Method and device for predicting thickness of concentration polarization layer of reverse osmosis membrane based on electrical impedance imaging

Abstract

This invention discloses a method and apparatus for predicting the thickness of the concentration polarization layer in a reverse osmosis membrane based on electrical impedance imaging, belonging to the field of non-destructive monitoring technology of membrane processes. The method includes: constructing a simulation model based on an electrode array membrane filter sensor; setting virtual media with different conductivities on the membrane surface and reconstructing the simulated conductivity image using the conjugate gradient least squares algorithm and sensitivity matrix, and training an improved neural network using known conductivity; reconstructing the measured conductivity image using a measured boundary voltage dataset; predicting the estimated conductivity value of the membrane surface using the trained improved neural network and mapping the concentration polarization layer thickness. The method solves the problem of difficult concentration polarization layer thickness calibration by generating conductivity images with conductivity labels through numerical simulation. Furthermore, by training the improved neural network, it can predict the true conductivity value based on the conductivity image. Combined with membrane mass transfer theory, an interpretable mapping of the concentration polarization layer thickness is performed, enabling online non-destructive quantitative detection of the concentration polarization layer thickness.

Description

Technical Field

[0001] This invention relates to the field of non-destructive monitoring technology for membrane processes, and in particular to a method and apparatus for predicting the thickness of the concentration polarization layer in a reverse osmosis membrane based on electrical impedance imaging. Background Technology

[0002] Reverse osmosis membranes are widely used in seawater desalination, wastewater recycling, and pure water production. During operation, solutes accumulate on the membrane surface, forming a concentration polarization layer. This leads to problems such as increased local concentration, decreased transmembrane flux, and increased energy consumption, and in severe cases, it can accelerate membrane fouling. The thickness of the concentration polarization layer is an important parameter for the mass transfer state and operating performance of the reverse osmosis membrane. However, because the formation region is close to the membrane surface and is very small, it is difficult to achieve online, non-destructive quantitative measurement using conventional methods.

[0003] Existing technologies often rely on macroscopic process quantities such as flux changes, pressure differences, or salt permeability to briefly estimate the degree of concentration polarization, resulting in limited accuracy. Alternatively, offline characterization methods such as laser interferometry and fluorescence tracing can be used, which cannot achieve continuous monitoring in closed systems. Electrical impedance imaging (EIT) technology applies current through an electrode array, acquires voltage, and reconstructs the conductivity distribution, offering advantages such as non-invasiveness and high temporal resolution. However, when used for reverse osmosis membrane process monitoring, especially for detecting the thickness of the concentration polarization layer, it suffers from insufficient sensitivity in the normal direction of the membrane surface, susceptibility to ambiguity and noise artifacts, and a lack of accurate thickness calibration data. Consequently, it lacks coupling with the membrane mass transfer mechanism and struggles to accurately reflect changes in polarization layer thickness. Summary of the Invention

[0004] This invention provides a method and apparatus for predicting the concentration polarization layer thickness of a reverse osmosis membrane based on electrical impedance imaging, in order to solve the technical problems of insufficient resolution, difficulty in calibration, and difficulty in corresponding the results with the physical mechanism of membrane mass transfer in reverse osmosis membrane process monitoring using electrical impedance imaging.

[0005] In a first aspect, embodiments of the present invention provide a method for predicting the thickness of the concentration polarization layer of a reverse osmosis membrane based on electrical impedance imaging, comprising:

[0006] S101, based on a membrane filtration sensor with an electrode array, simulates concentration polarization by setting virtual dielectric layers with different conductivity at different heights in the normal direction of the membrane surface, and uses adjacent excitation measurement, combined with the finite element method to analyze the potential distribution on the membrane surface, and calculates the sensitivity matrix sequence at different heights in the normal direction of the membrane surface based on the electrode excitation boundary conditions, and constructs a simulated membrane filtration evaluation pool model.

[0007] S102, based on the preset background conductivity, virtual media with different conductivity are set at different heights of the membrane surface normal and simulated boundary voltage datasets at different heights are obtained respectively. Then, the image is reconstructed using the conjugate gradient least squares algorithm and sensitivity matrix sequence to form a simulated conductivity image.

[0008] S103: Using simulated conductivity images and different conductivity values ​​of virtual media at different heights, a calibration training dataset is constructed to train the improved image conductivity mapping neural network.

[0009] S104, the measured boundary voltage dataset is measured using a membrane filter sensor and the conductivity image is reconstructed to form a measured conductivity image. The trained improved image conductivity mapping neural network is then used to predict the estimated value of the membrane surface conductivity.

[0010] S105. Based on the predicted membrane surface conductivity estimate, the concentration polarization layer thickness is mapped using classical membrane mass transfer theory to obtain the membrane surface concentration polarization layer thickness.

[0011] Secondly, embodiments of the present invention provide a reverse osmosis membrane concentration polarization layer thickness prediction device based on electrical impedance imaging, comprising:

[0012] The model building unit is used to construct a simulated membrane filtration evaluation pool model by setting virtual dielectric layers with different conductivity at different heights of the membrane surface normal and using adjacent excitation measurement based on the electrode array membrane filtration sensor.

[0013] The image reconstruction unit is used to set up virtual media with different conductivity at different heights in the normal direction of the membrane surface based on the preset background conductivity, and to reconstruct the image using the conjugate gradient least squares algorithm and sensitivity matrix sequence to form a simulated conductivity image.

[0014] The network training unit is used to construct a calibration training dataset using simulated conductivity images and different conductivity values ​​of virtual media at different heights, and to train the improved image conductivity mapping neural network.

[0015] The conductivity prediction unit is used to predict the estimated value of the membrane surface conductivity by using a trained improved image conductivity mapping neural network to reconstruct the measured conductivity image based on the measured boundary voltage dataset.

[0016] The thickness mapping unit is used to map the thickness of the concentration polarization layer on the membrane surface based on the predicted membrane surface conductivity estimate and classical membrane mass transfer theory.

[0017] Thirdly, embodiments of the present invention provide an electronic device, including:

[0018] One or more processors;

[0019] Storage device for storing one or more programs.

[0020] When the one or more programs are executed by the one or more processors, the one or more processors implement the above-described method for predicting the thickness of the concentration polarization layer of a reverse osmosis membrane based on electrical impedance imaging.

[0021] Fourthly, embodiments of the present invention provide a storage medium containing computer-executable instructions, which, when executed by a computer processor, are used to perform the above-described method for predicting the concentration polarization layer thickness of a reverse osmosis membrane based on electrical impedance imaging.

[0022] This invention provides a method and apparatus for predicting the thickness of the concentration polarization layer in a reverse osmosis membrane based on electrical impedance imaging. The method involves constructing an electrode array membrane filtration sensor, establishing a simulated membrane filtration evaluation pool model, setting virtual media with different conductivities at different heights normal to the membrane surface to obtain a simulated boundary voltage dataset, reconstructing the simulated conductivity image using the conjugate gradient least squares algorithm and sensitivity matrix sequence, constructing a calibration training dataset of conductivity image-known conductivity, and training an improved neural network including segmentation and regression branches. Based on the simulation model, the measured conductivity image can be reconstructed using the measured boundary voltage, and the trained improved neural network can be used to predict the conductivity estimate. Finally, the thickness of the concentration polarization layer is obtained based on membrane mass transfer theory. By generating conductivity image data with precise conductivity labels through numerical simulation, the difficulties in experimental calibration and data acquisition caused by the small scale and closed formation region of the concentration polarization layer thickness are solved. Then, by training a deep learning model, it is made capable of predicting the true conductivity value based on the conductivity image. Combined with membrane mass transfer theory, the concentration polarization layer thickness can be interpreted and mapped. This enables online, non-destructive, and quantitative detection of the concentration polarization layer thickness on the reverse osmosis membrane surface without damage or interruption of the production process. Attached Figure Description

[0023] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an undue limitation of the invention. In the drawings:

[0024] Figure 1 This is a flowchart of a method for predicting the thickness of a concentration polarization layer in a reverse osmosis membrane based on electrical impedance imaging, as described in Embodiment 1 of the present invention.

