Physical field data restoration method and system based on diffusion and iterative resampling

Abstract

The invention discloses a physical field data restoration method and system based on diffusion and iterative resampling, and the method comprises the steps: initialization: filling a missing region with random noise in to-be-restored physical field data, and obtaining an initial noisy field; forward diffusion: gradually adding noise into the complete data until the complete data becomes complete random noise data; noise model pre-training: training random noise added in each step in forward diffusion; inverse diffusion denoising: gradually restoring the image from the initial random noise through the noise predicted by the model and an iterative formula; and iterative resampling correction: in the reverse diffusion process, iterative circulation is carried out in a de-noising-noise adding-re-de-noising mode, so that the model can be effectively forced to spread information of a known area to a missing area, and the physical consistency and smooth transition of a repair result and a known data boundary are ensured. Any prior information of the missing area does not need to be preset, the repairing precision is high, and the physical consistency is good.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of engineering thermophysics, and particularly relates to a physical field data repairing method and system based on diffusion and iterative resampling. BACKGROUND

[0002] In high-complexity systems such as aircraft engines, experimental measurement is the core method for obtaining internal flow fields, temperature fields and other physical parameters. However, due to the extreme environment and the difficulty of sensor placement, the measured data often has spatial incompleteness. For example, the measurement of key areas such as blade passages and combustion chambers may result in data loss due to the inability of the probe to reach or signal interference, resulting in the obtained flow field information being only a local fragment. Such incomplete data seriously restricts the comprehensive analysis of complex flow phenomena in the engine.

[0003] In recent years, intelligent algorithms represented by deep learning have provided a new paradigm for physical field data reconstruction. Neural networks learn the spatial correlation rules in a large amount of flow field data to infer the global physical field from local measurements. In early methods, the generative adversarial network (GAN) generates complete data through the game between the generator and the discriminator, but it is easy to collapse the mode, resulting in physical inconsistency between the completed region and the real flow field; the convolutional neural network (CNN) performs well in regular missing scenarios due to its local feature extraction capability, but it relies on the pre-set shape of the missing region mask, making it difficult to adapt to irregular missing scenarios. The core limitation of traditional methods is that they usually require pre-defined geometric boundaries of the missing region (such as rectangles, circles), and assume that the missing pattern is fixed. In the actual missing scenario of an aircraft engine, the position, shape and size of the missing region often change dynamically with the working condition, and this strong pre-setting limits the generalization ability of traditional methods in engineering practice.

[0004] The rise of diffusion models provides a breakthrough solution to this dilemma. As a class of deep learning models based on probabilistic generation, diffusion models simulate the gradual generation process of "noise addition-noise removal", and can gradually recover complete flow fields that conform to physical laws from random noise. Its core advantages lie in two aspects: first, the probabilistic generation mechanism learns the global statistical distribution of flow field data, and can adaptively generate supplementary information consistent with the physical characteristics of the complete region in the missing region without relying on pre-set missing shapes; second, the adaptive mask processing capability enables the model to use the complete region in the measured data as a strong constraint condition to dynamically adjust the inference weight of the missing region in the denoising iteration, ensuring that the completion result meets the local measurement value. This feature perfectly adapts to the irregular missing scenario of the aircraft engine flow field data, opening up a new path for physical field completion in complex power systems. SUMMARY

[0005] The purpose of this invention is to provide a physical field data repair method and system based on diffusion and iterative resampling, which solves the problem of repairing missing data of arbitrary irregular physical fields in a high-precision and high-physical-consistency manner.

[0006] The objective of this invention is achieved through the following technical solution:

[0007] Step 1: Obtain the velocity field dataset of the downstream section of the turbine channel through CFD simulation calculation.

[0008] Step 2: Obtain the velocity field of the missing data by randomly deleting data of random size at random locations. The missing data samples include two types: one with a rectangular shape but random length, width, location, and area; the other is a completely random irregular shape obtained through a random growth method. Missing data is defined as:

[0009]

[0010] Where u(i, x) represents the velocity value at position x at time i; u m This represents the velocity field after the missing data is generated. A mask matrix is ​​constructed based on the missing and non-missing regions. The original data in the missing regions is replaced with standard Gaussian noise, while the original data in the non-missing regions is left unchanged, resulting in an initial noisy field dataset.

[0011] Step 3: Construct the forward diffusion process and gradually add noise to a Gaussian distribution.

[0012] Step 4: Build a U-Net noise prediction model and learn the noise mapping relationship.

