DTV model two-stage signal processing method based on digital twinning

Abstract

The invention discloses a DTV model two-stage signal processing method based on digital twinning, relates to the technical field of natural gas pipeline signal completion, and solves the problems of low efficiency, poor effect and the like when an existing pipeline signal completion method is used for processing complex, multi-dimensional and high-spatial-temporal-correlation data missing problems. And efficient completion of the natural gas pipeline pressure signal is realized through combination of a digital twinborn model and deep learning. Firstly, a digital twinning model is established according to a physical entity. Secondly, a DTV model two-stage signal processing method is provided, in the first stage of the method, a probability graph model mechanism of a variational auto-encoder is used, diversified outputs are generated, and the comprehensiveness of data completion is ensured; and in the second stage, complementation data is generated through a generator by utilizing a model mechanism of mutual confrontation and mutual optimization of the generative network and the discriminant network of the generative confrontation network, and the authenticity of the data is judged through a discriminator. Complementation and verification of natural gas pipeline pressure data are realized.

Description

Technical Field

[0001] The present invention relates to the field of natural gas transmission, and in particular to a two-stage signal processing method of a DTV model based on digital twin. Background Art

[0002] As an important infrastructure for energy supply, natural gas pipelines undertake the key task of transporting natural gas from production sites to various consumption areas. With the increase in global demand for clean energy, natural gas has become one of the main energy resources, and its safe and efficient transportation is crucial to ensuring energy security and reducing environmental pollution. Pipelines can achieve large-scale long-distance transmission, reduce the loss of natural gas during transportation, improve resource utilization, and promote sustainable economic and social development. However, due to the long pipeline route and complex environment, the risk of pipeline leakage always exists, which may pose a threat to the ecological environment and the safety of surrounding residents.

[0003] In the operation and monitoring process of natural gas pipelines, sensor networks are widely used to monitor various operating parameters inside pipelines in real time, which is one of the most commonly used and key technical means. Through high-precision data acquisition and transmission, sensor networks can provide a large amount of key data on the operation of natural gas pipelines. By analyzing these data, potential safety hazards can be identified in time. However, relying solely on the data collected by sensors is not enough to fully ensure the reliability and accuracy of the monitoring system. This is because during the data acquisition and transmission process, it may be interfered by various factors, such as changes in the external environment (such as temperature, humidity, electromagnetic interference, etc.), aging and performance degradation of sensor equipment, errors in the installation process, and transmission delays or data packet loss in the communication network. These interferences will not only cause data distortion or loss, but may also introduce noise, thereby reducing the credibility of the data, and then affecting the system's recognition and judgment of abnormal conditions, thereby affecting the scientificity and effectiveness of the safe operation, fault diagnosis and maintenance decisions of the pipeline, resulting in a decrease in the monitoring effect. In turn, it affects the safe operation, fault diagnosis and maintenance decisions of the pipeline. Therefore, in order to ensure the safety and efficiency of natural gas pipelines, how to solve the problems of signal loss and noise interference in the operation monitoring of natural gas pipelines has become an important research direction.

[0004] Early data completion methods mainly rely on some simple mathematical and statistical techniques, the purpose of which is to infer missing data points when data is missing or incomplete. Such as mean / median imputation, nearest neighbor imputation, regression imputation, and expectation-maximization (EM), these methods usually assume that the pattern of missing data is random, and fill in the missing parts through some simple rules or assumptions. Although simple to implement and computationally efficient, these methods often cannot effectively handle complex missing data patterns and nonlinear relationships between data. Moreover, the assumptions proposed by these methods, such as data missing is random, or there is a simple linear dependency between data, are often not valid in many practical applications.

