An EDI module control method and system based on an electric field-flow field coupling model

Abstract

The application relates to the technical field of physical field modeling of electrochemical water treatment, and discloses an EDI module control method and system based on an electric field-flow field coupling model, which comprises the following steps: establishing an EDI module multi-physical field coupling model, spatially discretizing multiple regions, and obtaining a high-dimensional space state; normalizing the electric field and the flow field direction of each node and calculating a direction consistency index; adaptively weighting a joint direction vector to generate a direction coupling state variable through spatial aggregation; performing intrinsic orthogonal decomposition of a multi-working-condition snapshot to reduce the order, embedding the direction coupling state variable into a reduced-order state space as an independent dimension, and establishing a direction-enhanced reduced-order dynamic model; combining online observation data to establish a physical constraint prediction model, rolling predicting future internal states and direction risks; and constructing a multi-objective optimization function to adjust working current and flow in advance through model predictive control. The application changes EDI control from result feedback to internal state predictive control, and eliminates control lag.

Description

Technical Field

[0001] This invention relates to the field of physical field modeling technology for electrochemical water treatment, and more specifically, to an EDI module control based on an electric field-flow field coupling model. Background Technology

[0002] Electrodeionization (EDI) is a water treatment process that deeply integrates electrodialysis and ion exchange technologies. This technology fills a desalination chamber with ion exchange resin, enabling the directional migration of ions in the water under a direct current electric field. Simultaneously, the resin is continuously regenerated in situ using hydrogen and hydroxide ions generated by water electrolysis, thus achieving continuous production of high-purity water without the need for acid-base chemical regeneration. Since its industrial application in the 1980s, EDI technology has been widely adopted in fields such as power, electronics, pharmaceuticals, and chemicals. The resistivity of the produced water can stably reach above 15 MΩ·cm, making it a core purification process in the field of ultrapure water preparation.

[0003] The internal structure of the EDI module includes alternating cation exchange membranes and anion exchange membranes, with desalination chambers and concentrate chambers formed between the membranes. The desalination chambers are filled with mixed ion exchange resins.

[0004] During operation, multiple physicochemical processes are coupled, including ion electromigration driven by an electric field, ion exchange adsorption and desorption on the resin surface, fluid convection transport, ion diffusion, and water electrolysis. The study points out that although mathematical modeling helps understand the behavior of EDI units, there is currently a lack of models that reliably correlate relevant operating parameters with EDI performance. Existing models are mostly based on the Nernst-Planck equation to describe ion migration flux, but they are insufficient in describing the spatial coupling relationship between the electric field, flow field, and concentration field. The coupled model framework provides a theoretical basis for describing the transport of charged particles in fluids, but its application in EDI engineering modeling still faces difficulties due to its high computational dimensionality and the challenge of real-time solution.

[0005] In their research on the commissioning and operation of EDI membrane stacks published in "Membrane Science and Technology" (Vol. 27, No. 4, 2007), Wu Hongxing et al. summarized that the main parameters for on-site adjustment are influent flow rate, electrode water flow rate, concentrate flow rate, operating voltage, and operating current. The adjustment is based on the changing trend of effluent conductivity. In current engineering practice, EDI operation control is generally based on the single indicator of effluent conductivity for feedback adjustment. When the effluent conductivity exceeds the set threshold, the operating current or influent flow rate is adjusted to respond.

[0006] The existing control modes have the following inherent defects:

[0007] From the occurrence of electric field distribution distortion, local concentration polarization, or flow field anomaly within the EDI to the eventual manifestation of increased effluent conductivity, there is a significant time lag, making it impossible for the controller to intervene in the early stages of the problem.

[0008] The key operating states of the EDI module, such as the spatial distribution of the electric field, the velocity distribution of the flow field, the ion concentration field distribution, and the temperature field distribution, cannot be directly obtained through external sensors, resulting in a fundamental lack of information for operators to perceive the internal state.

[0009] The control objective focuses solely on the quality of the effluent, lacking a synergistic consideration of energy consumption costs and the health of the internal state. While simply increasing the current can improve water quality in the short term, it also exacerbates the Joule heating effect and concentration polarization of the membrane surface, accelerating the aging of the ion exchange membrane in the long term.

[0010] Understandably, concentration polarization and membrane scaling are the main problems affecting the long-term stable operation of EDI. When the ion concentration in the concentrate chamber is too high, the pH value on the surface of the anion exchange membrane increases, which easily leads to the formation of inorganic scale such as calcium carbonate and calcium sulfate, resulting in increased pressure drop in the concentrate chamber and reduced current efficiency.

[0011] In existing technologies, the Proper Orthogonal Decomposition (POD) method has been widely used in fields such as fluid mechanics, nuclear reactor physics, and electrochemical systems. The POD method extracts dominant modes by performing singular value decomposition on multi-condition snapshot data, transforming the solution of high-dimensional partial differential equation systems into the solution of low-dimensional ordinary differential equation systems, thus significantly reducing computational costs. However, traditional POD reduction methods only extract and truncate the amplitude information of field variables. When two operating states have similar field variable amplitudes but fundamentally different spatial orientations, traditional reduction models map them to similar low-dimensional coordinates, losing the ability to distinguish directional differences. In actual EDI operation, non-uniform electric field distribution, local eddies, and irregular flow channels in the resin-filled region all lead to complex spatial variations in the electric field direction and flow field direction. Amplitude information alone cannot accurately describe these operating condition differences.

[0012] Existing EDI technology has shortcomings in operation modeling, state awareness, and order reduction calculation. Specifically, the multi-physics coupling model has too high a dimensionality for online application; there is a lack of effective means to characterize the directional coupling relationship between the internal electric field and the flow field; and traditional order reduction methods cannot distinguish directional differences. Therefore, there is an urgent need for a method that can characterize the multi-physics state inside EDI in a low dimension, effectively depict the directional coupling relationship between the electric field and the flow field, and achieve early control based on internal state prediction.

[0013] In summary, it is necessary to design an EDI module control based on an electric field-flow field coupling model to solve the problems existing in the current technology. Summary of the Invention

[0014] In view of this, the present invention proposes an EDI module control based on an electric field-flow field coupling model, which aims to solve the shortcomings of existing EDI technology in terms of operation modeling, state perception, and order reduction calculation.

[0015] In one aspect, this invention proposes an EDI module control method based on an electric field-flow field coupling model, comprising:

[0016] Step S1: Establish a multi-physics coupling model of the EDI module’s electro-thermal-fluid-ion migration. Spatially discretize the desalination chamber, concentrate chamber, ion exchange membrane and resin filling region of the EDI module. Solve for the electric field, flow field, ion concentration field and temperature field respectively to obtain a high-dimensional spatial state including electric field state, flow field state, concentration field state and temperature field state.

[0017] Step S2: Based on the high-dimensional spatial state, construct the directional coupling state between the electric field direction and the flow field direction. Specifically, normalize the electric field direction and the flow field direction of each node in the space, calculate the directional consistency index between the electric field driving force direction and the fluid transport direction at each node, adaptively determine the correction weight of the flow field on the electric field direction based on the directional consistency index, construct a joint direction vector, and then generate directional coupling state variables that characterize the degree of risk of mismatch between the electric field and the flow field directions through spatial aggregation.

[0018] Step S3: Based on multi-condition snapshot data, perform intrinsic orthogonal decomposition to reduce the order of the high-dimensional space state to obtain a low-dimensional state vector. After normalization, the directional coupled state variables are embedded into the reduced-order state space as independent state dimensions to form a directional enhanced reduced-order state. Establish a reduced-order dynamic model in which the directional risk state participates in the temporal evolution of the internal state as an independent driving term.

