Three-dimensional electro-catalytic oxidation device temperature field collaborative regulation method based on digital twinning

Abstract

The present application relates to the technical field of heat digital twinborn analysis, in particular to a three-dimensional electro-catalytic oxidation device temperature field collaborative regulation method based on digital twinborn. The specific implementation process includes: extracting current ripple features and fluid damping fluctuation data in the operation process of the three-dimensional electro-catalytic oxidation device, and constructing an energy distribution domain in the digital twinborn body; tracking the energy accumulation center in the energy distribution domain and correcting the heat conduction; carrying out evolution simulation to predict the spatial migration and temperature change trend; superimposing based on the prediction result to generate control waveform flow for device regulation; constructing an energy interaction link to collaboratively regulate the global temperature field. The present application combines multi-source data fusion, full-field reconstruction and prediction-driven control strategy, improves the limitations of relying on limited measurement points and lag feedback regulation, realizes high-precision perception, prediction and collaborative optimization control of the three-dimensional electro-catalytic oxidation device temperature field, and improves the stability of the device operation.

Description

Technical Field

[0001] This invention relates to the field of thermal digital twin analysis technology, specifically a method for coordinated temperature field control of a three-dimensional electrocatalytic oxidation device based on digital twins. Background Technology

[0002] Electrocatalytic oxidation technology is an advanced oxidation process that generates highly oxidizing free radicals through electrochemical means to degrade recalcitrant organic pollutants. Three-dimensional electrocatalytic oxidation devices introduce particle electrodes into the traditional two-dimensional flat plate electrode system, significantly improving the effective electrode area and mass transfer efficiency, and have been widely used in industrial wastewater treatment. Existing three-dimensional electrocatalytic oxidation devices (such as CN117756237A) have solved problems such as particle electrode caking and modular replacement, but no publicly disclosed technical solution exists for temperature field control. During actual operation, the device continuously generates heat due to the Joule heating effect, and is also affected by multiple factors such as electric field distribution, fluid flow regime, and particle electrode filling state, resulting in a typical time-varying and non-uniform temperature distribution within the device.

[0003] However, existing temperature field control technologies have inherent limitations in practical applications. Due to the limited number of measuring points, they can only reflect the temperature state at a few locations within the device, failing to reconstruct the complete three-dimensional temperature field spatial distribution and severely lacking the ability to perceive the overall evolution trend of the temperature field within the device. In scenarios where multiple control variables are coupled, it is difficult to achieve feedforward prediction and collaborative optimization of the temperature field, resulting in significant lag in the control response and limited overall control accuracy. Digital twin technology, by constructing a high-fidelity dynamic mapping model of the physical entity in virtual space and driving continuous model updates with real-time acquired operational data, achieves real-time perception, full-field reconstruction, and trend prediction of the physical system state, providing a new technical path for solving the above problems. However, existing digital twin research mainly targets systems with relatively simple physical field structures and has not yet established a twin model that can effectively characterize the complex mapping relationship between the temperature field and multiple operating parameters in a three-dimensional electrocatalytic oxidation device. Regarding model synchronization mechanisms, existing methods lack effective means for high-precision online reconstruction and adaptive correction of the full-field state based on limited measuring point data. In terms of control strategies, a systematic control framework that can integrate twin model prediction information and implement collaborative optimization of multiple actuators has not yet been formed.

[0004] In summary, existing technologies are insufficient to sense the operating status of a device, dynamically reconstruct the internal temperature distribution, and predict its electrothermal evolution trend. Consequently, they are unable to form a digital twin closed-loop control system in virtual space to coordinate control decisions and provide feedback guidance for the linkage of multiple actuators in the physical device.

[0005] To address this, a method for coordinated temperature field control of a three-dimensional electrocatalytic oxidation device based on digital twins is proposed. Summary of the Invention

[0006] The purpose of this invention is to provide a method for coordinated temperature field control of a three-dimensional electrocatalytic oxidation device based on digital twins, so as to coordinately control the temperature field of the three-dimensional electrocatalytic oxidation device.

[0007] To achieve the above objectives, the present invention provides the following technical solution: A method for coordinated temperature field control of a three-dimensional electrocatalytic oxidation device based on digital twins includes: The current ripple characteristics and fluid damping fluctuation data during the operation of the three-dimensional electrocatalytic oxidation device are extracted and field synthesis is performed in a digital twin. The heat distribution inside the channel is reverse deduced and reconstructed using the electrothermal effect residual image generated by the current ripple in the gap between the particle electrodes, and an energy distribution domain is generated. Thermal anchor points are deployed and drifted in the energy distribution domain, dynamically locking and tracking the energy accumulation center as the energy gradient evolves; the thermal inertia accumulation rate of the thermal anchor points at the energy accumulation center is calculated to correct the thermal conduction hysteresis of the digital twin online. Evolution simulation is performed using the corrected digital twin to identify hotspot evolution trends within the future prediction period; a dynamic response strategy is adopted to superimpose the frequency conversion pulse of the circulating pump with the frequency modulation command of the power supply to form a control waveform flow that cancels local heat accumulation and projects it onto the three-dimensional electrocatalytic oxidation device. The fluid damping fluctuation data after the three-dimensional electrocatalytic oxidation device performs regulation actions are then re-synthesized in the field. By establishing an energy interaction link between the digital twin and the three-dimensional electrocatalytic oxidation device, the global temperature field is coordinated and regulated.

[0008] Preferably, the specific implementation process of extracting current ripple characteristics and fluid damping fluctuation data during the operation of the three-dimensional electrocatalytic oxidation device and performing field synthesis within the digital twin includes: deploying current sensors at the sampling nodes of the main circuit of the three-dimensional electrocatalytic oxidation device to collect the current waveform time series during device operation; applying fast Fourier transform processing to the current waveform time series to extract the amplitude and phase information of each harmonic component and construct current ripple characteristics; deploying differential pressure sensors in the inlet and outlet channels of the device to collect the pressure difference time series at both ends of the channel, and applying differential filtering operation to the pressure difference time series to obtain fluid damping fluctuation data; injecting the current ripple characteristics and fluid damping fluctuation data as multidimensional excitation parameters into the digital twin, and performing field synthesis on the electric field distribution data and flow field distribution data.

[0009] Preferably, the specific implementation process of using the electrothermal effect residual image generated by the current ripple in the particle electrode gap to reversely deduce and reconstruct the heat distribution inside the channel and generate an energy distribution domain includes: extracting the phase delay sequence of each harmonic component on the time axis from the current ripple features as the time delay feature of the electrothermal response at the particle electrode interface; establishing an electrothermal coupling transfer function model at the particle electrode gap based on the geometric configuration parameters and equivalent admittance distribution of the particle electrodes; inputting the current ripple features into the electrothermal coupling transfer function model to calculate the instantaneous heat generation density distribution at each gap location; applying the time delay feature correction of the electrothermal effect to the instantaneous heat generation density distribution, deducting the heat flux component that has been conducted outward, and extracting the electrothermal effect residual image retained inside the channel structure; reconstructing the electrothermal effect residual image by spatial interpolation according to the particle electrode filling topology to restore the heat distribution inside the channel; applying an energy gradient threshold segmentation to the heat distribution, extracting the boundary of the heat accumulation region, and generating an energy distribution domain.

[0010] Preferably, the specific implementation process of deploying hot anchor point drift in the energy distribution domain and dynamically locking and tracking the energy gathering center according to the evolution direction of the energy gradient includes: identifying local energy maxima in the energy distribution domain and initializing the spatial coordinate set of the maxima as a hot anchor point set; performing gradient field calculation on the energy distribution domain to obtain the energy gradient vector field at each spatial location; performing spatial displacement of each hot anchor point along the direction of the energy gradient vector in each simulation time step to update the coordinate position of the hot anchor point; calculating the magnitude of the coordinate displacement vector of the hot anchor point in adjacent time steps, and determining that the hot anchor point has converged to the energy gathering center when the magnitude is lower than a preset convergence threshold; recording the spatial coordinates of the hot anchor point in the convergence state as the position marker of the energy gathering center at the current moment; and performing periodic reset and re-drift on the hot anchor point set as the energy distribution domain evolves and updates over time in the digital twin to dynamically track the energy gathering center.

[0011] Preferably, the specific implementation process of online correction of the thermal conduction hysteresis of the digital twin by calculating the thermal inertia accumulation rate of the thermal anchor point at the energy accumulation center includes: recording the coordinate trajectory sequence of the thermal anchor point during its drift towards the energy accumulation center within a continuous time window; performing a ratio calculation on the difference in coordinates of the thermal anchor point in adjacent time steps and the corresponding magnitude of the energy gradient vector to obtain the ratio parameter of the thermal anchor point drift rate to the energy gradient, which is defined as the thermal inertia accumulation rate; performing a deviation comparison calculation on the thermal inertia accumulation rate and the thermal conduction time constant in the digital twin; generating a thermal conduction time constant correction increment after processing the deviation through proportional-integral filtering; and superimposing the correction increment into the time delay parameter of the digital twin to perform online correction of the thermal conduction hysteresis.