[0005] Based on these reasons, some scholars choose to use tensor completion methods to complete data signals. Tensor completion methods extend traditional matrix completion techniques. This method solves the problem of missing multivariate data by extending to multidimensional data structures (i.e., tensors). The earliest tensor completion methods use low-rank tensor decomposition techniques, such as CP decomposition and Tucker decomposition, to represent tensors in the form of low-rank decomposition, thereby estimating the missing parts through known data. Chen et al. proposed a synchronous tensor decomposition and completion (STDC) method, which combines the advantages of rank minimization and Tucker decomposition by performing tensor decomposition and missing entry completion simultaneously, and cleverly uses factor prior information to significantly improve the effect of tensor completion tasks. It can not only effectively restore missing entries, but also accurately capture the underlying structure of tensors. Bai et al. proposed an adaptive correction method (ACA) for tensor completion, aiming to reduce the error accumulation caused by inaccurate initial estimates and provide more robust tensor completion results. Solve the problem of multilinear data recovery under limited sampling to improve the accuracy of tensor completion, especially in the case of sparse sampling, and better restore data. Another group of scholars chose to use neural network methods to complete data signals. Neural networks have strong nonlinear modeling capabilities and can capture complex patterns in data. Therefore, neural networks show excellent performance, especially when processing missing value completion of time series data or high-dimensional data. Li et al. proposed a diffusion mechanism for lidar data completion to address the problem of missing data or noise interference during data acquisition. They introduced a diffusion Transformer network and used it as a generator, combined with a self-attention unit discriminator. Danielep et al. proposed a data completion method based on sparse recognition and data assimilation. This method shows high efficiency and robustness when dealing with scarce or missing data, and can effectively correct and enrich existing models and improve prediction accuracy. Zhang et al. proposed a new traffic data completion model based on graph convolutional networks (GCNs) to solve the problem of missing values ​​in real-world traffic data. In order to deal with global spatial dependency and temporal dependency, the model integrates a self-attention mechanism. This self-attention mechanism is applied to the spatial and temporal dimensions respectively, enabling the model to focus on important areas and time periods when inputting missing values. However, as the data dimension increases, the computational complexity of tensor completion methods increases significantly, especially when processing large-scale tensor data, the computational and storage costs are often expensive; secondly, tensor completion methods have a strong dependence on the sparsity of data. If the data missing pattern is too complex or the amount of missing data is too large, the completion effect may be significantly reduced. Although neural network methods can capture complex nonlinear relationships, they consume a lot of computing resources and lack good interpretability. Summary of the invention

[0006] The present invention mainly overcomes the shortcomings of the prior art, and the purpose of the present invention is to provide a two-stage signal processing method for a DTV model based on digital twins, so as to solve the problems of low efficiency and poor effect of existing pipeline signal completion methods in processing complex, multi-dimensional, and time-space-correlated data missing problems.

[0007] In order to achieve the above technical objectives, the present invention adopts the following technical solutions:

[0008] Based on the digital twin technology, this paper proposes a two-stage signal processing method for long-distance natural gas pipelines based on the DTV model. This method builds a virtual pipeline model that is highly consistent with the physical system, integrates real-time sensor data and historical operation information, comprehensively monitors the status of the pipeline system and obtains a large amount of operation data. Based on these data, the missing parts of the pipeline pressure signal are extracted, and the network architecture of the combined generative adversarial network (tnGAN) and variational autoencoder (VAE) is used for data completion; a mathematical model of pipeline pressure changes based on the Darcy-Weisbach equation is established, and simulation signals are generated to verify the completion effect and optimize system operation.

[0009] Furthermore, based on the physical model, three-dimensional modeling and rendering are performed through 3DMax.

[0010] Furthermore, 3DMax is saved as a utodesk FBX format file with the suffix .fbx file, and then imported into Unity for real-time simulation of the pipeline model.

[0011] Furthermore, based on the virtual pipeline model, real-time sensor data and historical operation information are integrated through the MongoDB database.

[0012] Furthermore, the virtual pipeline model is combined for simulation to comprehensively monitor the operation status of the pipeline system. Through sensor simulation and real-time data feedback, a large amount of data related to pipeline operation is obtained.

