Method for correcting missing data of a physically guided two-phase flow conductivity probe

Abstract

This invention discloses a physical-guided method for correcting missing data from a two-phase flow conductivity probe, relating to the field of two-phase flow parameter measurement. The method includes: acquiring probe time data from a four-sensor conductivity probe; calculating the physical parameters of the effective bubble as a conditional vector based on a two-phase flow parameter calculation model for the four-sensor conductivity probe; constructing a physical-guided generative adversarial network (GAN) for filling in the missing probe time data; generating complete probe time data by filling in the missing probe time data using a generator; inputting the generator's output into a discriminator and a physical loss function, respectively; and alternately training the generator and the discriminator based on the discriminant loss and the physical loss function until the network converges. This invention solves the data integrity problem faced by existing multi-sensor conductivity probes in local two-phase flow parameter measurement.

Description

Technical Field

[0001] This invention relates to the field of two-phase flow parameter measurement, and specifically to a method for correcting missing data of a two-phase flow conductivity probe based on physical guidance. Background Technology

[0002] Two-phase flow refers to the phenomenon of mutual influence between the two phases in a gas-liquid two-phase system during its movement. It is widely present in the flow processes of boilers, nuclear reactors, oil and gas well production equipment, chemical reaction equipment, and many other devices in various industrial and natural processes. In reactors, gas-liquid two-phase flow is crucial, as it relates to the reactor's safety and effectiveness. Especially during reactor design, obtaining accurate two-phase flow parameters, particularly the interfacial area concentration (IAC), is extremely important for ensuring the normal and safe operation of the reactor.

[0003] In two-phase flow analysis within nuclear reactor procedures, a two-fluid model is employed, treating the gas and liquid phases as a continuous, penetrating medium. Conservation equations are derived separately, and the two phases are coupled through interphase interaction terms. Interfacial area concentration, a geometric parameter characterizing the size of the interphase interface area per unit volume of mixture, directly influences mass, momentum, and energy transfer between the two phases and is a crucial parameter in the two-fluid model. Furthermore, statistical parameters of bubbles, such as void fraction, bubble velocity vector, and bubble diameter, also reflect a complete set of parameters for two-phase flow.

[0004] However, due to the complex and varied flow patterns of two-phase flows (bubble flow, slug flow, stirred flow, etc.), and the transient, multi-scale, and three-dimensional structural characteristics of the phase interface, traditional volume-averaged or cross-sectional-averaged measurement methods are insufficient to meet the needs of fine characterization of local interface structures. Therefore, developing local two-phase flow parameter measurement techniques and establishing a reliable database of interfacial area concentration and bubble parameters are of significant scientific and engineering value for deepening the understanding of two-phase flow mechanisms and improving the predictive capabilities of reactor system analysis models. Summary of the Invention

[0005] To address the aforementioned shortcomings in existing technologies, this invention provides a method for correcting missing data in a two-phase flow conductivity probe based on physical guidance, which solves the data integrity problem faced by existing multi-sensor conductivity probes in the measurement of local two-phase flow parameters.

[0006] To achieve the aforementioned objectives, the present invention employs the following technical solution: a method for correcting missing data from a physically guided two-phase flow conductivity probe, comprising the following steps: Acquire probe time data of the four-sensor conductivity probe, the probe time data including the contact time and departure time of each sensor from the bubble; Based on the complete probe time data of the effective bubble, the physical parameters of the effective bubble are calculated as a condition vector according to the four-sensor conductivity probe two-phase flow parameter calculation model. The physical parameters include the bubble diameter and the bubble velocity vector. A physical-guided generative adversarial filling network is constructed, which includes a generator and a discriminator. The input of the generator includes the original probe time data, mask matrix, noise vector and condition vector. The generator fills in the missing probe time data to generate complete probe time data. The output of the generator is input into the discriminator and the physical loss function, respectively. The physical loss function includes time sequence constraints, minimum time difference constraints, axial velocity consistency constraints, and lateral velocity lower limit constraints. Based on the discriminant's discriminant loss and the physical loss function, the generator and the discriminant are trained alternately until the network converges; A trained physical-guided generative adversarial infilling network is used to fill in and correct missing probe time data.

[0007] Furthermore, the time sequence constraint for:

[0008] in, This represents the total number of bubble samples. ReLU penalty ，k For probe number, The contact time between the bubble and each probe is [missing information]. This represents the time it takes for the bubble to leave each probe. i Number the bubbles.

[0009] Furthermore, the minimum time difference constraint for:

[0010]

[0011] in, To calculate the minimum time difference between the contact of the probes before and after the test using the training dataset, Bubbles from 0 to k The contact time difference of the probe after the number Bubbles from 0 to k The time difference between the departure of the probe after the number Let be the distance vector between probe 0 and probe 1. and The mean and standard deviation of the velocity are calculated using the complete training set data.

