AEM cathode and anode safe release control method based on differential pressure estimation

Abstract

The invention provides an AEM cathode and anode safe release control method based on differential pressure estimation, and relates to the technical field of electrolysis safety control. Collecting multi-source operation data and performing online compensation; constructing a differential pressure estimation model fusing gas production, two-phase resistance, loop pressure loss and a membrane support effect, and outputting transmembrane differential pressure estimation; a self-adaptive grading threshold value and a rate limiting value are generated by combining a membrane and pile body tolerance curve and are predicted and evaluated, and a grading triggering decision is formed; the cathode and anode release valves are controlled in a linkage mode according to the minimum differential pressure gradient, and estimation and uncertainty are updated in a closed-loop mode; when abnormity occurs, opposite-side enhanced release and derating forced voltage sharing are triggered; and after stabilization, model parameters, threshold values and control gains are updated online and filed, and the problem that differential pressure estimation and cooperative release are unstable under multiple working conditions and uncertain conditions is solved.

Description

Technical Field

[0001] This invention relates to the field of electrolysis safety control technology, and in particular to an AEM anode and cathode safety release control method based on differential pressure estimation. Background Technology

[0002] In anion exchange membrane electrolysis systems, hydrogen evolution at the cathode and oxygen evolution at the anode cause asymmetric gas-liquid distribution and flow pressure loss on both sides. The transmembrane differential pressure fluctuates rapidly with current, temperature, alkali concentration, and cyclic operating conditions. Traditional safety release methods mainly rely on absolute pressure thresholds or single-point sensor triggers, employing fixed timing or unilateral pressure relief, which fails to reflect the transient and cumulative effects of the transmembrane differential pressure. This leads to delayed discharge, excessive discharge, or false triggering, ultimately causing membrane mechanical fatigue, gas cross-contamination, and efficiency loss. For applications with high current density and frequent start-stop cycles, the industry is shifting from static threshold control to a "state estimation + differential pressure management" approach. Through multi-source data fusion, online model estimation, and adaptive thresholds, a closed-loop control of transmembrane differential pressure prediction, verification, and release is achieved. This is further enhanced by fault diagnosis and degraded operation to improve inherent safety and availability.

[0003] However, existing technologies generally lack a unified and robust framework for transmembrane differential pressure estimation and uncertainty management. They are unable to maintain reliable differential pressure reconstruction when sensors are sparse, drifting, or data is missing. The release criteria are not sufficiently coupled with threshold, rate of change, and prediction information, making it difficult to suppress peak membrane stress. The dual-valve linkage and circulation-side coordination are insufficient, which easily leads to secondary differential pressure peaks. Furthermore, the lack of failure safety strategies with clear event priorities and online adaptive reset mechanisms results in the inability to stably constrain transmembrane differential pressure when valves are stuck or measurements fail, affecting the safety, lifespan, and efficiency of the system. Summary of the Invention

[0004] To overcome the shortcomings of the prior art, the purpose of this invention is to provide a safe release control method for AEM anode and cathode based on differential pressure estimation. This invention solves the problem that the prior art lacks a robust closed-loop method for transmembrane differential pressure estimation, graded triggering, and coordinated release of anode and cathode under multiple operating conditions and uncertainties, making it difficult to continuously constrain the transmembrane differential pressure within a safe range.

[0005] To achieve the above objectives, the present invention provides the following solution:

[0006] A method for safe release control of AEM cathode and anode based on differential pressure estimation, comprising:

[0007] Multi-source operational data related to transmembrane differential pressure were collected and online bias and noise compensation were performed to obtain compensated multi-source data.

[0008] Based on compensated multi-source data, a differential pressure estimation model is constructed that integrates gas production, two-phase resistance, loop pressure loss and membrane support effect, and state observation is performed to output the transmembrane differential pressure estimate.

[0009] Based on the transmembrane differential pressure estimation and combined with the membrane and stack tolerance curves, an adaptive grading threshold and differential pressure change rate limit are set and predicted and evaluated to determine the current grading level and triggering cause, thus obtaining the grading triggering decision.

[0010] Based on the hierarchical triggering decision, with the goal of minimizing the transmembrane differential pressure gradient, the opening and duration of the cathode and anode release valves are controlled in conjunction and unilateral transitions are limited. The transmembrane differential pressure estimate and uncertainty are updated in real time to meet the requirements of safety belt and hysteresis, and the coordinated release execution result is obtained.

[0011] When valve jamming, abnormal valve position, or drift of key sensors causes the coordinated release execution result to deviate from the target, the counter-side enhanced release is triggered based on transmembrane differential pressure estimation and graded triggering decision to implement derated operation and forced pressure equalization, thus obtaining a failure safety handling result.

[0012] After both the coordinated release execution results and the failure safety handling results showed that the transmembrane differential pressure was stable within the safety zone, the model parameters, thresholds, and control gains were updated using compensated multi-source data and historical records of transmembrane differential pressure estimation, and event archiving was completed, resulting in adaptive reset and online optimization results.