[0013] Step 5: The expression for reverse diffusion can be derived from the forward diffusion process in Step 3:

[0014] u t-1 =μ θ (u t ,t)+σ t

[0015] Where σ t μ represents the standard deviation of a predefined Gaussian distribution. θ (u t ,t) represents the mean, which depends on the U-Net network, and the specific calculation formula is as follows:

[0016]

[0017] where ε(u t ,t) is the prediction result of the U-Net network in step 4.

[0018] Step 6: Complete the missing data field by resampling.

[0019] Furthermore, the U-Net denoising network model in step 4 includes: first, building a basic U-Net network, including a downsampling module, an upsampling module, and skip connections. Features are extracted through a progressive downsampling encoding process, and the results are predicted through a progressive upsampling decoding process. The encoding and decoding processes are combined through skip connections. Then, a sinusoidal positional encoding method is used to encode the denoising time steps. After each downsampling and upsampling, the encoded temporal information is added to the original data through a fully connected layer, embedding the time step information. After embedding the temporal information, residual connections and an attention mechanism are introduced to enhance the ability to perceive features.

[0020] Furthermore, the specific steps for completing the missing data field in step 6 include:

[0021] Step 6-1: For the missing regions, based on the trained U-Net model and the inverse diffusion formula, backtrack the noisy velocity field state. Perform forward diffusion on the non-missing regions. The inverse generation process is completed after both reach the same time step.

[0022] Step 6-2: In the specific interval generated by reverse engineering, a forward diffusion process is added to both the missing and non-missing regions to add noise, thereby better integrating the feature information of the missing and non-missing regions.

[0023] Step 6-3: After adding noise for a certain number of steps in step 6-2, the noise-added state is corrected a second time using the reverse generation method in step 6-2.

[0024] Step 6-4: Repeat steps 6-1 and 6-3 for the specified number of iterations until the noise is completely removed and the missing velocity field data is completed.

[0025] Furthermore, the velocity field u during the forward diffusion process described in step 3 t Only with the u from the previous step t-1 This process is considered a Markov chain and satisfies:

[0026]

[0027] in, Represents a normal distribution with a mean of 1 / 2. The variance is β t t represents the number of steps in the forward process. Therefore, the probability distribution of the velocity field after T steps of noise addition from the initial velocity field u0 can be expressed as:

[0028]

[0029] By simplifying the iterative formula, the relationship between the velocity field corresponding to any forward step t and the initial velocity field can be obtained as follows:

[0030]

[0031] Where ε represents standard Gaussian noise.

[0032] The core of this invention is an iterative repair process based on a pre-trained noise prediction model. This process first generates data in the missing regions through a reverse diffusion mechanism. The key to this mechanism is that after each denoising step, the corresponding regions in the prediction results are forcibly replaced with original, real, known data, thus using known information as a strong boundary condition to guide the generation of the missing regions.

[0033] However, simple reverse diffusion can lead to unnatural artifacts or physical discontinuities at the boundary between the generated and known regions. To address this issue, the key innovation of this invention lies in introducing an iterative resampling correction strategy. This strategy selectively and periodically pauses denoising during the reverse denoising process and applies a brief forward noise addition to the partially repaired field (containing both the original known data and the newly generated repaired data). This "step back and then forward" operation effectively "blurs" and "fuses" the boundary between the known and generated regions, allowing the physical information from the known regions to propagate and permeate more naturally into the missing regions. Subsequently, the algorithm continues reverse denoising from this new, slightly noisier state.

[0034] By combining the mechanisms of back diffusion and iterative resampling, this invention enables high-fidelity restoration of physical field data without any missing shape priors.

[0035] The beneficial effects of this invention are:

[0036] 1. High generalization ability: This invention introduces arbitrary irregular missing mask during the training phase, enabling the model to handle data missing scenarios with completely random shapes, positions, and sizes in the real world, without the need to preset the missing pattern, and has strong generalization ability.

[0037] 2. High repair accuracy: By combining the probabilistic generation capability of the diffusion model with the iterative correction mechanism of the resampling strategy, this method can generate repair data that is highly consistent with the physical characteristics of the surrounding known area, and the average velocity error of the repaired physical field is less than 5%.

[0038] 3. Good physical consistency: The diffusion model learns the overall distribution pattern of the data, rather than the local pixel mapping, which ensures that the repair results conform to physical laws at both the macro and micro scales, avoiding artifacts and discontinuities that may be produced by traditional methods. Attached Figure Description

[0039] Figure 1Turbine channel geometry diagram.

[0040] Figure 2 Schematic diagram of forward and reverse diffusion processes.

[0041] Figure 3 Schematic diagram of the U-Net noise model structure.

[0042] Figure 4 Error variation curves for the training and test sets.

[0043] Figure 5 Overall process framework diagram

[0044] Figure 6 Prediction results for the first test set sample of the rectangular missing data.