[0012] Preferably, the specific implementation process of using the corrected digital twin for evolutionary simulation to identify the hotspot evolution trend within the future prediction period includes: performing evolutionary simulation using the digital twin after thermal conduction correction; driving the digital twin to perform forward time step iterations within the prediction window with the simulation step size; updating the full-field temperature distribution data based on the coupled solution results of the thermal conduction equation and the flow field equation within each simulation time step; extracting the coordinates of extreme temperature points and the magnitude of extreme temperatures from the full-field temperature distribution data of each time step to form a hotspot time-series trajectory set; performing trend fitting on the hotspot time-series trajectory set to extract the spatial migration vector sequence and temperature growth slope sequence of the hotspots; merging and outputting the spatial migration vector sequence and temperature growth slope sequence of the hotspots to form a hotspot evolution trend prediction map.

[0013] Preferably, the specific implementation process of using a dynamic response strategy to superimpose the variable frequency pulses of the circulating pump with the frequency modulation commands of the power supply to form a control waveform stream that cancels local heat accumulation and projects it onto the three-dimensional electrocatalytic oxidation device includes: extracting the spatial coordinates and temperature gradient amplitude of the target hotspot from the hotspot evolution trend prediction map, calculating the fluid heat exchange demand, and obtaining the target flow allocation matrix required to cancel the target hotspot; generating the variable frequency pulse waveform sequence of the circulating pump through the flow-frequency inverse mapping relationship based on the target flow allocation matrix; simultaneously extracting the predicted energy input law of the target hotspot from the hotspot evolution trend prediction map, and calculating the frequency modulation command sequence of the power supply through the energy-frequency inverse mapping relationship; performing phase alignment and superposition operations on the variable frequency pulse waveform sequence and the frequency modulation command sequence to generate a control waveform stream carrying anti-phase energy cancellation characteristics; and mapping the control waveform stream to the circulating pump frequency converter control interface and the power supply frequency modulation control interface respectively to complete the projection output of the control command.

[0014] Preferably, the process of performing field synthesis again on the fluid damping fluctuation data after the three-dimensional electrocatalytic oxidation device performs regulation actions, and establishing an energy interaction link between the digital twin and the three-dimensional electrocatalytic oxidation device to achieve coordinated regulation of the global temperature field includes: collecting newly generated fluid damping fluctuation data after the three-dimensional electrocatalytic oxidation device performs regulation actions, and injecting it into the digital twin to perform a new round of field synthesis, updating the multi-physics fusion state variables; establishing an energy interaction link between the digital twin and the three-dimensional electrocatalytic oxidation device based on the multi-physics fusion state variables, and coordinating the regulation of the global temperature field.

[0015] Compared with the prior art, the beneficial effects of the present invention are as follows: 1. This invention introduces multi-physics field fusion of current ripple characteristics and fluid damping fluctuation data to achieve field synthesis of electric field, flow field and thermal field within a digital twin. It also utilizes the electrothermal effect residual image to reconstruct the internal heat distribution of the channel, thereby improving the limitation of relying on a limited number of temperature measurement points. This enables high-precision reconstruction and refined perception of the full-domain temperature field inside the three-dimensional electrocatalytic oxidation device, and enhances the spatial distribution resolution capability and state perception integrity of the temperature field.

[0016] 2. This invention achieves dynamic tracking of energy accumulation centers by constructing a mechanism for calculating the drift of thermal anchor points and the accumulation rate of thermal inertia, and performs online adaptive correction of the thermal conduction hysteresis of the digital twin, enabling the twin model to continuously approximate the thermal dynamic response characteristics of the real system. This effectively solves the problems of insufficient synchronization accuracy and dynamic response hysteresis, and improves the accuracy and real-time performance of temperature field prediction and simulation.

[0017] 3. Based on the prediction results of hot spot evolution trends, this invention proposes a dynamic response strategy that superimposes the frequency conversion pulse of the circulating pump and the frequency modulation command of the power supply. Combined with the energy interaction link, a closed-loop collaborative control mechanism is formed to realize the linkage optimization control of multiple actuators. This not only suppresses local heat accumulation in advance and avoids hot spot diffusion, but also realizes the collaborative optimization control of the temperature field across the entire domain, thereby improving the stability and energy efficiency of the device operation. Attached Figure Description

[0018] Figure 1 This is a flowchart of the temperature field coordinated control method for a three-dimensional electrocatalytic oxidation device based on digital twins proposed in this invention. Figure 2 This is a schematic diagram of the field synthesis proposed in this invention; Figure 3 This is a schematic diagram of the energy interaction link proposed in this invention. Detailed Implementation

[0019] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be described in detail below with reference to the accompanying drawings and specific embodiments. It must be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to constitute any limitation on the scope of protection of this invention. Therefore, all equivalent changes or modifications conceived by those skilled in the art based on the content disclosed in this invention without inventive effort should fall within the scope of protection claimed by this invention.

[0020] Reference Figures 1 to 3 This invention provides a method for coordinated temperature field control of a three-dimensional electrocatalytic oxidation device based on digital twins. The technical solution is as follows:

[0021] Example 1: Refer to Figure 1This embodiment proposes a method for coordinated temperature field control of a three-dimensional electrocatalytic oxidation device based on digital twins, including: The current ripple characteristics and fluid damping fluctuation data during the operation of the three-dimensional electrocatalytic oxidation device are extracted and field synthesis is performed in a digital twin. The heat distribution inside the channel is reverse deduced and reconstructed using the electrothermal effect residual image generated by the current ripple in the gap between the particle electrodes, and an energy distribution domain is generated. Thermal anchor points are deployed and drifted in the energy distribution domain, dynamically locking and tracking the energy accumulation center as the energy gradient evolves; the thermal inertia accumulation rate of the thermal anchor points at the energy accumulation center is calculated to correct the thermal conduction hysteresis of the digital twin online. Evolution simulation is performed using the corrected digital twin to identify hotspot evolution trends within the future prediction period; a dynamic response strategy is adopted to superimpose the frequency conversion pulse of the circulating pump with the frequency modulation command of the power supply to form a control waveform flow that cancels local heat accumulation and projects it onto the three-dimensional electrocatalytic oxidation device. The fluid damping fluctuation data after the three-dimensional electrocatalytic oxidation device performs regulation actions are then re-synthesized in the field. By establishing an energy interaction link between the digital twin and the three-dimensional electrocatalytic oxidation device, the global temperature field is coordinated and regulated.

[0022] Furthermore, the specific implementation process of extracting current ripple characteristics and fluid damping fluctuation data during the operation of the three-dimensional electrocatalytic oxidation device and performing field synthesis within the digital twin includes: deploying current sensors at the sampling nodes of the main circuit of the three-dimensional electrocatalytic oxidation device to collect the current waveform time series during device operation; applying fast Fourier transform processing to the current waveform time series to extract the amplitude and phase information of each harmonic component, constructing current ripple characteristics; deploying differential pressure sensors in the inlet and outlet channels of the device to collect the pressure difference time series at both ends of the channel, and applying differential filtering operation to the pressure difference time series to obtain fluid damping fluctuation data; injecting the current ripple characteristics and fluid damping fluctuation data as multidimensional excitation parameters into the digital twin, and performing field synthesis on the electric field distribution data and flow field distribution data.

[0023] Reference Figure 2Specifically, at least three sampling nodes are set in the main circuit of the three-dimensional electrocatalytic oxidation device. A Hall effect current sensor is installed at each node, and the sampling frequency is set to no less than 10,000 times per second to ensure the capture of the current waveform sequence caused by electrode polarization, changes in particle electrode contact resistance, and power supply ripple superposition within the 10 Hz to 5000 Hz frequency band. The output of the current sensor is connected to an edge computing node with real-time data caching capabilities. The edge computing node segments the continuously acquired current waveform time series using a sliding window method, with each window length set to 0.1 seconds and the overlap ratio between adjacent windows set to 50% to balance time resolution and spectral continuity. A Fast Fourier Transform is applied to each segment of the current waveform time series to decompose and obtain the amplitude and phase information corresponding to the 2nd to 20th harmonic components. The amplitude vector and phase vector of each harmonic component are concatenated into a 38-dimensional feature vector as the current ripple feature.

[0024] Differential pressure sensors with a range of 0 to 5 kPa are installed between the inlet and outlet channels of the device, and the sampling frequency of the differential pressure sensors is set to 1000 times per second. Because the flow of wastewater in the particle electrode packing chamber is affected by multiple factors such as uneven distribution of particle electrode gaps, aeration backwash bubble disturbance, and electric field-induced fluid motion, the collected differential pressure time series contains a superimposed low-frequency trend component and a high-frequency noise component. The differential pressure time series is first passed through a low-pass filter with a cutoff frequency of 100 Hz to remove high-frequency noise, and then a first-order differential filtering operation is applied. Each element of the differentially derived sequence is divided by the sampling time interval to obtain a differential pressure change rate sequence in kPa per second. The average absolute value of this change rate sequence is taken as the quantitative index of fluid damping fluctuation data, reflecting the average change amplitude of channel resistance per unit time.