[0025] Figure 2 This is a flowchart of a method for predicting the thickness of a reverse osmosis membrane concentration polarization layer based on electrical impedance imaging, as described in Embodiment 2 of the present invention.

[0026] Figure 3This is a schematic diagram of the 16-electrode membrane filter sensor array described in Embodiment 2 of the present invention;

[0027] Figure 4 This is a schematic diagram of the reconstructed two-dimensional conductivity image described in Embodiment 2 of the present invention;

[0028] Figure 5 This is a flowchart of a method for predicting the thickness of a reverse osmosis membrane concentration polarization layer based on electrical impedance imaging, as described in Embodiment 3 of the present invention.

[0029] Figure 6 This is a schematic diagram of the structure of the improved image conductivity mapping neural network described in Embodiment 3 of the present invention;

[0030] Figure 7 This is a schematic diagram of the structure of a reverse osmosis membrane concentration polarization layer thickness prediction device based on electrical impedance imaging as described in Embodiment 4 of the present invention.

[0031] Figure 8 This is a structural diagram of the electronic device described in Embodiment 5 of the present invention. Detailed Implementation

[0032] The present invention will now be described in further detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and not intended to limit it. Furthermore, it should be noted that, for ease of description, the accompanying drawings show only the parts relevant to the present invention, and not all of the structures.

[0033] Example 1

[0034] Figure 1 The flowchart of the method for predicting the concentration polarization layer thickness of a reverse osmosis membrane based on electrical impedance imaging according to Embodiment 1 of the present invention specifically includes the following steps:

[0035] S101, based on a membrane filtration sensor with an electrode array, simulates concentration polarization by setting virtual dielectric layers with different conductivity at different heights in the normal direction of the membrane surface. Adjacent excitation measurements are used, and the potential distribution on the membrane surface is analyzed by combining the finite element method. Based on the electrode excitation boundary conditions, the sensitivity matrix sequence at different heights in the normal direction of the membrane surface is calculated, and a simulated membrane filtration evaluation pool model is constructed.

[0036] By setting an electrode array on the reverse osmosis membrane, the voltage distribution on the membrane surface can be collected to reflect the conductivity distribution of the concentration polarization layer on the membrane surface. For example, a square monitoring area with a side length of 2 cm is defined, and 16 electrodes are evenly arranged at the edge of the area to form an electrode array. The distance between the electrodes and the membrane surface is approximately 1 mm to approximate the actual installation state, thus constructing a membrane filtration sensor. Under the same conditions, a simulated membrane filtration evaluation cell model is built in simulation software to simulate the electric field distribution of the concentration polarization layer with different conductivity levels. This model uses adjacent excitation measurements, cyclically measuring the voltage between each pair of electrodes to form a boundary voltage dataset. Based on this, the background region of the membrane surface is divided into several triangular elements using the finite element method to solve for the potential distribution. Then, based on the electrode excitation boundary conditions, the normal direction of the membrane surface is solved. z Sensitivity matrices at different heights S Sensitivity matrix S The influence of conductivity variations on voltage measurements is described. The constructed simulation model is consistent with the actual measurement model, and a virtual medium with known conductivity can be incorporated into the simulation model to simulate the concentration polarization layer, serving as the data basis for subsequent conductivity image mapping.

[0037] S102, based on the preset background conductivity, virtual media with different conductivity are set at different heights in the normal direction of the membrane surface and simulated boundary voltage datasets at different heights are obtained respectively. Then, the image is reconstructed using the conjugate gradient least squares algorithm and sensitivity matrix sequence to form a simulated conductivity image.

[0038] Based on the constructed simulated membrane filtration evaluation pool model, a background conductivity is pre-set to simulate the initial conductivity of a solution (such as sodium chloride solution) under real conditions, serving as the basis for concentration polarization variations. Virtual media with different (known) conductivities are placed at different heights normal to the membrane surface. The conductivity combinations of the virtual media at each height layer are systematically changed (e.g., simulating mild, moderate, and severe polarization respectively) to simulate the concentration polarization layer formation process under different operating conditions. Then, the boundary voltage corresponding to each conductivity distribution is obtained by solving the forward impedance problem, forming a simulated boundary voltage dataset to describe the voltage response of the membrane surface under different conductivity distributions. Subsequently, the inverse problem is solved using the conjugate gradient least squares (CGLS) algorithm based on the simulated boundary voltage dataset. Combined with the sensitivity matrix, the conductivity distribution of the membrane surface is inferred from the voltage data. The CGLS algorithm iteratively minimizes the objective function to reconstruct a two-dimensional conductivity image of the membrane surface reflecting the set conductivity distribution, forming a simulated conductivity image. This achieves the simulation generation of a reconstructed conductivity image from a known conductivity distribution.

[0039] S103 utilizes simulated conductivity images and the different conductivity of virtual media at different heights to construct a calibration training dataset, and trains the improved image conductivity mapping neural network.

[0040] By utilizing a simulated membrane filtration evaluation pool model, a concentration polarization layer is simulated using virtual media with artificially set conductivity values. This generates regression labels with known conductivity values. Simulated conductivity images are reconstructed using boundary voltages, sensitivity matrices, and the CGLS algorithm, creating a one-to-one correspondence between the simulated and known conductivity values. This forms a controllable calibration training dataset with paired conductivity images and conductivity value labels, providing a large number of training samples for deep learning models. The constructed calibration training dataset is divided into training, validation, and test sets (e.g., 7:2:1) to train the deep learning model. Supervised training is performed using simulated conductivity images as input and corresponding conductivity values ​​as supervised labels. After training, the model possesses data-driven concentration polarization layer prediction capabilities, capable of reconstructing conductivity images from physically simulated conductivity images to known conductivity value labels. This data can be used to reconstruct conductivity images by measuring the electric field distribution of concentration polarization layers, and then the trained deep learning model can be used to predict the actual conductivity values, serving as the data basis for mapping concentration polarization layer thickness.

[0041] S104. The measured boundary voltage dataset is measured using a membrane filter sensor and the conductivity image is reconstructed to form a measured conductivity image. The trained improved image conductivity mapping neural network is then used to predict the estimated value of the membrane surface conductivity.

[0042] In actual reverse osmosis membrane filtration measurement experiments, a measurement method consistent with the simulated membrane filtration evaluation cell model is adopted. Voltage is generated through current excitation, and a measured boundary voltage dataset is collected. To eliminate system baseline drift, background voltage measurement is usually required. The relative boundary voltage difference between the measured boundary voltage and the background voltage at the initial filtration time (empty field) is calculated, and then input into the CGLS algorithm. Combined with the sensitivity matrix, conductivity image reconstruction is performed to form a measured conductivity image. The reconstructed measured conductivity image is then input into a trained improved image conductivity mapping neural network (i.e., the aforementioned deep learning model), which uses its predictive capabilities to output a predicted estimate of the membrane surface conductivity.