[0013] The present invention discloses the following technical effects:

[0014] This invention provides a method for safe release control of AEM anode and cathode based on differential pressure estimation, comprising: collecting multi-source operating data related to transmembrane differential pressure and performing online biasing and noise compensation to obtain compensated multi-source data; constructing a differential pressure estimation model integrating gas production, two-phase resistance, loop pressure loss, and membrane support effect based on the compensated multi-source data and performing state observation to output transmembrane differential pressure estimation; setting an adaptive grading threshold and differential pressure change rate limit based on the transmembrane differential pressure estimation and combining the membrane and reactor body tolerance curves, and performing prediction and evaluation to determine the current grading level and triggering cause, thus obtaining a grading triggering decision; and controlling the release of cathode and anode in conjunction with the grading triggering decision with the goal of minimizing the transmembrane differential pressure gradient. The valve opening degree and duration were controlled, and unilateral transitions were limited. The transmembrane differential pressure estimate and uncertainty were updated in real time in a closed loop to meet the safety zone and hysteresis requirements, resulting in a coordinated release execution result. When the coordinated release execution result deviated from the target due to valve jamming, abnormal valve position, or drift of key sensors, the opposite side was triggered to implement derated operation and forced pressure equalization based on the transmembrane differential pressure estimate and graded triggering decision, resulting in a failure safety handling result. After both the coordinated release execution result and the failure safety handling result indicated that the transmembrane differential pressure was stable within the safety zone, the model parameters, thresholds, and control gains were updated using compensated multi-source data and historical records of the transmembrane differential pressure estimate, and event archiving was completed, resulting in adaptive reset and online optimization results. This invention accurately estimates transmembrane differential pressure through online compensation and fusion modeling of multi-source data. Addressing the issues of misjudgment, hysteresis, and frequent false triggering caused by traditional single-sensor and fixed threshold methods, it introduces adaptive graded thresholds and rate limits constrained by tolerance curves to achieve trend-oriented prediction. Based on graded triggering decisions, it executes coordinated release of anode and cathode, minimizing the differential pressure gradient and suppressing oscillations with hysteresis and a safety belt, significantly reducing secondary instability caused by unilateral transitions. In the event of valve jamming or sensor drift, it automatically triggers enhanced release and derating operation on the opposite side, ensuring forced pressure equalization and operational continuity. After stabilization, online updates and archiving of parameters, thresholds, and gains form a verifiable closed-loop adaptive optimization, improving estimation accuracy, control robustness, and safety margin, while reducing maintenance costs and downtime risks. Attached Figure Description

[0015] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0016] Figure 1 The flowchart illustrates a method for safe release control of AEM cathode and anode based on differential pressure estimation, as provided in an embodiment of the present invention. Detailed Implementation

[0017] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0018] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0019] like Figure 1 As shown, this invention provides a method for safe release control of AEM cathode and anode based on differential pressure estimation, comprising:

[0020] Step 100: Collect multi-source operating data related to transmembrane differential pressure and perform online bias and noise compensation to obtain compensated multi-source data;

[0021] Step 200: Construct a differential pressure estimation model that integrates gas production, two-phase resistance, loop pressure loss and membrane support effect based on compensated multi-source data, and perform state observation to output the transmembrane differential pressure estimate;

[0022] Step 300: Based on the transmembrane differential pressure estimation and combined with the membrane and stack tolerance curves, set an adaptive grading threshold and differential pressure change rate limit, perform prediction and evaluation, determine the current grading level and triggering cause, and obtain the grading triggering decision;

[0023] Step 400: Based on the hierarchical trigger decision, with the goal of minimizing the transmembrane differential pressure gradient, the opening and duration of the cathode and anode release valves are controlled in a coordinated manner, and unilateral transitions are restricted. The transmembrane differential pressure estimate and uncertainty are updated in real time in a closed loop to meet the requirements of the safety belt and hysteresis, and the coordinated release execution result is obtained.

[0024] Step 500: When valve jamming, abnormal valve position, or key sensor drift causes the coordinated release execution result to deviate from the target, the counter-side enhanced release is triggered based on transmembrane differential pressure estimation and graded triggering decision to implement derated operation and forced pressure equalization, thus obtaining the failure safety handling result;

[0025] Step 600: After both the coordinated release execution results and the failure safety handling results indicate that the transmembrane differential pressure is stable within the safety zone, the model parameters, thresholds, and control gains are updated using compensated multi-source data and historical records of transmembrane differential pressure estimation, and event archiving is completed, resulting in adaptive reset and online optimization results.

[0026] Furthermore, the specific implementation process of step 100 is as follows:

[0027] This embodiment first clarifies the minimum multi-source dataset and time organization method related to transmembrane differential pressure to ensure the traceability of the acquisition entry point and the measurement quality. Specifically, this embodiment, based on the transmembrane differential pressure formation mechanism and loop coupling relationship, determines the minimum multi-source dataset, including four types of measurements: pressure, flow, temperature, and current. During the startup phase, a unified time reference is generated, and the sampling frequency, timestamp format, and maximum allowable clock deviation for each channel are configured to form a time-aligned sampling configuration. Under this configuration, parallel acquisition and clock alignment are performed, recording missing and abnormal annotations for each measurement, and outputting time-aligned raw multi-source data. Online bias estimation and drift correction are performed on the raw multi-source data. Physical constraints and redundancy consistency checks are used to determine the bias term and scaling factor. A recursive update strategy for redundant channels is used to perform sliding updates on the bias and scaling factor, and out-of-limit or abrupt data are removed or rolled back to obtain bias-corrected multi-source data. Subsequently, without changing the relevant dynamics of the transmembrane differential pressure, denoising and filtering smoothing are performed to filter out electromagnetic interference and high-frequency artifacts. Parameter selection ensures that the response bandwidth covers the dominant frequency and rising edge characteristics of the transmembrane differential pressure, outputting filtered and smoothed multi-source data.

[0028] To ensure consistency with the target update cycle of subsequent differential pressure estimation, this embodiment performs resampling and physical constraint interpolation based on the bias-corrected and filtered smoothed data. The resampling strategy uses a fixed-period grid aligned with the target estimation cycle. When short-term missing data or heterogeneous time delays occur, constraints are applied to the interpolated values ​​according to mass conservation, energy conservation, and reasonable upper and lower limits to avoid introducing non-physical fluctuations and output consistent multi-source data. Based on this, this embodiment performs cross-channel confidence weighted fusion. For multi-channel redundant sources of similar measurements, channel-level confidence is constructed using channel historical stability, instantaneous residuals, physical coupling consistency, and environmental sensitivity. Conflicting measurements are constrained based on coupling relationships to ensure that the fusion results satisfy the linkage relationship between flow rate and pressure, temperature and physical property parameters, and the consistency between current and gas production rate, resulting in consistent multi-source data and channel-level confidence.