[0025] The extracted current ripple characteristics and fluid damping fluctuation data are used as multidimensional excitation parameters. After standardization, these parameters are injected into a pre-constructed digital twin containing electric field and flow field distributions. The digital twin construction process is as follows: Based on the solid geometric drawings of the three-dimensional electrocatalytic oxidation device, a geometric model corresponding one-to-one with the inlet and outlet channels, particle electrode filling chamber, and electrode plate structure of the device is established in a three-dimensional coordinate system. An unstructured tetrahedral mesh is used to partition the internal region of the filling chamber. The mesh in the boundary layer region of the filling chamber is refined to 0.5 mm, and the mesh size in the far field region does not exceed 5 mm, generating approximately 1.5 million mesh nodes in total. The electric field distribution uses steady-state Laplace as the governing equation; the flow field distribution uses incompressible Reynolds-averaged Navier-Stokes and standard k-ε turbulence as the governing equations. The inlet boundary condition is set as a uniform velocity inlet, the outlet boundary condition is set as a zero-pressure outlet, and the wall condition uses a no-slip boundary. The material parameters of the above model (equivalent thermal conductivity and electrical conductivity of particle electrodes) are measured offline and written into the parameter database. After the model completes the steady-state solution under the initial working conditions, its global electric field intensity distribution and flow velocity and pressure distribution are used as the initial state variables of the digital twin.

[0026] During field synthesis, the harmonic components of the current ripple characteristics serve as electric field excitation boundary conditions, driving the electric field distribution model to perform transient solutions at corresponding frequencies, thereby obtaining electric field intensity distribution data at various spatial locations within the particle electrode filling chamber. The fluid damping fluctuation data serve as flow field excitation parameters, correcting the turbulence dissipation coefficient and the equivalent hydraulic diameter of the particle electrode gap in the flow field distribution model, thus updating the velocity and pressure distribution data at each spatial location. The transient electric field solution and the quasi-steady-state flow field solution are decoupled using a split approach: within each excitation update cycle, the transient solution is first completed using the electric field distribution to obtain the electric field intensity distribution at each grid node. According to the Joule heating density formula Write the electric heat source term into the heat conduction term, where For conductivity, For Joule heat generation density, For three-dimensional space coordinate axes, The current velocity field is used as the time variable; then the current flow velocity field drives the convective heat transfer calculation, and the convective heat transfer coefficient is used as the third type of boundary condition input for heat conduction to complete the solution of the temperature distribution of the whole field.

[0027] This embodiment improves upon the limitation of relying solely on sparse point sensors to fully perceive the internal temperature field distribution of a device by injecting current ripple characteristics and fluid damping fluctuation data as dual-channel excitation parameters into the digital twin and performing field synthesis. The harmonic information in the current ripple carries details of the dynamic process of the electrodes, while the fluid damping fluctuation data directly reflects the changes in the filling state of the particle electrodes. The synergistic injection of these two types of signals enables the digital twin to track the temperature field evolution process with high temporal resolution, providing a reliable real-time data foundation for subsequent active temperature field control.

[0028] Furthermore, the specific implementation process of using the electrothermal effect residual image generated by the current ripple in the particle electrode gap to reverse-engineer and reconstruct the heat distribution inside the channel and generate the energy distribution domain includes: extracting the phase delay sequence of each harmonic component on the time axis from the current ripple features as the time delay feature of the electrothermal response at the particle electrode interface; establishing an electrothermal coupling transfer function model at the particle electrode gap based on the geometric configuration parameters and equivalent admittance distribution of the particle electrodes; inputting the current ripple features into the electrothermal coupling transfer function model to calculate the instantaneous heat generation density distribution at each gap location; applying the time delay feature correction of the electrothermal effect to the instantaneous heat generation density distribution, deducting the heat flux component that has been conducted outward, and extracting the electrothermal effect residual image retained inside the channel structure; reconstructing the electrothermal effect residual image by spatial interpolation according to the particle electrode filling topology to restore the heat distribution inside the channel; applying an energy gradient threshold segmentation to the heat distribution, extracting the boundary of the heat accumulation region, and generating the energy distribution domain.

[0029] Specifically, from the extracted current ripple features, the phase values ​​of each harmonic component are tracked over a continuous time window, and the phase difference sequence between adjacent time windows is calculated. This phase difference sequence is the phase delay sequence of each harmonic component on the time axis. The phase delay sequence reflects the time lag of the electrothermal response at the particle electrode interface, and its physical essence lies in the time constant difference between the particle electrode absorbing electromagnetic energy and generating a detectable thermal response.

[0030] The electrothermal coupling transfer function model uses the angular frequencies of each harmonic component. Using lumped parameter thermal path method as the independent variable, the equivalent thermal path is constructed. For a single contact point at the gap, its equivalent thermal path consists of an electrothermal conversion gain element and a first-order thermal inertia element connected in series: electrothermal conversion gain... Defined as the first The product of the real part of the admittance of the second harmonic component and the square of the harmonic amplitude reflects the instantaneous resistive power dissipation of the harmonic component at the contact point; the thermal inertial element is represented by the thermal time constant. Describes the dynamic hysteresis between electrical power input and temperature rise response, where thermal resistance Based on the equivalent diameter of the contact point Thermal conductivity of particle electrode materials Through relational formulas Estimate heat capacity Based on the volume of the contact point With specific heat capacity of materials pass Calculation, where The density of the electrode material and the equivalent area of ​​the contact point. and volume The contact point geometry parameters were determined using X-ray computed tomography (CT) scans. The transfer function at each gap location was also determined. ,in The imaginary unit is used to represent the first number. After substituting the complex current amplitude of the subharmonic component, the contributions of each harmonic component are linearly superimposed to obtain the instantaneous heat generation density at each gap location.

[0031] When applying time-delay correction to the instantaneous heat generation density distribution for the electrothermal effect, the heat flux component that has been conducted outward from the pore structure within the delay time window before the current moment is calculated based on the phase delay sequence corresponding to each harmonic component. The calculation of the conducted heat flux component is based on Fourier's law of heat conduction, combined with the equivalent thermal conductivity of the particle electrode material and the pore geometry, to estimate the amount of heat diffusion along the pore wall direction within the corresponding delay time. The equivalent thermal conductivity is determined by steady-state thermal conductivity experiments on the particle electrode stack. After subtracting the conducted heat flux component from the instantaneous heat generation density distribution, the remaining heat is the electrothermal effect remnant that is still trapped inside the pore structure and has not yet been conducted outward.

[0032] When reconstructing the electrothermal effect residual image using spatial interpolation based on the particle electrode filling topology, the three-dimensional coordinate distribution of the particle electrodes obtained by X-ray computed tomography (CT) scan is used as the skeleton. Before the device's initial commissioning, the CT scan is performed on particle electrode samples from the same batch as the official device to obtain the statistical regularity of the three-dimensional coordinate distribution of the particle electrodes and the geometric parameter distribution of the contact points. These statistical parameters are stored as fixed prior parameters in the digital twin parameter database. During device operation, if the differential pressure sensor detects that the mean value of the fluid damping fluctuation data exceeds 20% of the initial value, a particle electrode status update alarm is triggered, and it is recommended that the operator perform a sampling CT scan of the particle electrode samples to update the parameter database. A radial basis function interpolation method is used to expand the sparsely distributed electrothermal effect residual image values ​​at the grid nodes into a heat distribution field covering all continuous spatial locations within the channel. The radial basis function adopts a thin-plate spline form, and its shape parameters... Determined as follows: Take the average diameter of the particle electrode sample. According to the relation The shape parameters are set so that the effective influence radius of the interpolation basis function is on the same order of magnitude as the average diameter of the particle electrode, to ensure a smooth transition in heat distribution between adjacent particle electrode nodes while preserving the details of heat accumulation at the pore scale.

[0033] When applying an energy gradient threshold segmentation to the heat distribution, the gradient amplitudes of the heat distribution field in three spatial directions are first calculated. The three-dimensional gradient amplitudes at each location are then synthesized into a scalar gradient field. Subsequently, using 1.5 times the mean of the scalar gradient field as the energy gradient threshold, the boundaries of all regions exceeding the threshold are extracted. Interconnected regions exceeding the threshold are marked as independent heat accumulation units, generating an energy distribution domain. The energy gradient threshold is determined by the following method: under standard operating conditions, the gradient amplitude distribution of the heat distribution field for at least 100 operating cycles is statistically analyzed. The standard operating conditions are defined as follows: the main circuit current equals the rated current (20 amperes in this embodiment), the influent flow rate equals the design flow rate (the rated flow rate of the circulating pump at 30 Hz in this embodiment), the influent temperature is room temperature (20 ± 5 degrees Celsius), and the device has been running for more than 2 hours with the temperature field reaching a quasi-steady state. The percentile value corresponding to the mean of the gradient amplitude distribution plus 1.5 times the standard deviation (approximately 1.4 to 1.6 times the mean of the gradient field, with the specific value determined according to the device operating conditions) is used as the basis for selecting the threshold multiple to confirm the signal-to-noise ratio between the over-threshold region and the background noise. The energy distribution domain is stored in a digital twin in the form of a three-dimensional voxel set, carrying attribute information such as the spatial coordinates, volume, peak heat density, and heat transfer direction between each heat accumulation unit and adjacent accumulation units, providing accurate spatial positioning basis for the subsequent formulation of temperature field coordinated control strategies.

[0034] This embodiment introduces a phase delay sequence as a time delay feature and constructs an electrothermal coupling transfer function model. It utilizes the electrothermal effect afterimage to separate conducted heat flux from retained heat, avoiding temperature field misjudgments caused by heat aliasing. The combined application of spatial interpolation reconstruction and energy gradient threshold segmentation enables the generation of the energy distribution domain to possess both continuous spatial coverage and the ability to identify heat accumulation regions. This provides an energy state sensing basis for the coordinated temperature field control of the three-dimensional electrocatalytic oxidation device, improving the device's safety margin and processing efficiency stability under complex operating conditions.