[0043] S105. Based on the predicted membrane surface conductivity estimate, the concentration polarization layer thickness is mapped using classical membrane mass transfer theory to obtain the membrane surface concentration polarization layer thickness.

[0044] Using the estimated predicted membrane surface conductivity, and based on the known relationship between conductivity and solute concentration in electrolyte solution theory, the conductivity is converted into the corresponding solute concentration at the membrane surface. Then, the concentration polarization layer thickness is mapped based on classical membrane mass transfer theory. For example, the concentration polarization layer thickness... From the membrane mass transfer theory, the formula is as follows:

[0045]

[0046] in, Indicates the diffusion coefficient. This indicates the membrane flux (which can be determined from the reverse osmosis membrane parameters, such as in a membrane filtration experiment). Indicates the concentration of the bulk liquid phase. This represents the solute concentration at the membrane surface. It is based on the mapping relationship between conductivity and solute concentration at the membrane surface. The predicted membrane surface conductivity estimate is converted into the membrane surface solute concentration. .

[0047] This embodiment constructs an electrode array membrane filtration sensor, establishes a simulated membrane filtration evaluation pool model, sets virtual media with different conductivities at different heights normal to the membrane surface, and obtains a simulated boundary voltage dataset. The simulated conductivity image is reconstructed using the conjugate gradient least squares algorithm and sensitivity matrix sequence. A calibration training dataset of conductivity image and known conductivity is constructed to train an improved neural network including segmentation and regression branches. Based on the simulation model, the measured conductivity image can be reconstructed using the measured boundary voltage, and the trained improved neural network can be used to predict the conductivity estimate. Finally, the concentration polarization layer thickness is obtained based on membrane mass transfer theory. By generating conductivity image data with precise conductivity labels through numerical simulation, the difficulties in experimental calibration and data acquisition caused by the small scale and closed formation region of the concentration polarization layer thickness are solved. Furthermore, by training a deep learning model, it is given the ability to predict the true conductivity value based on the conductivity image. Combined with membrane mass transfer theory, the concentration polarization layer thickness can be interpreted and mapped online, non-destructively, and quantitatively detected without damage or interruption of the production process.

[0048] Example 2

[0049] Figure 2 This is a flowchart of a method for predicting the concentration polarization layer thickness of a reverse osmosis membrane based on electrical impedance imaging, as described in Embodiment 2 of the present invention. This embodiment is an optimization based on the above embodiment. In this embodiment, S101 is specifically optimized as follows:

[0050] A membrane filtration sensor array was constructed on the reverse osmosis membrane under test using 16 electrodes;

[0051] Adjacent excitation measurement is used, and current is injected alternately between two adjacent electrodes. The boundary voltage sequence is measured through other adjacent electrodes to form a boundary voltage dataset.

[0052] Based on the simulated boundary voltage dataset, the potential distribution on the membrane surface is calculated using the finite element method.

[0053] Based on the potential distribution on the membrane surface, the sensitivity matrix sequence at different heights in the normal direction of the membrane surface is calculated based on the electrode excitation boundary conditions.

[0054] Accordingly, the reverse osmosis membrane concentration polarization layer thickness prediction method based on electrical impedance imaging provided in this embodiment specifically includes:

[0055] S201, a membrane filtration sensor array is constructed on the reverse osmosis membrane to be tested using 16 electrodes.

[0056] A membrane filtration sensor array is constructed by uniformly arranging multiple electrodes along the edge of the reverse osmosis membrane to be tested. For example, 16 electrodes are uniformly arranged along the edge of a 2cm × 2cm square observation area, with the electrodes aligned in the normal direction to the membrane surface. z (Axial direction) is maintained at a distance of about 1 mm from the surface of the reverse osmosis membrane to form a membrane filter sensor array, which is used to measure the voltage distribution on the surface of the reverse osmosis membrane.

[0057] S202 employs adjacent excitation measurement, injecting current alternately between two adjacent electrodes and measuring the boundary voltage sequence through other adjacent electrodes to form a boundary voltage dataset.

[0058] Adjacent excitation measurement involves injecting alternating current onto one pair of adjacent electrodes and measuring the boundary voltage across other adjacent electrode pairs. For example, ... Figure 3 As shown, firstly, an excitation current of 3 mA is injected between electrode 1 and electrode 2, and the relative potentials between the other 14 electrodes are measured, resulting in 13 voltage values. Then, the injected electrodes are changed from the original electrodes 1 and 2 to electrodes 2 and 3, and the relative voltage values ​​of the 14 electrodes other than electrodes 2 and 3 are measured, resulting in 13 voltage values. This process is repeated cyclically until all 16 excitation pairs are traversed. Finally, a single complete scan can measure 208 independent boundary voltage values ​​from 16 excitation pairs * 13 measurement pairs, forming a boundary voltage dataset.

[0059] S203, based on the simulated boundary voltage dataset, calculate the potential distribution on the membrane surface using the finite element method.

[0060] Similarly, in simulation software (such as COMSOL), a simulation model, namely the simulated membrane filtration evaluation pool model, is reproduced with the same structure. This simulation model can be injected with a virtual medium of known conductivity to simulate the conductivity of the concentration polarization layer at different distances from the reverse osmosis membrane surface in the normal direction. The potential distribution of the simulated boundary voltage dataset measured by the electrode array is solved using the Finite Element Method (FEM). The background region is divided into several triangular elements, and the local information of these triangular elements is used to approximate the solution for the entire region. The electric field within each element can be interpolated using nodal values ​​and a shape function to obtain a continuous and smooth potential distribution throughout the entire field, as shown in the following formula:

[0061]

[0062] in, This represents the electric field distribution across the entire membrane surface area; Indicates the first The shape function of each node is the local interpolation function of each element in the finite element method. It describes how the electric field value in each triangular element is interpolated according to the electric field value of each node, defines the distribution of the electric field in the element, and reflects the relationship between the electric field value of the element and the node value. Indicates the first The electric field value of each node is the electric field value obtained by solving the finite element method. The node represents the corner point of the triangular element. The electric field intensity at that location can be obtained by solving the electric field numerically. The number of nodes in a triangular element is used. Typically, each element in a two-dimensional triangular element has three nodes, representing the three corner points of that element. The membrane surface is discretized using the finite element method, and the electric field distribution across the entire membrane surface region is obtained by interpolation using the shape function of each element and the nodal electric field values. This transforms the complex electric field distribution problem into a discrete nodal electric field solution, thereby obtaining the complete distribution of the electric field within the region, which serves as the basis for calculating the change in conductivity of the membrane surface.

[0063] S204, based on the potential distribution on the membrane surface, calculate the sensitivity matrix sequence at different heights in the normal direction of the membrane surface according to the electrode excitation boundary conditions.

[0064] Since the concentration polarization layer on the membrane surface has different concentrations at different heights along the normal direction, it is necessary to describe the influence of the conductivity variation of the concentration polarization layer at different heights on the voltage measurement using sensitivity matrices at different heights. Based on electrode excitation boundary conditions and sensitivity theory, the concentration polarization layer at different heights within the observation region can be calculated. z A sensitivity matrix characterizing the impact of conductivity variation in each discrete triangular unit on each voltage measurement. S The formula is as follows:

[0065]

[0066] in, Indicates the first The electrode group is the first Sensitivity coefficient of each electrode group; and Indicates the first i The first electrode group and the first j Each electrode group is excited by currents of... The electric potential distribution in the time field, that is, the distribution of electric potential in different regions when current passes through the membrane surface, reflects the change of electric field in different regions of the membrane surface; Indicates that they are applied to the first The and the first The current on each electrode group; and express and The gradient operator reflects the spatial rate of change of the electric field, and By applying an excitation current to an electrode array and measuring the voltage signal, data on conductivity variations at different locations on the membrane surface can be obtained, along with how these variations affect the voltage signal, providing quantitative support for conductivity image reconstruction. z Repeated calculations at a high level yield a sensitivity matrix sequence. It is used to characterize the response of the electrode array to changes in the conductivity of different layers, thereby improving the normal resolution of the film surface.