[0029] This embodiment ultimately standardizes and encapsulates the fused, consistent multi-source data, corresponding confidence levels, and processing metadata to form a compensated multi-source data input for differential pressure estimation. The encapsulated content includes key metadata such as time base and resampling period, bias and scaling factor snapshots for each channel, filter type and bandwidth, interpolation markers and constraint usage records, channel confidence weights, and conflict resolution residuals. This supports the traceability, verifiability, and parameter reproducibility of the subsequent differential pressure estimation module. This input is directly used to construct a differential pressure estimation model that integrates gas production, two-phase resistance, loop pressure loss, and membrane support effects.

[0030] Furthermore, the specific implementation process of step 200 is as follows:

[0031] This embodiment decomposes the transmembrane differential pressure mechanism and constructs an identifiable parameter set based on compensated multi-source data and stack structure parameters. Specifically, this embodiment decomposes the transmembrane differential pressure into four parts: gas production phase holdup effect, two-phase resistance, loop pressure loss, and membrane support feedback. These correspond to the phase holdup change term caused by gas production rate and dissolution-precipitation, the additional pressure drop term caused by relative permeability and viscosity ratio in the two-phase region, the friction loss term along pipelines and valves and the support feedback term generated by membrane mechanical and electroosmotic coupling, respectively. Based on this, this embodiment establishes a minimum sufficient parameterization according to the conservation of energy and mass, and writes the pressure drop contribution of each part as a linear or quasi-linear mapping to the identifiable parameters. This includes, but is not limited to, the equivalent permeability coefficient of the two-phase region, the shape parameter of the saturation-relative permeability relationship, the temperature and gas-liquid property correction coefficient, the equivalent friction and local resistance coefficient of the loop, the membrane support stiffness and electroosmotic coupling gain, etc., and gives the physical boundaries and monotonicity constraints of the parameters, forming a mechanism decomposition framework and parameter prior set.

[0032] This embodiment constructs a coupled mechanism model based on the mechanistic decomposition framework, and achieves sub-model coupling with unified dimensions, unified time base, and consistent interface variables. Specifically: This embodiment establishes a gas production-phase holdup sub-model, deriving the gas production rate from current and temperature, and obtaining local saturation and phase holdup through phase equilibrium approximation; it establishes a two-phase resistance sub-model, mapping saturation to relative permeability and equivalent viscosity, and giving the channel section pressure drop; it establishes a loop pressure loss sub-model, calculating friction loss and local losses based on geometry and flow rate; and it establishes a membrane support effect sub-model, mapping the transmembrane electro-fluid-force interaction to equivalent pressure difference feedback using membrane support stiffness and electroosmotic coupling gain. This embodiment defines a state vector including saturation components, equivalent permeability and property corrections, slowly varying parameters such as membrane support and coupling gain, and transmembrane differential pressure; and defines an observation vector including compensated multi-source measurements and a derivable loop pressure difference proxy. To balance process and measurement uncertainties, this embodiment constructs a robust observer. Through a recursive estimation strategy that combines uncertainty ellipsoids or interval limits with gain scheduling, it performs online consistency checks on the initial state and noise covariance, outputs the initial transmembrane differential pressure estimate and uncertainty, and implements threshold suppression and hysteresis processing on abnormal residuals to ensure the stability and interpretability of the estimate.

[0033] This embodiment employs residual and uncertainty-driven online learning to recursively correct and redistribute weights for key mechanistic parameters, and completes reinjection and re-observation to output robust criteria. Specifically, based on the statistical characteristics and sensitivity matrix of the normalized residuals, this embodiment selects a subset of parameters that contribute significantly to transmembrane differential pressure and have sufficient identifiability. It uses an incremental update law constrained by physical boundaries and monotonicity for small-step recursion, introducing a forgetting factor when necessary to address operational drift. For conflict sources, it uses a combined weighting of channel confidence and mechanistic consistency to suppress the misleading effect of single measurement mismatch on parameters. Once the residual distribution has stabilized and the uncertainty has converged, this embodiment reinjects the adaptively updated mechanistic parameters into the coupled mechanistic model, re-observes on the same time base, and outputs a robust transmembrane differential pressure estimate as input for subsequent threshold setting and control criteria. It also records parameter snapshots, residual statistics, and covariance evolution to support traceable verification and subsequent version solidification.

[0034] Specifically, this embodiment provides a coupled mechanism model based on mechanism decomposition and its unified interface construction method. It takes compensated multi-source data as input and outputs a transmembrane pressure difference estimate for subsequent state observation and control criteria. First, this embodiment establishes a sub-model of gas production and phase holdup: the gas production volumetric flow rate is calculated using compensated current and temperature, and after thermophysical property correction, it is converted into the gas volume fraction increment along the channel path; considering bubble nucleation, coalescence, removal, and wall adhesion effects, an effective utilization coefficient characterizes the above combined effects, and an upper limit pruning operator restricts the phase holdup to not exceed the physically achievable upper limit; since the phase holdup obstructs the available cross-section of the sub-channel, a usable porosity and cross-section reduction coefficient caused by the gas phase are defined to obtain the reduced liquid phase volumetric flow rate; simultaneously, a time constant formed by the combination of phase holdup convection and local hysteresis is introduced to characterize the spatial and temporal hysteresis of gas production dynamics.

