A supersonic isolated section flow field reconstruction method integrating CNN and FCNN

Abstract

This invention relates to the field of high-altitude work equipment technology and discloses a method for reconstructing the flow field in a supersonic isolation section by integrating CNN and FCNN. The method includes the following steps: acquiring wall pressure data and schlieren image sequences in a wind tunnel test system; using synchronous light signals for time alignment and preprocessing; constructing a training dataset containing normalized pressure feature vectors and a matrix of real flow field schlieren images; constructing a parallel dual-branch deep learning model; using a convolutional neural network branch to reshape the pressure data into a matrix to extract spatial structure features; and using a fully connected neural network branch to directly extract numerical correlation features. The outputs of both are merged in a feature fusion layer. After optimizing the model parameters using the training dataset, the real-time acquired wall pressure is input into the trained model, and the reconstructed flow field grayscale image is output. This invention solves the problem of difficulty in reconstructing complex flow fields from sparse pressure data and achieves high-precision real-time monitoring of the flow field in a supersonic isolation section.

Description

Technical Field

[0001] This invention relates to the field of high-altitude work equipment technology, specifically to a supersonic isolation section flow field reconstruction method that integrates CNN and FCNN. Background Technology

[0002] The supersonic isolator is a core aerodynamic component in the propulsion system of an air-breathing hypersonic vehicle, located between the inlet throat and the combustion chamber inlet. The internal flow field of the isolator exhibits complex shock wave and boundary layer interactions, forming a shock train structure that effectively prevents back pressure from the combustion chamber from propagating forward and interfering with the inlet startup. Understanding the flow field parameter distribution and shock train evolution within the isolator is crucial for ensuring the stable operation of the propulsion system across its wide flight envelope and for implementing active flow control strategies.

[0003] Existing methods for acquiring supersonic flow fields mainly fall into two categories: computational fluid dynamics (CFD) numerical simulation and experimental measurement. CFD numerical simulation, based on physical conservation laws, solves the fluid control equations and provides detailed information about the entire flow field. Experimental measurement methods primarily rely on pressure sensors mounted on the flow channel walls for contact measurements, or utilize optical equipment such as schlieren and particle image velocimeters for non-contact measurements. Wall pressure measurement methods are characterized by high response frequency, simple structure, high temperature resistance, and ease of integration, making them a primary data acquisition source for aircraft engineering applications.

[0004] Computational fluid dynamics numerical simulation methods require complex mesh generation and lengthy iterative calculations, resulting in low computational efficiency and failing to meet the need for millisecond-level real-time monitoring of flow field states during aircraft flight. Optical measurement equipment systems are complex, bulky, and require extremely high optical path collimation, making them difficult to implement on flight platforms with severe vibrations and limited space. Sparse pressure data obtained solely from wall pressure sensors can only reflect local pressure changes at the flow channel boundary and cannot directly observe the shock wave structure and flow field topology in the central region inside the isolation section. Existing methods for inverting the flow field using pressure data are limited by insufficient feature extraction capabilities, making it difficult to establish a high-precision nonlinear mapping model between sparse one-dimensional pressure values ​​and dense two-dimensional flow field images. This results in blurred details in the reconstructed flow field images, failing to accurately capture the fine structure of shock waves. Therefore, this invention proposes a supersonic isolation section flow field reconstruction method integrating CNN and FCNN to address the shortcomings of existing technologies. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention provides a supersonic isolation section flow field reconstruction method that integrates CNN and FCNN, solving the problem in existing technologies that it is difficult to use sparse wall pressure data to perform high-precision, real-time reconstruction of the complex flow field structure inside the supersonic isolation section.

[0006] To achieve the above objectives, the present invention provides the following technical solution: a method for reconstructing the flow field in a supersonic isolation section based on the fusion of convolutional neural networks and fully connected neural networks, comprising the following steps: In the supersonic direct-drive wind tunnel test system, a pressure sensor array is used to collect wall pressure data sequences, and a schlieren imaging system is used to collect flow field schlieren image sequences. The wall pressure data sequence and the flow field schlieren image sequence are time-synchronized, aligned, and preprocessed to construct a training dataset containing normalized pressure feature vectors and real flow field schlieren image matrices. A parallel dual-branch deep learning model is constructed, which includes a parallel convolutional neural network branch and a fully connected neural network branch, as well as a feature fusion layer and an output reconstruction layer connected to the outputs of the two. The convolutional neural network branch is configured to reshape the input normalized stress feature vector into a two-dimensional matrix to extract spatial structure features, and the fully connected neural network branch is configured to directly process the normalized stress feature vector to extract numerical correlation features. The parallel dual-branch deep learning model is trained using the training dataset, and the model parameters are iteratively updated by minimizing the loss function to obtain the trained parallel dual-branch deep learning model. The real-time wall pressure data is input into the trained parallel dual-branch deep learning model, and the reconstructed flow field grayscale image is output.

[0007] Preferably, the time synchronization alignment specifically includes: determining the zero point of time using the synchronization light signal generated by the laser light-emitting diode; retrieving the data sequence recording the voltage signal of the laser light-emitting diode and the image sequence containing the light emission state of the laser light-emitting diode respectively, and determining their respective starting indices; calculating the extraction step size according to the ratio of the wall pressure sampling frequency to the schlieren image shooting frame rate, and establishing an index mapping relationship between each frame of schlieren image and the original pressure data points based on the extraction step size, so as to achieve a one-to-one correspondence of data.

[0008] Preferably, the construction of the normalized pressure feature vector specifically includes: selecting equidistant pressure sensors located on the lower wall of the isolation section test piece and back pressure sensors at the outlet from the pressure sensor group to form a sensor subset; establishing a first-in-first-out data cache queue, performing an arithmetic mean calculation based on a sliding time window on the original pressure data of the sensor subset to obtain a smoothed pressure value; obtaining the maximum and minimum pressure values ​​in historical test samples, performing min-max normalization processing on the smoothed pressure value, and generating the normalized pressure feature vector.

[0009] Preferably, the construction of the real flow field schlieren image matrix specifically includes: cropping an image portion containing only the visible area of ​​the flow field inside the isolation section from the original schlieren image using a pixel coordinate mask; performing spatial dimension downsampling compression on the cropped image using a bilinear interpolation algorithm; enhancing and denoising the image using a Laplacian sharpening operator and a Gaussian smoothing filter; and mapping the image pixel grayscale values ​​to floating-point numbers between zero and one.

[0010] Preferably, the construction method of the convolutional neural network branch includes: setting a fully connected initialization layer to map and reshape the normalized pressure feature vector into a three-dimensional initial feature tensor with height, width, and number of channels; setting a transposed convolutional layer to upsample the three-dimensional initial feature tensor to enlarge the spatial size; setting a deep feature extraction module composed of multiple cascaded two-dimensional convolutional layers to extract the topological features of the flow field space; and setting a feature compression vectorization module including a max pooling layer and a flattening layer to output a one-dimensional convolutional feature vector.

[0011] Preferably, each two-dimensional convolutional layer in the deep feature extraction module adopts an edge-filling strategy to keep the feature map space size unchanged, and as the number of layers increases, the number of output channels of each two-dimensional convolutional layer increases layer by layer.