[0013] Furthermore, the pipeline pressure signal data is analyzed, the pressure signals with missing parts are extracted, and they are divided into two parts, a and b. The data of parts a and b are preprocessed and standardized.

[0014] Furthermore, a variational autoencoder is used, which is composed of an encoder module, a decoder module and a loss function module, and the mean square error (MSE) is used for error reconstruction.

[0015] Furthermore, by introducing a probabilistic graphical model, the variational autoencoder can effectively learn the potential distribution of data and generate samples similar to real data. Also, because VAE uses the form of probabilistic distribution in the encoding and decoding process, it will generate diverse outputs with certain noise robustness. The steps are as follows:

[0016] Step 1: The encoder module takes the preprocessed and standardized part a data as the training set Mapping to latent space.

[0017] Step 2: Use the mean μ(x) of the latent variable a ) and logarithmic variance log(σ 2 (x a ))These two values ​​define the distribution of the latent variable z:

[0018]

[0019] Step 3: Generate latent variable z through mean and variance:

[0020]

[0021] Where I means that the covariance matrix is ​​the identity matrix (that is, the variance of each dimension is 1, and the dimensions are independent.

[0022] Step 4: The decoder module takes the latent variable z as input, remaps it back to the data space (recovering the original data or performing data completion), and outputs the decoded data

[0023]

[0024] Step 5: Introduce the prior distribution p(z) into the latent space. At this time, the encoder and decoder define the conditional distribution P enc (z|x a ) and P dec (x a |z):

[0025] p(z)=∫ x p(z|x a )P(x a )dx≈∫ x P enc (z|x a )P(x a )dx=P enc (z),

[0026] P(x a )=∫ z p(x a |z)p(z)dz≈∫z P dec (x a |z)p(z)dz=P dec (x a ).

[0027] Here P enc (z|x a ) is obtained by encoder calculation, P dec (x a |z) is obtained using the decoder. The goal of this process is to ensure that the output of the encoder is approximately consistent with the prior distribution, that is, p(z)≈P enc (z), the encoder output is close to the high-fidelity prior distribution P(x a )≈P dec (x a ).

[0028] Step 6: Perform training on the training set by minimizing the mean square error (MSE) through weight regularization. The purpose of regularization is to avoid overfitting the training data. The original data x is measured according to the reconstruction error. a and reconstruction data The difference between:

[0029]

[0030] R uses the stochastic gradient descent algorithm to minimize the total loss function. ∝ determines the degree of weight regularization.

[0031] Step 7: Use KL divergence as another regularization parameter to help ensure that the distribution of the latent space is as close to the standard normal distribution as possible. a ) and the prior distribution p(z):

[0032]

[0033] Step 8: Establish a loss function to optimize the model parameters. During the training process, adjust the model by minimizing this loss so that the model gradually learns a suitable latent space representation so that the samples generated from the latent space can be as similar to the original data as possible:

[0034] L VAE =L AE +L KL

[0035] Furthermore, a mathematical model of the natural gas pipeline is constructed based on the Darcy-Weisbach equation, and the generated simulation data can provide pressure loss data based on physical principles. For gas flow, the density ρ changes with pressure and temperature, so the state equation of compressed gas is needed to solve the density. Commonly used gas state equations:

[0036] P=ρRT

[0037] Where P is the gas pressure, ρ is the gas density, R is the gas constant, and T is the gas temperature.

[0038] Furthermore, in order to obtain effective simulation data, it is necessary to determine the basic parameters of the pipeline and the physical properties of natural gas, such as pipeline length, pipeline diameter, surface roughness, temperature, pressure, volume flow, etc.

[0039] Furthermore, the friction factor f of the gas flow is calculated, which mainly depends on the Reynolds number R e It is related to the surface roughness of the pipe and also to the flow type (laminar or turbulent).