[0067] S205, based on the preset background conductivity, sets virtual media with different conductivity at different heights in the normal direction of the membrane surface and obtains simulation boundary voltage datasets at different heights. Then, the image is reconstructed using the conjugate gradient least squares algorithm and sensitivity matrix sequence to form a simulation conductivity image.

[0068] Specifically, based on the preset background conductivity, the simulated boundary voltage dataset of the virtual medium is solved by the positive impedance problem, which satisfies the Laplace equation.

[0069] After setting virtual dielectrics with different conductivity at different heights normal to the membrane surface, the corresponding boundary voltage dataset is obtained by solving the forward impedance problem, where the forward impedance problem satisfies the Laplace equation:

[0070]

[0071] in, For conductivity distribution, The potential is obtained; the measurement operator is obtained under given electrode boundary conditions. AWith sensitivity matrix and along the membrane surface normal at multiple heights z The stratified sensitivity matrix sequence was calculated. This is used to generate simulated voltage data under different altitudes and conductivity conditions. To eliminate system steady-state bias and electrode contact resistance drift, and to enhance the contrast sensitivity to concentration polarization, background voltage also needs to be measured in an empty field. Between the actual voltage measured in the object field (with a virtual medium) The difference is used to calculate the relative boundary voltage difference. ,Right now relative boundary voltage difference As the corresponding boundary voltage dataset, it can effectively suppress common-mode interference such as electrode contact impedance drift.

[0072] The conductivity image is reconstructed by using the conjugate gradient least squares algorithm and combining it with the sensitivity matrix sequence at different heights to form a simulated conductivity image.

[0073] Using the conjugate gradient least squares (CGLS) algorithm, conductivity images are reconstructed from the simulated boundary voltage dataset through inverse problem derivation to obtain the simulated conductivity image. For example, a preset background conductivity... Virtual dielectrics with conductivity of 3051 µS / cm, 2871 µS / cm, 2701 µS / cm, and 2541 µS / cm were placed at different heights along the normal direction of the membrane surface to simulate conductivity at different distances from the membrane. After obtaining the corresponding boundary voltage dataset by solving the impedance problem, the CGLS algorithm was used to inversely deduce the membrane surface conductivity distribution from the boundary voltage dataset. The conductivity image was then obtained using the sensitivity matrix sequence at different heights, forming a simulated conductivity image of the membrane surface. The CGLS algorithm, at most... k Within each iteration, the objective function is minimized. ,in A This is the sensitivity matrix. The relative boundary voltage difference, The desired conductivity distribution is given. The iterative process includes: initialization process. That is, starting from a completely black image where the conductivity of all pixels remains unchanged; residual Let the first search direction be... This is used to backproject the voltage residual into the image space to obtain a rough initial orientation that indicates which areas may need adjustment; the goal is to obtain... Minimum value, and Indicates an iterative loop Then iterate through the process:

[0074]

[0075] The above iterative process can be described as follows: First, calculate the step size. That is, along the current search direction Determine the optimal distance to travel; then update the image. That is, along the direction Walk After the step, a new and better estimated image is obtained; then the residuals are updated. This involves updating the image to predict the voltage, calculating the new difference between the predicted voltage and the actual measured value, and then calculating the new gradient direction. (The direction of steepest descent); then calculate the conjugate coefficient. This is the core of the CGLS algorithm, ensuring new search directions. Conjugate (or orthogonal) with all previous directions, thus avoiding zigzag wandering and greatly accelerating convergence; then calculate the convergence monitoring residual norm. This indicates the degree of mismatch between the current image prediction and the measured data. It generally decreases with iteration; if it no longer decreases, it indicates convergence. Then, a new search direction is determined. This involves combining the current gradient direction with the previous search direction, and iterating accordingly. The final iteration is obtained by iteratively using the relative boundary voltage difference. The solution vector after this Number of iterations The residual norm is determined based on the convergence monitoring to avoid underfitting or overfitting.

[0076] Among them, optionally for Gram-Schmidt reorthogonality is performed to suppress numerical accumulation error, and the results are recorded during iteration. These serve as metrics for convergence and regularity, respectively. By establishing a membrane filtering model consistent with the experimental system in a numerical simulation platform, and by applying current excitation and solving for the electric field distribution and boundary voltage, the simulation generation of a reconstructed conductivity image from a known conductivity distribution is achieved. A large number of simulated conductivity images and their corresponding conductivity values ​​can be used as ground truth labels to provide calibration data training samples for deep learning models, realizing data-driven concentration polarization layer prediction from physical simulation.

[0077] S206 utilizes simulated conductivity images and the different conductivity of virtual media at different heights to construct a calibration training dataset, and trains the improved image conductivity mapping neural network.

[0078] S207 uses a membrane filter sensor to measure the measured boundary voltage dataset and reconstruct the conductivity image to form a measured conductivity image. Then, a trained improved image conductivity mapping neural network is used to predict the estimated value of the membrane surface conductivity.

[0079] Optionally, a membrane filtration sensor containing a 16-electrode array is used to measure a dataset of measured boundary voltages at different heights in the membrane normal, based on a simulated membrane filtration evaluation cell model.

[0080] A membrane filtration sensor was constructed using a 16-electrode array consistent with the simulation model, forming a real measurement system consistent with the simulated membrane filtration evaluation cell model. The boundary voltage of the concentration polarization layer at different heights in the membrane normal was measured using the same adjacent excitation, forming a measured boundary voltage dataset.

[0081] Based on the measured boundary voltage dataset, the conductivity image is reconstructed using the conjugate gradient least squares algorithm combined with the sensitivity matrix sequence at different heights, thus forming the measured conductivity image.

[0082] After obtaining the actual boundary voltage data, the same image reconstruction algorithm is used to generate the corresponding layered sensitivity matrix sequence. As the sensitivity matrix A, the voltage difference vector is used as the relative boundary voltage difference. ,exist Minimize the solution within the next iteration. To gradually optimize the conductivity distribution vector The iterative process also includes residual updates and search direction determination processes consistent with those described above. A regularized early stopping strategy can also be introduced to avoid noise amplification. The final output is a reconstructed two-dimensional measured conductivity image, such as... Figure 4 As shown.

[0083] By using a trained improved image conductivity mapping neural network, the measured conductivity image is predicted to obtain the estimated value of the predicted membrane surface conductivity.

[0084] The reconstructed measured conductivity image is used as input data. The improved image conductivity mapping neural network, which is trained, has the ability to predict the true conductivity value from the conductivity image. The predicted surface conductivity estimate is output, providing a data basis for concentration polarization layer thickness mapping.

[0085] S208. Based on the predicted membrane surface conductivity estimate, the concentration polarization layer thickness is mapped using classical membrane mass transfer theory to obtain the membrane surface concentration polarization layer thickness.