[0012] Furthermore, the axial velocity consistency constraint for:

[0013] in, The axial velocity was calculated by back-calculating the probe time data after filling. Let be the prior target axial velocity in the conditional vector. The mean axial velocity is calculated using the training dataset.

[0014] Furthermore, the lower limit constraint of the lateral velocity for:

[0015] in, This is the lower limit threshold for lateral velocity. To compensate for lateral velocity.

[0016] Furthermore, the total loss of the physical-guided generative adversarial filling network... for:

[0017] in, For physical loss function, To reconstruct the loss, To combat the losses, This is due to discriminator loss.

[0018] Furthermore, before acquiring probe time data, the process includes a step of generating a bubble-probe interaction time dataset through Monte Carlo simulation: based on the assumption of spherical bubbles and the assumption that the bubble velocity direction is uniformly distributed in space, the bubble velocity direction and bubble diameter are randomly generated, the bubble spherical equation is solved to obtain the contact time and departure time between each sensor and the bubble, and bubble-probe interaction time datasets under different axial flow velocities and velocity fluctuation conditions are generated in batches.

[0019] Furthermore, both the generator and the discriminator are multi-layer fully connected neural networks. The generator contains three hidden layers with 256, 256, and 8 neurons in each hidden layer, respectively, and the discriminator contains three hidden layers.

[0020] Further, training the generator and the discriminator includes: dividing the effective bubble dataset into a training set, a validation set, and a test set in a 7:2:1 ratio; training the physical-guided generative adversarial filling network on the training set; adjusting the network hyperparameters on the validation set; and evaluating the filling accuracy on the test set.

[0021] The beneficial effects of this invention are: This invention injects the diameter and velocity vector of the effective bubble as a conditional vector into the generator, so that the network is constrained by the physical prior of "given bubble size and approximate velocity distribution range" when filling missing time, avoiding unconstrained wandering in 8-dimensional time space, and the filling result has physical rationality.

[0022] This invention designs a physical loss function that includes time sequence constraints, minimum time difference constraints, axial velocity consistency constraints, and lateral velocity lower limit constraints, so that the filling result strictly satisfies the kinematic laws of the four-sensor probes—the bubble must contact the leading probe first and then the following probe, and the same probe must contact first and then leave—fundamentally avoiding the problem of physical paradoxes generated by traditional data-driven methods.

[0023] This invention jointly optimizes the physical loss function with the adversarial loss and reconstruction loss of the generative adversarial network, so that the filling result conforms to both the statistical distribution of data and the physical laws. It has a significant advantage over the traditional correction factor method in predicting interface area concentration. The prediction error can be controlled within 10% under various flow rate conditions, while the error of the traditional method increases significantly with the increase of the missing bubble ratio under high speed and high fluctuation conditions. Attached Figure Description

[0024] Figure 1 This is a flowchart of a method for correcting missing data from a physical-guided two-phase flow conductivity probe.

[0025] Figure 2 Diagram of the physical-guided GAIN neural network architecture.

[0026] Figure 3 This is a box-shaped diagram of a violin.

[0027] Figure 4 The graph shows the evolution of bubble diameter and velocity modulus with flow velocity for different datasets under high-velocity fluctuations.

[0028] Figure 5 This is a graph showing the evolution of axial and lateral velocities with flow velocity for different datasets under high-speed fluctuations.

[0029] Figure 6 This figure shows the evolution of bubble diameter and velocity modulus as a function of velocity fluctuations in different datasets under high flow conditions.

[0030] Figure 7 This is a graph showing the evolution of axial and lateral velocities as a function of velocity fluctuations in different datasets under high flow conditions.

[0031] Figure 8 A comparison chart of predicted interfacial area concentrations under different flow rate conditions.

[0032] Figure 9This is a diagonal error plot for two methods under different flow rate conditions.

[0033] Figure 10 A comparison chart of predicted interfacial area concentration values ​​under different velocity fluctuation conditions.

[0034] Figure 11 The diagram shows the diagonal error of the two methods under different speed fluctuation conditions. Detailed Implementation

[0035] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0036] The four-sensor conductivity probe of this invention consists of four sensors with an outer diameter of 0.25 mm, including one longer upstream sensor (sensor 0) and three shorter downstream sensors (sensors 1, 2, and 3). The sensors are made of 316L stainless steel wire, coated with an electrically insulating layer, and the four sensors are fixedly encapsulated in a four-hole insulating tube made of Al2O3. The axial distance between the probes is 2.5 mm, and the lateral spacing is 0.25 mm, ensuring that the measured minimum bubble size is accurate to the millimeter level.