[0045] Figure 7 Prediction results for the second test set sample with missing rectangular data.

[0046] Figure 8 Prediction results for the third test set sample with missing rectangular data.

[0047] Figure 9 Prediction results for the first test set sample of the random shape missing data.

[0048] Figure 10 Prediction results for the second test set sample of the random shape missing data.

[0049] Figure 11 Prediction results for the third test set sample of the random shape missing data. Detailed Implementation

[0050] The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain the invention, and should not be construed as limiting the invention.

[0051] The embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0052] A physical field data inpainting method based on diffusion and iterative resampling performs an iterative inpainting process on a pre-trained noise prediction model, including the following steps:

[0053] Step 1: Obtain the velocity field dataset of the downstream section of the turbine channel through CFD simulation. The channel shape and the location of the downstream section are shown in the figure. Figure 1 As shown.

[0054] Step 2: Miss data of random size at random locations to obtain the velocity field of the missing data. The missing locations are determined by random numbers and can be anywhere within the entire cross-section. The missing size is limited to between 10% and 30%. A mask matrix is ​​built based on the missing and non-missing regions. The original data in the missing regions is replaced with standard Gaussian noise, while the original data in the non-missing regions remains unchanged, ultimately resulting in an initial noisy data set.

[0055] Step 3: As Figure 2 As shown, a forward diffusion process is constructed, and noise is gradually added to a Gaussian distribution.

[0056] The specific steps for constructing the forward diffusion process include:

[0057] Step 3-1: Set the maximum forward step count T to 700 and the noise figure β. t As t monotonically increases from 0.0001 to 0.99, the auxiliary parameter α... t Parameters such as these.

[0058] Step 3-2: Define the forward diffusion process, starting from the initial velocity field u0 and passing through T steps of noise addition.

[0059] Step 3-3: By simplifying the iterative formula, the velocity field corresponding to any forward step t can be obtained.

[0060] Step 4: As Figure 3 As shown, a U-Net noise prediction model is built to learn the noise mapping relationship.

[0061] The specific steps for building a U-Net noise prediction model include:

[0062] Step 4-1: Build the basic U-Net network, including a downsampling module, an upsampling module, and skip connections. Features are extracted through a progressive downsampling encoding process, and the results are predicted through a progressive upsampling decoding process. The encoding and decoding processes are combined through skip connections.

[0063] Step 4-2: Use a sinusoidal positional encoding method to encode the denoising time steps at a resolution of 256. After each downsampling and upsampling, the encoded time information is added to the original data through a fully connected layer to embed the time step information. After embedding the time information, residual connections and attention mechanisms are introduced to enhance the ability to perceive features.

[0064] Step 4-3: Import the data obtained in Step 2, standardize it, and randomly shuffle it into training and test sets. Input these sets into the model for calculation. Use the mini-batch stochastic gradient descent algorithm and set the training parameters as follows: batch = 32, learning rate = 0.001, training steps = 300. Figure 4The error variation curves of the training set and test set during the training process are shown.

[0065] Step 5: The backward diffusion expression can be derived through the forward diffusion process in Step 3, and the prediction result of the previous step at a specific time step can be obtained based on the U-Net network.

[0066] Step 6: The overall process is as follows Figure 5 As shown, the missing data field is completed by resampling.

[0067] Furthermore, the specific steps for completing the missing data field in step 6 include:

[0068] Step 6-1: For the missing regions, based on the trained U-Net model and the inverse diffusion formula, backtrack the noisy velocity field state. Perform forward diffusion on the non-missing regions. The inverse generation process is completed after both reach the same time step.

[0069] Step 6-2: During the reverse generation process, a forward diffusion process is added every 10 time steps to add noise to both the missing and non-missing regions, thus better fusing the feature information of the missing and non-missing regions. That is, resampling is performed at time steps such as t=690, 680, and 670.

[0070] Step 6-3: After adding noise for 10 time steps and looping 5 times in step 6-2, the noise-added state is corrected a second time using the reverse generation method in step 6-2.

[0071] Step 6-4: Repeat steps 6-1 and 6-3 until the noise is completely removed and the missing velocity field data is completed. Figure 6 , Figure 7 , Figure 8 The data presents the true velocity field data for different samples of the rectangular missing data set, the missing velocity field data, the completed velocity field data, and the error between the predicted and true results. The maximum error for a single sample is 11.3%, the maximum average error for a single sample is 4.7%, and the average error for all samples is 1.78%. Figure 9 , Figure 10 , Figure 11 This paper presents the true velocity field data, missing velocity field data, and imputed velocity field data for different samples of data with completely irregular missing shapes, along with the error between the predicted and true results. The results show that even with completely random missing data, the missing data can be imputed well, with an average error of 1.62% for all samples.