[0040] Furthermore, the gas density ρ of natural gas is calculated according to the gas state equation and substituted into the Darcy-Weisbach equation to calculate the pressure loss. The calculation process needs to consider the changes in gas density and flow rate, that is, the gas density ρ is dynamic and needs to be calculated based on the current pressure and temperature.

[0041]

[0042] Furthermore, a generative adversarial network is used, which uses a generator network G and a discriminator network D to compete with each other and optimize each other. The generator generates virtual data similar to the real data, and the discriminator judges the authenticity of the data. In order to enable the network model to process more data, an auxiliary network for specific tasks is added to the original adversarial network. The added auxiliary network can improve the accuracy of data completion and enhance the model's ability to process different types of missing data. The steps are as follows:

[0043] Step 1: The simulation data generated by the mathematical model constructed according to the Darcy-Weisbach equation constitutes the data sample x D , normalize the extracted missing pressure signal b and transform it into the complementary data generated by the self-encoding Synthesize into a new data sample x N .

[0044] Step 2: Use the generator to receive data samples x N , and generate complete pressure data G(w) based on these inputs.

[0045] Step 3: Use the discriminator to distinguish whether the input data is real data or fake data generated by the generator. D As the input of the discriminator, it gives the possibility D(x) that the input data is real data.

[0046] Step 4: Use x D Represents real data samples, using w instead of x N Represent the input of G, with x D ~p data Represents x D Data distribution, w~p w Represents the data distribution of w. In order to enhance and control the data generation performance, additional information c can be added and merged into both G and D for iterative training. In order to achieve the generator's desire to maximize the probability of false data output by the discriminator, the discriminator's desire to minimize the probability of false data output by the generator, and maximize the probability of real data, the minimum maximum objective function is used to conduct adversarial training on the signal. The formula is as follows:

[0047]

[0048] Where D(·) represents the probability that the input belongs to the original sample, and the value range of D(·) is 0 to 1.

[0049] Step 5: Since the input of the discriminator network is based on the simulation data of the Darcy-Weisbach equation, in order to integrate the physical laws into the deep learning model, physical constraints need to be guided. Physical constraints guide the optimization of the generator by introducing additional loss terms to ensure that the generated data does not violate the physical laws. The physical loss function is defined as:

[0050] L py =‖f Darcy-Weisbach (x)-G(w)‖

[0051] Where: G(w) is the pressure signal generated by the generator. py Represents the difference between the generated data and the theoretical pressure loss data.

[0052] Step 6: Construct the final loss function:

[0053] L total =L GAN +λL py

[0054] Where λ is a weight parameter used to balance the weight between statistical generation and physical constraints. total , the generator can not only generate pressure signals that conform to the real distribution, but also satisfy the physical constraints of the Darcy-Weisbach equation. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] In order to more clearly illustrate the technical solution of the present invention, the drawings required for the present invention are described below.

[0056] Figure 1 It is a flowchart of the two-stage signal processing method of the DTV model under the digital twin model described in the present invention;

[0057] Figure 2 This is the structure of the encoder and the decoder in the variational autoencoder described in the present invention.

[0058] Figure 3 This is a flowchart of the generative adversarial network signal completion process in the present invention. DETAILED DESCRIPTION

[0059] In order to better understand the above technical solution, a clear and complete description will be given below in conjunction with the accompanying drawings and specific implementation methods.

[0060] Figure 1 The figure is a flowchart of a two-stage signal processing method of a DTV model under a digital twin model, which is used to complete an incomplete pressure signal of a natural gas pipeline. The method includes the following steps:

[0061] Step S100: Modeling using 3DMax;

[0062] In this embodiment, information such as the size and model of the physical entity is collected, and the pipeline model is constructed through 3DMax.