[0037] Conductivity probes utilize the difference in conductivity between the gas and liquid phases to measure two-phase parameters. During measurement, the sensor tip and the outer casing serve as the positive and negative electrodes, respectively, and a specific voltage is applied to each sensor. When the exposed sensor tip is immersed in the liquid phase with higher conductivity, the circuit closes, generating a low-baseline signal in the loop; when the tip contacts the gas phase with lower conductivity, the circuit opens, generating a high-pulse signal in the loop. Based on the four sets of voltage signals measured by the four-probe conductivity probes and the probe dimensions and structure, a series of relevant parameters of the two-phase flow can be calculated.

[0038] Before acquiring probe time data, this invention also includes a step of generating a bubble-probe interaction time dataset through Monte Carlo simulation: based on the assumption of spherical bubbles and the assumption that the bubble velocity direction is uniformly distributed in space, the bubble velocity direction and bubble diameter are randomly generated, and the bubble spherical equation is solved to obtain the contact time and departure time between each sensor and the bubble, thus generating bubble-probe interaction time datasets in batches under different axial flow velocities and velocity fluctuation conditions. The specific implementation is as follows: This invention is based on the following two fundamental assumptions: (1) Spherical bubble assumption: The distance from any point on the bubble surface to the center satisfies the spherical equation, and the bubble diameter follows a normal distribution.

[0039] (2) Assumption of uniform velocity distribution: The direction of bubble velocity is uniformly distributed in space. The bubble velocity vector is represented as:

[0040]

[0041]

[0042] in, Let be the axial velocity of the bubble. For relative velocity fluctuation components, The maximum relative velocity fluctuation component can be derived experimentally from the formula. lateral velocity The unit vector, as shown in the formula, is derived from the angle. , Sure( ∈[0, ], ∈[0, 2π]), , , They are respectively x , y , z The unit vector of the axis.

[0043] Monte Carlo simulation first generates the initial bubble velocity using random numbers, transforming the question of "whether the probe should capture the bubble" into a question of whether a quadratic equation has a solution. Based on the solution to the equation, the bubbles are divided into valid bubbles and missing bubbles. Simultaneously, a large sample size is repeatedly sampled to obtain statistical values ​​of the bubble motion patterns, thereby studying the influence of a certain factor on the probe measurement results. The specific steps are as follows: (1) Given probe positions: The four sensors are divided into one front probe (0) and three rear probes. In the global coordinate system o-xyz, the distance from the bubble center to all probes is obtained according to the vector triangle.

[0044] (2) Initialize bubble position: The bubble center is evenly distributed on a circular plane 20mm away from the plane of probe 0, and the bubble velocity is obtained by randomly generating the direction angle.

[0045] (3) Initialize bubble diameter: Based on the assumption of spherical bubble, the bubble diameter follows a normal distribution.

[0046] (4) Coordinate transformation: Rotate the local coordinate system to be parallel to the direction of bubble velocity to simplify the calculation.

[0047] (5) Solve the spherical equation: Transform the contact problem between the probe and the bubble into solving a quadratic equation in terms of time t to obtain the contact time between the bubble and each probe. and departure time (k=0,1,2,3).

[0048] (6) Bubble Classification: Based on the solution to the spherical equation, bubbles are classified into effective bubbles (contacting all four probes), missing bubbles (not contacting all probes), and escape bubbles (not contacting any probes). The ratio of missing bubbles to... Defined as:

[0049] in, This represents the number of missing bubbles. This represents the number of valid bubbles.

[0050] This invention establishes a two-phase flow parameter calculation model using a four-sensor conductivity probe, as detailed below: In this invention, complete probe time data (8 time values) of the effective bubble are used to calculate the bubble diameter, velocity vector, and interfacial area concentration. These physical quantities are also used as conditional vector input generators.

[0051] (1) Calculation of bubble velocity Due to the curvature of the spherical interface, the transmission time of a single interface cannot be directly used for velocity calculation. This is achieved by establishing a connection between sensor 0 and... By examining the vector polygonal relationship between the two interfaces, it was found that taking the harmonic average of the measurable displacement velocities of the two interfaces can eliminate the uncertainty caused by the interface curvature.

[0052] in, For sensor 0 The measurable bubble displacement velocity of the number For the first h The interface before the bubble and the probe before number 0 k The time difference between the probes after the number For the first h The interface after the bubble and the probe before number 0 k The time difference between the probes after the number For probe 0 and k The distance vector of the probe after the number. Further utilizing the unit vector of the bubble velocity direction. relative to probe direction Geometric projection relationship Solving the system of equations for the three pairs of sensors yields a linear equation system concerning the cosine of the velocity direction. The magnitude of the bubble velocity is then obtained using Cramer's rule.