[0012] Preferably, the fully connected neural network branch adopts a multilayer perceptron architecture, which includes multiple fully connected layers connected in sequence; each of the multiple fully connected layers uses a weight matrix to perform a linear transformation on the input vector and superimposes a bias vector, and then outputs it through a rectified linear unit activation function; the fully connected neural network branch finally outputs a one-dimensional fully connected feature vector.

[0013] Preferably, the feature fusion layer performs a vector concatenation operation, merging the convolutional feature vectors output by the convolutional neural network branch and the fully connected feature vectors output by the fully connected neural network branch in the channel dimension to generate a joint feature vector; the output reconstruction layer includes a fusion fully connected layer and an output fully connected layer, the number of neurons in the output fully connected layer is equal to the total number of pixels in the target flow field image, and is configured to map the features back to the pixel space and reshape them into a two-dimensional reconstructed flow field grayscale image matrix.

[0014] Preferably, the step of iteratively updating the model parameters by minimizing the loss function employs a mean squared error function; the mean squared error function is used to calculate the average of the sum of squares of the differences in grayscale values ​​between the reconstructed flow field grayscale image matrix output by the model and the real flow field schlieren image matrix at each corresponding pixel position.

[0015] Preferably, training the parallel dual-branch deep learning model using the training dataset specifically includes: initializing the model weight parameters using a normal distribution initialization method; selecting an adaptive moment estimation optimizer and adjusting the learning rate to update the model parameters based on the exponential moving average of the gradient; and executing a learning rate decay strategy at preset epoch intervals during the training process.

[0016] This invention provides a method for reconstructing the supersonic isolated flow field by integrating CNN and FCNN. It has the following beneficial effects: 1. This invention constructs a parallel dual-branch deep learning model that includes a convolutional neural network branch and a fully connected neural network branch. It can simultaneously use the convolutional neural network to extract the spatial topological features after the pressure distribution is reshaped, and use the fully connected neural network to extract the nonlinear correlation features of the pressure numerical sequence. The two types of features are merged in the channel dimension through a feature fusion layer, so that the model has both the ability to perceive the spatial structure of the flow field and retains the sensitivity of the original values. This improves the accuracy of reconstructing dense flow field schlieren images from sparse wall pressure data and can restore the shock train structure in the supersonic isolation section.

[0017] 2. This invention utilizes the synchronization light signal generated by a laser light-emitting diode as a physical reference to establish a strict time alignment relationship between the wall pressure data sequence and the flow field schlieren image sequence at different sampling frequencies. Furthermore, it employs an arithmetic mean calculation based on a sliding time window to denoise the original pressure data. This hardware signal-based synchronization mechanism and data preprocessing strategy eliminates timing deviations between multimodal data acquisition systems, suppresses interference from high-frequency sensor noise on model training, ensures high quality and strong coupling of the training dataset, and thus improves the model's generalization ability.

[0018] 3. This invention utilizes a pre-trained parallel dual-branch deep learning model to establish an end-to-end mapping relationship from low-dimensional wall pressure data to high-dimensional flow field grayscale images. In practical applications, it eliminates the need for a schlieren imaging system; only real-time acquired wall pressure data needs to be input to output a visualized flow field image. Compared to traditional computational fluid dynamics numerical simulation methods, this invention avoids complex mesh generation and iterative calculation processes, reduces the time delay of flow field reconstruction, and achieves non-contact real-time monitoring of the flow field state inside the supersonic isolation section. Attached Figure Description

[0019] Figure 1 This is a three-dimensional diagram of the experimental system architecture of the present invention; Figure 2 This is a schematic diagram of the system architecture of the present invention; Figure 3 This is a schematic diagram of the overall process of the method of the present invention.

[0020] The components include: 1. Storage tank; 2. Pneumatic control valve; 3. Stabilization section; 4. Nozzle; 5. Isolation section test piece; 6. Exhaust pipe; 7. Fused silica observation window; 8. Back pressure baffle device; 9. Servo motor; 10. Pressure sensor group; 11. Data acquisition system; 12. Z-type schlieren imaging system; 13. High-speed camera; and 14. Laser light-emitting diode. Detailed Implementation

[0021] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0022] See attached document Figure 1 With appendix Figure 2 The present invention provides a supersonic isolated section flow field reconstruction method that integrates CNN and FCNN, the execution of which depends on a supersonic direct-connection wind tunnel test system and a supporting data acquisition and synchronous observation system.

[0023] See attached document Figure 1 The supersonic direct-drive wind tunnel testing system comprises, in sequence along the airflow direction: a high-pressure air storage tank 1, a pneumatic control valve 2, a stabilization section 3, a nozzle 4, an isolation section test piece 5, and an exhaust pipe 6. The high-pressure air storage tank 1 provides the high-pressure air source required for the test; its total pressure is set at 13 MPa, and its volume is 10 cubic meters. The pneumatic control valve 2 is located downstream of the high-pressure air storage tank 1 and is used to control the opening and closing of the airflow. The stabilization section 3 connects the pneumatic control valve 2 and the nozzle 4, and is used to rectify the airflow to obtain uniform incoming flow conditions. The nozzle 4 is selected with different profiles according to the test requirements to generate supersonic airflow at a specific Mach number. In this embodiment, by changing the nozzle 4, incoming flow conditions with inlet Mach numbers of 1.8 and 2.4 are obtained respectively.

[0024] The isolation section test piece 5 is connected downstream of the nozzle 4, with a flow channel cross-section of 50 mm wide, 30 mm high, and 320 mm long. Fused silica observation windows 7, each 260 mm long and 30 mm high, are installed on both side walls of the isolation section test piece 5 to provide a visual observation channel for the flow field. The exhaust pipe 6, with a diameter of 400 mm, is connected to the downstream outlet of the isolation section test piece 5 to discharge the gas after the test into the atmosphere.

[0025] To generate a shock train within the isolation section test specimen 5 and simulate the effect of combustion chamber back pressure on the flow field, a back pressure baffle device 8 is installed at the top of the outlet of the isolation section test specimen 5. The back pressure baffle device 8 includes a mechanical baffle disposed inside the flow channel and a servo motor 9 that drives the mechanical baffle to rotate. The mechanical baffle is installed at the bottom position 30 mm from the top of the isolation section test specimen 5. The servo motor 9 has an output torque of 15 N·m, a power of 2.5 kW, an angular resolution of 0.006 degrees, and a maximum response angular velocity of 11 degrees / second. Before the test begins, the mechanical baffle angle is set to 0 degrees, in a fully raised state; during the test, the servo motor 9 drives the mechanical baffle to increase the angle, reducing the flow channel outlet area, thereby increasing the outlet back pressure through physical throttling, and inducing a shock train structure inside the isolation section test specimen 5.

[0026] See attached document Figure 2 To obtain wall pressure distribution data of the flow field, pressure sensor arrays 10 are symmetrically arranged along the centerline on the upper and lower walls of the isolation section test specimen 5. The pressure sensor array 10 includes a first pressure sensor array 10a (corresponding to measurement points T1 to T10) arranged on the upper wall and a second pressure sensor array 10b (corresponding to measurement points T11 to T20) arranged on the lower wall, totaling 20 dynamic pressure sensors. In addition, a back pressure sensor 10c (corresponding to measurement point BT) is installed at the outlet of the isolation section test specimen 5 to measure the outlet back pressure value. The pressure sensor array 10 uses the TMNS-3 model, with a measurement range of 0 to 1 MPa, an effective response frequency of 20 kHz, and a comprehensive measurement accuracy of ±0.1%.