[0063] Step S110: Use Unity to build a pipeline digital twin model and obtain pipeline operation data;

[0064] In this embodiment, 3DMax is saved as a utodesk FBX file with the suffix .fbx file, and then imported into Unity to build a pipeline digital twin model. Real-time sensor data and historical operation information are integrated through the MongoDB database. Combined with the virtual pipeline model for simulation, the operating status of the pipeline system is fully monitored. Through sensor simulation and real-time data feedback, a large amount of pipeline operation-related data is obtained.

[0065] Step S120: Variational Autoencoder

[0066] In this embodiment, the collected incomplete pipeline pressure signal is input into the variational autoencoder module. The variational autoencoder can effectively learn the potential distribution of the data and generate samples similar to the real data by introducing the probabilistic graph model. And because the probability distribution is used in the encoding and decoding process, it will generate diversified outputs, which helps to enrich the data form.

[0067] Step S130: Darcy-Weisbach equation mathematical model;

[0068] In this embodiment, the Darcy-Weisbach equation is used to construct a mathematical model of the natural gas pipeline based on the basic parameters of the pipeline and the physical properties of natural gas, such as pipeline length, pipeline diameter, surface roughness, temperature, pressure, volume flow, etc. The generated simulation data can provide pressure loss data based on physical principles. The purpose of this process is to generate idealized pipeline pressure simulation data, which is used as the input of the generative adversarial network discriminator to optimize the entire data completion process.

[0069] Step S140: Generate an adversarial network;

[0070] In this embodiment, the model mechanism of the generative adversarial network G and the discriminative network D confronting and optimizing each other is utilized, virtual data similar to real data is generated by the generator, and the authenticity of the data is judged by the discriminator.

[0071] Step S150: Detect whether the generated completion signal meets the requirements;

[0072] In this embodiment, the collected incomplete pressure signal is input into the above signal processing method and goes through steps S120-S140 to determine whether the completed signal meets the requirements.

[0073] Please refer to Figure 3 In this embodiment, further, step S140 may include the following sub-steps:

[0074] Step S300: Using a generator to receive a data sample x N , and generate complete pressure data G(w) based on these inputs.

[0075] In this example, the missing pressure signal b extracted from S110 is normalized and converted into the complementary data generated by the self-encoding Synthesize into a new data sample x N According to the pressure matrix X = [x1, x2, x3, ..., x n ] T ∈R n×t (where n is the number of pressure data and t is the length of the pressure data) defines the incomplete data matrix

[0076] X N =Γ·X

[0077] in

[0078]

[0079] is the kth data value in the i-th pressure data. The incomplete data matrix is ​​input into the generator, and the complete pressure data G(w) is generated based on these inputs.

[0080] Step S310: The simulation data x D Input discriminator;

[0081] The discriminator is used to distinguish whether the input data is real data or fake data generated by the generator. The simulated data generated by the mathematical model based on the Darcy-Weisbach equation constitutes the data sample x D As the input of the discriminator, it gives the possibility D(x) that the input data is real data.

[0082] Step S320: Perform adversarial training

[0083] Using x D Represents real data samples, using w instead of x N Represent the input of G, with x D ~p data Represents x D Data distribution, w~p w Represents the data distribution of w. In order to enhance and control the data generation performance, additional information c can be added and merged into both G and D for iterative training. In order to achieve the generator's desire to maximize the probability of false data output by the discriminator, the discriminator's desire to minimize the probability of false data output by the generator, and maximize the probability of real data, the minimum maximum objective function is used to conduct adversarial training on the signal. The formula is as follows:

[0084]

[0085] Where D(·) represents the probability that the input belongs to the original sample, and the value range of D(·) is 0 to 1.