[0035] Secondly, driven by the phase content, this embodiment jointly establishes a two-phase resistance and loop pressure loss sub-model: the two-phase frictional pressure drop is calculated over the characteristic channel length, and the single-phase pressure drop is corrected by the two-phase friction amplification factor. The amplification factor is given by classically related coefficients and parameters, and the dimensions are unified by the apparent flow velocity, cross-sectional area and hydraulic scale of the mixed phase. The loop pressure loss is composed of the superposition of friction along the path and local losses of valves, which is equivalent to the loop-level comprehensive pressure loss. The linear part is determined by the equivalent linear resistance coefficient of the loop and the mixed phase volumetric flow rate, and the nonlinear part is given by the equivalent valve pressure loss function determined by the opening of the anode and cathode valves. This function is obtained by calibration test and satisfies monotonicity and smoothness, which is convenient for numerical solution and gain scheduling.

[0036] Furthermore, this embodiment establishes a membrane support effect sub-model: the mechanical response of the membrane and support structure to the transmembrane pressure difference is equivalent to the coupling relationship of pressure difference input, small deformation, deformation time derivative, and back feedback; the equivalent stiffness and equivalent damping can be adaptively updated with temperature and membrane water content to reflect the changes in mechanical properties caused by material aging and water content coupling; the additional weak feedback formed by hysteresis and springback is described by a small gain coefficient and equipped with a hysteresis time constant to constrain the phase delay; in order to achieve consistency between thermodynamic and mechanical dimensions, this embodiment introduces a proportionality coefficient to unify pressure difference and deformation dynamics, so that the back feedback term can be superimposed on the fluid pressure difference input under the same metric.

[0037] Subsequently, this embodiment unifies the dimensions and time bases of the three sub-models and establishes interface variables and directional specifications: all fluxes are positively expressed as volumetric flow rate in the upward direction of the channel, pressure drop is positively expressed as inlet minus outlet, and deformation is positively expressed as the small displacement of the membrane towards the low-pressure side caused by pressure; the interface variables of each sub-model, including phase content, reduced liquid flow rate, miscibility density, miscibility velocity, loop pressure loss, valve pressure loss, and membrane reverse feedback pressure difference, are all aligned with a unified timestamp and sampling period.

[0038] Finally, this embodiment uses a unified interface to couple the sub-models in a consistent manner, and constructs an overall mechanism model oriented towards state observation: the transmembrane pressure difference is determined by the two-phase frictional pressure drop, the loop integrated pressure loss and the membrane support back feedback, and is recursively calculated on the same time base; in order to avoid numerical instability, this embodiment introduces boundary constraints and smooth saturation treatment for the shading coefficient, amplification factor and valve pressure loss function.

[0039] Phase holdup refers to the volume fraction of the gas phase within the channel, reflecting the gas-liquid ratio and determining the effective flow cross-section; the upper limit cutoff value refers to the maximum achievable phase holdup determined by geometry and physical properties, used to prevent non-physical overflow; equivalent porosity refers to the usable flow volume fraction after considering structure and wetting conditions; usable porosity due to the gas phase refers to the remaining volume fraction available for liquid phase flow at a given phase holdup; miscibility density and miscibility velocity are the volume fraction-weighted densities of the gas and liquid phases and the channel average velocity, respectively; the two-phase friction amplification factor is used to amplify the single-phase frictional pressure drop to two-phase conditions, and its parameters are determined experimentally or given by authoritative sources; the loop equivalent linear drag coefficient is used to characterize the loop under small Reynolds conditions or... Equivalent resistance within the linear interval; the equivalent valve pressure loss function describes the nonlinear effect of valve opening on pressure loss, and must satisfy the monotonic characteristic that the larger the opening, the smaller the pressure loss; membrane reverse feedback pressure difference refers to the equivalent reverse pressure difference applied to the fluid side by the deformation of the membrane and support structure after bearing the pressure difference and through structural constraints; equivalent stiffness and equivalent damping are used to describe the linearized mechanical response of the membrane support within a small displacement range, which changes slowly with temperature and membrane water content; the hysteresis time constant is used to characterize the viscoelasticity and rebound effect of the membrane material; the proportionality coefficient is used to unify the dimensions of pressure difference and deformation variables, so that the coupling terms can be superimposed under the same dimension; the membrane water content index is used to reflect the membrane water content state and affect the equivalent stiffness and damping.

[0040] The sources and methods for determining the values ​​of the above parameters are as follows: current, temperature, pressure, and flow rate are obtained from compensated multi-source data; geometric parameters, including channel length, cross-sectional area, and hydraulic dimensions, are provided by the reactor structure; physical property parameters, including gas-liquid density and viscosity, are provided by the database or in-service estimation; effective utilization coefficient, shielding coefficient, amplification factor, correlation coefficient, loop equivalent linear resistance coefficient, equivalent valve pressure loss function, equivalent stiffness, equivalent damping, weak feedback coefficient, hysteresis time constant, and proportional coefficient are obtained through type testing, step and sweep frequency excitation, or in-service identification, and are subject to physical boundary constraints and monotonicity constraints, with typical value ranges based on calibration reports; intermediate variables such as miscibility density, miscibility velocity, and phase content are calculated from the above basic quantities according to unified rules. The parameters serve the following functions: the effective utilization coefficient is used to correct the gas removal efficiency at the microscale; the shading coefficient reflects the reduction of the effective cross-section by bubbles; the amplification factor and correlation coefficient are used for nonlinear amplification of the two-phase frictional pressure drop; the loop equivalent linear resistance coefficient and the valve pressure drop function jointly determine the loop pressure drop; the equivalent stiffness and damping determine the strength and phase of the membrane back feedback; the weak feedback coefficient and hysteresis time constant are used to characterize the material rebound and memory effects; and the proportionality coefficient ensures the dimensional consistency of the coupling terms. Through the above steps, the coupling mechanism model formed in this embodiment can stably and reproducibly output a real-time estimate of the transmembrane pressure difference under known input conditions, and provide verifiable mechanistic support for subsequent observer design, threshold setting, and coordinated release control.