[0027] All output channels of the pressure sensor group 10 are connected to the data acquisition system 11. The data acquisition system 11 includes two high-speed voltage input modules, model IOtech6220. The data acquisition system 11 is configured with a sampling frequency of 10 kHz for recording the voltage signal sequence output by each pressure sensor.

[0028] See attached document Figure 2 To obtain a true flow field structure image of the internal flow field of the isolation section as a reconstruction target, a Z-type schlieren imaging system 12 was deployed at the test site. The optical path of the Z-type schlieren imaging system 12 passes through the fused silica observation windows 7 on both sides of the isolation section test specimen 5. The Z-type schlieren imaging system 12 is equipped with a high-speed camera 13, model PhantomV12, used to record transient schlieren images of the flow field. The spatial resolution of the high-speed camera 13 is configured as 1280 pixels by 300 pixels, covering the visualization area of ​​the isolation section test specimen 5. The exposure time of the high-speed camera 13 is set to 0.2 milliseconds, and the shooting frame rate is set to 1000 frames per second.

[0029] To ensure the temporal consistency between the pressure data collected by the pressure sensor group 10 and the schlieren image captured by the high-speed camera 13, the system is equipped with a synchronization triggering device. This device includes a laser light-emitting diode 14 connected to one input channel of the data acquisition system 11. The data acquisition system 11 synchronously records the pressure signal from the pressure sensor group 10 and the voltage signal from the laser light-emitting diode 14, marking the time origin by the changes in the brightness of the laser light-emitting diode 14, thereby achieving time alignment between the pressure data sequence and the image data sequence.

[0030] After acquiring the raw wall pressure data, in order to eliminate sensor range differences and meet the input requirements of the subsequent neural network model, the pressure data needs to be dimensionless. Define any time... The original pressure value at any measuring point collected by the pressure sensor group 10 is The normalized pressure value after processing Calculate according to the following formula: ; in, This shows the original pressure value at any measuring point measured by the pressure sensor group 10; This indicates the minimum pressure value recorded at the measuring point throughout the entire test. This indicates the maximum pressure value recorded at the measuring point throughout the entire test; This represents the normalized pressure value after minimum-maximum normalization, and its value ranges from 0 to 1. This forms the basis of the input data for the subsequent flow field reconstruction model.

[0031] See attached document Figure 3 In the supersonic isolation section flow field reconstruction task, constructing a high-quality training dataset is the foundation for model training. Since the sampling frequency of the data acquisition system 11 for acquiring wall pressure data is not consistent with the frame rate of the high-speed camera 13 for capturing schlieren images, and the two are controlled by different hardware clocks, strict time synchronization and data alignment operations must be performed to establish a one-to-one correspondence between the wall pressure state and the flow field structure.

[0032] In this embodiment, the wall pressure sampling frequency configured in the data acquisition system 11 is... The frequency is 10,000 Hz, meaning 10,000 pressure data points are collected per second; while the high-speed camera 13 is equipped with a schlieren image capture frame rate of 10,000 Hz. The sampling rate is 1000 frames per second. Because the wall pressure sampling frequency is higher than the schlieren image capture frame rate, the raw pressure data sequence recorded by the data acquisition system 11 contains redundant data relative to the schlieren image sequence. To eliminate the frequency difference and achieve data alignment, this invention employs a fixed-step decimation method based on a hardware trigger signal.

[0033] First, the zero point of time is determined using the synchronization light signal generated by the laser light-emitting diode 14. During the experiment's initiation phase, an analog voltage input channel of the data acquisition system 11 records the voltage signal across the laser light-emitting diode 14 in real time. Simultaneously, the high-speed camera 13 captures a field-of-view image including the luminous state of the laser light-emitting diode 14. The moment when the back pressure baffle device 8 begins to operate (i.e., the moment when the back pressure begins to change) is defined as the experiment's time origin. During data processing, the voltage signal sequence recorded by the data acquisition system 11 is retrieved, and the moment when the voltage signal undergoes a step change is marked as the starting index of the pressure data sequence. Simultaneously, the image sequence captured by the high-speed camera 13 is retrieved, and frames where the brightness of the laser light-emitting diode 14 changes abruptly are marked as the starting frame index of the image sequence. .

[0034] After establishing the time origin, the extraction step size is calculated based on the ratio between the pressure sampling frequency and the image capture frame rate. Extract step size The calculation formula is as follows: ; in, This indicates the wall pressure sampling frequency configured in the data acquisition system 11; This indicates the frame rate at which the high-speed camera 13 captures schlieren images.

[0035] Based on extraction step size The original pressure data sequence is downsampled to match the image sequence. For the first image in the image sequence... Frame Schlieren Image The corresponding wall pressure data vector Extracted from the original pressure data sequence, the extraction rules satisfy the following index mapping relationship: ; in, This indicates the frame number of the currently processed schlieren image in the original image sequence; The frame where the brightness of the laser light-emitting diode 14 suddenly changes is marked as the starting frame index of the image sequence; This indicates that the moment when the voltage signal undergoes a step change is marked as the starting index of the pressure data sequence; Indicates the extraction step size; Indicates the relationship with the first The frame schlieren image precisely corresponds in time to the index position of the original pressure data point in the pressure data sequence.

[0036] Through the aforementioned synchronization and extraction steps, the continuously acquired wall pressure time series is converted into a discrete pressure sample vector sequence, and the continuously captured schlieren video stream is converted into a discrete flow field image matrix sequence. Each pressure sample vector and a flow field schlieren image matrix acquired at the same time form a training sample pair. In this embodiment, by processing experimental data with an isolation section inlet Mach number of 1.8 and an isolation section inlet Mach number of 2.4, 10,000 sample pairs are generated respectively, ultimately constructing an isolation section flow field reconstruction dataset containing 20,000 sample pairs. This dataset covers the complete dynamic evolution process of the shock train from generation and upstream movement to unsteady oscillation, providing spatiotemporal correlation data containing rich flow field features for subsequent neural network model training.

[0037] See attached document Figure 3 When constructing a supervised learning dataset for training deep neural networks, the original schlieren image sequence acquired by the high-speed camera 13 is used as the target label for flow field reconstruction. Since the original schlieren images contain background interference from the test bench and have too high data dimensionality, direct use will introduce redundant features and increase computational overhead. Therefore, a series of standardized preprocessing steps are required to convert the original schlieren images into a standardized flow field grayscale matrix.

[0038] First, a region of interest (ROI) cropping operation is performed on the image. Since the field of view of the high-speed camera 13 covers not only the internal flow channel region of the isolation section test piece 5, but also the metal frame, mounting brackets, and other laboratory background environment outside the upper and lower walls of the isolation section test piece 5, the pixel information of these non-flow field regions is invalid interference information for the flow field reconstruction task. Therefore, using a pre-set pixel coordinate mask, the image portion containing only the visible area of ​​the internal flow field of the isolation section is cropped from each frame of the original schlieren image. The cropped image retains the shock train structure, boundary layer, and background wave system characteristics within the isolation section flow channel, while removing the imaging areas of all external experimental devices.