[0086] Step S330: Construct the final loss function based on the physical loss function

[0087] Since the input of the discriminator network is based on the simulation data of the Darcy-Weisbach equation, in order to integrate the physical laws into the deep learning model, physical constraints need to be guided. Physical constraints guide the optimization of the generator by introducing additional loss terms to ensure that the generated data does not violate the physical laws. The physical loss function is defined as:

[0088] L py =‖f Darcy-Weisbach (x)-G(w)‖

[0089] Where: G(w) is the pressure signal generated by the generator. py Represents the difference between the generated data and the theoretical pressure loss data. The loss function is determined based on adversarial training and the defined physical loss function:

[0090] L total =L GAN +λL py

[0091] Where λ is a weight parameter used to balance the weight between statistical generation and physical constraints. total , the generator can not only generate pressure signals that conform to the real distribution, but also satisfy the physical constraints of the Darcy-Weisbach equation.

[0092] In summary, 3DMax is first used to build the pipeline model. The built model is then imported into Unity to build a digital twin model. Real-time sensor data and historical operation information are integrated through the MongoDB database. Combined with the virtual pipeline model for simulation, the operating status of the pipeline system is fully monitored, and a large amount of data related to pipeline operation is obtained. The variational autoencoder uses the mechanism of probabilistic graph model to effectively learn the potential distribution of data and generate samples similar to real data. Because the probability distribution is used in the encoding and decoding process, diversified outputs will be generated, ensuring the comprehensiveness of data completion. The Darcy-Weisbach equation is used to build a mathematical model of the natural gas pipeline, generate idealized pipeline pressure simulation data, and use it as the input of the generative adversarial network discriminator to optimize the entire data completion process. The model mechanism of the generative adversarial network's generative network G and discriminant network D confronts and optimizes each other, and the generator generates virtual data similar to the real data, and the discriminator judges the authenticity of the data. By reconstructing the errors in the variational autoencoder and the generative adversarial network, the final loss function of the model is constructed, and the L is optimized. total , the generator can generate a pressure signal that conforms to the real distribution.

Claims

1. A two-stage signal processing method for a DTV model based on digital twins, characterized in that: The following steps are involved: S1: Use 3DMax to perform 3D modeling and rendering based on the physical model; S2: Use Unity to build a pipeline digital twin model based on the 3D modeling constructed in S1, integrate real-time sensor data and historical operation information through the MongoDB database, and obtain a large amount of pipeline operation-related data; S3: Input the incomplete signal in the pipeline operation related data obtained by S2 into the variational autoencoder module; S4: According to the Darcy-Weisbach equation, a mathematical model of the natural gas pipeline is constructed to generate idealized pipeline pressure simulation data; S5: Use the simulation data generated in S4 as the input of the generative adversarial network discriminator; S6: Generate data by using the model mechanism of the generative adversarial network's generative network and discriminative network to compete with and optimize each other, and use the discriminator to judge the authenticity of the data.

2. According to claim 1, a two-stage signal processing method for a DTV model based on digital twins is characterized in that: The step S1 performs three-dimensional modeling using 3DMax based on the physical model.

3. According to claim 1, a two-stage signal processing method for a DTV model based on digital twins is characterized in that: Save 3DMax as a utodesk FBX file with the suffix .fbx file, and then import it into Unity to build a pipeline digital twin model. Integrate real-time sensor data and historical operation information through the MongoDB database, combine it with the virtual pipeline model for simulation, and comprehensively monitor the operating status of the pipeline system. Through sensor simulation and real-time data feedback, obtain a large amount of pipeline operation-related data.