[0053]

[0054] and the direction of velocity:

[0055] In the formula, Let be the coefficient determinant formed by the cosines of the probe direction. , , To be The first, second, and third columns are replaced with column vectors in sequence. The resulting determinant, , , Let the distance vectors of probe 0 (front) and probe 1 (back) be the angles between them and the coordinate axes; similarly... , , , , , Let be the angles between the distance vectors of probe 0 (front) and probe 2 (back) and the coordinate axes. , , Let be the angles between the distance vectors of probe 0 (front) and probe 3 (rear) and the coordinate axes. These together constitute the explicit solution to the bubble's three-dimensional velocity vector.

[0056] Furthermore, the isosceles triangle relationship from the bubble center to the sensor's zero contact point satisfies the following conditions regarding the velocity magnitude, diameter, and interface normal:

[0057] in, For the first h The duration of the bubble on probe 0, The diameter of the bubble. For the first h The unit velocity vector of a bubble, Let be the normal unit vector of the front interface of the bubble at probe 0. Let be the normal unit vector at probe 0 on the back interface of the bubble. This formula will serve as a crucial bridge connecting the speed and diameter.

[0058] (2) Calculation of bubble diameter To determine the bubble diameter First, the normal unit vectors of the front and back interfaces need to be obtained. The sensor projects the chord length along the connecting line direction. It is explicitly given by the measurement time, speed, and probe spacing:

[0059] in, For the duration of stay Known combinations of interface transmission time (taken from the previous interface) Take it from the back interface ), For the first lInterface contact 0 k Time difference between probe pairs Number 0 k The unit distance vector of the probe pair. Projecting the three pairs of sensors. , , Simultaneously solve the equations, using Cramer's rule to find the direction cosine of the interface normal, and combine... Normalization constraints for unit vectors:

[0060] In the formula, , , Normal unit vector The angle between the coordinate axis and the coordinate axis.

[0061] Eliminating the direction cosine yields the explicit expression for the diameter:

[0062] In the formula, , , To be The first, second, and third columns are replaced with projection vectors in sequence. The resulting determinant. Solving for the bubble diameter. The process relies on only 8 probe timing information and probe geometric parameters.

[0063] (3) Calculation of interfacial area concentration benchmark To quantitatively evaluate the accuracy of the subsequent physical-guided GAIN neural network filling results, a baseline true value for the interfacial area concentration (IAC) needs to be established in a Monte Carlo simulation. In the Monte Carlo simulation, the baseline true value of the interfacial area concentration (IAC) can be obtained from the known geometric parameters used when generating the bubbles through classical relationships.

[0064] For spherical or near-spherical bubble swarms, the local interfacial area concentration... With local cavitation share Sauter's average diameter Satisfying strict relations:

[0065] Therefore, the calculation of the interfacial area concentration baseline is transformed into calculating separately. and .

[0066] Voiding Defined as the volume fraction of the gas phase within the control volume. Let the sampling time... Internal volume control The total number of bubbles is The void fraction is then the ratio of the total bubble volume to the control volume:

[0067] In the formula, In order to control volume The Middle The volume occupied by each bubble.

[0068] Defined as the diameter of an equivalent sphere, which has the same volume-to-surface-area ratio as the bubble swarm under investigation. In Monte Carlo simulations, the bubbles are assumed to be spheres, and their surface area is... and volume Calculated based on the set parameters. Therefore:

[0069] The true value of the interface area concentration under simulated conditions is obtained through this benchmark algorithm, which serves as the standard true value for evaluating the physically guided GAIN neural network.

[0070] The construction of the physics-guided GAIN neural network is the core of this invention. The physics-guided GAIN neural network makes two key improvements to the traditional GAIN framework: first, it adds a conditional vector to the generator input; second, it adds a physics loss term to the loss function.

[0071] Compared to the traditional GAIN neural network framework, the physical-guided GAIN neural network adds a condition vector C to the data processing and generator input parts. It is calculated from the effective bubble time data in the Monte Carlo simulation dataset. It serves as a priori physical condition that the simulation data should have, and during the training process, it ensures that the final output result conforms to the simulation conditions.

[0072] Secondly, traditional GAIN neural network loss functions only include generator loss and discriminator loss. To ensure that the final output meets the requirements of real physics, a physics loss term is added to the loss function. By using the physical equations that need to be satisfied in this scenario, GAIN not only learns the data distribution during training, but also learns to fill in the missing values ​​that satisfy the physical conditions.