[0035] Furthermore, the specific implementation process of deploying hot anchor point drift in the energy distribution domain and dynamically locking and tracking the energy accumulation center according to the evolution direction of the energy gradient includes: identifying local energy maxima in the energy distribution domain and initializing the spatial coordinate set of the maxima as a hot anchor point set; performing gradient field calculation on the energy distribution domain to obtain the energy gradient vector field at each spatial location; performing spatial displacement of each hot anchor point along the energy gradient vector direction in each simulation time step to update the coordinate position of the hot anchor point; calculating the magnitude of the coordinate displacement vector of the hot anchor point in adjacent time steps, and determining that the hot anchor point has converged to the energy accumulation center when the magnitude is lower than a preset convergence threshold; recording the spatial coordinates of the hot anchor point in the convergence state as the position marker of the energy accumulation center at the current moment; and performing periodic reset and re-drift on the hot anchor point set as the energy distribution domain evolves and updates over time in the digital twin to dynamically track the energy accumulation center.

[0036] Specifically, when identifying local maxima in the energy distribution domain, the three-dimensional heat distribution field that generates the energy distribution domain is used as input. At each voxel location, a cubic neighborhood with a side length of 3 voxel units is constructed with that location as the center. The heat density values ​​of the 26 adjacent voxels are compared one by one with the center location. The location is determined to be a local maximum if and only if the heat density of the center location is strictly greater than that of all 26 neighboring locations.

[0037] When performing gradient field calculations on the energy distribution domain, the central difference method is used to calculate the partial derivatives of the heat density with respect to the spatial coordinates in three coordinate directions. The partial derivatives in these three directions together constitute the three-dimensional energy gradient vector at that location, and the direction of the gradient vector is the direction in which the heat density increases most rapidly in space. Within the digital twin, the above gradient vector calculation is performed on each voxel node covered by the energy distribution domain. The resulting global energy gradient vector field is stored in a sparse matrix structure, with each node recording its three-dimensional coordinates, heat density scalar value, and three-dimensional gradient vector components.

[0038] When performing spatial displacement of each hot anchor point along the energy gradient vector direction within each simulation time step, trilinear interpolation is first performed on the current hot anchor point coordinate position to obtain the three-dimensional gradient vector at that position from the energy gradient vector field. The unit direction vector of the gradient vector is used as the drift direction, and the result of multiplying the preset drift step size by the unit direction vector is used as the coordinate displacement increment within that time step. After the displacement increment is superimposed on the current coordinates of the hot anchor point, the coordinate position is updated. The drift step size is set to 0.3 times the side length of the voxel unit of the energy distribution domain, i.e., 0.15 mm, to ensure a balance between spatial accuracy and iterative stability in the drift process. The step size of the simulation time step is synchronized with the time update cycle of the energy distribution domain and is set to 0.5 seconds.

[0039] When calculating the magnitude of the coordinate displacement vector of the hot anchor point within adjacent time steps, the coordinate vector of the hot anchor point at the end of the nth time step is subtracted from the coordinate vector of the hot anchor point at the end of the n-1th time step to obtain the coordinate displacement vector within the current time step. The Euclidean norm of this displacement vector in three-dimensional space is then calculated, and the resulting scalar value is the magnitude of the coordinate displacement vector of the hot anchor point within the current time step. The preset convergence threshold is set based on the side length of the voxel unit in the energy distribution domain, and is set to 0.1 times the side length of the voxel unit, i.e., 0.05 mm. This threshold balances the floating-point precision of numerical calculation with the requirement of determining whether the hot anchor point has approached the energy accumulation center in the actual physical sense. When the magnitude of the coordinate displacement vector calculated within three consecutive time steps is lower than the convergence threshold, a convergence judgment is triggered, and the hot anchor point is marked as converged. Setting a composite convergence criterion that satisfies the condition for three consecutive steps, rather than judging in a single step, is to eliminate the pseudo-convergence phenomenon caused by local perturbations in the energy distribution domain of the digital twin within a certain time step.

[0040] When recording the spatial coordinates of the thermal anchor points during convergence and using them as the location markers of the energy accumulation center at the current moment, the three-dimensional coordinates of the thermal anchor points that meet the convergence conditions, along with the corresponding heat density values ​​and the timestamp of the convergence time, are written into the energy accumulation center location record table. When multiple thermal anchor points converge to adjacent positions with a spatial distance of less than 5 millimeters, these thermal anchor points are determined to have converged to the same energy accumulation center. The weighted average of the heat density of the coordinates of each converged thermal anchor point is taken as the representative coordinates of this accumulation center to avoid redundant center duplication due to the excessively dense distribution of initial maximum points.

[0041] When the set of hot anchor points is periodically reset and re-drifted as the energy distribution domain evolves and updates within the digital twin, the reset period is an integer multiple of the energy distribution domain's update cycle. Specifically, a full reset is performed every 10 energy distribution domain updates (5 seconds). During the reset, the records of converged hot anchor points are first cleared. Local maximum point identification is then performed again within the newly updated energy distribution domain. The newly identified set of maximum point coordinates is used as the initial set of hot anchor points for the next drift iteration, and a new drift iteration begins. To ensure that hot anchor point resets do not cause tracking breakpoints when the energy distribution domain undergoes significant morphological changes, the coordinates of the previously converged energy aggregation center are used as a reference. When a newly identified maximum point is more than 15 millimeters away from the previous aggregation center, an alarm is triggered and marked as an energy aggregation center migration event within the digital twin for priority response by upper-level control strategies.

[0042] This embodiment achieves dynamic positioning of the energy accumulation center during the operation of a three-dimensional electrocatalytic oxidation device by constructing a thermal anchor point drift tracking mechanism driven by an energy gradient vector field. The synergistic application of the convergence threshold determination mechanism and the periodic reset strategy enables the thermal anchor point tracking to maintain high-precision positioning under steady-state conditions where the energy distribution domain evolves slowly, and to respond quickly and capture migration events when the energy accumulation pattern changes abruptly. This improves the adaptive sensing capability and predictive control of the digital twin of the temperature field of the three-dimensional electrocatalytic oxidation device under complex dynamic conditions.

[0043] Furthermore, the specific implementation process of online correction of the thermal conduction hysteresis of the digital twin by calculating the thermal inertia accumulation rate of the thermal anchor point at the energy accumulation center includes: recording the coordinate trajectory sequence of the thermal anchor point during its drift towards the energy accumulation center within a continuous time window; performing a ratio calculation on the difference in coordinates of the thermal anchor point in adjacent time steps and the corresponding magnitude of the energy gradient vector to obtain the ratio parameter of the thermal anchor point drift rate to the energy gradient, which is defined as the thermal inertia accumulation rate; performing a deviation comparison calculation between the thermal inertia accumulation rate and the thermal conduction time constant in the digital twin; generating a thermal conduction time constant correction increment after processing the deviation through proportional-integral filtering; and superimposing the correction increment into the time delay parameter of the digital twin to perform online correction of the thermal conduction hysteresis.

[0044] Specifically, when recording the coordinate trajectory sequence of a hot anchor point drifting towards the energy accumulation center within a continuous time window, the starting point is the moment when the hot anchor point completes initialization and starts drift iteration. An independent coordinate trajectory buffer is created for each hot anchor point within the digital twin. After each simulation time step, the three-dimensional spatial coordinates of the hot anchor point at the end of that time step, along with the corresponding timestamp, are written into its respective buffer, forming a continuous coordinate trajectory sequence. The length of the continuous time window is set to the set of all time steps experienced by the hot anchor point from its initial position until convergence is achieved, i.e., a complete record of all intermediate coordinate states during a single drift convergence process. To ensure the integrity of the trajectory sequence and the numerical stability of subsequent ratio calculations, when a hot anchor point's gradient interpolation becomes singular due to its location near the boundary of the energy distribution domain within a certain time step, an anomaly flag is marked on the coordinate record of that time step. This time step is then skipped in subsequent ratio calculations, and the coordinate difference between adjacent normal time steps is used to complete the calculation.

[0045] When performing a ratio calculation on the difference in coordinates of the thermal anchor points between adjacent time steps and the corresponding magnitude of the energy gradient vector, the three-dimensional coordinate vectors of the nth time step and the (n-1)th time step in the coordinate trajectory sequence are subtracted to calculate the coordinate displacement vector within that time step. The Euclidean norm of this vector is then used as the scalar representation of the coordinate displacement, representing the actual displacement distance of the thermal anchor point in three-dimensional space within the current time step. Simultaneously, the energy gradient vector at the end of the (n-1)th time step is extracted from the energy gradient vector field, and its Euclidean norm is calculated as the magnitude of the energy gradient vector corresponding to the current time step. Dividing the coordinate displacement scalar by the magnitude of the energy gradient vector yields a ratio that is the single-step estimate of the thermal inertia accumulation rate for that time step. Physically, this represents the actual displacement of the thermal anchor point in space driven by a unit energy gradient, reflecting the relative strength of the resistance to external conduction caused by heat accumulation in the current energy distribution domain. The arithmetic mean of the single-step estimates for all effective time steps in the complete coordinate trajectory sequence is used to obtain the representative value of the thermal inertia accumulation rate for this drift convergence process.