[0019] Step S4: Based on the reduced-order dynamic model, a physical constraint state prediction model is established by combining online observation data to perform rolling prediction of the future internal state of the EDI module. The prediction output includes the future direction and risk state.

[0020] Step S5: Based on the predicted results of the future internal state, construct a multi-objective optimization function with the objectives of water quality compliance, energy consumption minimization, and directional risk minimization. Solve for the optimal control quantity through model predictive control, and adjust the operating current and flow rate of the EDI module in advance before the directional risk state actually increases.

[0021] It is understood that the present invention performs steps S1 to S3 offline to complete the establishment of a multi-physics coupling model, the determination of the directional coupling state construction logic, the generation of multi-condition snapshots, and the training and parameter identification of the directional enhancement and order reduction dynamic model.

[0022] The online real-time control in steps S4 to S5 of the present invention is based on the online collected current, voltage, flow and conductivity data. In each control cycle, state prediction and model predictive control optimization are rolled out, and control commands are sent to the current regulation mechanism and flow regulation mechanism of the EDI module.

[0023] Preferably, in step S1, the establishment of the electro-thermal-fluid-ion migration multiphysics coupling model of the EDI module includes:

[0024] Electric field modeling is performed by solving the spatial electric potential distribution based on the electric potential conservation equation. The spatial electric field distribution is obtained by taking the negative gradient of the electric potential, where the conductivity is coupled and corrected as a function of the temperature field and the concentration field.

[0025] Flow field modeling is performed by solving the velocity field based on the momentum conservation equation for incompressible fluids, where the volume force of the electric field on charged ions is introduced as a source term into the momentum equation.

[0026] Ion migration modeling is based on the Nernst-Planck equation to describe the migration flux of each ion component. The migration flux includes three parts: diffusion term, electromigration term, and convective transport term. The concentration field is obtained by solving the mass conservation equation of each ion component.

[0027] Temperature modeling is performed by solving the temperature field based on the energy conservation equation, where the Joule heat caused by the electric field is used as a volume heat source term. The Joule heat is determined by the product of electrical conductivity and the square of the electric field strength.

[0028] The four fields are solved through bidirectional coupling iteratively using the temperature-concentration dependence of conductivity.

[0029] Preferably, in step S2, constructing the directional coupling state includes:

[0030] The electric field vector at each node in space is divided by its magnitude and a regularization term is added to obtain the electric field direction normalized vector; the flow field velocity vector at each node in space is divided by its magnitude and a regularization term is added to obtain the flow field direction normalized vector.

[0031] The direction consistency index is obtained by calculating the inner product of the electric field direction normalization vector and the flow field direction normalization vector at each node. The value range of the direction consistency index is from negative one to positive one. A positive value indicates that the direction of the electric field driving force is consistent with the direction of fluid transport, and a negative value indicates that the two directions conflict.

[0032] A joint direction vector is constructed by superimposing the electric field direction normalized vector with the flow field direction normalized vector weighted by the direction consistency index and the flow field direction correction coefficient, and then normalizing the superposition result. When the direction consistency index is positive, the flow field direction contribution is enhanced; when the direction consistency index is negative, the flow field direction contribution is suppressed. The flow field direction correction coefficient is a preset constant or adaptively determined based on the flow field Reynolds number.

[0033] The outer product is constructed using the joint direction vector of each node, and then the sum is weighted by the node weights and aggregated into a global directional coupling tensor; where the node weights are determined based on the contribution of each node's region to the ion migration flux.

[0034] The maximum and minimum eigenvalues ​​of the directional coupling tensor are calculated. The directional anisotropy index is defined by the ratio of the maximum to the minimum eigenvalues. The directional risk state is obtained by subtracting the reciprocal of the directional anisotropy index from one. The larger the value of the directional risk state, the more severe the directional mismatch between the electric field and the flow field.

[0035] Preferably, the step S3 of establishing the directional enhancement reduced-order state model includes:

[0036] By changing the operating current, flow rate, influent concentration, and temperature parameters under various operating conditions, the multiphysics coupling model is solved to generate multiple sets of high-dimensional spatial state snapshots covering different operating states.

[0037] Singular value decomposition is performed on the snapshot matrix composed of the multiple snapshots. The first few principal modes are selected as basis functions according to the energy contribution rate. The high-dimensional space state is projected onto the low-dimensional subspace spanned by the basis functions to obtain the low-dimensional state vector.

[0038] Preferably, the step S3 of establishing the directional enhancement reduced-order state model further includes:

[0039] The directional coupling state variables are normalized to obtain the directional enhancement state, which is then appended as an independent state dimension to the low-dimensional state vector to form the directional enhancement reduced-order state. The normalization process involves mapping the directional coupling state variables to the [0,1] interval, using the minimum and maximum values ​​of the directional coupling state variables in the multi-condition snapshots as boundaries for linear mapping.

[0040] A discrete-time state transition equation is established with the current low-dimensional state, the direction-enhancing state, and the control input as independent variables. The direction-enhancing state acts on the evolution of the low-dimensional state at the next time step through an independent coupling matrix, so that the direction mismatch information not only exists as a static index, but also changes the state transition structure of the reduced-order model.

[0041] Preferably, in step S4, the construction of the physical constraint state prediction model includes:

[0042] The prediction model consists of two superimposed parts: a physical prediction term and a model error compensation term. The physical prediction term is deduced deterministically based on the state transition equation of the reduced-order dynamic model, and the model error compensation term is used to correct the prediction bias caused by the reduction-order truncation and model simplification.

[0043] The input to the prediction model is the current operating current and flow rate; online observations include current, voltage, flow rate, and conductivity.

[0044] The prediction model operates in a rolling manner: in each control cycle, it extrapolates multiple steps forward based on the current measured state and the reduced-order dynamic model to obtain the reduced-order state prediction value at each time in the future prediction time domain. The prediction value includes the directional risk state prediction value at each time in the future.

[0045] Preferably, in step S5, model predictive control includes:

[0046] Define the prediction time domain and the control time domain, and in each control cycle, predict the internal state trajectory for multiple future steps based on the physical constraint state prediction model.

[0047] A multi-objective optimization function is constructed, which consists of a weighted sum of three terms. The first term is the water quality objective, which represents the deviation between the predicted effluent concentration and the target concentration. The second term is the energy consumption objective, which represents the product of the predicted voltage and the operating current. The third term is the directional risk objective, which represents the square of the predicted directional risk state.

[0048] Preferably, in step S5, model predictive control further includes:

[0049] Under the conditions of satisfying the upper and lower limits of current, upper and lower limits of flow rate, upper limit of directional risk, and upper limit of effluent quality, the minimum value of the multi-objective optimization function is solved to obtain the optimal current and optimal flow rate.

[0050] The optimal current and optimal flow rate are output as the execution quantities for the next control cycle, thereby enabling advance adjustment of the operating parameters of the EDI module;

[0051] When the predicted directional risk state exceeds the preset safety threshold, the weight and priority of the directional risk target are increased in the optimization solution, so that the controller can suppress the deterioration of directional mismatch first under the premise of meeting water quality constraints.

[0052] In existing technologies, online monitoring methods for EDI modules are extremely limited, typically only able to acquire external macroscopic electrical parameters such as operating current, terminal voltage, and effluent conductivity. Due to the physical enclosure of the ion exchange membrane and resin-filled areas, critical operating conditions within the EDI module, such as the spatial distribution of the electric field, flow velocity distribution, ion migration flux distribution, and temperature field distribution, cannot be directly measured using conventional sensors. This means that operators can only indirectly infer the internal operating status based on the final effluent water quality results, resulting in a fundamental lack of information regarding the internal state.