[0073] like Figure 1 and Figure 2 As shown, a method for correcting missing data of a two-phase flow conductivity probe based on physical guidance includes the following steps: S1: Acquire probe time data of the four-sensor conductivity probe, the probe time data including the contact time and departure time of each sensor from the bubble; S2: Based on the complete probe time data of the effective bubble, the physical parameters of the effective bubble are calculated as the condition vector C according to the four-sensor conductivity probe two-phase flow parameter calculation model. The physical parameters include the bubble diameter and the bubble velocity vector.

[0074] in, For the effective bubble diameter vector, The effective bubble velocity vector is used. These two physical quantities are used as conditional vectors because the effective bubble has complete information from the eight probe times, which can be used to calculate the relevant parameters of the effective bubble; and both the effective bubble and the missing bubble are obtained by randomly generating bubble diameter and velocity vectors using the Monte Carlo principle, so these two types of bubbles have the same diameter and velocity range under simulation conditions.

[0075] S3: Construct a physically guided generative adversarial filling network, which includes a generator and a discriminator. The input of the generator includes the original probe time data, mask matrix, noise vector and conditional vector. Both the generator and the discriminator are multi-layer fully connected neural networks. The generator contains three hidden layers with 256, 256, and 8 neurons in each hidden layer, respectively. The discriminator also contains three hidden layers.

[0076] S4: The missing probe time data is filled in by the generator to generate complete probe time data; S5: Input the output of the generator into the discriminator and the physical loss function respectively. The physical loss function includes time sequence constraints, minimum time difference constraints, axial velocity consistency constraints, and lateral velocity lower limit constraints. This invention addresses the issue of total loss function. Adding a physical loss term yields a new total loss function. This ensures that the filling results meet the actual physical background and improves the rationality of the data.

[0077] Physically guided generative adversarial methods fill the total loss of the network. for:

[0078] in, For physical loss function, To reconstruct the loss, To combat the losses, This is due to discriminator loss.

[0079] Time sequence constraints for: Based on the physical fact that bubbles pass through the probes sequentially, it is required that the entry time of the same probe is earlier than its exit time, and that reference probe 0 is contacted before the other probes:

[0080] in, This represents the total number of bubble samples. ReLU penalty ，k For probe number, The contact time between the bubble and each probe is [missing information]. This represents the time it takes for the bubble to leave each probe. i Number the bubbles.

[0081] Minimum Time Difference Constraint for: To prevent the calculation results from diverging due to the extremely small time difference after filling, the probe spacing is used as a reference. Derivation of the physical minimum time difference from the modulus statistics of the training set velocity:

[0082]

[0083] in, To calculate the minimum time difference between the contact of the probes before and after the test using the training dataset, Bubbles from 0 to k The contact time difference of the probe after the number Bubbles from 0 to k The time difference between the departure of the probe after the number Let be the distance vector between probe 0 and probe 1. and The mean and standard deviation of the velocity are calculated using the complete training set data.

[0084] Axial velocity consistency constraint for: By using the filling time to inversely calculate the bubble velocity vector, the magnitude of the bubble velocity can be obtained. And the filling axial velocity is obtained by the angle between the velocity directions. Compare it with the prior target axial velocity in the condition vector. Comparison, define the normalized mean square error:

[0085] in, The axial velocity was calculated by back-calculating the probe time data after filling. Let be the prior target axial velocity in the conditional vector. The mean axial velocity is calculated using the training dataset.

[0086] Lateral velocity lower limit constraint for:

[0087] in, This is the lower limit threshold for lateral velocity. To compensate for lateral velocity.

[0088] This constraint ensures that the missing bubble in the probe still retains a lateral motion component consistent with the flow field conditions, preventing the filling result from degenerating into pure axial motion.

[0089] S6: Based on the discriminant's discriminant loss and the physical loss function, train the generator and the discriminant alternately until the network converges; The effective bubble dataset was divided into training, validation, and test sets in a 7:2:1 ratio. The physical-guided generative adversarial filling network was trained on the training set, the network hyperparameters were tuned on the validation set, and the filling accuracy was evaluated on the test set.

[0090] S7: Use a trained physical-guided generative adversarial incomplete network to fill in and correct missing probe time data.

[0091] In one embodiment of the present invention, the missing patterns of missing bubbles under different speed fluctuations were statistically analyzed. Table 1 shows the statistical results of a certain simulation. In the table, the missing patterns correspond to the presence or absence of time information from the eight probes. Positions 1 and 2 correspond to probes before probe 0, positions 3 and 4 correspond to probes after probe 1, positions 5 and 6 correspond to probes after probe 2, and positions 7 and 8 correspond to probes after probe 3. 1 indicates missing, and 0 indicates presence. Observation of the existing missing patterns revealed that bubbles only simultaneously lack all time information from the same probe; and the number of missing 2 probes is the most common, with very few missing 3 or 1 probes.