[0041] Specifically, this embodiment first constructs a unified diagnostic input within each observation period. This embodiment aligns the predicted quantities of each mechanistic sub-model at the same timestamp with the corresponding measured quantities from compensated multi-source data, using a unified time base and sampling period for synchronization to ensure a one-to-one correspondence. For each observation, the residual is calculated, and its corresponding uncertainty is scaled to obtain the normalized residual. The uncertainty originates from the process uncertainty of the observer output and the measurement uncertainty obtained from the measurement chain calibration. The normalized residual is used to eliminate dimensional and range differences, allowing direct comparison of errors between different channels. This embodiment calculates a consistency index on the normalized residual within a sliding time window to characterize the degree of matching between the model output and the measurement. The consistency index integrates residual magnitude, directional stability, and physical constraint compliance, and employs hysteresis thresholds and gentle pruning for sudden outliers to avoid misleading learning. To reflect channel quality differences, this embodiment introduces channel reliability, which is a weighted fusion of normalized residuals and consistency indicators to obtain a single unified diagnostic input that can be compared across channels. The channel reliability is jointly evaluated by recent drift, sensor health and mechanism consistency, and is updated over time to maintain sensitivity to changes in environment and operating conditions.

[0042] This embodiment, after obtaining the unified diagnostic input, performs uncertainty decomposition on both the process and measurement sides and generates a learning schedule set to control the learning step size and gain. Specifically, based on the process and measurement uncertainty priors provided by the observer, this embodiment decomposes the unified diagnostic input into process and measurement contributions using the minimum deviation principle. When the measurement contribution is dominant, it is determined that the measurement chain bias or transient interference is dominant, the learning step size is suppressed, the gain is reduced, and the update priority of that channel is lowered. When the process contribution is dominant, it is determined that the model structure or mechanism parameter bias is dominant, the learning step size is relaxed, the gain is increased, and the update priority of highly sensitive parameters is increased. Based on this, this embodiment automatically generates a learning schedule set, which includes the target step size, gain weight, allowed update frequency, priority label, and boundary strategy for each parameter to be updated. The boundary strategy includes three types: physical feasible region constraints, monotonicity constraints, and stability constraints, used to prevent out-of-bounds updates and numerical discontinuities. In addition, this embodiment configures priority queues for computing resources for different channels. When the computing budget is limited, parameter updates that contribute more to the improvement of consistency indicators are executed first. The learning schedule set is archived periodically to record the source of step size and gain, channel credibility weight and uncertainty decomposition results for auditing and reproduction.

[0043] This embodiment calculates the sensitivity of each sub-model output to candidate parameters based on a unified diagnostic input within the current observation period, and performs closed-loop updates and channel weight redistribution using weighted least squares. Sensitivity is obtained analytically or through numerical perturbation, with the output being the local rate of change of the observed parameters. This embodiment projects the sensitivity vector into the physically feasible region, eliminating directions that conflict with stability and monotonicity, and selecting identifiable directions with good condition numbers based on the learning schedule set to obtain the parameter sensitivity. Subsequently, this embodiment constructs a weighted least squares objective, with weights jointly determined by the gain weights of the learning schedule set, channel confidence, and consistency index, and incorporates small-amplitude regularization to suppress parameter collinearity and ill-conditioned amplification. After obtaining the parameter increment, step size constraints and boundary saturation are applied, and trust regions or line search are used when necessary to avoid overshoot. Simultaneously, this embodiment performs a consistency-driven normalized redistribution of the mechanistic channel weights: channels that significantly reduce the unified diagnostic input in the current period are appropriately weighted, while channels that do not improve or worsen are appropriately weighted, in order to emphasize more reliable information sources in subsequent observations; the weight redistribution follows the constraints of a sum of one and a minimum weight lower bound to prevent information loss.

[0044] Furthermore, the specific implementation process of step 300 is as follows:

[0045] This embodiment first constructs effective differential pressure data based on transmembrane differential pressure estimates, which can be used for threshold generation and judgment. This embodiment performs a two-stage processing on the continuous estimation sequence: first, a smoothing filter covering the dominant operating condition changes with a bandpass response bandwidth is used to remove high-frequency artifacts; then, a consistency check is used to eliminate outliers introduced by channel drift or short-term mismatch. The consistency check, based on the uncertainty output by the aforementioned observer and the unified diagnostic input, verifies the compliance of the differential pressure mean, variance, and jump amplitude within each time window. After verification, a usable data sequence and interval range are generated, and the effective differential pressure data is output. Subsequently, this embodiment reads the tolerance curves of the membrane and the stack, including the allowable pressure difference and allowable rate of change of the material and structure under different temperatures, moisture contents, and aging conditions. To eliminate the difference in conditions, this embodiment unifies the dimensions and operating conditions of the tolerance curves with the current operating conditions. Specifically, this includes mapping the temperature, moisture content, and pressure level to reference conditions consistent with the current cycle, and introducing margin parameters to the allowable values ​​to cover manufacturing discreteness and in-service degradation. The three boundary functions of safety, early warning, and risk, as well as the corresponding margins, are extracted to form tolerance boundary parameters for subsequent threshold and rate limit generation.