[0039] Secondly, downsampling is performed on the cropped image. The original schlieren image has a high spatial resolution and dense pixels. Directly using it as the output target of the neural network would cause the number of parameters in the network output layer to increase exponentially, exceeding the memory load of the edge computing device. In this embodiment, a bilinear interpolation algorithm is used to compress the spatial dimension of the cropped high-resolution image, uniformly adjusting the image size to 40 pixels (height direction) multiplied by 319 pixels (width direction). The dimension of the downsampled image matrix is ​​40×319, which directly determines the total number of nodes in the output layer of the subsequent neural network model. Despite the reduced resolution, the image matrix of this size still completely preserves the key flow field topological features such as the shock wave leading edge position, shock wave tilt angle, and wave system intersection points.

[0040] Furthermore, to highlight the high-frequency features in the flow field and suppress sensor thermal noise, the downsampled image was sharpened and denoised. Since schlieren imaging essentially visualizes the first or second derivative of the flow field density gradient optically, the shock wave location appears as an edge feature where light and dark meet. By applying the Laplacian sharpening operator to convolve the image, the contrast of the shock wave edges in the image was enhanced, making the shock wave structure clearly discernible even in low-resolution images. Simultaneously, a Gaussian smoothing filter was used to slightly smooth the image to remove random isolated noise points caused by camera sensor light-sensing noise, ensuring that changes in image grayscale values ​​only reflect changes in flow field density.

[0041] Finally, the image pixel grayscale values ​​are normalized. The original schlieren image has a pixel depth of 8 bits, and its grayscale values ​​are... The value range is 0 to 255 (where 0 represents pure black and 255 represents pure white). To adapt to the sensitive range of the neural network activation function and accelerate the convergence of the gradient descent algorithm, integer pixel gray values ​​are mapped to floating-point numbers between 0 and 1. For any coordinate in the image matrix... pixel grayscale value at Its normalized pixel value Calculate using the following formula: ; in, Represents arbitrary coordinates in the image matrix The pixel grayscale value at that location; This represents the maximum possible number of gray levels in an 8-bit grayscale image. This represents the pixel value after normalization in the neural network loss function.

[0042] After the above cropping, downsampling, enhancement, and normalization processes, each frame of schlieren image is transformed into a two-dimensional matrix with values ​​distributed between 0 and 1. This two-dimensional matrix, together with the wall pressure vector synchronized in the previous steps, constitutes a complete training sample, which is stored in the training database for model learning.

[0043] See attached document Figure 3 Before inputting the physical pressure signal into the neural network model, feature filtering, noise smoothing and numerical normalization must be performed on the raw voltage signal output by the data acquisition system 11 to construct an input feature vector with high signal-to-noise ratio and consistent numerical distribution.

[0044] First, a feature selection operation for sparse pressure measurement points is performed. Although 20 pressure sensors and 1 back pressure sensor are arranged on the upper and lower walls of the isolation section test piece 5, in this embodiment, in order to reduce the computational load of the edge computing device and improve the model inference speed, a feature dimensionality reduction strategy is adopted to select a specific subset of sensors from all available sensors as key feature inputs. Specifically, the selected sensor subset includes pressure sensor T12 (number 12), pressure sensor T14 (number 14), pressure sensor T16 (number 16), pressure sensor T18 (number 18), and pressure sensor T20 (number 20) arranged on the lower wall of the isolation section test piece 5, and back pressure sensor T21 arranged at the outlet of the isolation section test piece 5. This sensor subset covers five equally spaced measurement points distributed along the flow direction and one outlet boundary condition measurement point, for a total of 6 pressure measurement points. The data processing module extracts only the pressure value sequences corresponding to the 6 pressure measurement points and discards the data of the remaining measurement points, thereby fixing the input layer dimension of the neural network to 6 dimensions.

[0045] Secondly, noise smoothing based on a sliding time window is performed. Due to the complex electromagnetic interference and mechanical vibrations in the ground wind tunnel testing environment, the raw pressure data output by the pressure sensor group 10 contains high-frequency random noise and spikes. To filter out noise while preserving the dynamic changes in the flow field, this invention constructs a [missing information - likely a specific type of window or array] with a length of [missing information - likely a specific length]. A first-in, first-out (FIFO) data cache queue. In this embodiment, the cache queue length... The value is set to 10. For each pressure sensor in the aforementioned sensor subset, the system maintains an independent buffer queue in real time. When new raw pressure data... Upon arrival, Push the oldest data to the tail of the queue and remove the oldest data from the head of the queue, keeping the queue length unchanged. Then, calculate the arithmetic mean of all data in the current cache queue as the smoothed pressure value at the current moment. .

[0046] For the A selected pressure sensor at time Smooth pressure value The calculation formula is as follows: ; in, This indicates the index of the selected pressure sensor, with values ​​corresponding to T12, T14, T16, T18, T20, and T21. Indicates a time-lag index; This represents the length of the buffer queue for the moving average window (in this example, the value is 10). Indicates the first A pressure sensor in Raw pressure values ​​collected at all times; Indicates the first A pressure sensor at time Smoothed pressure value after moving average filtering.

[0047] Finally, min-max normalization of the pressure data is performed. Because the absolute magnitudes of pressure sensor measurements at different locations vary significantly (e.g., the inlet pressure and outlet back pressure of the isolation section may be on different orders of magnitude), the smoothed pressure values ​​need to be normalized to eliminate the influence of dimensions and map the data to the sensitive activation regions of the neural network. For the first... A pressure sensor at time Smooth pressure value Its normalized input pressure value Calculate using the following formula: ; in, Indicates the smoothing pressure value; Indicates the first The minimum pressure value recorded by each pressure sensor in all historical test samples used to construct the dataset; Indicates the first The maximum pressure value recorded by each pressure sensor in all historical test samples used to construct the dataset; This represents the input pressure value that is ultimately input to the input layer of the neural network model, and its value is limited to the range of 0 to 1.

[0048] After the above feature selection, moving average filtering, and normalization processing, at any time... The system generates a normalized pressure feature vector containing 6 elements. : ; Normalized pressure eigenvector It will be used directly as the input tensor of the fused neural network model.

[0049] See attached document Figure 3 This invention proposes and constructs a parallel dual-branch deep learning model that integrates convolutional neural networks and fully connected neural networks, hereinafter referred to as the PS model. The PS model aims to establish a nonlinear reconstruction mapping relationship between low-dimensional discrete wall pressure data and high-dimensional continuous flow field schlieren image data. The overall data flow structure of the PS model includes four main parts: input layer, parallel feature extraction layer, feature fusion layer, and output reconstruction layer.

[0050] The input layer of the PS model receives the normalized pressure feature vector generated by the aforementioned data preprocessing steps. In a specific embodiment, the normalized pressure feature vector It contains 6 floating-point numerical elements, corresponding to the normalized pressure values ​​at six pressure measurement points: T12, T14, T16, T18, T20, and T21. The input layer of the PS model will use the normalized pressure feature vector. Simultaneously, the data is copied and transmitted to two independent branches in the parallel feature extraction layer.