[0092] Table 1. Statistics on Missing Bubble Patterns

[0093] Because the temporal information of missing bubbles obtained from Monte Carlo simulations is incomplete, the true values ​​at the missing locations cannot be obtained, thus the network cannot evaluate the filling effect. Therefore, based on the physically real missing patterns, artificially created missing bubbles of the same pattern are generated and partitioned in the effective Monte Carlo simulation bubble dataset. The network's filling values ​​are compared with the true values ​​to evaluate the network's filling accuracy. The trained network is then applied to the missing bubbles to obtain the network's extrapolation and generalization ability. The specific use and partitioning of the Monte Carlo simulation dataset are shown in Table 2 below. The network parameter settings are shown in Table 3.

[0094] Table 2 Dataset Partitioning

[0095] Table 3. Physically Guided GAIN Neural Network Parameter Settings

[0096] When evaluating the accuracy of the physically guided GAIN network in filling in missing data, the distributions of bubble diameter and velocity were compared between the training and test sets, using a violin plot instead of a box plot alone. Box plots only provide quantiles, while violin plots, through kernel density estimation, present the overall outline of the probability density, allowing for intuitive judgment of whether the distribution is skewed, whether the tails are elongated, and whether outliers are clustered. Examining these distribution characteristics from a statistical perspective verifies the physical plausibility of the neural network's incomplete results. Figure 3 In the violin plot, the median is marked with a thick horizontal solid line. ), the vertical solid line connects the first quartile ( ) and the third quartile ( The vertical dashed line extends to the boundary at 1.5 times the interquartile range ( ). , ) is used to mark potential outliers.

[0097] The results from the training set, the artificially created missing test set, and the real missing dataset are plotted side-by-side. By comparing the contour envelope shape, median overlap, and interquartile range overlap, it is determined whether the network has restored the statistical distribution of the original bubble parameters. If the test set contour is basically covered by the training set envelope and the median is highly consistent, it can be considered that the diameter and velocity of the filled bubble still maintain the original distribution characteristics at the statistical level.

[0098] (1) Effect of bubble velocity on GAIN filling performance: At the maximum speed fluctuation ( With the value set to 0.5, three training sets were generated by changing the axial velocity of the bubbles in the Monte Carlo simulation: low flow rate ( =0.35 m / s), medium velocity ( =0.8 m / s) and high flow velocity ( =1.2 m / s), to investigate the filling performance of GAIN network under different flow velocities. Figure 4 and 5 The distributions of diameter, velocity modulus, axial velocity, and lateral velocity obtained by back-calculation after network filling are shown under three working conditions. The velocity modulus is also calculated. axial velocity and lateral speed The formula is as follows:

[0099] Based on the training set, with a fixed fluctuation of 0.5, the axial velocity increases with increasing flow velocity. With velocity modulus Increase, lateral velocity The velocity also increased from approximately 0.1 m / s to 0.35 m / s, while the diameter distribution remained stable around 4–6 mm. The diameter distribution of the artificial missing test set remained consistently low, and the lateral velocity… The results are significantly higher than those of the training set, indicating that the network, after physical guidance, learned to increase the lateral velocity component during the filling process, demonstrating the effectiveness of physical constraints.

[0100] The diameter of the true missing data set is relatively small, with the median consistently remaining between 2.5 and 3 mm, significantly lower than the 5 mm of the training set. Furthermore, the extreme outliers become more pronounced as the flow velocity increases, indicating that the true missing bubbles are predominantly small to medium in diameter.

[0101] In summary, under a fixed high volatility ( Under the condition of 0.5, the accuracy of the network in filling in the axial velocity of artificially missing bubbles improves with increasing flow velocity, and the consistency between the test set and the training set reaches its best at high flow velocities. However, the inverse calculation results of real missing bubbles become increasingly discrete with increasing flow velocity, manifested in an increase in extreme outliers in diameter and a widening of the velocity distribution range. This indicates that under high flow velocity and high fluctuation conditions, the physical mechanism of real missing bubbles differs too much from the artificial random missing bubbles in the training set, and the introduction of conditional vectors weakens the effect on real missing bubbles. (2) The effect of velocity fluctuation on GAIN filling performance: To verify the filling capability of the physically guided GAIN proposed in this invention under different velocity fluctuations, under high flow velocity conditions ( =1.2 m / s), the maximum velocity fluctuation parameter of the Monte Carlo simulation was gradually increased from 0.1 to 0.5 to generate five training sets, and imputation experiments were carried out under the same missing mode. Figure 6 and Figure 7 The distribution of diameter, velocity modulus, axial velocity, and lateral velocity of the training set, the artificial missing test set, and the real missing bubbles under various velocity fluctuations is presented.