[0086] This embodiment employs adjacent excitation measurements with 16 electrodes and calculates the sensitivity matrix layer by layer to accommodate the different conductivity of the concentration polarization layer at different heights (different distances from the membrane surface) in the normal direction of the membrane surface, thereby improving the accuracy of conductivity image reconstruction, especially in the normal direction of the membrane surface. zThe spatial resolution (in the axial direction) can more clearly reflect the longitudinal distribution characteristics of the concentration polarization layer. Image reconstruction is performed using the conjugate gradient least squares algorithm combined with the layered sensitivity matrix. The iterative process derived from the inverse problem is suitable for handling the ill-conditioned nature of the conductivity inverse problem, suppressing blur and noise artifacts in the reconstructed image, and obtaining a more quantitative conductivity distribution image.

[0087] Example 3

[0088] Figure 5 This is a flowchart of a method for predicting the concentration polarization layer thickness of a reverse osmosis membrane based on electrical impedance imaging, as described in Embodiment 3 of the present invention. This embodiment is an optimization based on the above embodiment. In this embodiment, S103 is specifically optimized as follows:

[0089] A pairing relationship is established between the simulated conductivity image and the corresponding true conductivity value of the virtual medium to construct a calibration training dataset;

[0090] Using simulated conductivity images as input and corresponding true values ​​of virtual dielectric conductivity as supervision labels, an improved image conductivity mapping neural network is trained.

[0091] Accordingly, the reverse osmosis membrane concentration polarization layer thickness prediction method based on electrical impedance imaging provided in this embodiment specifically includes:

[0092] S301, based on a membrane filtration sensor with an electrode array, simulates concentration polarization by setting virtual dielectric layers with different conductivity at different heights in the normal direction of the membrane surface. Adjacent excitation measurements are used, and the potential distribution on the membrane surface is analyzed by combining the finite element method. Based on the electrode excitation boundary conditions, the sensitivity matrix sequence at different heights in the normal direction of the membrane surface is calculated, and a simulated membrane filtration evaluation pool model is constructed.

[0093] S302, based on the preset background conductivity, sets virtual media with different conductivity at different heights in the normal direction of the membrane surface and obtains simulation boundary voltage datasets at different heights. Then, the image is reconstructed using the conjugate gradient least squares algorithm and sensitivity matrix sequence to form a simulation conductivity image.

[0094] S303 establishes a pairing relationship between the simulated conductivity image and the corresponding true conductivity value of the virtual medium to construct a calibration training dataset.

[0095] The conductivity image obtained through simulation is paired with the known true conductivity value of the virtual medium to form a calibration data pair between input and output data. This calibration training dataset is then used to train the deep learning model, enabling the deep learning model to learn the regression ability to output the predicted true conductivity value based on the input conductivity image.

[0096] Optionally, after size normalization, grayscale standardization, and masking of the conductivity image, it is input into the improved image conductivity mapping neural network, and the conductivity value used as the supervision label is standardized.

[0097] To ensure the input data is suitable for model processing, the conductivity image needs to be normalized in size, standardized in grayscale, and masked before being input into the model. During size normalization, bilinear interpolation is used to uniformly scale the input image to 256×256 resolution; during grayscale standardization, linear normalization is performed on the image pixel values. ,in Original grayscale The normalized gray level. and The mean and standard deviation of the entire image are used. During masking, physical thresholding is applied to the image through color mark inversion (LUT nearest neighbor mapping), linear thresholding, and background removal (color distance thresholding) to obtain the target region mask and remove other interfering regions. Then, all samples are randomly divided into training, validation, and test sets in a 7:2:1 ratio for model training and optimization. The conductivity value, used as the supervision label, also needs to be standardized, i.e., min-max normalization is performed to map the conductivity to a uniform scale range, eliminating differences in data dimensions.

[0098] S304 uses simulated conductivity images as input and the corresponding true values ​​of virtual dielectric conductivity as supervision labels to train an improved image conductivity mapping neural network.

[0099] An improved convolutional neural network is used to form a neural network model specifically for image-conductivity mapping. The input data of the model is the conductivity image, and the output data is the conductivity value. During the training phase, the simulated conductivity image is used as input, and the corresponding virtual medium conductivity true value is used as the supervision label for regression task training, so that the trained model has the ability to predict the mapping from conductivity image to conductivity true value.

[0100] Specifically, such as Figure 6 As shown, the improved image conductivity mapping neural network includes:

[0101] An improved U-Net backbone network is used for feature extraction, and residual convolutional blocks are used to replace the standard convolutional layers in the encoder, introducing cross-layer skip connections and dilated convolutions in the downsampling path.

[0102] An improved image conductivity mapping neural network, using U-Net as its backbone, is employed for feature extraction from conductivity images. To address the vanishing gradient and high-frequency texture loss issues inherent in traditional U-Net structures when fusing shallow and deep features, improvements were made. Specifically, in the encoder's downsampling path, standard convolutional layers were replaced with residual convolutional blocks to introduce cross-layer skip connections, enhancing gradient propagation and effectively mitigating the vanishing gradient problem, ensuring deep features are not lost during training. Furthermore, dilated convolutional blocks were embedded in the encoder's downsampling path, enabling the acquisition of a larger receptive field without increasing the number of parameters or excessively sacrificing spatial resolution. This allows for the capture of local details and broader contextual information, achieving multi-scale feature capture of concentration polarization layers of varying thicknesses on the membrane surface.

[0103] In the upsampling path of the improved U-Net backbone network decoder, deconvolution and skip connections are used to form a segmentation branch. Then, mask weights and weighted pooling are used to form a mask weighted pooling branch, and color space transformation and mask weights are used to form a color statistical feature branch.

[0104] At the end of the upsampling path in the U-Net decoder, after the backbone U-Net decodes to the last level feature map, deconvolution is used and fused with the features of the corresponding layer in the encoder through skip connections to gradually restore the spatial resolution of the feature map and reconstruct the spatial features. The output feature tensor This feature tensor comprehensively represents the influence of conductivity variations at different locations on the film surface on image brightness and texture, reflecting the spatial characteristics of concentration polarization regions. This feature tensor is then input into a 1×1 convolutional layer for pixel-level channel compression, outputting the probability value of each pixel belonging to the concentration polarization layer, i.e., the output concentration polarization region probability map. This forms a segmentation branch used to identify the pixel distribution between polarized and non-polarized regions on the film surface, as shown in the following formula:

[0105]

[0106] in, This represents the probability value for each pixel to belong to the concentration polarization region. Here, x and y represent the pixel coordinates, and sigmoid is the activation function used to achieve a smooth transition from continuous features to binary classification. The weights are 1×1 convolution kernel weights. The input feature tensor is output by the decoder. This is a bias term used to adjust the response threshold of each pixel, making the output probability more consistent with the distribution difference between the polarization layer and the background region. The final output of the segmentation branch... Mask probability maps are used to generate binary segmentation images of concentration polarization regions, providing a basis for spatial localization of conductivity distribution.