[0046] When performing a deviation comparison calculation between the thermal inertia accumulation rate and the heat conduction time constant in the digital twin, it is necessary to first clarify the initial setting basis and physical meaning of the heat conduction time constant within the digital twin. The heat conduction time constant is a parameter in the digital twin's heat conduction model that reflects the characteristic time required for heat to diffuse outward from its generation location to reach a steady state. Its initial value is calculated using a lumped-parameter thermal capacity model based on the equivalent thermal conductivity of the particle electrode material, the average diameter of the particle electrode, and the filling porosity. The representative value of the thermal inertia accumulation rate calculated during this drift convergence process is then compared with the aforementioned heat conduction time constant after dimensional normalization. The proportional coefficient of the proportional-integral filter... Set to 0.18, integral coefficient The value is set to 0.042, and the integration time window is set to the historical sequence of deviations corresponding to the last 5 drift convergence cycles, i.e., the cumulative historical deviation value over a period of approximately 50 seconds. The proportional term directly generates an instantaneous correction component based on the current deviation to quickly respond to the thermal conductivity parameter shift caused by sudden changes in operating conditions; the integral term generates a slow correction component based on the cumulative trend of historical deviations to eliminate the influence of random errors caused by numerical fluctuations during a single drift process on the correction result. The sum of the two is the incremental correction for the thermal conductivity time constant generated this time. The tuning method for the proportional and integral coefficients is as follows: using the z-domain transfer function of the digital twin thermal conductivity correction... Based on, among which The drift convergence period is defined as follows. The pole placement method is used to place the closed-loop poles within a circle of radius 0.75 on the z-plane (corresponding to a continuous domain damping ratio of approximately 0.7) to ensure that the correction increment converges within 10 updates. The reference value ranges for the resulting proportional and integral coefficients are [0.12, 0.25] and [0.03, 0.06], respectively. When the device's thermal conduction time constant changes by an order of magnitude, the parameters should be readjusted using the above method.

[0047] When performing online correction of thermal conduction hysteresis by superimposing the correction increment onto the time delay parameters of the digital twin, the generated thermal conduction time constant correction increment is updated to the time delay parameter nodes of the digital twin thermal conduction model in an incremental superposition manner. This superposition operation is performed immediately after each drift convergence cycle, without interrupting the normal evolution simulation process of the digital twin. The corrected time delay parameters are synchronously transmitted to the time integral format of thermal conduction in the digital twin, driving subsequent simulation steps to use the corrected time constant to perform thermal diffusion calculations when updating the overall temperature distribution data, ensuring that the phase accuracy of the simulation results on the time axis remains dynamically consistent with the actual thermal response of the device. To prevent extreme values ​​of the correction increment caused by a single abnormal drift cycle from compromising the simulation stability of the digital twin, upper and lower limits are set for each generated correction increment: the upper limit is 15% of the current time delay parameter value, and the lower limit is 15% of the negative current time delay parameter value. Correction increments exceeding the constraint range are truncated to the boundary value before superposition, and the truncation event simultaneously triggers anomaly logging.

[0048] This embodiment calculates the cumulative rate of thermal inertia of the thermal anchor point coordinate trajectory sequence and introduces online iterative correction of the heat conduction time constant driven by proportional-integral filtering, achieving adaptive correction of the heat conduction hysteresis of the digital twin. By combining the fast response of the proportional term with the slow correction of the integral term, the accuracy and stability of the correction results are maintained in both scenarios of stable operating conditions and sudden changes in operating conditions. This ensures that the heat conduction simulation accuracy of the digital twin continuously approaches that of the real physical system throughout the entire life cycle of the device, effectively improving the overall accuracy of the coordinated control of the temperature field of the three-dimensional electrocatalytic oxidation device and the long-term stable operation capability of the device.

[0049] Furthermore, the specific implementation process of using the corrected digital twin for evolutionary simulation to identify the hotspot evolution trend within the future prediction period includes: performing evolutionary simulation using the thermally corrected digital twin, driving the digital twin to perform forward time-step iterations within the prediction window using the simulation step size; updating the full-field temperature distribution data based on the coupled solution results of the thermal conduction equation and the flow field equation within each simulation time step; extracting the coordinates of extreme temperature points and the magnitude of extreme temperatures from the full-field temperature distribution data of each time step to form a hotspot time-series trajectory set; performing trend fitting on the hotspot time-series trajectory set to extract the spatial migration vector sequence and temperature growth slope sequence of the hotspots; merging and outputting the spatial migration vector sequence and temperature growth slope sequence of the hotspots to form a hotspot evolution trend prediction map.

[0050] Specifically, evolutionary simulation is performed using a digital twin that has undergone thermal conduction correction. The current full-field temperature distribution data, flow field distribution data, and multi-physics fusion state variables of the digital twin after online correction are used as the initial conditions for simulation. The external excitation parameter input at the current moment is frozen, and the system switches to forward prediction mode. In the forward prediction mode, the digital twin no longer receives real-time sensor data updates from the physical device. Instead, it starts from the state variables at the current moment and advances towards the future time axis entirely through iterative solutions coupled internally, in order to achieve independent prediction of the future operating state of the device.

[0051] The prediction window length is set to an integer multiple of the heat conduction time constant; based on the heat conduction time constant, the prediction window length is set to 3 times the heat conduction time constant. The reason for selecting 3 times the heat conduction time constant as the prediction window is that within 1 time constant, the heat distribution only completes about 60% of the diffusion response, which is insufficient to reflect the complete trend of hotspot spatial migration; beyond 4 times the time constant, the simulation error amplifies significantly with the accumulation of time steps, and the prediction confidence drops to a level that does not meet the accuracy requirements of control decisions. The simulation step size is set to 0.5 seconds, consistent with the time update cycle of the energy distribution domain.

[0052] In each simulation time step, when updating the overall temperature distribution data based on the coupled solution results of heat conduction and flow field, the digital twin employs an operator splitting method to decouple the heat conduction solution and the flow field solution into two sequential sub-steps within each time step. In the heat conduction sub-step, using the initial overall temperature distribution of the current time step as input, the thermal diffusion is driven by the corrected heat conduction time constant to complete an explicit time integration within a 0.5-second step, updating the temperature values ​​of each grid node. Simultaneously, the Joule heat generation density generated between the particle electrodes is superimposed on the corresponding node as a volumetric heat source term. In the flow field solution sub-step, the temperature field output from the heat conduction sub-step is used as a buoyancy-driven term to update the velocity and pressure fields in the flow field distribution model. The convective heat transfer flux of the flow field is fed back to the boundary conditions of the heat conduction sub-step for use in the next time step, achieving unidirectional explicit coupling between the two fields.

[0053] When extracting the coordinates of extreme temperature points and the magnitude of extreme temperatures from the full-field temperature distribution data at each time step, after the full-field temperature distribution data for each time step is output, the temperature values ​​of all grid nodes are traversed, and the maximum temperature value and its corresponding three-dimensional spatial coordinates are extracted. These are used as the representative coordinates and magnitude of extreme temperatures of the hotspots at that time step, and are stored together with the corresponding simulation timestamp in the hotspot record array. When there are multiple temperature maxima points within a single time step and the difference between their temperature values ​​and the maximum temperature value is less than 0.5 degrees Celsius, all of these maxima points are included in the hotspot record to avoid tracking omissions caused by retaining only a single representative point for parallel hotspots that are spatially far apart. For the coordinate values ​​of each hotspot in the hotspot time-series trajectory set in the three coordinate directions, a first-order linear regression is performed with simulation time as the independent variable. The regression slopes in the three directions together constitute the spatial migration velocity vector of the hotspot. The spatial migration velocity vectors corresponding to each time step within the prediction window are arranged in chronological order to form a spatial migration vector sequence. For the extreme temperature magnitude time series data of each hot spot, a first-order linear regression was performed with simulation time as the independent variable. The resulting regression slope is the temperature growth slope, in degrees Celsius per second. The trend of temperature growth slope over several consecutive time steps was further fitted with a second-order polynomial to capture the nonlinear evolution characteristics of the temperature rise rate itself as it accelerates or slows down over time.

[0054] The spatial migration vector sequence and temperature growth slope sequence of hotspots are merged to form a hotspot evolution trend prediction map. Using each simulation time step within the prediction window as the time axis, the three-dimensional spatial coordinate trajectory, spatial migration vector sequence, extreme temperature magnitude sequence, and temperature growth slope sequence of each hotspot are encapsulated in a unified data structure to generate a structured hotspot evolution trend prediction map. The prediction map also includes a confidence score for each hotspot. The confidence score is calculated based on the statistical distribution of the hotspot's spatial positioning deviation in historical prediction periods. Hotspot prediction results with a confidence score below 0.75 are marked as reference items rather than mandatory trigger items in subsequent control decisions.

[0055] This embodiment constructs a time-step iterative prediction mechanism, combining linear regression and second-order trend fitting of hotspot time-series trajectories, to achieve quantitative prediction of the spatial migration path and temperature growth trend of hotspots within the future prediction window of a three-dimensional electrocatalytic oxidation device. The prediction window length is dynamically determined based on the heat conduction time constant, ensuring that the time span of the prediction results remains physically consistent with the actual thermal response characteristics of the device. This enhances the proactiveness of regulation while effectively avoiding the risk of erroneous intervention due to prediction errors.