[0102] From the training set, axial velocity With velocity modulus It remained relatively stable around 1.2~1.3 m / s, but the lateral velocity... The value increases significantly with increasing volatility, indicating that increasing velocity volatility in Monte Carlo simulations introduces a stronger lateral velocity component. The artificial missing test set shows improvements in diameter, and The three physical quantities maintained good consistency with the training set, indicating that under the condition of knowing part of the probe time, the GAIN network can accurately recover the missing time with the help of the constraint of the conditional vector C, and then calculate the reasonable physical quantities, which shows that the network has strong filling ability.

[0103] The calculated diameter, which is missing from the actual value, is still significantly smaller than expected. and The actual missing value is significantly lower than that in the training set and decreases with increasing fluctuations, which is in stark contrast to the test set where it remains stable at around 1.1 m / s. In cases of true missing values, the results consistently closely match those of the test set, significantly outperforming those of the training set under similar fluctuations.

[0104] The results of true missing data imputation further explain the formation of true missing bubbles. The local velocity vector of true missing bubbles has a large angle with the mainstream axis, and the probe's failure to contact them is not due to random loss, but because the bubble trajectory deviates from the mainstream direction. These bubbles themselves have a small diameter but a large lateral component, so the back-calculated results show the characteristics of small diameter, low axial velocity, and high lateral velocity. It is worth noting that as the velocity fluctuation increases, the concentration of the true missing diameter distribution improves, indicating that the larger velocity fluctuation allows the network to learn more types of data, slightly improving its adaptability to true missing data, but the systematic bias has not been eliminated.

[0105] In summary, under high flow rates, the physical-guided GAIN neural network is generally reliable in filling artificial missing parts, and the test set and training set of artificial missing parts are highly consistent in terms of diameter and axial velocity. However, due to the fundamental difference in physical mechanism between real missing bubbles and the training set, the back-calculation results show that the diameter is systematically smaller, the axial velocity is lower, and the lateral velocity is higher.

[0106] (3) Comparison of interfacial area concentration predictions: To verify the accuracy of the physically guided GAIN neural network in predicting interfacial area concentration, a control group was set up. The prediction results were compared with the simulated baseline and the traditional correction factor based on the missing bubble ratio, as shown in the equation:

[0107] In the formula, This is the corrected total interfacial area concentration. The contribution of effective bubbles to the interfacial area concentration, The missing bubble ratio is given by the formula. calculate. At a constant speed fluctuation ( Under the condition of 0.3), the predicted interfacial area concentration for three velocity conditions was obtained. Specific data can be found in [link to data]. Figure 8 The diagonal error plots for the two methods are shown below. Figure 9 The control group maintained a consistent missing rate. Under these conditions, the true value of the interfacial area concentration gradually decreased, following the principle that increased velocity leads to a shorter duration of bubble passage through the probe and a decrease in the time-averaged cavitation fraction, as shown by the formula... It can be seen that the interfacial area concentration decreases.

[0108] In terms of prediction accuracy, the neural network predictions are generally slightly lower than the true values, but the deviation is not large, and the relative error decreases with higher flow velocities. Traditional correction factors overestimate the value in almost all operating conditions. The compensation mechanism of this method is essentially an empirical compensation for the contribution of missing bubbles; once the missing bubble ratio changes, this empirical compensation struggles to accurately reproduce the actual contribution of missing bubbles. Quantitatively, the neural network keeps the prediction error of interfacial area concentration within 10% at various velocities; traditional methods, on the other hand, consistently deviate from the true value. For precise measurements of two-phase flow parameters, this level of accuracy is clearly insufficient. This demonstrates that the physically guided GAIN network filling strategy maintains good prediction consistency under different flow velocity conditions, providing a feasible technical path for correcting missing data from conductivity probes.

[0109] At high flow rates, such as Figure 10 The figure shows the prediction results under different speed fluctuations. Figure 11 The diagram shows the diagonal error. Traditional correction factors exhibit high accuracy in the low-fluctuation region (0.1~0.2), but the predicted values ​​increase rapidly as velocity fluctuations increase, indicating that traditional methods are highly sensitive to the size of missing bubbles. The neural network's predicted values ​​are lower than the true values ​​in the low-fluctuation region, suggesting that the training set lacks sufficient sample types and the constraint power of the conditional vector is weak, leading to bias in the generator's inference of low-fluctuation missing patterns. The neural network achieves the best prediction accuracy when velocity fluctuation reaches 0.3, indicating that the physical loss function effectively constrains the missing patterns when they become moderately complex. However, the prediction accuracy decreases as fluctuations increase, suggesting that as the missing patterns become more complex, the network generator tends to output conservative estimates to avoid physical loss penalties, resulting in decreased accuracy.