[0053] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0054] By establishing a multi-physics coupling model, the freshwater chamber, concentrated water chamber, ion exchange membrane, and resin filling region of the EDI module are completely spatially discretized, and the electric field, flow field, ion concentration field, and temperature field are solved respectively to obtain the high-dimensional spatial state.

[0055] Based on this, the high-dimensional field information with millions of degrees of freedom is compressed into a low-dimensional state vector through intrinsic orthogonal decomposition to reduce the order. Then, the rolling state is estimated by combining the physical constraint state prediction model with online measurable current, voltage, flow rate and conductivity data.

[0056] Therefore, without modifying the internal structure of the EDI module or adding a large number of invasive sensors, it is possible to indirectly acquire and reconstruct in real time the internal electric field distribution, flow field distribution, ion migration state and temperature distribution of the EDI, which are not directly measurable, thus fundamentally breaking through the limitations of simulating the operating state of EDI in the existing technology.

[0057] In existing technologies, EDI control strategies generally employ a feedback control method based on effluent water quality. This means that the controller only adjusts the current or flow rate when the effluent conductivity exceeds a set threshold. However, there is a significant time lag between the occurrence of electric field direction shifts and mismatches between fluid transport and electromigration directions within the EDI module, and the eventual deterioration of effluent water quality. This control mode, characterized by degradation before response, causes the EDI module to operate inefficiently or even with localized damage for a considerable time window, increasing energy consumption and accelerating the aging of the ion exchange membrane.

[0058] It is understood that the technical effects of the present invention include:

[0059] By minimizing directional risk, the controller proactively adjusts flow rate and current to ensure that electric field lines and streamlines are as parallel and coordinated as possible. This reduces ineffective migration paths and localized retention of ions within the resin bed, directly increasing desalination capacity per unit energy consumption and making the effluent quality more stable, while reducing water quality fluctuations caused by localized polarization.

[0060] This invention, by constraining directional risks, essentially forces the module to operate within a comfortable range of hydraulic-electric coordination. This effectively avoids excessively high local concentration gradients, thereby delaying ion exchange membrane fouling and resin degradation, and extending the lifespan of expensive consumables.

[0061] This invention transforms the invisible internal multiphysics coupling state into a quantifiable, predictable, and optimizable control variable by constructing a directional enhancement reduced-order state, thus bridging the gap between microscopic mechanisms and macroscopic control.

[0062] This invention employs POD order reduction combined with physical constraint error compensation, which not only preserves the high-precision description capability of multiphysics models for nonlinear dynamics, but also reduces the computational load to a level that embedded controllers can handle, thus solving the industry problem that high-precision mechanistic models cannot be applied online.

[0063] On the other hand, this application also provides an EDI module control system based on an electric field-flow field coupling model, applied to the above-mentioned EDI module control method based on an electric field-flow field coupling model, including:

[0064] The multiphysics modeling module establishes a multiphysics coupling model of the EDI module, which includes electric-thermal-fluid-ion migration. It spatially discretizes the freshwater chamber, concentrated water chamber, ion exchange membrane, and resin-filled region of the EDI module, and solves for the electric field, flow field, ion concentration field, and temperature field respectively, to obtain a high-dimensional spatial state that includes the electric field state, flow field state, concentration field state, and temperature field state.

[0065] The directional coupling state construction module constructs the directional coupling state of electric field direction and flow field direction based on the high-dimensional spatial state. Specifically, it normalizes the electric field direction and flow field direction of each node in space, calculates the directional consistency index between the electric field driving force direction and the fluid transport direction at each node, adaptively determines the correction weight of the flow field on the electric field direction based on the directional consistency index, constructs a joint direction vector, and then generates directional coupling state variables that characterize the degree of risk of mismatch between electric field and flow field directions through spatial aggregation.

[0066] The directional enhancement and order reduction modeling module performs intrinsic orthogonal decomposition on the high-dimensional space state based on multi-condition snapshot data to reduce the order, obtains a low-dimensional state vector, and embeds the directional coupled state variables as independent state dimensions into the reduced-order state space after normalization to form a directional enhancement and order reduction state. It also establishes a reduced-order dynamic model in which the directional risk state participates in the internal state time-series evolution as an independent driving term.

[0067] The state prediction module, based on the reduced-order dynamic model and combined with online observation data, establishes a physical constraint state prediction model to perform rolling predictions of the future internal state of the EDI module. The prediction output includes the future direction and risk state.

[0068] The predictive control module, based on the predicted results of the future internal state, constructs a multi-objective optimization function with the objectives of water quality compliance, energy consumption minimization, and directional risk minimization. It solves for the optimal control quantity through model predictive control and adjusts the operating current and flow rate of the EDI module in advance before the directional risk state actually increases.

[0069] It is understood that in this application:

[0070] The multiphysics modeling module is used to establish the electro-thermal-fluid-ion migration coupling model of the EDI module. It obtains the high-dimensional spatial state by solving the coupled iterative solution of electric field, flow field, ion migration field and temperature field.

[0071] The directional coupling state construction module is used to normalize the electric field direction and flow field direction of each node based on the high-dimensional spatial state and calculate the directional consistency index. Based on the directional consistency index, it adaptively weights and constructs a joint direction vector, generates a directional coupling tensor through spatial aggregation, and generates a directional coupling state variable representing the risk of electric field-flow field direction mismatch based on the eigenvalue anisotropy of the directional coupling tensor.

[0072] The directional enhancement reduction modeling module is used to perform intrinsic orthogonal decomposition on multi-condition snapshot data to obtain low-dimensional state vectors. The normalized directional coupling state variables are embedded as additional state dimensions into the reduced state space. The dynamic correlation between the state variables and the reduced modes is established through the directional risk coupling matrix. A reduced dynamic model in which the directional risk state participates in state transition through an independent coupling matrix is ​​established.

[0073] The state prediction module is used to predict the internal state of the EDI module in the future multiple steps in a rolling manner based on the reduced-order dynamic model and online observation data, and output the predicted trajectory including the future directional risk state.

[0074] The predictive control module is used to optimize the EDI module based on the predicted trajectory, under the condition of meeting the operating constraints, with multiple objectives of achieving water quality standards, minimizing energy consumption, and minimizing directional risk, and output the optimal operating current and optimal flow control commands to realize predictive control of the EDI module.

[0075] It is understandable that the EDI module control based on the electric field-flow field coupling model described above has the same beneficial effects, and will not be elaborated further here. Attached Figure Description

[0076] Various other advantages and benefits will become apparent to those skilled in the art upon reading the following detailed description of preferred embodiments. The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. Furthermore, the same reference numerals denote the same parts throughout the drawings. In the drawings:

[0077] Figure 1 A flowchart of an EDI module control method based on an electric field-flow field coupling model provided in an embodiment of the present invention;

[0078] Figure 2 The potential model of the interstitial liquid between cation exchange resin and anion exchange resin in the dilute solution chamber of the EDI module control method based on the electric field-flow field coupling model provided in the embodiments of the present invention;

[0079] Figure 3 A schematic diagram illustrating the principle of constructing the EDI potential distribution-direction coupling state of the EDI module control method based on the electric field-flow field coupling model provided in this embodiment of the invention.