[0056] Furthermore, a dynamic response strategy is adopted to superimpose the variable frequency pulses of the circulating pump with the frequency modulation commands of the power supply to form a control waveform stream that cancels local heat accumulation and projects it onto the three-dimensional electrocatalytic oxidation device. The specific implementation process includes: extracting the spatial coordinates and temperature gradient amplitude of the target hotspot from the hotspot evolution trend prediction map, calculating the fluid heat exchange demand, and obtaining the target flow allocation matrix required to cancel the target hotspot; generating the variable frequency pulse waveform sequence of the circulating pump through the flow-frequency inverse mapping relationship based on the target flow allocation matrix; simultaneously extracting the predicted energy input law of the target hotspot from the hotspot evolution trend prediction map, and calculating the frequency modulation command sequence of the power supply through the energy-frequency inverse mapping relationship; performing phase alignment and superposition operations on the variable frequency pulse waveform sequence and the frequency modulation command sequence to generate a control waveform stream carrying anti-phase energy cancellation characteristics; mapping the control waveform stream to the circulating pump frequency converter control interface and the power supply frequency modulation control interface respectively to complete the projection output of the control command.

[0057] Specifically, the spatial coordinates and temperature gradient amplitude of target hotspots are extracted from the hotspot evolution trend prediction map, and fluid heat exchange demand is calculated. Hotspots with a confidence score of not less than 0.75 are selected as target hotspots. The three-dimensional spatial coordinates and temperature gradient amplitude at the end of the prediction window for each target hotspot are extracted sequentially. The temperature gradient amplitude is obtained by performing three-dimensional central difference calculation on the full-field temperature distribution data at the end of the prediction window, and is a quantitative indicator reflecting the degree of spatial non-uniformity of the temperature field at the location of the target hotspot. A spherical heat exchange demand region with a radius equal to the equivalent influence range of the hotspot is delineated around the spatial coordinates of the target hotspot. The equivalent influence range is dynamically determined based on the ratio of the temperature gradient amplitude to a preset heat exchange intervention threshold; the larger the temperature gradient amplitude, the larger the equivalent influence range. Based on the spatial coordinates, temperature gradient amplitude, and equivalent influence range of the target hotspot, and combined with the flow contribution coefficients of each channel in the flow field distribution model within the digital twin to the heat exchange demand region, the target flow distribution matrix required to offset the target hotspot is calculated. When multiple target hotspots exist, the global target flow allocation matrix is ​​solved using a weighted linear programming method, with the temperature gradient amplitude of each target hotspot as a weight, under the constraint of the total design flow rate of the device. The flow contribution coefficient is defined as the ratio of the flow coverage area of ​​each channel in the flow field distribution model to the total area of ​​the target heat exchange demand area, reflecting the degree of contribution of the flow rate change of that channel to the cooling effect of the target hotspot. When the target flow allocation scheme for multiple hotspots is not feasible under the total flow rate constraint, the hotspots are satisfied sequentially according to their priority from high to low temperature gradient amplitude, and the flow increment required by low-priority hotspots is reduced proportionally.

[0058] The target flow allocation matrix is ​​constructed with each flow channel number as the row index and the target flow value as the column element. Flow channels with higher flow contribution coefficients are allocated larger target flow increments, while flow channels with flow contribution coefficients below 0.05 have their target flow increments set to zero to avoid ineffective intervention. Based on the target flow allocation matrix, a circulating pump variable frequency pulse waveform sequence is generated through an inverse mapping relationship between flow and frequency. First, a pre-calibrated circulating pump flow frequency calibration curve is retrieved. This calibration curve is obtained by measuring the inverter output frequency as the independent variable and the measured flow rate of each flow channel under the corresponding steady-state operating condition as the dependent variable, within the range of 10 Hz to 50 Hz in 1 Hz steps, with a total of 41 calibration points. The calibration accuracy is better than 1.5% of the full scale. For the target flow value of each flow channel in the target flow allocation matrix, the corresponding inverter target frequency value is solved by performing cubic spline interpolation inverse mapping on the calibration curve. Since the control strategy requires reaching the target flow rate at the end of the prediction window, i.e., 90 seconds later, the frequency converter needs to be ramped up from the current operating frequency to the target frequency using a linear ramp method. The ramp duration is set to 15 seconds to balance flow response speed and mechanical stress constraints. Based on the above frequency ramp parameters, a frequency converter pulse waveform sequence is generated. This waveform sequence contains 180 frequency command data points with a sampling interval of 0.5 seconds, forming a discrete frequency converter control timing sequence covering the entire prediction window.

[0059] Simultaneously, the predicted energy input pattern of the target hotspot is extracted from the hotspot evolution trend prediction map, and the power supply frequency modulation command sequence is calculated through the energy-frequency inverse mapping relationship. Differential operations are performed on the extreme temperature magnitude sequence of the target hotspot at each time step within the prediction window to obtain the predicted energy input rate time series. This energy input rate time series reflects the change in Joule heat generation power at the target hotspot over time. The peak energy input rate at the end of the prediction window is used as the reference energy input for power supply frequency modulation intervention. Inverse mapping is performed through the power supply power-frequency calibration curve to calculate the required reduction in power supply output frequency to offset the Joule heat generation power at the target hotspot to a safe level at the corresponding time. The power supply power-frequency calibration curve is calibrated in 5 Hz steps within the range of 20 Hz to 100 Hz, with a calibration accuracy better than 2% of the rated power.

[0060] The two waveform sequences are phase-aligned using a unified time base to ensure that the convective cooling effect from increased circulation pump flow and the Joule heating reduction effect from reduced power supply act synchronously on the target hotspot region on the time axis. The time deviation between the peak effect moments of the two interventions does not exceed one sampling interval, i.e., 0.5 seconds. The two phase-aligned waveform sequences are then weighted and superimposed at each sampling moment. The fluid convection heat transfer contribution... Defined as the product of the target flow rate increment, fluid density, specific heat capacity, and the temperature difference between the target hot spot and the inlet, it reflects the heat carried away by the change in circulation pump flow rate per unit time; power supply regulation contribution. Defined as the reduction in Joule heat generation power corresponding to power frequency adjustment. Weighting coefficients , Weighting coefficients The sum of the two is 1.

[0061] The resulting composite control waveform stream, after superposition, carries a comprehensive intervention intensity index at each sampling moment. This index reflects the total amount of energy cancellation at the target hotspot under the combined action of the circulating pump frequency converter and the power supply frequency regulator intervention methods, exhibiting the physical characteristic of anti-phase energy cancellation. The control waveform stream is mapped to the circulating pump frequency converter control interface and the power supply frequency regulator control interface respectively to complete the control command projection output. The digital twin writes the frequency conversion pulse waveform sequence into the preset register address of the circulating pump frequency converter in ModbusTCP format via the industrial Ethernet protocol and sets the trigger time flag. Simultaneously, the frequency regulation command sequence is written into the frequency regulation command buffer of the power controller via the CANopen protocol, and the same trigger time flag is set. The trigger time of both commands is set to the current simulation time plus a communication delay compensation amount, which is dynamically determined by online measurement of the round-trip delay of the communication link.

[0062] This embodiment employs dual-channel intervention calculations involving inverse flow frequency mapping and inverse energy frequency mapping, and introduces phase alignment and weighted superposition to generate a control waveform flow carrying anti-phase energy cancellation characteristics. This improves upon the problem that the circulating pump and power supply, as independent actuators, cannot achieve coordinated intervention, and that the energy efficiency of a single actuator is low. It enhances the energy utilization efficiency of thermal accumulation cancellation, providing technical support for achieving precise and low-energy temperature field coordinated control of a three-dimensional electrocatalytic oxidation device under complex dynamic conditions.

[0063] Furthermore, the fluid damping fluctuation data after the three-dimensional electrocatalytic oxidation device performs regulation actions is re-synthesized in the field. The specific implementation process of coordinating the regulation of the global temperature field by establishing an energy interaction link between the digital twin and the three-dimensional electrocatalytic oxidation device includes: collecting newly generated fluid damping fluctuation data after the three-dimensional electrocatalytic oxidation device performs regulation actions, and injecting it into the digital twin to perform a new round of field synthesis, updating the multi-physics fusion state variables; establishing an energy interaction link between the digital twin and the three-dimensional electrocatalytic oxidation device based on the multi-physics fusion state variables, and coordinating the regulation of the global temperature field.

[0064] Reference Figure 3Specifically, after the three-dimensional electrocatalytic oxidation device performs a control action, newly generated fluid damping fluctuation data is collected and injected into the digital twin to perform a new round of field synthesis and update the multiphysics fusion state variables. After the control waveform stream is projected and output, each actuator of the device begins to change its operating state according to the received command sequence. The flow velocity distribution, pressure distribution, and particle electrode gap resistance of the fluid in the filling chamber all change responsively. These changes are reflected in real time in the differential pressure time series collected by the differential pressure sensor in the form of damping fluctuation amplitude and spectral characteristics. The digital twin continuously monitors the real-time data stream of the differential pressure sensor. Starting from the moment the control waveform stream is projected, the newly generated differential pressure time series is continuously collected at a period of 0.5 seconds. The differential pressure data in each collection cycle is subjected to the same differential filtering operation as the initial fluid damping fluctuation data to extract the updated fluid damping fluctuation data. This updated fluid damping fluctuation data, along with the current waveform time series re-acquired after the control action, is injected into the digital twin as a new round of multidimensional excitation parameters. The injection operation is performed in an incremental update manner, that is, only the local grid regions whose state changes due to the control action are subjected to excitation parameter replacement and field reconstruction, while the far regions unaffected by the control retain the field synthesis results of the previous round, so as to reduce the consumption of computing resources and ensure that the update cycle does not exceed 0.5 seconds.