[0107] After the segmentation branch, the mask probability map output by the segmentation branch is used as the spatial attention weight to enhance the features of the polarization layer region. Then, the feature map extracted by the improved backbone U-Net is weighted pooled to form the mask weighted pooling branch, which yields the feature vector of the mask region. The formula is expressed as follows:

[0108]

[0109] in, To improve the extraction of the U-Net backbone, the first... c The feature map pixel values ​​of each channel represent the image in... The coordinates of the first c The 3D feature response describes how changes in conductivity are represented in the image space; This is a weight normalization factor to ensure that the aggregation result does not depend on the mask area, thus achieving scale invariance. This is a feature vector obtained after channel-level weighted pooling, representing the global features of the polarization layer region. It allows the neural network to focus on the concentration polarization region, improving the spatial sensitivity of conductivity estimation, suppressing background noise interference, and aggregating local spatial features into global statistical features representing the entire polarization region. This method performs spatially significant feature compression, retaining local information of the polarization layer while reducing features in irrelevant regions. This allows the input features of subsequent regression branches to be more concentrated in regions related to changes in conductivity, thereby improving prediction accuracy.

[0110] A Color Statistical Pooling branch, parallel to the mask weighted pooling branch, is then introduced. This branch extracts the color distribution features of the mask region by calculating the RGB mean and variance of the input image, capturing subtle color differences caused by conductivity variations. This feature is then concatenated with the deep feature vector to compensate for the loss of spectral information in pseudo-color images. Specifically, the original image is converted to the LAB color space, and the color distribution features within the mask region are calculated. The weighted mean and standard deviation of a channel are calculated using the following formula:

[0111]

[0112]

[0113] in, For the image in the LAB color space (Red and green axis) channel components, The components of the (yellow and blue axis) channel reflect the color difference between conductive and polarized regions in the image; The weighted average color value of the (red-green axis) channel represents the overall shift trend of the polarization layer color (i.e., average conductivity). The weighted standard deviation of the (red-green axis) channels characterizes the degree of color change within the polarization layer region (corresponding to the uniformity of conductivity distribution). This is the weighted average color value of the (yellow and blue axis) channels; This represents the weighted standard deviation of the (yellow and blue axis) channels. Output color statistical feature vector. It is used to assist in conductivity prediction and improve the model's sensitivity to weak polarization phenomena.

[0114] A regression fusion branch is formed by a global average pooling layer and multiple fully connected layers. This branch receives the outputs of the mask weighting branch and the color statistical feature branch and performs feature fusion. Then, the regression of the conductivity value is obtained through nonlinear mapping.

[0115] The regression fusion branch is located at the very end of the neural network and is the output module of the entire network. After receiving the parallel outputs of the mask weighting branch and the color statistical feature branch, it first concatenates the features of the two to form a fused feature vector, which is then input into a multilayer perceptron (MLP, usually 2-3 fully connected layers with ReLU activation function used for linear mapping) for conductivity prediction.

[0116]

[0117] in, The input parameters for the regression fusion branch are the fused feature vectors. This characterizes the spatial and color distribution information of the polarization layer; This represents a multilayer perceptron, consisting of fully connected layers, ReLU activation, and Dropout, used for nonlinear mapping from input features to output conductivity; This serves as the regression label for the output parameter, i.e., the true value of the conductivity. To enhance the model's generalization and domain adaptability, a learnable linear calibration layer is added to the output:

[0118]

[0119] in, and These are the scale and offset parameters learned during the training phase, i.e., the learning parameters (determined during the training phase). The predicted value of the true conductivity after back calibration, i.e., the final output parameter, represents the estimated average conductivity of the membrane surface under the current operating conditions, which is used for subsequent calculation of the thickness of the concentration polarization layer.

[0120] Optionally, the improved image conductivity mapping neural network is trained using a two-stage learning strategy with the Adam optimizer, a mask switching strategy, and a hierarchical learning rate, and optimized using a multi-variable joint loss function that includes segmentation loss and regression loss.

[0121] In the training phase of the neural network, a two-stage learning strategy using the Adam optimizer is employed. The improved U-Net backbone stabilizes feature extraction by freezing the pre-trained weights for several initial rounds. Color statistics and pooling in the early stages of training use realistic masks, while switching to predictive masks in the later stages eliminates the distributional differences between training and inference. A hierarchical learning rate strategy is adopted, independently adjusting the segmentation and regression fusion branches. Furthermore, multiple joint loss functions are used to collaboratively optimize the segmentation and regression tasks. To simultaneously ensure the accuracy of segmentation boundaries and conductivity regression, the multiple joint loss function is expressed as:

[0122]

[0123] in, The splitting loss is a mixture of Dice and cross-entropy; This is the mean squared error or Huber loss; The feature alignment loss is used to constrain the consistency between the predicted values ​​and the label mean and slope. It is calculated by Euclidean distance of the feature means within the segmented region. ,in The average feature vector of the segmented region. This is the average representation of the regression input features; This is the auxiliary absolute error term for the original spatial conductivity; , , , These are the loss weights, or hyperparameters, used to balance the importance of different subtasks or constraints in multi-task learning. The weights of each loss term are gradually adjusted during training to achieve a smooth transition from structured learning to numerical learning. The weights of convolutional layers, pooling layers, MLP weights and biases, and feature fusion weights in the neural network are optimized. After training, the mean squared error and correlation coefficient are evaluated on the validation set based on both the real and predicted masks to ensure the network balances segmentation and regression performance. Then, a calibration relationship between predicted and true conductivity is established through linear regression for adaptive correction in the experimental domain. Ultimately, the system achieves the ability to obtain conductivity predictions for each layer of the membrane surface simply by inputting the reconstructed experimental image.

[0124] S305 uses a membrane filter sensor to measure the measured boundary voltage dataset and reconstruct the conductivity image to form a measured conductivity image. Then, it uses a trained improved image conductivity mapping neural network to predict the estimated value of the membrane surface conductivity.

[0125] S306. Based on the predicted surface conductivity estimate, the concentration polarization layer thickness is mapped using classical membrane mass transfer theory to obtain the concentration polarization layer thickness on the membrane surface.

[0126] This embodiment improves the convolutional neural network by adopting an improved U-Net architecture that fuses segmentation and regression. The segmentation branch is responsible for accurately locating concentration polarization regions. Then, it combines parallel mask-weighted pooling and color statistical features, using the segmentation results as spatial attention weights to focus feature extraction on the target region and suppress background interference. Simultaneously, it extracts image color distribution information strongly correlated with the physical nature of conductivity, providing powerful auxiliary clues for the regression task. The regression fusion branch concatenates and fuses spatial and color features, then performs a nonlinear mapping to output a regression label for the true conductivity value, achieving accurate mapping from image to conductivity. The learnable linear calibration layer at the network's end allows the model to adaptively adjust its output, greatly enhancing its cross-domain generalization ability under different experimental conditions and sensor systems. The model is improved through a two-stage training strategy, mask switching, hierarchical learning rates, and multiple joint loss functions, ensuring high-precision and robust regression prediction of membrane surface conductivity even in complex noise environments.

[0127] Example 4

[0128] Figure 7 This is a schematic diagram of a reverse osmosis membrane concentration polarization layer thickness prediction device based on electrical impedance imaging according to Embodiment 4 of the present invention. In this embodiment, the reverse osmosis membrane concentration polarization layer thickness prediction device based on electrical impedance imaging includes:

[0129] Model building unit 810 is used for membrane filtration sensors based on electrode arrays and adjacent excitation measurements. It sets virtual dielectric layers with different conductivity at different heights of the membrane surface normal to measure the boundary voltage and build a simulated membrane filtration evaluation pool model.

[0130] The image reconstruction unit 820 is used to set virtual media with different conductivity at different heights in the normal direction of the membrane surface based on the preset background conductivity, and to reconstruct the image using the conjugate gradient least squares algorithm and sensitivity matrix sequence to form a simulated conductivity image.