[0080] Figure 4 This is a functional block diagram of an EDI module control system based on an electric field-flow field coupling model, provided in an embodiment of the present invention. Detailed Implementation

[0081] Exemplary embodiments of the present disclosure will now be described in more detail with reference to the accompanying drawings. While exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure may be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided to enable a more thorough understanding of the present disclosure and to fully convey the scope of the disclosure to those skilled in the art. It should be noted that, unless otherwise specified, embodiments and features in the embodiments of the present invention can be combined with each other. The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0082] See Figure 1-4 As shown, this embodiment proposes an EDI module control method based on an electric field-flow field coupling model, including:

[0083] Step S1: Establish a multi-physics coupling model of the EDI module’s electro-thermal-fluid-ion migration. Spatially discretize the desalination chamber, concentrate chamber, ion exchange membrane and resin filling region of the EDI module. Solve for the electric field, flow field, ion concentration field and temperature field respectively to obtain a high-dimensional spatial state including electric field state, flow field state, concentration field state and temperature field state.

[0084] Step S2: Based on the high-dimensional spatial state, construct the directional coupling state between the electric field direction and the flow field direction. Specifically, normalize the electric field direction and the flow field direction of each node in the space, calculate the directional consistency index between the electric field driving force direction and the fluid transport direction at each node, adaptively determine the correction weight of the flow field on the electric field direction based on the directional consistency index, construct a joint direction vector, and then generate directional coupling state variables that characterize the degree of risk of mismatch between the electric field and the flow field directions through spatial aggregation.

[0085] Step S3: Based on multi-condition snapshot data, perform intrinsic orthogonal decomposition to reduce the order of the high-dimensional space state to obtain a low-dimensional state vector. After normalization, the directional coupled state variables are embedded into the reduced-order state space as independent state dimensions to form a directional enhanced reduced-order state. Establish a reduced-order dynamic model in which the directional risk state participates in the internal state temporal evolution as an independent driving term.

[0086] Step S4: Based on the reduced-order dynamic model, a physical constraint state prediction model is established by combining online observation data to perform rolling prediction of the future internal state of the EDI module. The prediction output includes the future direction and risk state.

[0087] Step S5: Based on the prediction results of the future internal state, construct a multi-objective optimization function with the objectives of water quality compliance, energy consumption minimization, and directional risk minimization. Solve for the optimal control quantity through model predictive control, and adjust the operating current and flow rate of the EDI module in advance before the directional risk state actually increases.

[0088] It is understood that in this embodiment, steps S1 to S3 are executed offline to complete the establishment of the multi-physics coupling model, the determination of the directional coupling state construction logic, the generation of multi-condition snapshots, and the training and parameter identification of the directional enhancement and order reduction dynamic model.

[0089] In this embodiment, steps S4 to S5 involve online real-time control based on online collected current, voltage, flow, and conductivity data. In each control cycle, state prediction and model predictive control optimization are performed on a rolling basis, and control commands are sent to the current regulation mechanism and flow regulation mechanism of the EDI module.

[0090] Understandably, see Figure 2 As shown, this is a potential distribution model of the interparticle space between anion and cation exchange resin particles in a freshwater chamber. It is a classic microscopic mechanism diagram in electro-deionization technology, illustrating how the potential is distributed in the liquid between the ion exchange resin particles in the freshwater chamber and how ions migrate.

[0091] CM stands for Cation-exchange Membrane, located near the negative electrode, allowing only cations to pass through while blocking anions. AM stands for Anion-exchange Membrane, located near the positive electrode, allowing only anions to pass through while blocking cations.

[0092] - The negative sign indicates the cathode direction. Under the influence of an electric field, cations move in this direction.

[0093] The plus sign (+) indicates the anode direction. Under the influence of an electric field, anions move in this direction.

[0094] The black upward arrow indicates the direction of the raw water flow, meaning the water flows from bottom to top through the freshwater chamber.

[0095] The white spheres represent anion exchange resins. They have a positively charged surface and adsorb anions.

[0096] The black spheres represent cation exchange resins. They have a negatively charged surface and adsorb cations.

[0097] The wavy lines represent the water flow path, illustrating the meandering flow of water between closely packed resin particles.

[0098] CR stands for Cation-exchange Resin, which refers to cation exchange resin particles.

[0099] AR stands for Anion-exchange Resin, which refers to particles of anion exchange resin.

[0100] Na+ is a sodium ion, a cation. The diagram shows it desorbing from the cation exchange resin (CR) surface and migrating towards the left cathode / CM membrane; Cl− is a chloride anion. The diagram shows it desorbing from the anion exchange resin (AR) surface and migrating towards the right anode / AM membrane.

[0101] δ eff Effective Distance refers to the equivalent thickness or characteristic length of the liquid phase region between two resin particles. It is a key geometric parameter for calculating resistance and potential drop.

[0102] φ cr This refers to the potential inside the cation resin phase, i.e., the potential level inside the black sphere.

[0103] φ ar This refers to the potential inside the anion resin phase, i.e., the potential level inside the white sphere.

[0104] φ dsThe potential in the solution refers to the potential of the liquid between two resin particles. The diagonal line in the figure indicates that the potential decreases linearly in the solution.

[0105] Φ ds cr This is the solution-side potential at the cation exchange resin-solution interface, which is the solution potential immediately adjacent to the surface of the black resin. Due to the presence of the Donnan potential, it has a sudden change compared to the internal resin potential φcr.

[0106] Φ ds ar It is the solution-side potential at the anion resin-solution interface, which is the solution potential immediately adjacent to the surface of the white resin.

[0107] This reveals that EDI is a complex system deeply coupled with electric field, flow field, ion concentration field, and temperature field, and is by no means a uniform electric field path; the black arrows in the figure represent that the electric field lines or ion migration paths do not pass straight through, but bypass the resin particle spheres, exhibiting a curved and divergent state. This means that at the microscopic level, the direction of the electric field is highly spatially variable; the wavy lines represent water flow channels; the water flow must navigate through the gaps between these tightly packed resin particles; the magnified image shows the φ of the resin surface. cr ,φ ar With solution bulk φ ds φ ds The potential difference between the two phases indicates that the electric field exists not only in the solution but also deeply coupled at the interface between the resin phase and the solution phase. This rigorously demonstrates that the interior of the EDI is a porous medium environment with complex and variable electric field vector directions, and is strongly constrained by the fluid geometry.

[0108] Understandably, see Figure 3 The results show the potential model of the entire cell cross-section at half height (L / 2) of the EDI cell at t=1 hour under the following conditions: initial concentrations of 0.02M NaCl and 0.05M NaCO3 in the circulating tank, and a cell potential of 7V. It can be observed that under these specific conditions, applying the Nernst-Planck ion transport equation leads to a linear change in the potential in the resin-free compartment; simultaneously, the Donnan potential at the membrane interface in these compartments (ranging from 72 to 92 mV) is also observed. This implies that the current density continuously increases along the ion transport direction in various resins, resulting in a larger potential drop in that direction. The study confirms that in the resin-filled bed DC, the potential curve does not decrease linearly but exhibits curvature characteristics caused by the source term of the Poisson equation. This indicates that the electric field inside the resin bed is not a uniform field; its intensity and direction are continuously varied in space, further demonstrating the complexity of electric field-driven processes at the microscale.

[0109] Based on the aforementioned physical facts, this application further discovers and utilizes the following technical insights: Because the electric field inside the resin bed has significant curvature characteristics (i.e., its direction is divergent or curved), while the main fluid flow direction within the EDI module is typically a straight line along the longitudinal direction of the flow channel, this inevitably leads to a significant directional mismatch between the direction of the local electric field vector and the direction of the fluid velocity vector in specific regions of the resin bed, particularly near the membrane interface or where resin packing is uneven.