[0051] The parallel feature extraction layer of the PS model consists of a convolutional neural network (CNN) branch and a fully connected neural network (FCNN) branch. The CNN branch is configured to process spatial structure features. It first reshapes the one-dimensional normalized pressure feature vector into a two-dimensional feature matrix through dimensionality transformation, simulating the spatial distribution properties of the flow field data. Then, it uses convolutional kernels to perform sliding operations on the two-dimensional feature matrix to extract the spatial relationships and local gradient features implicit in the discrete pressure point distribution, ultimately outputting a one-dimensional CNN feature vector. The fully connected neural network branch is configured to process numerical regression features. This branch directly receives a one-dimensional normalized pressure feature vector and uses a hierarchical neuron connection weight matrix to perform a non-linear transformation on the pressure values. This process uncovers the coupling correlation strength between pressure measurement points at different locations, ultimately outputting a one-dimensional FCNN feature vector. .

[0052] The feature fusion layer of the PS model is connected to the output of the parallel feature extraction layer. The feature fusion layer performs vector concatenation, combining the CNN feature vectors output by the convolutional neural network branches. FCNN feature vectors output by fully connected neural network branches The channels are merged to generate a joint feature vector containing dual feature information. Joint eigenvectors The dimension is equal to the CNN feature vector. Dimensions and FCNN feature vectors The sum of dimensions.

[0053] The output reconstruction layer of the PS model is connected after the feature fusion layer. The output reconstruction layer consists of several fully connected layers used to combine the joint feature vectors. Decoding maps back to a high-dimensional pixel space. The last layer of the output reconstruction layer contains... There are 10 neuron nodes, of which Equal to the height of the target flow field image Multiply by width The one-dimensional vector output by the output reconstruction layer is ultimately reshaped into a vector of size . The two-dimensional matrix is ​​the final reconstructed grayscale image matrix of the flow field. .

[0054] See attached document Figure 3 In order to extract flow field features with spatial topological properties from discrete and unstructured wall pressure data, the convolutional neural network branch designed in this invention includes a feature space reconstruction module, a feature upsampling module, a deep feature extraction module, and a feature compression vectorization module.

[0055] First, the convolutional neural network branch receives the normalized stress feature vector from the input layer. The vector has a dimension of 6. Since convolution operations require two-dimensional or three-dimensional gridded data, the first layer of the convolutional neural network branch is set as a fully connected initialization layer (FC_I). The fully connected initialization layer contains 25 neurons and linearly maps the 6-dimensional normalized pressure feature vector to a 25-dimensional intermediate feature vector using a fully connected weight matrix. Subsequently, a feature reshaping operation is performed, rearranging the 25-dimensional intermediate feature vector into a three-dimensional initial feature tensor. Three-dimensional initial feature tensor The dimensions are set to 5 pixels in height, 5 pixels in width, and 1 channel (i.e., 5×5×1). This step converts the pressure values ​​without spatial location information into feature maps with a preliminary two-dimensional grid structure, providing a data carrier for subsequent convolution operations.

[0056] Secondly, in order to increase the spatial resolution of the feature map and simulate the flow field expansion process, the three-dimensional initial feature tensor The input is fed into the feature upsampling module. The feature upsampling module consists of a single transposed convolutional layer. This transposed convolutional layer has a kernel size of 3 pixels by 3 pixels, a stride of 2, and 64 output channels. After the transposed convolution operation, the input 5×5×1 feature tensor is amplified and mapped to a first-level feature tensor with a size of 11 pixels by 11 pixels and 64 channels. The operation of the transposed convolutional layer expands the feature map in spatial dimensions, thus enabling it to accommodate richer flow field details.

[0057] Next, the first-level feature tensor enters the deep feature extraction module, which consists of seven cascaded two-dimensional convolutional layers (denoted as Conv_1 to Conv_7). These seven convolutional layers all employ the same padding strategy: padding the edges of the feature map with zero values ​​to ensure that the spatial dimensions (height and width) of the feature map remain unchanged before and after the convolution operation, always maintaining an 11×11 size. The specific configuration of each convolutional layer is as follows: The first convolutional layer (Conv_1) and the second convolutional layer (Conv_2) have a kernel size of 3×3, a stride of 1, and 64 output channels.

[0058] The third convolutional layer (Conv_3) and the fourth convolutional layer (Conv_4) have a kernel size of 3×3, a stride of 1, and the number of output channels is increased to 128.

[0059] The fifth convolutional layer (Conv_5), the sixth convolutional layer (Conv_6), and the seventh convolutional layer (Conv_7) have a kernel size of 3×3, a stride of 1, and the number of output channels is further increased to 256.

[0060] Each convolutional layer is followed by a non-linear activation function. For any nth convolutional layer... Convolutional layers, whose input feature maps With output feature map The calculation relationship is described by the following formula: ; in, Represents any number of The first convolutional layer One output channel matrix; Indicates the first The first layer of the input feature map One input channel matrix; Indicates the first Layer connection input channel matrix With output channel matrix The two-dimensional convolution kernel weight matrix; This represents the two-dimensional convolution operator. Indicates the first Convolutional layer The bias scalar of each output channel; This represents the rectified linear unit activation function, used to introduce nonlinear features. By progressively increasing the number of channels (from 64 to 256), the convolutional neural network branches can extract flow field structure information from low-level edge features to high-level semantic features step by step.

[0061] Finally, the feature tensor (11×11×256) output by the seventh convolutional layer (Conv_7) enters the feature compression and vectorization module. This module contains a max-pooling layer and a flattening layer. The max-pooling layer has a pooling window size of 2×2 and a stride of 2. The max-pooling layer downsamples the feature tensor, selecting the most prominent features in local regions, compressing the spatial size of the feature map from 11×11 to 5×5, while keeping the number of channels unchanged at 256. Subsequently, the flattening layer unfolds this 5×5×256 three-dimensional tensor row-wise, converting it into a one-dimensional vector of length 6400. This one-dimensional vector is the CNN feature vector of the convolutional neural network branch. It encodes the topological distribution characteristics of the flow field after spatial transformation and depth extraction.

[0062] See attached document Figure 3 To complement the convolutional neural network branch's focus on local spatial feature extraction, this invention designs a fully connected neural network branch aimed at uncovering the implicit global numerical correlation and nonlinear regression features in wall pressure data. The fully connected neural network branch employs a multilayer perceptron architecture, directly performing high-dimensional feature mapping on the input pressure values ​​without altering the data's vectorized structure.

[0063] The fully connected neural network branch works in parallel with the convolutional neural network branch. The input of the fully connected neural network branch also receives the normalized pressure feature vector from the input layer. In this embodiment, the normalized pressure feature vector The dimension is 6. The fully connected neural network branch mainly consists of four sequentially connected fully connected layers (denoted as FC_1, FC_2, FC_3 and FC_4 respectively).

[0064] The first fully connected layer (FC_1) serves as the entry layer for the fully connected neural network branch and contains 64 neurons. The first fully connected layer receives a 6-dimensional normalized stress feature vector. After performing a linear transformation using the first weight matrix and superimposing biases, a first-layer feature vector of length 64 is output using a non-linear activation function. This process maps low-dimensional physical pressure values ​​to a higher-dimensional feature space.