[0065] During the execution of a new round of field synthesis, updated fluid damping fluctuation data and current ripple characteristics are synchronously injected into the electric field distribution model and flow field distribution model of the digital twin. The electric field intensity distribution and velocity / pressure distribution are resolved within the local grid region affected by the control action. Based on the updated flow field parameters, the convective heat transfer coefficient and local Reynolds number at each grid node are recalculated. The updated convective heat transfer coefficient is fed back into the boundary conditions of heat conduction, driving the heat conduction model to reconstruct the local temperature field within the affected region. Simultaneously, the Joule heat generation density at each gap location in the electric field distribution model is recalculated based on the current ripple characteristics after the control action. The updated Joule heat generation density is then used as the volumetric heat source term to replace the corresponding node in the heat conduction model, completing the synchronous refresh of the electric field heat source. After the incremental collaborative update of the multiphysics fields is completed, the digital twin outputs multiphysics fusion state quantities covering the entire device domain, including the overall temperature distribution, overall velocity distribution, overall electric field intensity distribution, and updated heat density values ​​for each energy accumulation unit.

[0066] When establishing an energy interaction link between the digital twin and the three-dimensional electrocatalytic oxidation device based on the multi-physics fusion state variables to coordinate the regulation of the global temperature field, the energy interaction link uses the multi-physics fusion state variables as the information carrier, the digital twin as the decision-making core, and the actuators of the physical device as the action terminals, forming a complete perception-decision-execution closed loop. At the perception layer of the energy interaction link, real-time data streams from differential pressure sensors and current sensors continuously transmit the current state information of the physical device to the digital twin at a period of 0.5 seconds, driving the continuous updating of the multi-physics fusion state variables of the digital twin. At the decision-making layer, the digital twin periodically initiates thermal anchor point drift tracking and hotspot evolution trend prediction based on the latest multi-physics fusion state variables, outputting a new round of control waveform stream after each prediction window ends. At the execution layer, the control waveform stream is synchronously sent to the circulating pump frequency converter and power controller via industrial Ethernet and fieldbus protocols. The device state changes generated after the actuators respond are again transmitted to the perception layer via sensors, forming a closed energy interaction link. The goal of the global coordinated control of the energy interaction link is not limited to eliminating local heat accumulation in a single target hotspot, but also simultaneously monitors the uniformity index of the global temperature distribution of the device. When the global temperature uniformity coefficient exceeds the preset upper limit threshold, the global optimization mode is triggered. In all energy accumulation centers, the corresponding control waveform streams are generated in order of priority from high to low heat density. The multiple control waveform streams are projected on the time axis in the order of non-overlapping execution time windows to avoid the superposition of flow field disturbances caused by the simultaneous action of multiple commands, which would lead to damping instability.

[0067] This embodiment injects fluid damping fluctuation data after regulation actions into the digital twin in real time using an incremental field synthesis method, and constructs a three-layer closed energy interaction link of perception, decision-making and execution using multi-physics field fusion state variables as information links. While ensuring the real-time performance of multi-physics field fusion state variables, it reduces the consumption of computing resources and realizes continuous adaptive optimization and regulation of the temperature field during the entire life cycle operation of the three-dimensional electrocatalytic oxidation device.

[0068] Example 2: In this example, the above-mentioned method for coordinated temperature field control of a three-dimensional electrocatalytic oxidation device based on digital twins is fully deployed in a continuous treatment system for chemical wastewater.

[0069] Furthermore, current ripple characteristics and fluid damping fluctuation data during the operation of the three-dimensional electrocatalytic oxidation device were extracted and field synthesis was performed within a digital twin. Specifically, four independent sampling nodes were deployed in the main loop of the device. The current waveform, acquired at a frequency of 12000 Hz, was divided into time series segments using edge computing nodes, with a segmentation window set to 0.2 seconds and maintaining a 50% data overlap rate. Subsequently, a Fast Fourier Transform algorithm was executed to extract the amplitude and phase information of the fundamental frequency (with a set mean of 20 amperes) and higher harmonics, forming a high-dimensional current ripple feature vector. Simultaneously, differential pressure sensors with a sampling rate of 2000 Hz were deployed in the inlet and outlet channels. A low-pass digital filter with a cutoff frequency of 120 Hz and first-order differential operations were applied to the differential pressure time series to obtain a fluid damping fluctuation data series with a mean of approximately 2.1 kPa and a normal fluctuation extreme value of 0.06 kPa / s. The system performs tensor splicing and standardization on the aforementioned multidimensional feature data, and then injects it as boundary excitation conditions into the digital twin based on finite element mesh registration. With a computation cycle of 0.4 seconds, it performs field synthesis calculations of electric field and flow field data on a mesh with a spatial resolution of 1 / 25 of the feature size.

[0070] Furthermore, utilizing the electrothermal effect remnant generated by the current ripple in the gap between the particle electrodes, the heat distribution inside the channel is deduced and reconstructed to generate an energy distribution domain. The system extracts the phase delay times of the 3rd and 5th harmonics from the feature vector, which are 8.5 ms and 4.8 ms, respectively, as the electrothermal response time delay characteristics of the particle electrodes (with an average diameter of 10.5 mm and a porosity of 0.42). These parameters are input into a pre-constructed electrothermal coupling transfer function model, and the instantaneous heat generation density distribution on the anode side, reaching a maximum of 1.15 millijoules per cubic centimeter per second, is calculated through element-wise multiplication of the admittance matrix and the current density tensor. Based on the time delay characteristics and Fourier's law of heat conduction, the system subtracts the diffused heat flux and extracts the electrothermal effect remnant, which accounts for approximately 35%. A spatial interpolation algorithm based on radial basis functions is used to reconstruct the discrete afterimage data globally, generating a continuous heat distribution field with a spatial resolution of 0.4 mm. An energy gradient threshold segmentation algorithm with a mean of 1.4 times is applied to calculate and generate an energy distribution domain containing 5 independent three-dimensional voxel sets.

[0071] Furthermore, hot anchor points are deployed in the energy distribution domain to dynamically lock and track energy accumulation centers as the energy gradient evolves. A local maximum point identification algorithm is used to select 12 initial coordinate points within the energy distribution domain as a set of hot anchor points. The system employs the central difference method to construct a global three-dimensional energy gradient vector field, with the maximum gradient vector magnitude calculated to be 0.045 millijoules per millimeter. Within each 0.4-second simulation time step, each hot anchor point is driven to perform a spatial iterative displacement of 0.2 millimeters along the gradient vector direction. By continuously calculating the Euclidean norm of the hot anchor point displacement vector, convergence is determined when the norm for three consecutive steps is below the convergence threshold of 0.06 millimeters. In actual calculations, each hot anchor point converges within 8 to 22 steps, and is then merged into four energy accumulation centers through coordinate weighted averaging. The system performs a memory record reset and re-drift calculation every 12 simulation steps (i.e., 4.8 seconds), thereby achieving dynamic and uninterrupted tracking of the coordinates of accumulation centers under complex flow conditions.

[0072] Furthermore, the three-dimensional coordinate trajectory sequence of a certain thermal anchor point over 15 simulation steps (approximately 6 seconds) is extracted from the cache. The ratio of the single-step displacement scalar to the corresponding gradient magnitude is calculated to obtain the average thermal inertia accumulation rate. This value is then compared with the initial 28.5-second heat conduction time constant set by the digital twin for dimensional conversion and deviation analysis. By calling a proportional-integral digital filter with a proportionality coefficient of 0.18 and an integral coefficient of 0.042, the historical deviation data from the last 5 drift cycles is processed to generate a time constant correction increment with upper and lower limits (±12%). This increment is then superimposed in real-time onto the time delay parameter matrix of the heat conduction partial differential equation within the twin, completing online adaptive correction in the entire digital domain.

[0073] Furthermore, evolutionary simulations are performed using the corrected digital twin to identify hotspot evolution trends within the future prediction period. The system freezes the external sensor input stream and drives the operator splitting model to perform 210 forward explicit integral iterations within a prediction window with a time constant of 3 times the correction value, using a step size of 0.4 seconds. After each iteration, the system executes an extreme point search algorithm to extract the highest temperature and coordinates. Through first-order linear regression and second-order polynomial fitting algorithms, it calculates and generates spatial migration vector sequences and temperature growth slope sequences for each hotspot in three-dimensional space. The system filters out interference nodes with confidence levels below 0.80 and encapsulates the effective sequences into a structured hotspot evolution trend prediction map.

[0074] Furthermore, a dynamic response strategy is adopted to superimpose the variable frequency pulses of the circulating pump with the frequency modulation commands of the power supply to form a control waveform flow that cancels out local heat accumulation and projects it onto the three-dimensional electrocatalytic oxidation device. The system analyzes the target hotspot location (gradient amplitude up to 0.45 degrees Celsius per millimeter) from the spectrum and calculates the heat exchange demand domain with an equivalent influence radius of 38 millimeters. Using digital mapping relationships, the target flow distribution matrix is ​​solved, and a 12-second linear ramp pulse sequence of the frequency converter is generated through cubic spline interpolation. The corresponding energy input cancellation rate is calculated synchronously, generating a frequency modulation command sequence in the range of 25 Hz to 120 Hz. The system performs phase alignment and weighted superposition of the two commands with a weight ratio of 0.65 and 0.35. After compensating for a 95-millisecond network communication delay, the data packet carrying the anti-phase energy cancellation characteristics is projected to the hardware control interface.