[0110] In some embodiments of this application, step S1, establishing the electro-thermal-fluid-ion migration multiphysics coupling model of the EDI module, includes:

[0111] Electric field modeling is performed by solving the spatial electric potential distribution based on the electric potential conservation equation. The spatial electric field distribution is obtained by taking the negative gradient of the electric potential, where the conductivity is coupled and corrected as a function of the temperature field and the concentration field.

[0112] Flow field modeling is performed by solving the velocity field based on the momentum conservation equation for incompressible fluids, where the volume force of the electric field on charged ions is introduced as a source term into the momentum equation.

[0113] Ion migration modeling is based on the Nernst-Planck equation to describe the migration flux of each ion component. The migration flux includes three parts: diffusion, electromigration and convective transport. The concentration field is obtained by solving the mass conservation equation of each ion component.

[0114] Temperature modeling is performed by solving the temperature field based on the energy conservation equation, where the Joule heat caused by the electric field is used as a volume heat source term. The Joule heat is determined by the product of electrical conductivity and the square of the electric field strength.

[0115] The four fields are solved through bidirectional coupling iteratively using the temperature-concentration dependence of conductivity.

[0116] It is understood that in this embodiment, the multiphysics coupling model described in step S1 is implemented using the existing electro-thermal-fluid-ion migration coupling simulation framework.

[0117] Since the governing equations of each physical field, including potential conservation, momentum conservation, Nernst-Planck migration and energy conservation, as well as the coupled iterative algorithm based on conductivity temperature-concentration dependence, are all mature existing technologies, this specification will not elaborate on their specific mathematical expressions and solution details.

[0118] The essence of this step is to use the existing model mentioned above as a digital twin tool to solve and output a high-dimensional spatial state containing electric field, flow field, concentration field and temperature field offline, thereby providing a data foundation for the directional coupling state extraction in step S2 and the eigenorthogonal decomposition in step S3.

[0119] In some embodiments of this application, step S2, constructing the directional coupling state, includes:

[0120] The electric field vector at each node in space is divided by its magnitude and a regularization term is added to obtain the electric field direction normalized vector; the flow field velocity vector at each node in space is divided by its magnitude and a regularization term is added to obtain the flow field direction normalized vector.

[0121] The direction consistency index is obtained by calculating the inner product of the electric field direction normalization vector and the flow field direction normalization vector at each node. The value range of the direction consistency index is from negative one to positive one. A positive value indicates that the direction of the electric field driving force is consistent with the direction of fluid transport, and a negative value indicates that the two directions conflict.

[0122] A joint direction vector is constructed by superimposing the electric field direction normalized vector with the flow field direction normalized vector weighted by the direction consistency index and the flow field direction correction coefficient, and then normalizing the superposition result. When the direction consistency index is positive, the flow field direction contribution is enhanced; when the direction consistency index is negative, the flow field direction contribution is suppressed. The flow field direction correction coefficient is a preset constant or adaptively determined based on the flow field Reynolds number.

[0123] The outer product is constructed using the joint direction vector of each node, and then the sum is weighted by the node weights and aggregated into a global directional coupling tensor; where the node weights are determined based on the contribution of each node's region to the ion migration flux.

[0124] The maximum and minimum eigenvalues ​​of the directional coupling tensor are calculated. The directional anisotropy index is defined by the ratio of the maximum to the minimum eigenvalues. The directional risk state is obtained by subtracting the reciprocal of the directional anisotropy index from one. The larger the value of the directional risk state, the more severe the directional mismatch between the electric field and the flow field.

[0125] Specifically, the technical approach of this embodiment includes:

[0126] Within the framework of continuum mechanics, the electric driving force and fluid convection transport constitute the two main vector fields for ion migration. At any discrete node in space... Above, define the unit vector of the electric field direction. Unit vector of the flow field direction Calculate the interior dot product of the two: Mathematically, this is equivalent to solving for the direction cosines of the two vector fields. Geometrically, this index characterizes the collinearity of the local electric field vector and the flow field vector.

[0127] In response, when At this time, the two vector fields are locally coupled in the same direction, and the electric force and convective transport work together to promote ion migration;

[0128] when At this time, the two vector fields are locally opposed, and the electric field migration flux and the convective transport flux locally cancel each other out. This is the hydrodynamic root of inducing concentration polarization (and local ion accumulation).

[0129] Specifically, the technical approach of vector adaptive weighting based on physical feedback and joint direction vector includes:

[0130] To highlight the dangerous condition of directional conflict at the control level, the embodiment introduces a nonlinear adaptive weighting mechanism.

[0131] Let the joint direction vector be... The construction logic is as follows:

[0132] ;

[0133] Among them, the weight function It is a monotonically increasing function of the directional consistency index; from the perspective of control theory, this is a state-dependent gain scheduling strategy.

[0134] In the collaborative region Increase the flow field vector weight to enhance the system's perception of normal transport conditions;

[0135] In the confrontation zone Suppress the flow field vector weights, so that the joint vector Geometrically, it leans more towards the direction of the electric field.

[0136] The physical significance of this structure is that when a severe electric field-flow field inverse conflict occurs locally, it can reduce the confidence level of the flow field information, forcing the control algorithm to focus on the abnormal migration behavior dominated by the electric field, thereby making the controller more sensitive to the risk of local mismatch.

[0137] Specifically, the technical approach to spectral analysis and scalar dimensionality reduction of global tensors, i.e., directional risk states, includes:

[0138] In order to aggregate distributed local orientation information into a single global control variable, the embodiment uses tensor outer product and spectral analysis methods;

[0139] The construction of the global directional coupling tensor refers to the weighted outer product and summation of the joint direction vectors of each node to construct a second-order symmetric tensor. The second-order symmetric tensor Constructed using the following formula:

[0140] ;

[0141] This tensor is mathematically equivalent to the covariance matrix of the local direction vectors, and it characterizes the overall anisotropic distribution of the direction field of the entire module.

[0142] Perform eigenvalue decomposition on tensor T to obtain the largest eigenvalue. and minimum eigenvalue .

[0143] Understandable It represents the energy concentration in the most dominant transport direction in the directional field; It represents the degree of energy dispersion in the weakest direction.

[0144] Define directional anisotropy index The formula is: ;

[0145] Understandably, in an ideal matching state, the orientation field is highly ordered. The value is relatively large; however, when there is a large area of ​​chaotic electric field-flow field direction and severe local reverse opposition within the module, the direction vector tends to diverge uniformly in space, leading to... and Approaching The value decreased.

[0146] Therefore, the directional risk state is defined as:

[0147] ;

[0148] Understandably, this is a standard normalized risk measure; when When, it indicates This means that the global directional field is highly isotropic, which is a chaotic state where the electric field and the flow field are severely mismatched on a macroscopic scale; while when When the direction field is highly anisotropic and exhibits an ordered state, it indicates that the field is in an ideal state of cooperative transport.

[0149] In summary, this embodiment constructs a mathematical mapping of centralized scalar control states by measuring local collinearity through vector inner product, highlighting adversarial regions through adaptive weighting, and extracting global anisotropy through tensor spectrum analysis.

[0150] In some embodiments of this application, step S3, establishing a directional enhancement reduced-order state model, includes:

[0151] By changing the operating current, flow rate, influent concentration and temperature parameters under multiple operating conditions, the multiphysics coupling model is solved to generate multiple sets of high-dimensional spatial state snapshots covering different operating states.

[0152] Singular value decomposition is performed on the snapshot matrix composed of multiple snapshots. The first few principal modes are selected as basis functions according to the energy contribution rate. The high-dimensional state is projected onto the low-dimensional subspace spanned by the basis functions to obtain the low-dimensional state vector.