[0065] The second fully connected layer (FC_2) follows the first fully connected layer and contains 128 neurons. The second fully connected layer receives the first layer feature vector of length 64 and maps it to the second layer feature vector of length 128, further increasing the width of the feature representation to capture more complex numerical combinations.

[0066] The third fully connected layer (FC_3) follows the second fully connected layer and contains 512 neurons. The third fully connected layer receives the second layer feature vector of length 128 and maps it to the third layer feature vector of length 512.

[0067] The fourth fully connected layer (FC_4), as the final layer of the fully connected neural network branch, contains 2048 neurons. The fourth fully connected layer receives the feature vector of the third layer (length 512) and maps it to a fourth layer feature vector (length 2048). This 2048-bit vector is the FCNN feature vector of the fully connected neural network branch. .

[0068] In a fully connected neural network branch, the data transmission and computation process of each layer follows a unified mathematical model. For the first layer of a fully connected neural network branch... Fully connected layer (of which) (The values ​​are 1, 2, 3, and 4), and its input vector is... The output vector is The calculation process is described by the following formula: ; Among them, when At that time, that is for Specifically refers to the input of a fully connected neural network branch, i.e., the normalized stress feature vector. ; Indicates the first The weight matrix of a fully connected layer has the number of rows equal to the number of neurons in that layer and the number of columns equal to the number of neurons in the previous layer. This represents matrix multiplication. Indicates the first The bias vector of a fully connected layer has a length equal to the number of neurons in that layer; This represents the activation function of the rectified linear unit.

[0069] Through the step-by-step dimensionality-increasing mapping of the four fully connected layers, the fully connected neural network branches transform the original pressure vector containing six physical quantities into an FCNN feature vector containing 2048 abstract numerical features. This vector can characterize the complex nonlinear global mapping relationship between the pressure distribution on the isolation section wall and the flow field state, providing numerical dimension feature support for subsequent feature fusion.

[0070] See attached document Figure 3 The feature fusion and image generation module is located at the end of the PS model. Its function is to integrate spatial structural features from the convolutional neural network branch and numerical regression features from the fully connected neural network branch, and then decode the integrated features into a high-resolution flow field grayscale image matrix. The feature fusion and image generation module mainly consists of a feature stitching layer, a fusion fully connected layer, and an output fully connected layer.

[0071] First, the feature concatenation layer receives two input vectors: one is the CNN feature vector output from a branch of the convolutional neural network. One is 6400 in length; the other is the FCNN feature vector from the output of a fully connected neural network branch. Its length is 2048. The feature concatenation layer performs a vector concatenation operation, combining the FCNN feature vectors... Directly appended to the CNN feature vector The tail of the vector is used to construct a new joint feature vector. Joint eigenvectors The length is equal to the CNN feature vector. Length of FCNN feature vector The sum of the lengths is 6400 + 2048 = 8448. The mathematical expression of the feature splicing layer is shown in the following formula: ; in, This represents the vector concatenation operation; Represents the convolutional feature vector (CNN) feature vector. The first in One element; Represents the FCNN feature vector The first in One element; This represents the vector transpose symbol. Through the feature concatenation layer, the PS model simultaneously preserves the local topological information and global parameter correlation information of the flow field within the same feature space.

[0072] Secondly, joint feature vectors The input is fed into a fused fully connected layer (FC_O). The fused fully connected layer contains 4096 neurons. The fused fully connected layer utilizes the weight matrix on the joint feature vector of dimension 8448. A linear weighted summation is performed, and a bias term is added. Then, a nonlinear transformation is applied using the rectified linear unit activation function (ReLU) to output a fused hidden layer vector of length 4096. The role of the fully connected fusion layer is to perform deep interaction and dimensionality reduction integration of the spliced ​​dual-source features, and extract a compact feature representation that can characterize the global state of the flow field.

[0073] Next, fuse the hidden layer vectors. The input is fed into the output fully connected layer. The output fully connected layer is the last network layer in the entire PS model, and the number of neurons in the output fully connected layer is strictly set to match the total number of pixels in the target flow field image. In this embodiment, the height of the target flow field image... 40 pixels wide The value is 319 pixels, therefore the number of nodes in the output fully connected layer is [number]. The value is set to 40 × 319 = 12760. The output fully connected layer will have a fused hidden layer vector of length 4096. Mapped to an image pixel vector of length 12760 The calculation process for the fully connected layer is shown in the following formula: ; in, This represents the weight matrix of the output fully connected layer, with a size of 12760×4096; This represents the bias vector of the output fully connected layer, with a length of 12760.

[0074] Finally, image reshaping is performed. This involves reshaping the one-dimensional image pixel vector... The flow field is converted into a visualized two-dimensional image. The feature fusion and image generation module adjusts the image width according to the target image width. and height For image pixel vectors Perform matrix rearrangement. Specifically, rearrange the image pixel vectors... The front of the middle The first element is used as the pixel value of the first row of the image, and the following elements... Each element is used as the pixel value for the second row of the image, and so on, until the image is filled. Okay. After the reshaping operation, a reconstructed flow field grayscale image matrix with a size of 40×319 is finally generated. in, Each element value in the diagram represents the grayscale intensity of the flow field schlieren at the corresponding spatial location, thus realizing a complete reconstruction process from wall pressure to visualization of the internal flow field.

[0075] See attached document Figure 3During the training phase of the PS model, the core task is to iteratively adjust the weight and bias parameters within the PS model so that the reconstructed flow field grayscale image matrix output by the PS model approximates the numerical distribution of the actually observed flow field schlieren image matrix. Since this invention defines the flow field reconstruction task as a pixel-wise regression problem in a high-dimensional space, it uses mean squared error as the loss function to quantify the model's prediction performance.

[0076] The mean squared error loss function is used to calculate the average of the sum of squares of the differences in grayscale values ​​between the reconstructed image and the ground truth image at each corresponding pixel location. In each training iteration, a batch of sample pairs is randomly selected from the training dataset. For any training sample, its corresponding ground truth flow field schlieren image matrix is ​​defined as... Define the reconstructed flow field grayscale image matrix generated by the PS model based on the pressure input of the sample. .

[0077] Define the set of all learnable weight parameters and bias parameters in the PS model as follows: Target loss function Calculate according to the following formula: ; in, This represents the total loss value calculated from the current training samples. This value is a non-negative scalar used to characterize the current prediction error level of the model. This represents the row index in the image matrix, with values ​​ranging from 1 to a height of 1. number of rows; This represents the column index in the image matrix, with values ​​ranging from 1 to a width of [value missing]. Number of columns; The true flow field schlieren image matrix is ​​represented as In the line, number The normalized pixel grayscale value at the column coordinate is derived from the label data generated during the data preprocessing stage, and its value ranges from 0 to 1. Indicates the current parameter set Under the influence of the PS model, the reconstructed flow field grayscale image matrix is ​​output. In the line, number The predicted pixel grayscale value at the column coordinate is calculated by the aforementioned feature fusion and image generation module, and its value ranges from 0 to 1.