[0075] Furthermore, the fluid damping fluctuation data after the three-dimensional electrocatalytic oxidation device performs regulation actions is re-synthesized in the field. By establishing an energy interaction link between the digital twin and the three-dimensional electrocatalytic oxidation device, coordinated regulation of the global temperature field is achieved. Upon receiving instructions, the device hardware generates a new flow distribution. The system uses an incremental update mechanism to re-inject fluctuation data only into the local meshes where the state has changed, updating the multiphysics fusion state variables and optimizing the allocation of computational resources for the underlying processor. This bidirectional energy interaction data link enables global closed-loop control based on real-time data processing and predictive analysis.

[0076] This embodiment achieves proactive prediction and adaptive cancellation of local thermal runaway through digital field reconstruction based on inverse deduction of electrical signal micro-ripples and fluid fluctuation data, and by utilizing thermal anchor convergence and proportional-integral filtering correction. This not only avoids electrode plate caking and lifespan loss caused by localized overheating within the device, but also optimizes the cooling fluid and electrical energy input through the calculation of the flow and power distribution matrix, thereby reducing the overall operating energy consumption of the three-dimensional electrocatalytic oxidation device.

[0077] It should be clarified that the embodiments described above are merely exemplary and are intended to aid in understanding the present invention, not to limit it. Those skilled in the art can make various changes and modifications after grasping the core ideas of the present invention. Therefore, the scope of protection of the present invention is defined by the appended claims and their equivalents.

Claims

1. A method for coordinated temperature field control of a three-dimensional electrocatalytic oxidation device based on digital twins, characterized in that, include: Current sensors are installed at the sampling nodes of the main circuit of the three-dimensional electrocatalytic oxidation device to collect the time series of current waveforms during the operation of the device. Apply Fast Fourier Transform to the current waveform time series to extract the amplitude and phase information of each harmonic component and construct the current ripple feature. Differential pressure sensors are installed in the inlet and outlet flow channels of the device to collect the pressure difference time series at both ends of the flow channel, and differential filtering is applied to the pressure difference time series to obtain fluid damping fluctuation data. The current ripple characteristics and fluid damping fluctuation data are injected into the digital twin as multidimensional excitation parameters, and field synthesis is performed on the electric field distribution data and flow field distribution data. The phase delay sequence of each harmonic component on the time axis is extracted from the current ripple characteristics and used as the time delay feature of the electrothermal response at the particle electrode interface. Based on the geometric configuration parameters and equivalent admittance distribution of the particle electrodes, an electrothermal coupling transfer function model is established at the gap between the particle electrodes. The current ripple characteristics are input into the electrothermal coupling transfer function model to calculate the instantaneous heat generation density distribution at each gap location. The time delay characteristic correction of the electrothermal effect is applied to the instantaneous heat generation density distribution to deduct the heat flux component that has been conducted outward and extract the electrothermal effect residual image retained inside the pore structure. The electrothermal effect residual image is spatially interpolated and reconstructed according to the particle electrode filling topology to restore the heat distribution inside the pore. An energy gradient threshold segmentation is applied to the heat distribution to extract the boundary of the heat accumulation region and generate an energy distribution domain. Thermal anchor point drift is deployed in the energy distribution domain to dynamically lock onto and track the energy accumulation center as the energy gradient evolves. The thermal conduction hysteresis of the digital twin is corrected online by calculating the rate of accumulation of thermal inertia of the thermal anchor point at the energy accumulation center; Evolution simulation is performed using the corrected digital twin to identify hotspot evolution trends within the future prediction period; a dynamic response strategy is adopted to superimpose the frequency conversion pulse of the circulating pump with the frequency modulation command of the power supply to form a control waveform flow that cancels local heat accumulation and projects it onto the three-dimensional electrocatalytic oxidation device. The fluid damping fluctuation data after the three-dimensional electrocatalytic oxidation device performs regulation actions are then re-synthesized in the field. By establishing an energy interaction link between the digital twin and the three-dimensional electrocatalytic oxidation device, the global temperature field is coordinated and regulated.

2. The method for coordinated temperature field control of a three-dimensional electrocatalytic oxidation device based on digital twins according to claim 1, characterized in that, The specific implementation process of deploying hot anchor points in the energy distribution domain and dynamically locking and tracking the energy accumulation center according to the evolution direction of the energy gradient includes: identifying local energy maxima in the energy distribution domain and initializing the spatial coordinate set of the maxima as a hot anchor point set; performing gradient field calculation on the energy distribution domain to obtain the energy gradient vector field at each spatial location; performing spatial displacement of each hot anchor point along the direction of the energy gradient vector in each simulation time step to update the coordinate position of the hot anchor point; calculating the magnitude of the coordinate displacement vector of the hot anchor point in adjacent time steps, and determining that the hot anchor point has converged to the energy accumulation center when the magnitude is lower than a preset convergence threshold; recording the spatial coordinates of the hot anchor point in the convergence state as the position marker of the energy accumulation center at the current moment; and performing periodic reset and re-drift on the hot anchor point set as the energy distribution domain evolves and updates over time in the digital twin to dynamically track the energy accumulation center.

3. The method for coordinated temperature field control of a three-dimensional electrocatalytic oxidation device based on digital twins according to claim 1, characterized in that, The specific implementation process of online correction of the thermal conduction hysteresis of the digital twin by calculating the thermal inertia accumulation rate of the thermal anchor point at the energy accumulation center includes: recording the coordinate trajectory sequence of the thermal anchor point drifting towards the energy accumulation center within a continuous time window; performing a ratio calculation on the coordinate difference of the thermal anchor point in adjacent time steps and the corresponding energy gradient vector magnitude to obtain the ratio parameter of the thermal anchor point drift rate to the energy gradient, which is defined as the thermal inertia accumulation rate; performing a deviation comparison calculation on the thermal inertia accumulation rate and the thermal conduction time constant in the digital twin; generating a thermal conduction time constant correction increment after the deviation is processed by proportional-integral filtering; and superimposing the correction increment into the time delay parameter of the digital twin to perform online correction of the thermal conduction hysteresis.

4. The method for coordinated temperature field control of a three-dimensional electrocatalytic oxidation device based on digital twins according to claim 1, characterized in that, The specific implementation process of using a corrected digital twin for evolutionary simulation to identify the hotspot evolution trend within a future prediction period includes: performing evolutionary simulation using a digital twin corrected for thermal conduction; driving the digital twin to perform forward time-step iterations within the prediction window using the simulation step size; updating the overall temperature distribution data based on the coupled solution results of the thermal conduction equation and the flow field equation within each simulation time step; extracting the coordinates of extreme temperature points and the magnitude of extreme temperatures from the overall temperature distribution data at each time step to form a hotspot time-series trajectory set; performing trend fitting on the hotspot time-series trajectory set to extract the spatial migration vector sequence and temperature growth slope sequence of the hotspots; and merging and outputting the spatial migration vector sequence and temperature growth slope sequence of the hotspots to form a hotspot evolution trend prediction map.

5. The method for coordinated temperature field control of a three-dimensional electrocatalytic oxidation device based on digital twins according to claim 4, characterized in that, The specific implementation process of superimposing the variable frequency pulses of the circulating pump and the frequency modulation command of the power supply to form a control waveform stream that cancels local heat accumulation and projects it onto the three-dimensional electrocatalytic oxidation device using a dynamic response strategy includes: extracting the spatial coordinates and temperature gradient amplitude of the target hotspot from the hotspot evolution trend prediction map, calculating the fluid heat exchange demand, and obtaining the target flow allocation matrix required to cancel the target hotspot; generating the variable frequency pulse waveform sequence of the circulating pump through the flow-frequency inverse mapping relationship based on the target flow allocation matrix; simultaneously extracting the predicted energy input law of the target hotspot from the hotspot evolution trend prediction map, and calculating the frequency modulation command sequence of the power supply through the energy-frequency inverse mapping relationship; performing phase alignment and superposition operations on the variable frequency pulse waveform sequence and the frequency modulation command sequence to generate a control waveform stream carrying anti-phase energy cancellation characteristics; and mapping the control waveform stream to the circulating pump frequency converter control interface and the power supply frequency modulation control interface respectively to complete the projection output of the control command.

6. The method for coordinated temperature field control of a three-dimensional electrocatalytic oxidation device based on digital twins according to claim 1, characterized in that, The process of re-synthesizing the fluid damping fluctuation data after the three-dimensional electrocatalytic oxidation device performs regulation actions, and establishing an energy interaction link between the digital twin and the three-dimensional electrocatalytic oxidation device to coordinately regulate the global temperature field includes: collecting newly generated fluid damping fluctuation data after the three-dimensional electrocatalytic oxidation device performs regulation actions, injecting it into the digital twin to perform a new round of field synthesis, and updating the multi-physics fusion state variables; establishing an energy interaction link between the digital twin and the three-dimensional electrocatalytic oxidation device based on the multi-physics fusion state variables to coordinately regulate the global temperature field.

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