[0153] In some embodiments of this application, step S3, establishing the directional enhancement reduced-order state model, further includes:

[0154] The directional coupling state variables are normalized to obtain the directional enhancement state, which is then appended to the low-dimensional state vector as an independent state dimension to form the directional enhancement reduced-order state. The normalization process involves mapping the directional coupling state variables to the [0,1] interval, and performing a linear mapping with the minimum and maximum values ​​of the directional coupling state variables in the multi-condition snapshot as the boundaries.

[0155] A discrete-time state transition equation is established with the current low-dimensional state, the direction-enhancing state, and the control input as independent variables. The direction-enhancing state acts on the evolution of the low-dimensional state at the next time step through an independent coupling matrix, so that the direction mismatch information not only exists as a static index, but also changes the state transition structure of the reduced-order model.

[0156] In some embodiments of this application, step S4, the construction of the physical constraint state prediction model, includes:

[0157] The prediction model consists of two superimposed parts: a physical prediction term and a model error compensation term. The physical prediction term is based on the state transition equation of the reduced-order dynamic model and is used to correct the prediction bias caused by the reduction-order truncation and model simplification.

[0158] The inputs to the prediction model are the current operating current and flow rate; online observations include current, voltage, flow rate, and conductivity.

[0159] The prediction model operates in a rolling manner: in each control cycle, it extrapolates multiple steps forward based on the current measured state and the reduced-order dynamic model to obtain the reduced-order state prediction values ​​at each time in the future prediction time domain. The prediction values ​​include the directional risk state prediction values ​​at each time in the future.

[0160] In some embodiments of this application, step S5, model predictive control, includes:

[0161] Define the prediction time domain and the control time domain, and predict the internal state trajectory for multiple future steps based on the physical constraint state prediction model in each control cycle;

[0162] A multi-objective optimization function is constructed, which consists of a weighted sum of three terms. The first term is the water quality objective, which represents the deviation between the predicted effluent concentration and the target concentration. The second term is the energy consumption objective, which represents the product of the predicted voltage and the operating current. The third term is the directional risk objective, which represents the square of the predicted directional risk state.

[0163] In some embodiments of this application, step S5, model predictive control, further includes:

[0164] Under the conditions of satisfying the upper and lower limits of current, upper and lower limits of flow rate, upper limit of directional risk, and upper limit of effluent quality, the minimum value of the multi-objective optimization function is solved to obtain the optimal current and optimal flow rate.

[0165] The optimal current and optimal flow rate are output as the execution quantities for the next control cycle, thereby enabling advance adjustment of the operating parameters of the EDI module;

[0166] When the predicted directional risk state exceeds the preset safety threshold, the weight and priority of the directional risk target are increased in the optimization solution, so that the controller can suppress the deterioration of directional mismatch first under the premise of meeting water quality constraints.

[0167] It is understood that the technical effects of this embodiment include:

[0168] Compared with the prior art, the beneficial effects of this embodiment are as follows:

[0169] This application uses a directional coupling state construction method to perform point-by-point normalization and inner product operation on the electric field driving force direction and fluid transport direction of each node in space to obtain a directional consistency index. Furthermore, it constructs a joint direction vector through adaptive weighting, generates a directional coupling tensor through spatial aggregation, and extracts the anisotropy ratio of eigenvalues ​​to finally generate directional coupling state variables.

[0170] This variable can reflect the trend of electromigration direction shift, fluid transport direction mismatch, and local ion migration efficiency decline even before observable changes occur in the effluent water quality.

[0171] Through the rolling prediction mechanism of model predictive control, the controller can adjust the operating current and flow rate in advance before the directional risk state actually increases, transforming the control mode of EDI from traditional result feedback control to internal state predictive control, eliminating control lag, and reducing the risk of membrane fouling and local polarization caused by the continuous development of directional mismatch.

[0172] In existing technologies, order reduction methods based on intrinsic orthogonal decomposition only extract and truncate the amplitude information of field variables. This means that when two operating states have similar electric field strength and flow velocity amplitudes, but the coupling relationship between the electric field direction and the flow field direction is fundamentally different, traditional order reduction models will map them to similar low-dimensional coordinates, thus losing the ability to distinguish directional differences. In actual EDI operation, non-uniform electric field distribution, local eddies, and irregular flow channels in the resin-filled region all lead to complex spatial variations in the electric field direction and the flow field direction. Amplitude information alone cannot accurately describe these differences in operating conditions.

[0173] Compared with the prior art, the beneficial effects of this embodiment are as follows:

[0174] By using the orientation-state embedding mechanism, the normalized orientation-coupled state variables are appended as independent state dimensions to the low-dimensional state vector to form an orientation-enhanced reduced-order state.

[0175] More importantly, in reduced-order dynamic modeling, the orientation-enhancing state acts on the next time step evolution of the low-dimensional state through an independent coupling matrix, so that the orientation mismatch information not only exists as an additional static label, but also directly changes the state transition structure of the reduced-order model.

[0176] Therefore, the reduced-order model can clearly distinguish operating states with similar amplitudes but different directional relationships, significantly improving the description accuracy and prediction reliability of the internal state of EDI under non-uniform electric fields, non-uniform flow fields, and complex operating condition switching conditions.

[0177] In existing technologies, if a high-fidelity multiphysics coupling model is directly used for online control, each control cycle requires a complete coupled iterative solution of electric field, flow field, ion migration, and temperature field on a million-level spatial grid. The computation time for a single calculation far exceeds the sampling cycle requirement of the EDI control system, making real-time control impractical in engineering. Therefore, existing EDI systems typically have to abandon control strategies based on internal states and degenerate into control methods based on empirical formulas or simple transfer functions.

[0178] Compared with the prior art, the beneficial effects of this embodiment are as follows:

[0179] By reducing the order through intrinsic orthogonal decomposition, the high-dimensional space state is projected into a low-dimensional subspace spanned by at least a few principal modes. Then, the physical constraint state prediction model is used to advance multiple steps in a rolling manner. The computational dimension of the entire prediction process is reduced from millions of grid degrees of freedom to single-digit reduced state dimensions.

[0180] The calculation of directionally coupled state variables involves only low-complexity operations such as normalization, inner product, outer product, and eigenvalue decomposition, without introducing additional computational bottlenecks.

[0181] Therefore, while maintaining a complete description of key physical state information such as electric field distribution, flow field distribution, ion migration state, and orientation mismatch risk, the computation time of a single online predictive control is reduced by several orders of magnitude, making real-time model predictive control based on internal states feasible in engineering. Technical Effect 5: Achieving Multi-Objective Collaborative Optimization

[0182] In existing technologies, the control objective of EDI (Electronic Direct Identification) typically focuses solely on achieving effluent water quality standards, with the controller's only adjustment method being to increase or decrease the operating current. However, while simply increasing the current can improve effluent water quality in the short term, it also leads to increased Joule heating, higher energy consumption, and exacerbates membrane concentration polarization and local electric field distortion. In the long run, this can actually accelerate membrane performance degradation. Existing control strategies lack a synergistic consideration of energy consumption costs and internal health, making it difficult to achieve a balance among multiple interdependent operational objectives.

[0183] Compared with the prior art, the beneficial effects of this embodiment are as follows:

[0184] By using a multi-objective optimization function, the objectives of water quality compliance, energy consumption minimization, and directional risk minimization are uniformly incorporated into the optimization framework through a weighted summation method.

[0185] Among them, the introduction of directional risk objectives enables the controller to actively constrain the deterioration of the directional mismatch between the electric field and the flow field while pursuing optimal water quality and energy consumption.

[0186] When the predicted directional risk state exceeds the preset safety threshold, the weight priority of the directional risk objective in the optimization solution is automatically increased, so that the controller can suppress the further development of directional mismatch while meeting water quality constraints.