[0131] The network training unit 830 is used to construct a calibration training dataset using simulated conductivity images and different conductivity values ​​of virtual media at different heights, and to train the improved image conductivity mapping neural network.

[0132] The conductivity prediction unit 840 is used to predict the estimated value of the membrane surface conductivity by using a trained improved image conductivity mapping neural network to predict the measured conductivity image obtained by image reconstruction based on the measured boundary voltage dataset.

[0133] Thickness mapping unit 850 is used to map the thickness of the concentration polarization layer on the membrane surface based on the predicted membrane surface conductivity estimate and classical membrane mass transfer theory.

[0134] In this embodiment, a simulated membrane filtration evaluation pool model is constructed based on an electrode array membrane filtration sensor by a model building unit. An image reconstruction unit uses the conjugate gradient least squares algorithm and sensitivity matrix sequence to reconstruct the image and form a simulated conductivity image. A network training unit trains an improved image conductivity mapping neural network using the simulated conductivity image and the different conductivity of virtual media at different heights. A conductivity prediction unit uses the trained improved image conductivity mapping neural network to predict the estimated value of membrane surface conductivity based on the measured conductivity image. A thickness mapping unit maps the thickness of the concentration polarization layer on the membrane surface based on the predicted membrane surface conductivity estimate and classical membrane mass transfer theory. By generating conductivity image data with precise conductivity labels through numerical simulation, the difficulties in experimental calibration and data acquisition caused by the small scale and closed formation region of the concentration polarization layer thickness are solved. Then, by training a deep learning model, it is made capable of predicting the true conductivity value based on the conductivity image. Combined with membrane mass transfer theory, the concentration polarization layer thickness can be interpreted and mapped. This enables online, non-destructive, and quantitative detection of the concentration polarization layer thickness on the reverse osmosis membrane surface without damage or interruption of the production process.

[0135] The reverse osmosis membrane concentration polarization layer thickness prediction device based on electrical impedance imaging provided in this embodiment of the invention can execute the reverse osmosis membrane concentration polarization layer thickness prediction method based on electrical impedance imaging provided in any embodiment of the invention, and has the corresponding functional modules and beneficial effects of the method.

[0136] Example 5

[0137] Figure 8 This is a structural diagram of an electronic device according to Embodiment 5 of the present invention. Figure 8 A block diagram is shown of an exemplary electronic device 12 suitable for implementing embodiments of the present invention. Figure 8 The electronic device 12 shown is merely an example and should not impose any limitation on the functionality and scope of use of the embodiments of the present invention.

[0138] like Figure 8As shown, the electronic device 12 is represented in the form of a general-purpose computing device. The components of the electronic device 12 may include, but are not limited to: one or more processors or processing units 16, system memory 28, and bus 18 connecting different system components (including system memory 28 and processing unit 16).

[0139] Bus 18 represents one or more of several bus architectures, including a memory bus or memory controller, a peripheral bus, a graphics acceleration port, a processor, or a local bus using any of the various bus architectures. For example, these architectures include, but are not limited to, the Industry Standard Architecture (ISA) bus, the Micro Channel Architecture (MAC) bus, the Enhanced ISA bus, the Video Electronics Standards Association (VESA) local bus, and the Peripheral Component Interconnect (PCI) bus.

[0140] Electronic device 12 typically includes a variety of computer system readable media. These media can be any available media that can be accessed by electronic device 12, including volatile and non-volatile media, removable and non-removable media.

[0141] System memory 28 may include computer system readable media in the form of volatile memory, such as random access memory (RAM) 30 and / or cache memory 32. Electronic device 12 may further include other removable / non-removable, volatile / non-volatile computer system storage media. By way of example only, storage system 34 may be used to read and write non-removable, non-volatile magnetic media (… Figure 8 Not shown; usually referred to as a "hard drive"). Although Figure 8 Not shown, a disk drive for reading and writing to a removable non-volatile disk (e.g., a "floppy disk") and an optical disk drive for reading and writing to a removable non-volatile optical disk (e.g., a CD-ROM, DVD-ROM, or other optical media) may be provided. In these cases, each drive may be connected to bus 18 via one or more data media interfaces. System memory 28 may include at least one program product having a set (e.g., at least one) of program modules configured to perform the functions of the embodiments of the present invention.

[0142] A program / utility 40 having a set (at least one) of program modules 42 may be stored, for example, in system memory 28. Such program modules 42 include, but are not limited to, an operating system, one or more application programs, other program modules, and program data. Each or some combination of these examples may include an implementation of a network environment. Program modules 42 typically perform the functions and / or methods described in the embodiments of the present invention.

[0143] Electronic device 12 can also communicate with one or more external devices 14 (e.g., keyboard, pointing device, display 24, etc.), and with one or more devices that enable a user to interact with the electronic device 12 / server / computer, and / or with any device that enables the electronic device 12 to communicate with one or more other computing devices (e.g., network card, modem, etc.). This communication can be performed through input / output (I / O) interface 22. Furthermore, electronic device 12 can also communicate with one or more networks (e.g., local area network (LAN), wide area network (WAN), and / or public networks, such as the Internet) via network adapter 20. Figure 8 As shown, network adapter 20 communicates with other modules of electronic device 12 via bus 18. It should be understood that, although... Figure 8 As not shown, other hardware and / or software modules may be used in conjunction with electronic device 12, including but not limited to: microcode, device drivers, redundant processing units, external disk drive arrays, RAID systems, tape drives, and data backup storage systems.

[0144] The processing unit 16 executes various functional applications and data processing by running programs stored in the system memory 28, such as implementing the reverse osmosis membrane concentration polarization layer thickness prediction method based on electrical impedance imaging provided in the embodiments of the present invention.

[0145] Example 6

[0146] Embodiment 6 of the present invention also provides a storage medium containing computer-executable instructions, which, when executed by a computer processor, are used to perform the reverse osmosis membrane concentration polarization layer thickness prediction method based on electrical impedance imaging as provided in the above embodiments.

[0147] The computer storage medium of this invention can be any combination of one or more computer-readable media. A computer-readable medium can be a computer-readable signal medium or a computer-readable storage medium. A computer-readable storage medium can be, for example,—but not limited to—an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination thereof. More specific examples of computer-readable storage media (a non-exhaustive list) include: an electrical connection having one or more wires, a portable computer disk, a hard disk, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), optical storage device, magnetic storage device, or any suitable combination thereof. In this document, a computer-readable storage medium can be any tangible medium that contains or stores a program that can be used by or in conjunction with an instruction execution system, apparatus, or device.

[0148] Computer-readable signal media may include data signals propagated in baseband or as part of a carrier wave, carrying computer-readable program code. Such propagated data signals may take various forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination thereof. Computer-readable signal media may also be any computer-readable medium other than computer-readable storage media, capable of sending, propagating, or transmitting programs for use by or in connection with an instruction execution system, apparatus, or device.

[0149] Program code contained on a computer-readable medium may be transmitted using any suitable medium, including—but not limited to—wireless, wire, optical fiber, RF, etc., or any suitable combination thereof.

[0150] Computer program code for performing the operations of this invention can be written in one or more programming languages ​​or a combination thereof, including object-oriented programming languages ​​such as Java, Smalltalk, and C++, as well as conventional procedural programming languages ​​such as "C" or similar programming languages. The program code can be executed entirely on the user's computer, partially on the user's computer, as a standalone software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In cases involving remote computers, the remote computer can be connected to the user's computer via any type of network—including a local area network (LAN) or a wide area network (WAN)—or can be connected to an external computer (e.g., via the Internet using an Internet service provider).