[0078] The target loss function It has a clear physical meaning: by squaring the pixel differences, the target loss function... Larger prediction errors will be penalized with greater weight. In supersonic flow field images, the shock wave location (manifested as an edge with a sharp change in grayscale) usually corresponds to a large pixel gradient. When the shock wave location predicted by the PS model does not coincide with the actual shock wave location, a significant difference in pixel grayscale will occur in the corresponding region, thus causing the target loss function to... The value increases significantly. Therefore, minimizing this objective loss function... The process is essentially about driving the PS model to adjust its parameters. This allows it to accurately capture and align high-frequency features in the flow field, such as shock wave train structures, shock wave reflection points, and boundary layer separation regions, thereby achieving high-fidelity flow field reconstruction. The calculated... This will be used as input to the subsequent backpropagation algorithm to calculate the parameter gradients and update the network weights.

[0079] See attached document Figure 3 In order to ensure that the PS model proposed in this invention can effectively search for the global optimum or a high-quality local optimum in the high-dimensional parameter space, and to prevent the model from getting stuck in the gradient vanishing or gradient exploding dilemma during training, strict parameter initialization standards and optimizer configuration schemes must be formulated.

[0080] Network parameter initialization strategy: Before model training begins, initialize all weight parameter matrices in the PS model. and bias vector Initial values ​​need to be assigned. Since the PS model widely uses rectified linear units as activation functions in both convolutional neural network branches and fully connected neural network branches, this invention uses the He normal distribution initialization method to initialize the weight parameters, maintaining the variance consistency of the signal during transmission in deep networks.

[0081] For any network layer (including convolutional or fully connected layers) in the PS model, assuming the number of input neurons (or the number of receptive field units corresponding to the input channels) of that network layer is... The weight parameter matrix of this network layer The initial values ​​are generated by random sampling from a truncated normal distribution with a mean of 0 and a standard deviation of 0. Determined based on the following formula: ; in, This indicates the number of input neurons in the network layer; Represents the standard deviation of the normal distribution used to generate the initial weights; the bias vector of all network layers in the PS model. The initial value is uniformly set to a constant 0.

[0082] Optimizer selection and configuration: This invention uses the Adaptive Moment Estimation (Adam) optimizer to perform the gradient descent process. The Adam optimizer combines the advantages of momentum method and root mean square propagation, and can independently and adaptively adjust the learning rate for each parameter in the PS model.

[0083] In the In the next iteration, let the target loss function be... Regarding parameter adjustment The gradient is The Adam optimizer first calculates the first moment estimate of the gradient. and second-order moment estimation The calculation process is shown in the following formula: ; ; in, Indicates the first The first moment estimate of the next iteration (exponential moving average of the gradient); Indicates the first Second moment estimate of the next iteration (exponential moving average of the squared gradient). This represents the first-order moment attenuation coefficient, which is set to 0.9 in this embodiment; This represents the second-order moment attenuation coefficient, which is set to 0.999 in this embodiment; This represents the element-wise squaring operation of the gradient vector.

[0084] because and Initialized as a zero vector, it will have a bias in the early stages of training. Therefore, the Adam optimizer further calculates the bias-corrected first moment. and second moment As shown in the following formula: ; ; in, and They represent and of Power of 1.

[0085] Finally, the adjustment parameters of the PS model Update according to the following formula: ; in, This indicates the updated parameter value; This indicates the parameter value before the update; This represents the global initial learning rate; This represents a numerical stability constant set to prevent the denominator from being zero; in this embodiment, it is set to 10. -8 .

[0086] Specific settings for training hyperparameters: To ensure the stability and convergence speed of model training, this embodiment configures the key hyperparameters during training on a deep learning computing platform based on an NVIDIA RTX 3090 graphics processing unit (GPU) as follows: Batch size: Set to 64. This means that the PS model processes 64 stress schlieren sample pairs simultaneously in each parameter update iteration. This value is chosen to balance GPU memory usage with the oscillations of stochastic gradient descent.

[0087] Initial learning rate: set to 1×10 -4 This smaller learning rate helps the PS model avoid missing the global minimum of the loss function in the early stages of training.

[0088] Maximum number of iterations: set to 500. That is, the entire training dataset will be fed into the PS model for 500 complete iterations.

[0089] Learning rate decay strategy: A step decay strategy is adopted. Every 100 epochs of training, the global initial learning rate is decreased. Multiplying by a decay factor of 0.5 allows for more precise parameter fine-tuning of the PS model in the later stages of training.

[0090] Dataset partitioning: The 20,000 constructed sample pairs were randomly divided into a training set (80%) containing 16,000 samples and a test set (20%) containing 4,000 samples. The training set was used only for gradient calculation and parameter updates, while the test set was used only to evaluate the generalization performance of the PS model after each epoch and did not participate in gradient backpropagation.

[0091] By defining the parameter initialization method, the details of the Adam optimizer algorithm, and the specific hyperparameter values, the training environment and execution logic of the PS model were fully determined, ensuring the reproducibility of the technical solution.

[0092] See attached document Figure 3 The training process of the PS model is a gradient-based iterative optimization process, which aims to adjust the parameters of the PS model through repeated forward propagation, error calculation, backpropagation, and parameter update cycles. The training process converges to the optimal state. It mainly consists of a data batch loading step, a forward inference calculation step, a loss assessment step, an error backpropagation step, and a parameter weight update step.

[0093] Data Batch Loading and Input Initialization: At the beginning of each training epoch, the training dataset containing 16,000 sample pairs is first randomly shuffled. Then, according to the set batch size, the training dataset is divided into 250 consecutive data batches. The training process enters a batch loop, reading each data batch sequentially. For the currently read batch... From each data batch, the system extracts an input tensor containing 64 normalized pressure feature vectors. And a label tensor containing 64 corresponding real flow field schlieren image matrices. .Will The data is fed into the input layer of the PS model to begin forward computation.

[0094] Forward Propagation and Flow Field Feature Derivation: PS Model Receives Input Tensor This step involves controlling the positive flow of signals within the network. It comprises two sub-processes executed in parallel: First, input tensor Entering the convolutional neural network branch, the convolutional feature vectors are generated in batches through operations such as fully connected initialization layers, feature reshaping, transposed convolutional layers, seven 2D convolutional layers, max pooling layers, and flattening layers. ; Secondly, input tensor Simultaneously, the vectors enter the fully connected neural network branch, sequentially undergoing linear mapping and activation function operations through four fully connected layers to generate batches of fully connected feature vectors. .

[0095] Subsequently, the feature fusion and image generation module will and The images are stitched and fused, and the reconstructed flow field grayscale image matrix tensor for the current batch is finally output through calculations using the fully connected layer. During the entire forward propagation process, the adjustment parameters of the PS model are... Keep it fixed.

[0096] Loss function calculation: Using the defined mean squared error loss function formula, the difference between the predicted result and the true label for the current batch is calculated. The system will reconstruct the flow field grayscale image matrix tensor. Label tensor of real flow field schlieren image matrix Substituting into the loss function, the average loss scalar of the current batch is calculated. , The overall error level of the PS model for flow field reconstruction under the current parameter configuration was quantified.

[0097] Error backpropagation and gradient calculation: based on the calculated average loss scalar The chain rule is used to calculate the partial derivative (i.e., gradient) of the loss function with respect to each learnable parameter layer by layer from the output layer to the input layer.