[0187] This avoids the drawbacks of traditional single-objective control that sacrifices energy consumption and membrane life to achieve short-term water quality standards, and realizes the optimal coordinated operation of the EDI module in terms of water quality, energy consumption and internal state.

[0188] Compared with the prior art, the beneficial effects of this embodiment are as follows:

[0189] By using a multi-objective optimization function, the objectives of water quality compliance, energy consumption minimization, and directional risk minimization are uniformly incorporated into the optimization framework through a weighted summation method.

[0190] Among them, the introduction of directional risk objectives enables the controller to actively constrain the deterioration of the directional mismatch between the electric field and the flow field while pursuing optimal water quality and energy consumption.

[0191] When the predicted directional risk state exceeds the preset safety threshold, the weight priority of the directional risk objective in the optimization solution is automatically increased, so that the controller can suppress the further development of directional mismatch while meeting water quality constraints.

[0192] This avoids the drawbacks of traditional single-objective control that sacrifices energy consumption and membrane life to achieve short-term water quality standards, and realizes the optimal coordinated operation of the EDI module in terms of water quality, energy consumption and internal state.

[0193] On the other hand, this application also provides an EDI module control system based on an electric field-flow field coupling model, applied to the above-mentioned EDI module control method based on an electric field-flow field coupling model, including:

[0194] The multiphysics modeling module establishes a multiphysics coupling model of the EDI module, which includes electric-thermal-fluid-ion migration. It spatially discretizes the freshwater chamber, concentrated water chamber, ion exchange membrane, and resin-filled region of the EDI module, and solves for the electric field, flow field, ion concentration field, and temperature field respectively, to obtain a high-dimensional spatial state that includes the electric field state, flow field state, concentration field state, and temperature field state.

[0195] The directional coupling state construction module constructs the directional coupling state between the electric field direction and the flow field direction based on the high-dimensional spatial state. Specifically, it normalizes the electric field direction and the flow field direction at each node in space, calculates the directional consistency index between the electric field driving force direction and the fluid transport direction at each node, adaptively determines the correction weight of the flow field on the electric field direction based on the directional consistency index, constructs a joint direction vector, and then generates directional coupling state variables that characterize the degree of risk of mismatch between the electric field and the flow field directions through spatial aggregation.

[0196] The directional enhancement and order reduction modeling module performs intrinsic orthogonal decomposition on the high-dimensional space state based on multi-condition snapshot data to reduce the order, obtains a low-dimensional state vector, and embeds the directional coupled state variables as independent state dimensions into the reduced-order state space after normalization to form a directional enhancement and order reduction state. It also establishes a reduced-order dynamic model in which the directional risk state participates in the internal state time-series evolution as an independent driving term.

[0197] The state prediction module, based on a reduced-order dynamic model, combines online observation data to establish a physical constraint state prediction model, and performs rolling predictions of the future internal state of the EDI module. The prediction output includes the future direction and risk state.

[0198] The predictive control module constructs a multi-objective optimization function based on the prediction results of future internal states, with the objectives of water quality compliance, energy consumption minimization, and directional risk minimization. It solves for the optimal control quantity through model predictive control and adjusts the operating current and flow rate of the EDI module in advance before the directional risk state actually increases.

[0199] It is understood that in this application:

[0200] The multiphysics modeling module is used to establish the electro-thermal-fluid-ion migration coupling model of the EDI module. It obtains the high-dimensional spatial state by solving the coupled iterative solution of electric field, flow field, ion migration field and temperature field.

[0201] The directional coupling state construction module is used to normalize the electric field direction and flow field direction of each node based on the high-dimensional spatial state and calculate the directional consistency index. Based on the directional consistency index, it adaptively weights and constructs a joint direction vector, generates a directional coupling tensor through spatial aggregation, and generates directional coupling state variables that characterize the risk of electric field-flow field direction mismatch based on the eigenvalue anisotropy of the directional coupling tensor.

[0202] The directional enhancement reduction modeling module is used to perform intrinsic orthogonal decomposition on multi-condition snapshot data to obtain low-dimensional state vectors. The normalized directional coupling state variables are embedded as additional state dimensions into the reduced state space. The dynamic correlation between the state variables and the reduced modes is established through the directional risk coupling matrix. A reduced dynamic model in which the directional risk state participates in state transition through an independent coupling matrix is ​​established.

[0203] The state prediction module is used to predict the internal state of the EDI module in the future multiple steps in a rolling manner based on the reduced-order dynamic model and online observation data, and output the predicted trajectory including the future directional risk state.

[0204] The predictive control module is used to optimize the EDI module based on the predicted trajectory, under the condition of meeting the operating constraints, with multiple objectives such as water quality compliance, energy consumption minimization, and directional risk minimization, and output the optimal operating current and optimal flow control commands.

[0205] It is understandable that the EDI module control based on the electric field-flow field coupling model described above has the same beneficial effects, and will not be elaborated further here.

[0206] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program goods. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program goods embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0207] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program goods according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0208] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0209] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0210] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of the present invention. Any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention should be covered within the scope of protection of the claims of the present invention.

Claims

1. A control method for an EDI module based on an electric field-flow field coupling model, characterized in that, include: Step S1: Establish a multi-physics coupling model of the EDI module’s electro-thermal-fluid-ion migration. Spatially discretize the desalination chamber, concentrate chamber, ion exchange membrane and resin filling region of the EDI module. Solve for the electric field, flow field, ion concentration field and temperature field respectively to obtain a high-dimensional spatial state including electric field state, flow field state, concentration field state and temperature field state. Step S2: Based on the high-dimensional spatial state, construct the directional coupling state of the electric field direction and the flow field direction. Specifically, normalize the electric field direction and the flow field direction of each node in the space, calculate the directional consistency index between the electric field driving force direction and the fluid transport direction at each node, adaptively determine the correction weight of the flow field on the electric field direction based on the directional consistency index, construct a joint direction vector, and then generate directional coupling state variables that characterize the degree of risk of mismatch between the electric field and the flow field directions through spatial aggregation. Step S3: Based on multi-condition snapshot data, perform intrinsic orthogonal decomposition to reduce the order of the high-dimensional space state to obtain a low-dimensional state vector. After normalization, the directional coupled state variables are embedded into the reduced-order state space as independent state dimensions to form a directional enhanced reduced-order state. Establish a reduced-order dynamic model in which the directional risk state participates in the temporal evolution of the internal state as an independent driving term. Step S4: Based on the reduced-order dynamic model, a physical constraint state prediction model is established by combining online observation data to perform rolling prediction of the future internal state of the EDI module. The prediction output includes the future direction and risk state. Step S5: Based on the predicted results of the future internal state, construct a multi-objective optimization function with the objectives of water quality compliance, energy consumption minimization, and directional risk minimization. Solve for the optimal control quantity through model predictive control, and adjust the operating current and flow rate of the EDI module in advance before the directional risk state actually increases.

2. The EDI module control method based on the electric field-flow field coupling model according to claim 1, characterized in that, In step S1, the establishment of the electro-thermal-fluid-ion migration multiphysics coupling model of the EDI module includes: Electric field modeling is performed by solving the spatial electric potential distribution based on the electric potential conservation equation. The spatial electric field distribution is obtained by taking the negative gradient of the electric potential, where the conductivity is coupled and corrected as a function of the temperature field and the concentration field. Flow field modeling is performed by solving the velocity field based on the momentum conservation equation for incompressible fluids, where the volume force of the electric field on charged ions is introduced as a source term into the momentum equation. Ion migration modeling is based on the Nernst-Planck equation to describe the migration flux of each ion component. The migration flux includes three parts: diffusion term, electromigration term, and convective transport term. The concentration field is obtained by solving the mass conservation equation of each ion component. Temperature modeling is performed by solving the temperature field based on the energy conservation equation, where the Joule heat caused by the electric field is used as a volume heat source term. The Joule heat is determined by the product of electrical conductivity and the square of the electric field strength. The four fields are solved through bidirectional coupling iteratively using the temperature-concentration dependence of conductivity.

