fine-tuning module for fine-tuning the pre-trained model using the second dataset to obtain a fusion model; an interpretable analytical formula extraction module for extracting explicit analytical formulas from the fusion model using a symbolic regression algorithm; and an initiation criterion generation and application module for calculating the predicted initiation distance based on the analytical formula, comparing it with the actual length of the wedge to generate an initiation criterion, and applying it to the combustion chamber design evaluation.

10. The method for predicting oblique detonation initiation using multi-source data fusion and interpretable deep learning as described in claim 9, characterized in that, The detonation criterion generation and application module is also used to output the generated detonation criteria to the combustion chamber design unit, fuel adaptability assessment unit, flight envelope analysis unit, or real-time detonation status monitoring unit of the oblique detonation engine, so as to guide the combustion chamber structure design, select suitable fuels, assess the detonation reliability within the flight envelope, or generate active control commands.

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