[0046] This embodiment generates multi-level differential pressure thresholds and differential pressure change rate limits based on the relative distance and uncertainty between effective differential pressure data and tolerance boundary parameters. Specifically, this embodiment calculates the distance between the current differential pressure center value and each level of boundary function, and constructs confidence intervals based on the estimated uncertainty, automatically increasing the safety margin for cases with small distances and high uncertainty. On this basis, corresponding differential pressure threshold sets and differential pressure change rate limit sets are generated according to three levels: safety, warning, and risk. The rate limit is used to capture dynamic overspeed situations that rapidly cross the boundary. To suppress frequent switching, this embodiment designs entry and exit values ​​for each threshold and rate limit in pairs, forming a hysteresis interval, and performs time-domain smoothing on the threshold trajectory to avoid jitter caused by short-term noise. For scenarios where the boundary function is condition-dependent, this embodiment introduces an adaptive scaling factor, so that the threshold automatically tightens with the operating condition under high temperature or high current density, and moderately relaxes under low load and low temperature, while constraining the scaling factor to change within the calibration range to ensure verifiability and traceability. After the above processing, the threshold and rate limit set are output, and the distance metric, uncertainty, scaling factor and hysteresis settings used during generation are recorded for the next cycle of iteration update.

[0047] This embodiment simultaneously evaluates both static and dynamic overspeed criteria within the current observation period to complete the classification and trigger cause identification. Specifically, this embodiment uses the current value of the effective differential pressure data and the short-term extrapolated value of the most recent time window as input. The extrapolation adopts a stable local trend model and weights the extrapolation uncertainty. The static criterion detects whether the current value exceeds the threshold at each level and considers the hysteresis conditions for entry and exit. The dynamic criterion detects whether the rate of change of differential pressure exceeds the rate limit of the corresponding level and responds to dynamic overspeed with higher priority to avoid hysteresis risk. When both static and dynamic overspeed are triggered simultaneously, this embodiment selects the more conservative level according to the preset priority and the degree of proximity to the boundary. To pinpoint the triggering cause, this embodiment correlates and analyzes the unified diagnostic input, sub-model residual distribution, and trend information. The trigger is attributed to one or a combination of factors, including approaching tolerance boundaries, sudden rate increases, abrupt changes in operating conditions, or decreased measurement reliability. It outputs actionable triggering decisions and handling suggestions, including threshold levels, action time limits, coupling constraints on anode and cathode release, and rate suppression strategies. Simultaneously, it records the current effective differential pressure data, tolerance boundary parameters, extrapolation results, and final criteria for adaptive adjustment of thresholds and rate limits in the next cycle, and serves as the basis for event archiving and auditing. Through these steps, this embodiment can achieve adaptive, tiered triggering decisions based on operating conditions and uncertainties without relying on conventional fixed thresholds, reducing false and missed triggers, and ensuring stable and controllable transmembrane differential pressure within safety limits and hysteresis requirements.

[0048] Furthermore, the specific implementation process of step 400 is as follows:

[0049] Upon receiving the graded trigger decision, this embodiment sets the current control objective as minimizing the transmembrane differential pressure gradient and generates an executable constraint set under the same time reference. Specifically, based on the effective differential pressure data and tolerance boundary parameters output in the previous cycle, this embodiment sets the upper and lower boundaries of the safety belt and the hysteresis bands for entry and exit, requiring the transmembrane differential pressure to converge towards the center of the safety belt within the control window and not to cross the outer boundary. To suppress transient shocks, this embodiment sets the maximum allowable rate of change and the maximum allowable transition amplitude, simultaneously limiting the time derivative and discrete increment of the differential pressure. To avoid unilateral pressure abrupt changes introduced by the uncoordinated actions of the valves on both sides, this embodiment provides unilateral transition restrictions, constraining the amplitude and time proportion of independent action of any valve on one side, and forcibly executing the coupling ratio range and phase synchronization window of the cathode and anode openings, so that the releases on both sides overlap in time and satisfy the upper and lower limits of the ratio in amplitude. The above-mentioned safety belt, hysteresis, rate and amplitude constraints, and unilateral transition restrictions constitute the control objective and constraint set, and form a traceable configuration snapshot for current solution and post-event verification.

[0050] This embodiment calculates the linkage opening degree and duration of the cathode and anode release valves based on the control objective and constraint set, and performs closed-loop monitoring within the control window. Specifically, this embodiment uses minimizing the transmembrane differential pressure gradient as the objective function and employs piecewise convex time-domain rolling optimization to jointly solve for the opening degree, holding time, and slope of the cathode and anode valves in each sub-interval. To avoid actuator saturation and mechanical shock, this embodiment limits the superposition rate of opening degree changes and amplitude saturation, and applies a smoother to the solution results to generate a traceable opening degree trajectory. The obtained valve linkage control command includes the opening degree trajectories on both sides, the trigger time, the minimum holding time, and the allowed fine-tuning step size. In this embodiment, control commands are sent to the actuator, and pressure, flow, temperature, and valve position feedback are collected at high frequency in the control window. At the same time, the valve drive current or stroke is recorded for health assessment. During the data collection process, this embodiment detects in real time whether the safety belt boundary is touched, whether there is a sudden increase in the differential pressure change rate, and whether there are signs of valve position hysteresis or jamming. If any protection condition is triggered, a slight retreat is immediately executed or the system enters a safety sub-mode to limit further release, and the event is marked to proceed to the next stage of estimation update and judgment.