3. The EDI module control method based on the electric field-flow field coupling model according to claim 2, characterized in that, In step S2, constructing the directional coupling state includes: The electric field vector at each node in space is divided by its magnitude and a regularization term is added to obtain the electric field direction normalized vector; the flow field velocity vector at each node in space is divided by its magnitude and a regularization term is added to obtain the flow field direction normalized vector. The direction consistency index is obtained by calculating the inner product of the electric field direction normalization vector and the flow field direction normalization vector at each node. The value range of the direction consistency index is from negative one to positive one. A positive value indicates that the direction of the electric field driving force is consistent with the direction of fluid transport, and a negative value indicates that the two directions conflict. A joint direction vector is constructed by superimposing the electric field direction normalized vector with the flow field direction normalized vector weighted by the direction consistency index and the flow field direction correction coefficient, and then normalizing the superposition result. When the direction consistency index is positive, the flow field direction contribution is enhanced; when the direction consistency index is negative, the flow field direction contribution is suppressed. The flow field direction correction coefficient is a preset constant or adaptively determined based on the flow field Reynolds number. The outer product is constructed using the joint direction vector of each node, and then the sum is weighted by the node weights and aggregated into a global directional coupling tensor; where the node weights are determined based on the contribution of each node's region to the ion migration flux. The maximum and minimum eigenvalues ​​of the directional coupling tensor are calculated. The directional anisotropy index is defined by the ratio of the maximum to the minimum eigenvalues. The directional risk state is obtained by subtracting the reciprocal of the directional anisotropy index from one. The larger the value of the directional risk state, the more severe the directional mismatch between the electric field and the flow field.

4. The EDI module control method based on the electric field-flow field coupling model according to claim 3, characterized in that, The step S3, establishing a directional enhancement reduced-order state model, includes: By changing the operating current, flow rate, influent concentration, and temperature parameters under various operating conditions, the multiphysics coupling model is solved to generate multiple sets of high-dimensional spatial state snapshots covering different operating states. Singular value decomposition is performed on the snapshot matrix composed of the multiple snapshots. The first few principal modes are selected as basis functions according to the energy contribution rate. The high-dimensional space state is projected onto the low-dimensional subspace spanned by the basis functions to obtain the low-dimensional state vector.

5. The EDI module control method based on the electric field-flow field coupling model according to claim 4, characterized in that, The step S3 of establishing the directional enhancement reduced-order state model further includes: The directional coupling state variables are normalized to obtain the directional enhancement state, which is then appended as an independent state dimension to the low-dimensional state vector to form the directional enhancement reduced-order state. The normalization process involves mapping the directional coupling state variables to the [0,1] interval, using the minimum and maximum values ​​of the directional coupling state variables in the multi-condition snapshots as boundaries for linear mapping. A discrete-time state transition equation is established with the current low-dimensional state, the direction-enhancing state, and the control input as independent variables. The direction-enhancing state acts on the evolution of the low-dimensional state at the next time step through an independent coupling matrix, so that the direction mismatch information not only exists as a static index, but also changes the state transition structure of the reduced-order model.

6. The EDI module control method based on the electric field-flow field coupling model according to claim 5, characterized in that, In step S4, the physical constraint state prediction model is constructed, including: The prediction model consists of two superimposed parts: a physical prediction term and a model error compensation term. The physical prediction term is deduced deterministically based on the state transition equation of the reduced-order dynamic model, and the model error compensation term is used to correct the prediction bias caused by the reduction-order truncation and model simplification. The input to the prediction model is the current operating current and flow rate; online observations include current, voltage, flow rate, and conductivity. The prediction model operates in a rolling manner: in each control cycle, it extrapolates multiple steps forward based on the current measured state and the reduced-order dynamic model to obtain the reduced-order state prediction value at each time in the future prediction time domain. The prediction value includes the directional risk state prediction value at each time in the future.

7. The EDI module control method based on the electric field-flow field coupling model according to claim 6, characterized in that, In step S5, model predictive control includes: Define the prediction time domain and the control time domain, and in each control cycle, predict the internal state trajectory for multiple future steps based on the physical constraint state prediction model. A multi-objective optimization function is constructed, which consists of a weighted sum of three terms. The first term is the water quality objective, which represents the deviation between the predicted effluent concentration and the target concentration. The second term is the energy consumption objective, which represents the product of the predicted voltage and the operating current. The third term is the directional risk objective, which represents the square of the predicted directional risk state.

8. The EDI module control method based on the electric field-flow field coupling model according to claim 7, characterized in that, In step S5, model predictive control further includes: Under the conditions of satisfying the upper and lower limits of current, upper and lower limits of flow rate, upper limit of directional risk, and upper limit of effluent quality, the minimum value of the multi-objective optimization function is solved to obtain the optimal current and optimal flow rate. The optimal current and optimal flow rate are output as the execution quantities for the next control cycle, thereby enabling advance adjustment of the operating parameters of the EDI module; When the predicted directional risk state exceeds the preset safety threshold, the weight and priority of the directional risk target are increased in the optimization solution, so that the controller can suppress the deterioration of directional mismatch first under the premise of meeting water quality constraints.

9. An EDI module control system based on an electric field-flow field coupling model, applied in the EDI module control method based on an electric field-flow field coupling model as described in any one of claims 1-8, characterized in that, include: The multiphysics modeling module establishes a multiphysics coupling model of the EDI module, which includes electric-thermal-fluid-ion migration. It spatially discretizes the freshwater chamber, concentrated water chamber, ion exchange membrane, and resin-filled region of the EDI module, and solves for the electric field, flow field, ion concentration field, and temperature field respectively, to obtain a high-dimensional spatial state that includes the electric field state, flow field state, concentration field state, and temperature field state. The directional coupling state construction module constructs the directional coupling state of electric field direction and flow field direction based on the high-dimensional spatial state. Specifically, it normalizes the electric field direction and flow field direction of each node in space, calculates the directional consistency index between the electric field driving force direction and the fluid transport direction at each node, adaptively determines the correction weight of the flow field on the electric field direction based on the directional consistency index, constructs a joint direction vector, and then generates directional coupling state variables that characterize the degree of risk of mismatch between electric field and flow field directions through spatial aggregation. The directional enhancement and order reduction modeling module performs intrinsic orthogonal decomposition on the high-dimensional space state based on multi-condition snapshot data to reduce the order, obtains a low-dimensional state vector, and embeds the directional coupled state variables as independent state dimensions into the reduced-order state space after normalization to form a directional enhancement and order reduction state. It also establishes a reduced-order dynamic model in which the directional risk state participates in the internal state time-series evolution as an independent driving term. The state prediction module, based on the reduced-order dynamic model and combined with online observation data, establishes a physical constraint state prediction model to perform rolling predictions of the future internal state of the EDI module. The prediction output includes the future direction and risk state. The predictive control module, based on the predicted results of the future internal state, constructs a multi-objective optimization function with the objectives of water quality compliance, energy consumption minimization, and directional risk minimization. It solves for the optimal control quantity through model predictive control and adjusts the operating current and flow rate of the EDI module in advance before the directional risk state actually increases.

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