[0098] First, the gradient of the loss function with respect to the parameters of the fully connected layer is calculated. Then, the error signal is passed to the feature fusion layer, where it splits: one part of the error gradient flows to the convolutional neural network branch to calculate the gradient of the convolutional kernel weights and biases; the other part of the error gradient flows to the fully connected neural network branch to calculate the gradient of the fully connected layer weights and biases.

[0099] Define adjustment parameters The Middle The parameters are Then the gradient corresponding to this parameter Calculate according to the following formula: ; The system iterates through all parameters in the PS model, calculates and stores the gradient vector containing the gradients of all parameters. .

[0100] Parameter weight update: when obtaining the gradient vector Then, the parameters of the PS model are adjusted using the Adam optimizer configured above. To update the model, the current gradient, historical first-moment and second-moment estimates are used to calculate the update step size for each parameter. The updated values ​​are then used to overwrite the original parameter values, thus completing one model iteration.

[0101] Iterative iteration and model validation: Repeat the data batch loading and input initialization steps up to the parameter weight update step until all 250 data batches of the current epoch have been traversed. At the end of each epoch, validate the updated PS model using test set data, calculate the average loss value on the test set, and if the test set loss value of the current epoch is lower than the historical lowest test set loss value, save the adjustment parameters of the current PS model. Use these as the optimal model weights. Repeat the above process until the preset maximum number of iterations (500) is reached, and finally output the trained PS model file.

Claims

1. A method for reconstructing the supersonic isolated section flow field by integrating CNN and FCNN, characterized in that, Includes the following steps: In the supersonic direct-drive wind tunnel test system, a pressure sensor array is used to collect wall pressure data sequences, and a schlieren imaging system is used to collect flow field schlieren image sequences. The wall pressure data sequence and the flow field schlieren image sequence are time-synchronized, aligned, and preprocessed to construct a training dataset containing normalized pressure feature vectors and real flow field schlieren image matrices. A parallel dual-branch deep learning model is constructed, comprising a convolutional neural network branch and a fully connected neural network branch set in parallel, as well as a feature fusion layer and an output reconstruction layer connected to the outputs of the two. The convolutional neural network branch is configured to reshape the input normalized stress feature vector into a two-dimensional matrix to extract spatial structure features, and the fully connected neural network branch is configured to directly process the normalized stress feature vector to extract numerical correlation features. The parallel dual-branch deep learning model is trained using the training dataset, and the model parameters are iteratively updated by minimizing the loss function to obtain the trained parallel dual-branch deep learning model. The real-time wall pressure data is input into the trained parallel dual-branch deep learning model, and the reconstructed flow field grayscale image is output.

2. The supersonic isolated section flow field reconstruction method integrating CNN and FCNN according to claim 1, characterized in that, The time synchronization alignment specifically includes: The zero point of time is determined by using the synchronization light signal generated by the laser light-emitting diode (LED). The data sequence recording the voltage signal of the LED and the image sequence containing the luminous state of the LED are retrieved respectively to determine their respective starting indices. The extraction step size is calculated based on the ratio of the wall pressure sampling frequency to the schlieren image capture frame rate, and an index mapping relationship between each frame of schlieren image and the original pressure data points is established based on the extraction step size to achieve a one-to-one correspondence of data.

3. The supersonic isolated section flow field reconstruction method integrating CNN and FCNN according to claim 1, characterized in that, The construction of the normalized pressure feature vector specifically includes: A subset of sensors is formed by selecting equally spaced pressure sensors located on the lower wall of the isolation section test piece and a back pressure sensor at the outlet from the pressure sensor group. A first-in-first-out (FIFO) data buffer queue is established, and the raw pressure data of the sensor subset is subjected to an arithmetic average calculation based on a sliding time window to obtain a smoothed pressure value. Obtain the maximum and minimum pressure values ​​from historical test samples, perform min-max normalization on the smoothed pressure values, and generate the normalized pressure feature vector.

4. The supersonic isolated section flow field reconstruction method integrating CNN and FCNN according to claim 1, characterized in that, The construction of the real flow field schlieren image matrix specifically includes: A pixel coordinate mask is used to crop out the image portion containing only the visible area of ​​the flow field inside the isolation section from the original schlieren image; The cropped image is compressed by spatial dimensional downsampling using a bilinear interpolation algorithm. The image is enhanced and denoised using the Laplacian sharpening operator and the Gaussian smoothing filter; Map image pixel grayscale values ​​to floating-point numbers between zero and one.

5. The supersonic isolated section flow field reconstruction method integrating CNN and FCNN according to claim 1, characterized in that, The methods for constructing the convolutional neural network branches include: A fully connected initialization layer is set up to map and reshape the normalized pressure feature vector into a three-dimensional initial feature tensor with height, width, and number of channels; A transposed convolutional layer is set to upsample and enlarge the spatial size of the three-dimensional initial feature tensor; A deep feature extraction module consisting of multiple cascaded two-dimensional convolutional layers is set up to extract the spatial topological features of the flow field; A feature compression vectorization module containing max pooling and flattening layers is set up to output a one-dimensional convolutional feature vector.

6. The supersonic isolated section flow field reconstruction method integrating CNN and FCNN according to claim 5, characterized in that, The deep feature extraction module employs an edge-filling strategy in each two-dimensional convolutional layer to maintain the feature map space size. Furthermore, as the number of layers increases, the number of output channels in each two-dimensional convolutional layer increases layer by layer.

7. The supersonic isolated section flow field reconstruction method integrating CNN and FCNN according to claim 1, characterized in that, The fully connected neural network branch adopts a multilayer perceptron architecture, which includes multiple fully connected layers connected in sequence; Each of the fully connected layers uses a weight matrix to perform a linear transformation on the input vector and superimposes a bias vector, which is then output through a rectified linear unit activation function; The fully connected neural network branch ultimately outputs a one-dimensional fully connected feature vector.

8. The supersonic isolated section flow field reconstruction method integrating CNN and FCNN according to claim 1, characterized in that, The feature fusion layer performs a vector concatenation operation, merging the convolutional feature vectors output by the convolutional neural network branch and the fully connected feature vectors output by the fully connected neural network branch in the channel dimension to generate a joint feature vector; The output reconstruction layer includes a fusion fully connected layer and an output fully connected layer. The number of neurons in the output fully connected layer is equal to the total number of pixels in the target flow field image. It is configured to map features back to pixel space and reshape them into a two-dimensional reconstructed flow field grayscale image matrix.

9. The supersonic isolated section flow field reconstruction method integrating CNN and FCNN according to claim 1, characterized in that, The method of iteratively updating model parameters by minimizing the loss function uses the mean square error function. The mean square error function is used to calculate the average of the sum of squares of the differences in grayscale values ​​between the reconstructed flow field grayscale image matrix output by the model and the real flow field schlieren image matrix at each corresponding pixel position.

10. The supersonic isolated section flow field reconstruction method integrating CNN and FCNN according to claim 1, characterized in that, The specific steps of training the parallel dual-branch deep learning model using the training dataset include: The model weight parameters are initialized using a normal distribution initialization method; An adaptive moment estimation optimizer is selected, and the learning rate is adjusted based on the exponential moving average of the gradient to update the model parameters; During training, a learning rate decay strategy is executed at preset round intervals.

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