[0072] This invention combines reverse diffusion and iterative resampling mechanisms to achieve high-fidelity restoration of physical field data without any missing shape priors.

Claims

1. A physical field data restoration method based on diffusion and iterative resampling, characterized in that, Based on a pre-trained noise prediction model, an iterative repair process is performed, including the following steps: Step 1: Data preparation, obtaining the original complete velocity field dataset; obtaining the velocity field dataset of the downstream section of the turbine channel through CFD simulation calculation; Step 2: In the physical field data to be repaired, fill the missing regions with random noise to obtain an initial noisy field dataset; at random locations, data of random size are missing to obtain the velocity field of the missing data. The missing locations are determined by random numbers and can be anywhere in the entire cross section; the missing size is limited to the range of 10% to 30%. A mask matrix is ​​established based on the missing and non-missing regions. The original data in the missing regions is replaced with standard Gaussian noise, while the original data in the non-missing regions is left unchanged, finally obtaining an initial noisy field dataset. Step 3: Construct the forward diffusion process and gradually add noise to a Gaussian distribution; Step 4: Build a U-Net noise prediction model and learn the noise mapping relationship; Step 5: Derive the back-diffusion expression through the forward diffusion process in Step 3, and obtain the previous step prediction result at a specific time step based on the U-Net network; Step 6: Complete the missing data field by resampling.

2. The physical field data restoration method based on diffusion and iterative resampling according to claim 1, characterized in that, Step 3, the specific steps for constructing the forward diffusion process include: Step 3-1: Set the maximum forward step count T to 700 and the noise figure β. t As t monotonically increases from 0.0001 to 0.99, the auxiliary parameter α... t ; Step 3-2: Define the forward diffusion process, starting from the initial velocity field u0 and passing through T steps of noise addition; Step 3-3: By simplifying the iterative formula, obtain the velocity field corresponding to any forward step t.

3. The physical field data restoration method based on diffusion and iterative resampling according to claim 1, characterized in that, In step 4, the noise prediction model is a neural network model based on the U-Net architecture, which integrates temporal encoding information to represent time step t and embeds residual modules and attention mechanisms.

4. The physical field data restoration method based on diffusion and iterative resampling according to claim 3, characterized in that, The specific steps for building a U-Net noise prediction model include: Step 4-1: Build a basic U-Net network, including a downsampling module, an upsampling module, and a skip connection part. Features are extracted through a progressive downsampling encoding process, and the results are predicted through a progressive upsampling decoding process. The encoding and decoding processes are combined through skip connections. Step 4-2: Use the sinusoidal positional encoding method to encode the denoising time step. After each downsampling and upsampling, add the encoded time information to the original data through a fully connected layer to embed the time step information. After embedding the time information, introduce residual connections and attention mechanisms to increase the ability to perceive features. Step 4-3: Import the dataset obtained in Step 2, standardize it, and randomly shuffle it into training and test sets, then input them into the model for calculation.

5. The physical field data restoration method based on diffusion and iterative resampling according to claim 1, characterized in that, In step 5, the expression for reverse diffusion is derived from the forward diffusion process: you t-1 =μ θ (u t ,t)+σ t Where σ t μ represents the standard deviation of a predefined Gaussian distribution. θ (u t ,t) represents the mean, which depends on the U-Net network, and the specific calculation formula is as follows: where ε(u t ,t) is the prediction result of the U-Net network.

6. The physical field data restoration method based on diffusion-free and iterative resampling according to claim 1, characterized in that, Step 6, the specific steps for completing the missing data field include: Step 6-1: For the missing region, based on the trained U-Net model and the reverse diffusion formula, backtrack the noisy velocity field state and perform forward diffusion on the non-missing region. After both reach the same time step, the reverse generation process is completed. Step 6-2: In the specific interval generated by reverse engineering, a forward diffusion process is added to add noise to both the missing and non-missing regions to better integrate the feature information of the missing and non-missing regions. Step 6-3: After adding noise for a certain number of steps in step 6-2, the noise-added state is corrected a second time using the reverse generation method in step 6-2; Step 6-4: Repeat steps 6-1 and 6-3 for the specified number of iterations until the noise is completely removed and the missing velocity field data is completed.

7. The physical field data restoration method based on diffusion-free and iterative resampling according to claim 1, characterized in that, The physical field data refers to the velocity field or temperature field data of the downstream section of the turbine channel.

8. A system for physical field data restoration based on diffusion and iterative resampling as described in claim 1, characterized in that, include: Processor; memory on which computer programs that execute processor commands are stored.

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