[0051] This embodiment updates the transmembrane differential pressure estimate and uncertainty in real time based on execution feedback and process data, and completes compliance verification and result archiving. Specifically, this embodiment performs outlier identification and gentle removal on incremental data within the control window, recursively observes transmembrane differential pressure and uncertainty using a unified time base, and adds confidence weighting to valve position anomalies and sensor drift. When the estimate shows proximity to the safety zone boundary or hysteresis zone edge, this embodiment triggers a fine-tuning strategy according to priority, reducing the valve opening step size and extending the holding time until the differential pressure change rate falls back to within the limit. After completing the window control, this embodiment checks whether the transmembrane differential pressure is stably located within the safety zone and whether the gradient has achieved the minimum objective. If not, it continues iteratively in the next sub-window. When the conditions are met, this embodiment records the final opening of the anode and cathode, duration of action, number of adjustments, trigger and rollback events, differential pressure and uncertainty trajectory, and generates reset conditions and initial values ​​for the next cycle, including hysteresis state position, estimated covariance scaling factor, and valve position baseline bias. The above records serve as the results of collaborative release execution and archived data, providing verifiable and reproducible basis for subsequent graded judgment iterations, adaptive threshold updates, and anomaly handling.

[0052] Furthermore, the results of the coordinated release execution include:

[0053] Control trajectory, final differential pressure, stability determination, and reset conditions.

[0054] Furthermore, the specific implementation process of step 500 is as follows:

[0055] This embodiment continuously monitors valve response, valve position readback, key sensor consistency, and coordinated release execution results online during the coordinated release control operation. This enables timely identification of valve jamming, abnormal valve position, or sensor drift, and determines deviations from the transmembrane differential pressure target and violations of safety zones and hysteresis. Specifically, this embodiment compares the valve drive current, valve position readback, and expected opening trajectory within each control window. A dual-threshold strategy using a delay window and amplitude error is employed to identify jamming and hysteresis. If the valve position readback is consistently lower than expected and the drive current abnormally increases, it is determined to be jamming; if the valve position readback oscillates outside the allowable error band, it is determined to be an abnormal valve position. Regarding the consistency of key sensors, this embodiment employs multi-channel cross-checking and mechanistic residual consistency testing: when the difference between channels exceeds the confidence interval and the mechanistic residual continuously deviates in the same direction, drift is determined to exist. Subsequently, this embodiment uses the transmembrane differential pressure estimation as a benchmark to calculate the distance between the center of the seat belt and the boundary. It combines the hysteresis state indicator and the change rate limit to check whether it exceeds the limit or speeds, and outputs the abnormal judgment and deviation level accordingly. The deviation level is divided into mild, moderate and severe, and this level serves as the triggering condition and intensity scale for subsequent treatment.

[0056] In this embodiment, after an anomaly is confirmed, based on the current transmembrane differential pressure estimate and the output graded triggering decision, enhanced release is triggered on the opposite side at the corresponding level, and derating operation constraints and forced pressure equalization target ranges are set simultaneously. Specifically: when a valve on one side is stuck or the valve position is abnormal, causing the coordinated release to fail to achieve the expected result, this embodiment immediately performs enhanced release on the non-failed side, increasing the opening degree and minimum holding time, and limiting the maximum slope to avoid secondary impact; to prevent drastic fluctuations in transmembrane differential pressure caused by unilateral transitions, this embodiment maintains the lower limit of the linkage ratio and the phase synchronization window, and even if enhanced release is performed on the opposite side, the amplitude and duration of unilateral transitions must not be exceeded. At the same time, this embodiment generates a set of derating operation constraints based on the deviation level: under slight deviation, the upper limit of power and circulating flow rate is slightly reduced and a change rate limit is set; under moderate deviation, the load and flow rate are further tightened and the control step size is shortened; under severe deviation, a conservative mode is entered, power and current density are forcibly limited, and the tolerable range of flow path pressure loss and valve pressure loss is narrowed. To ensure that the recovery target is clear and verifiable, this embodiment defines a forced equalization target range, that is, the transmembrane differential pressure should return to the convergence band near the median value of the safety belt within a limited time, and the rate of change within the band should be kept below the limit value, forming a set of constraints for contralateral enhanced release and derating, providing clear and auditable boundary conditions for the execution process.

[0057] This embodiment performs enhanced release and simultaneous derating operation on the non-failed side based on the contralateral enhanced release and derating constraint set, and updates the transmembrane differential pressure estimate and uncertainty in real time in a closed loop, completing compliance verification and outputting the handling results. Specifically, this embodiment issues the enhanced release opening trajectory and holding time, superimposes rate and amplitude limits, and collects pressure, flow, valve position, and drive signals at high frequency within the control window to form process feedback; after smoothing out anomalies and verifying consistency in the process feedback, it recursively updates the transmembrane differential pressure estimate and uncertainty, and checks whether it has entered the equalization target range and meets the safety belt and hysteresis requirements at the end of each sub-window; if not, it continues to release on the contralateral side according to the step-by-step strategy, and further derating according to the preset curve until the rate of change and boundary distance recover to within the safety threshold; when sensor drift signs persist or valve position hysteresis is not resolved, this embodiment simultaneously provides retesting suggestions, including zero-point retesting, bypass channel comparison, or valve stroke reset test. Once the transmembrane differential pressure stabilizes within the target pressure equalization range and meets the hysteresis condition, this embodiment generates a failure safety handling result, which includes the execution trajectory, pressure equalization status, derating configuration, and reset conditions. The above results are archived together with the current data for subsequent cycle adaptive parameter tuning and event auditing, ensuring that the transmembrane differential pressure can still be controlled within a safe range and traceability can be maintained in the event of valve or sensor failure.