[0110] In summary, under low volatility conditions, the number of missing bubbles is relatively low, and traditional methods perform well; neural networks perform well in the medium volatility range, but their predictive ability fluctuates under high volatility conditions.

[0111] Those skilled in the art will recognize that the embodiments described herein are intended to help the reader understand the principles of the invention, and should be understood that the scope of protection of the invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific modifications and combinations based on the technical teachings disclosed in this invention without departing from the spirit of the invention, and these modifications and combinations are still within the scope of protection of the invention.

Claims

1. A method for correcting missing data of a two-phase flow conductivity probe based on physical guidance, characterized in that, Includes the following steps: Acquire probe time data of the four-sensor conductivity probe, the probe time data including the contact time and departure time of each sensor from the bubble; Based on the complete probe time data of the effective bubble, the physical parameters of the effective bubble are calculated as a condition vector according to the four-sensor conductivity probe two-phase flow parameter calculation model. The physical parameters include the bubble diameter and the bubble velocity vector. A physical-guided generative adversarial filling network is constructed, which includes a generator and a discriminator. The input of the generator includes the original probe time data, mask matrix, noise vector and condition vector. The generator fills in the missing probe time data to generate complete probe time data. The output of the generator is input into the discriminator and the physical loss function, respectively. The physical loss function includes time sequence constraints, minimum time difference constraints, axial velocity consistency constraints, and lateral velocity lower limit constraints. Based on the discriminant's discriminant loss and the physical loss function, the generator and the discriminant are trained alternately until the network converges; A trained physical-guided generative adversarial infilling network is used to fill in and correct missing probe time data.

2. The method for correcting missing data of a two-phase flow conductivity probe based on physical guidance according to claim 1, characterized in that, The time order constraint for: in, This represents the total number of bubble samples. ReLU penalty ，k For probe number, The contact time between the bubble and each probe is [value missing]. This represents the time it takes for the bubble to leave each probe. i Number the bubbles.

3. The method for correcting missing data of a two-phase flow conductivity probe based on physical guidance according to claim 2, characterized in that, The minimum time difference constraint for: in, To calculate the minimum time difference between the contact of the probes before and after the test using the training dataset, Bubbles from 0 to k The contact time difference of the probe after the number Bubbles from 0 to k The time difference between the departure of the probe after the number Let be the distance vector between probe 0 and probe 1. and The mean and standard deviation of the velocity are calculated using the complete training set data.

4. The method for correcting missing data of a two-phase flow conductivity probe based on physical guidance according to claim 3, characterized in that, The axial velocity consistency constraint for: in, The axial velocity was calculated by back-calculating the probe time data after filling. Let be the prior target axial velocity in the conditional vector. The mean axial velocity is calculated using the training dataset.

5. The method for correcting missing data of a two-phase flow conductivity probe based on physical guidance according to claim 4, characterized in that, The lower limit constraint of lateral velocity for: in, This is the lower limit threshold for lateral velocity. To compensate for lateral velocity.

6. The method for correcting missing data of a two-phase flow conductivity probe based on physical guidance according to claim 5, characterized in that, The total loss of the physically guided generative adversarial filling network for: in, For physical loss function, To reconstruct the loss, To combat the losses, This is due to discriminator loss.

7. The method for correcting missing data of a two-phase flow conductivity probe based on physical guidance according to claim 1, characterized in that, Before acquiring probe time data, the process also includes generating a bubble-probe interaction time dataset through Monte Carlo simulation: based on the assumption of spherical bubbles and the assumption that the bubble velocity direction is uniformly distributed in space, the bubble velocity direction and bubble diameter are randomly generated, the bubble spherical equation is solved to obtain the contact time and departure time between each sensor and the bubble, and bubble-probe interaction time datasets under different axial flow velocities and velocity fluctuation conditions are generated in batches.

8. The method for correcting missing data of a two-phase flow conductivity probe based on physical guidance according to claim 1, characterized in that, Both the generator and the discriminator are multi-layer fully connected neural networks. The generator contains three hidden layers with 256, 256, and 8 neurons in each hidden layer, respectively. The discriminator also contains three hidden layers.

9. The method for correcting missing data of a two-phase flow conductivity probe based on physical guidance according to claim 1, characterized in that, Training the generator and the discriminator includes: dividing the effective bubble dataset into a training set, a validation set, and a test set in a 7:2:1 ratio; training the physical-guided generative adversarial filling network on the training set; adjusting the network hyperparameters on the validation set; and evaluating the filling accuracy on the test set.

Images