[0151] Note that the above description is merely a preferred embodiment of the present invention and the technical principles employed. Those skilled in the art will understand that the present invention is not limited to the specific embodiments described herein, and various obvious changes, readjustments, and substitutions can be made without departing from the scope of protection of the present invention. Therefore, although the present invention has been described in detail through the above embodiments, the present invention is not limited to the above embodiments, and may include many other equivalent embodiments without departing from the concept of the present invention, the scope of which is determined by the scope of the appended claims.

Claims

1. A method for predicting the thickness of the concentration polarization layer in a reverse osmosis membrane based on electrical impedance imaging, characterized in that, include: S101, based on a membrane filtration sensor with an electrode array, simulates concentration polarization by setting virtual dielectric layers with different conductivity at different heights in the normal direction of the membrane surface, and uses adjacent excitation measurement, combined with the finite element method to analyze the potential distribution on the membrane surface, and calculates the sensitivity matrix sequence at different heights in the normal direction of the membrane surface based on the electrode excitation boundary conditions, and constructs a simulated membrane filtration evaluation pool model. S102, based on the preset background conductivity, virtual media with different conductivity are set at different heights of the membrane surface normal and simulated boundary voltage datasets at different heights are obtained respectively. Then, the image is reconstructed using the conjugate gradient least squares algorithm and sensitivity matrix sequence to form a simulated conductivity image. S103: Using simulated conductivity images and different conductivity values ​​of virtual media at different heights, a calibration training dataset is constructed to train the improved image conductivity mapping neural network. S104. The measured boundary voltage dataset is measured using a membrane filter sensor consistent with the simulated membrane filter evaluation cell model, and the conductivity image is reconstructed to form a measured conductivity image. The trained improved image conductivity mapping neural network is then used to predict the estimated value of membrane surface conductivity. S105. Based on the predicted membrane surface conductivity estimate, the concentration polarization layer thickness is mapped using classical membrane mass transfer theory to obtain the membrane surface concentration polarization layer thickness. S105 includes: Using the estimated predicted membrane surface conductivity, and based on the known relationship between conductivity and solute concentration in electrolyte solution theory, the conductivity is converted into the corresponding solute concentration at the membrane surface. Then, based on classical membrane mass transfer theory, the concentration polarization layer thickness is mapped. From the membrane mass transfer theory, the formula is as follows: in, Indicates the diffusion coefficient. Indicates membrane flux, Indicates the concentration of the bulk liquid phase. Represents the solute concentration at the membrane surface; based on the mapping relationship between conductivity and solute concentration at the membrane surface. The predicted membrane surface conductivity estimate is converted into the membrane surface solute concentration. .

2. The method according to claim 1, characterized in that, S101 includes: A membrane filtration sensor array was constructed on the reverse osmosis membrane under test using 16 electrodes; Adjacent excitation measurement is used, and current is injected alternately between two adjacent electrodes. The boundary voltage sequence is measured through other adjacent electrodes to form a boundary voltage dataset. Based on the simulated boundary voltage dataset, the potential distribution on the membrane surface is calculated using the finite element method. Based on the potential distribution on the membrane surface, the sensitivity matrix sequence at different heights in the normal direction of the membrane surface is calculated based on the electrode excitation boundary conditions.

3. The method according to claim 1, characterized in that, S102 includes: Based on the preset background conductivity, the simulated boundary voltage dataset of the virtual medium is solved by the positive impedance problem, which satisfies the Laplace equation. The conductivity image is reconstructed by using the conjugate gradient least squares algorithm and combining it with the sensitivity matrix sequence at different heights to form a simulated conductivity image.

4. The method according to claim 1, characterized in that, S103 includes: A pairing relationship is established between the simulated conductivity image and the corresponding true conductivity value of the virtual medium to construct a calibration training dataset; Using simulated conductivity images as input and corresponding true values ​​of virtual dielectric conductivity as supervision labels, an improved image conductivity mapping neural network is trained.

5. The method according to claim 4, characterized in that, The improved image conductivity mapping neural network includes: An improved U-Net backbone network is used for feature extraction, and residual convolutional blocks are used to replace the standard convolutional layers in the encoder, introducing cross-layer skip connections and dilated convolutions in the downsampling path. In the upsampling path of the improved U-Net backbone network decoder, deconvolution and skip connections are used to form a segmentation branch, followed by mask weights and weighted pooling to form a mask weighted pooling branch, and color space transformation and mask weights to form a color statistical feature branch. A regression fusion branch is formed by a global average pooling layer and multiple fully connected layers. This branch receives the outputs of the mask weighting branch and the color statistical feature branch and performs feature fusion. Then, the regression of the conductivity value is obtained through nonlinear mapping.

6. The method according to claim 4, characterized in that, S103 further includes: After size normalization, grayscale standardization, and masking of the conductivity image, it is input into the improved image conductivity mapping neural network, and the conductivity value used as the supervision label is standardized. An improved image conductivity mapping neural network is trained using a two-stage learning strategy with the Adam optimizer, a mask switching strategy, and a hierarchical learning rate, and optimized using a multi-variable joint loss function that includes segmentation loss and regression loss.

7. The method according to claim 1, characterized in that, S104 includes: Using a membrane filtration sensor with a 16-electrode array, a dataset of measured boundary voltages at different heights in the membrane normal was measured based on a simulated membrane filtration evaluation cell model. Based on the measured boundary voltage dataset, the conductivity image is reconstructed by using the conjugate gradient least squares algorithm combined with the sensitivity matrix sequence at different heights, thus forming the measured conductivity image. By using a trained improved image conductivity mapping neural network, the measured conductivity image is predicted to obtain the estimated value of the predicted membrane surface conductivity.

8. A reverse osmosis membrane concentration polarization layer thickness prediction device based on electrical impedance imaging, used to implement the reverse osmosis membrane concentration polarization layer thickness prediction method based on electrical impedance imaging as described in any one of claims 1-7, characterized in that, include: The model building unit is used to construct a simulated membrane filtration evaluation pool model by setting virtual dielectric layers with different conductivity at different heights of the membrane surface normal and using adjacent excitation measurement based on the electrode array membrane filtration sensor. The image reconstruction unit is used to set up virtual media with different conductivity at different heights in the normal direction of the membrane surface based on the preset background conductivity, and to reconstruct the image using the conjugate gradient least squares algorithm and sensitivity matrix sequence to form a simulated conductivity image. The network training unit is used to construct a calibration training dataset using simulated conductivity images and different conductivity values ​​of virtual media at different heights, and to train the improved image conductivity mapping neural network. The conductivity prediction unit is used to predict the estimated value of the membrane surface conductivity by using a trained improved image conductivity mapping neural network to reconstruct the measured conductivity image based on the measured boundary voltage dataset. The thickness mapping unit is used to map the thickness of the concentration polarization layer on the membrane surface based on the predicted membrane surface conductivity estimate and classical membrane mass transfer theory.

9. An electronic device, characterized in that, The electronic device includes: One or more processors; Storage device for storing one or more programs. When the one or more programs are executed by the one or more processors, the one or more processors implement the reverse osmosis membrane concentration polarization layer thickness prediction method based on electrical impedance imaging as described in any one of claims 1-7.

10. A storage medium containing computer-executable instructions, which, when executed by a computer processor, are used to perform the reverse osmosis membrane concentration polarization layer thickness prediction method based on electrical impedance imaging as described in any one of claims 1-7.

Images