4. According to claim 1, a two-stage signal processing method for a DTV model based on digital twins is characterized in that: Input the incomplete pipeline pressure signal collected in step S3 into the variational autoencoder module, and utilize the mechanism of the variational autoencoder using the probabilistic graphical model to effectively learn the potential distribution of the data and generate diversified output samples similar to the real data; The steps are as follows: Step 1: Use the encoder module to take the preprocessed and standardized part a data as the training set Mapping to latent space; Step 2: Use the mean μ(x) of the latent variable a ) and logarithmic variance log(σ 2 (x a ))These two values ​​define the distribution of the latent variable z: Step 3: Generate latent variable z through mean and variance: Step 4: The decoder module takes the latent variable z as input, remaps it back to the data space (recovering the original data or performing data completion), and outputs the decoded data Step 5: Introduce the prior distribution p(z) into the latent space and use the encoder and decoder to define the conditional distribution P enc (z|x a ) and P dec (x a |z): p(z)=∫ x p(z|x a )P(x a )dx≈∫ x P enc (z|x a )P(x a )dx=P enc (z), P(x a )=∫ z p(x a |z)p(z)dz≈∫ z P dec (x a |z)p(z)dz=P dec (x a )。 Here P enc (z|x a ) is obtained by encoder calculation, P dec (x a |z) is obtained using the decoder. The goal of this process is to ensure that the output of the encoder is approximately consistent with the prior distribution, that is, p(z)≈P enc (z), the encoder output is close to the high-fidelity prior distribution P(x a )≈P dec (x a ); Step 6: Train the training set by minimizing the mean square error (MSE) through weight regularization, and measure the original data x according to the reconstruction error a and reconstruction data The difference between: Where R uses the stochastic gradient descent algorithm to determine the degree of weight regularization; Step 7: Use KL divergence as another regularization parameter to help ensure that the distribution of the latent space is as close to the standard normal distribution as possible, measuring the distribution of the encoder output P(x a ) and the prior distribution p(z): Step 8: Establish a loss function to optimize the model parameters: L VAE =L AE +L KL Step 9: Adjust the model by minimizing this loss during the training process so that the model gradually learns a suitable latent space representation so that the samples generated from the latent space can be as similar to the original data as possible.

5. According to claim 1, a two-stage signal processing method for a DTV model based on digital twins is characterized in that: The diversified completion data generated in step S4 and the simulation data generated according to the Darcy-Weisbach equation are respectively used as inputs of the generator network and the discriminator network in the generative adversarial network. The purpose is to utilize the operation mechanism of the generator network and the discriminator network of the generative adversarial network to confront and optimize each other, generate virtual data similar to the real data through the generator, and judge the authenticity of the data through the discriminator; The steps are as follows: Step 1: The simulation data generated by the mathematical model constructed according to the Darcy-Weisbach equation constitutes the data sample x D , normalize the extracted missing pressure signal b and transform it into the complementary data generated by the self-encoding Synthesize into a new data sample x N ; Step 2: Use the generator to receive data samples x N , and generate complete pressure data G(w) based on these inputs; Step 3: Use the discriminator to distinguish whether the input data is real data or fake data generated by the generator; take the data sample x D As the input of the discriminator, it gives the possibility D(x) that the input data is real data; Step 4: Use x D Represents real data samples, using w instead of x N Represent the input of G, with x D ~p data Represents x D Data distribution, w~p w Represents the data distribution of w; in order to enhance and control the data generation performance, additional information c can be added and merged into both G and D for iterative training; Step 5: In order to realize that the generator wants to maximize the probability of false data output by the discriminator, the discriminator wants to minimize the probability of false data output by the generator, and maximize the probability of real data, the minimum maximum objective function is used to perform adversarial training on the signal. The formula is as follows: Step 6: Since the input of the discriminator network is based on the simulation data of the Darcy-Weisbach equation, in order to integrate the physical laws into the deep learning model, physical constraints need to be guided. Physical constraints guide the optimization of the generator by introducing additional loss terms to ensure that the generated data does not violate the physical laws. The physical loss function is defined as: L py =‖f Darcy-Weisbach (x)-G(w)‖ Where: G(w) is the pressure signal generated by the generator. py Indicates the difference between the generated data and the theoretical pressure loss data; Step 7: Construct the final loss function: THE total =L GAN +λL py Where λ is a weight parameter used to balance the weight between statistical generation and physical constraints. total , the generator can not only generate pressure signals that conform to the real distribution, but also satisfy the physical constraints of the Darcy-Weisbach equation.

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