[0058] Furthermore, the specific implementation process of step 600 is as follows:

[0059] In this embodiment, after both the collaborative release execution result and the failure safety handling result are completed, a stability consistency check is first performed to determine whether to enter the reset and online optimization stage. Specifically, this embodiment applies a sliding window statistical method under a unified time reference to the estimated trajectory of the transmembrane differential pressure, calculates the center value, fluctuation amplitude, and rate of change within the window, and performs compliance checks based on the upper and lower boundaries of the safety zone and the hysteresis conditions for entry and exit. The requirements are that the center value is continuously within the safety zone, the fluctuation amplitude does not exceed the limit, the rate of change is continuously below the limit, and the dynamic overspeed criterion is not triggered. To eliminate short-term false stability, this embodiment introduces minimum maintenance duration and minimum data coverage constraints to ensure that the stable state covers several complete control sub-windows and is consistent with the "pressure equalization achieved" and "no protection triggered" flags in the collaborative release execution result and the failure safety handling result. At the same time, a cross-consistency check is performed using valve position readback, drive current, and unified diagnostic input of key sensors. If there is residual valve position hysteresis, sensor reliability degradation that has not been recovered, or abnormal markers that have not been cleared, it is determined that the conditions for entering the reset and optimization stage are not met. The stability confirmation conclusion obtained through the above verification will be used as the admission basis for subsequent data aggregation and online updates.

[0060] After obtaining stability confirmation, this embodiment aggregates compensated multi-source data and constructs a standardized training dataset. Subsequently, online updates of parameters, thresholds, and control gains are performed, and the data is solidified and initialized through offline verification and online sampling. Specifically, this embodiment collects observations such as current, temperature, pressure, flow rate, valve position readback, drive current, transmembrane differential pressure estimation, and uncertainty using a unified interface. Transitional data containing "protection action" and "failure handling" markers are removed. A standardized training dataset is formed using timestamp alignment, unit unification, and missing measurement interpolation. Simultaneously, unified diagnostic input, channel reliability, and residual statistics are retained for weight allocation. In the online update phase, this embodiment uses a weighted least squares closed-loop incremental update for the mechanistic parameters within the published learning scheduling set framework. For the grading thresholds, an adaptive scaling update based on tolerance boundary margin and historical approximation distance is used. For the control gain, small-step rolling tuning with added trust region constraints ensures that the update amount is constrained by physical boundaries, monotonicity, and stability. After the update is completed, this embodiment performs a two-step verification: offline verification uses historical window playback to check the changing trends of the safety band and hysteresis compliance and overshoot rate; online sampling verification uses sparsely injected small perturbations to check whether the closed-loop convergence speed and overshoot are controlled. After both pass, a fixed snapshot and initialization configuration are generated, including the updated model parameters, grading thresholds, control gain, boundaries and weights, as well as the initial value of the observer covariance and hysteresis state bits, which are used as the starting baseline for the next cycle.

[0061] After solidification and initialization, this embodiment performs event archiving and reset, and outputs adaptive reset and online optimization results. Specifically, this embodiment performs end-to-end archiving of the input, update process, and verification results of this process. The archived content includes a list of data sources and time ranges, stability confirmation conclusions, summary statistics of standardized training datasets, parameter and threshold update increments, control gain tuning records, evidence of pass for offline verification and online sampling verification, and anomaly and rollback records. At the same time, it generates snapshot version identifiers, parameter and threshold lists, control gain and observer initial value lists, recovery strategies, and rollback criteria to ensure reusability and auditability in subsequent cycles. This embodiment then performs a reset operation, switching the control mode from protection or derating state back to normal cooperative release mode, loading the initialization configuration and clearing resolved anomaly markers, while retaining the silence duration of key alarms and the debouncing settings for re-triggering thresholds. To ensure a smooth transition, this embodiment enables conservative gain and tightens rate limits in the first control window after reset, and gradually restores to normal gain after confirming that the transmembrane differential pressure remains stable within the safety zone and hysteresis is established. Finally, this embodiment outputs adaptive reset and online optimization results, including snapshot version, parameter and threshold list, control gain, verification record and reset status, and registers the results to the version management and event audit system for subsequent operation and retraining.

[0062] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. The same or similar parts between the various embodiments can be referred to each other.

[0063] This document uses specific examples to illustrate the principles and implementation methods of the present invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of the present invention. Furthermore, those skilled in the art will recognize that, based on the ideas of the present invention, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. An AEM anode-cathode safe release control method based on differential pressure estimation, characterized in that, The method comprises the following steps: Collecting multi-source operation data related to transmembrane differential pressure and performing online bias and noise compensation to obtain compensated multi-source data; Building a differential pressure estimation model integrating gas production, two-phase resistance, loop pressure loss and membrane support effect based on the compensated multi-source data and performing state observation to output transmembrane differential pressure estimation; Setting adaptive grading threshold and differential pressure change rate limit according to the transmembrane differential pressure estimation and combining membrane and stack tolerance curve and performing prediction evaluation to determine current grading level and trigger cause and obtain grading trigger decision; Controlling the opening degree and duration of cathode and anode release valves in linkage according to the grading trigger decision to minimize transmembrane differential pressure gradient and limiting unilateral transition, and updating transmembrane differential pressure estimation and uncertainty in real time to meet safety band and hysteresis requirements to obtain coordinated release execution result; When the valve is stuck, the valve position is abnormal or the key sensor drifts, triggering the opposite side enhanced release to implement derating operation and forced equalization based on the transmembrane differential pressure estimation and grading trigger decision to obtain failure safety disposal result; When the coordinated release execution result and the failure safety disposal result both show that the transmembrane differential pressure is stable in the safety band, updating the model parameters, threshold and control gain using the historical records of the compensated multi-source data and the transmembrane differential pressure estimation and completing event archiving to obtain adaptive reset and online optimization result.

2. The AEM anode and cathode safe release control method based on differential pressure estimation according to claim 1, characterized in that, The method comprises the following steps: Collecting multi-source operation data related to transmembrane differential pressure and performing online bias and noise compensation to obtain compensated multi-source data, comprising: Defining the minimum multi-source data set required for transmembrane differential pressure and completing time synchronization configuration, and establishing a unified time reference to obtain time-aligned sampling configuration; wherein the minimum multi-source data set includes pressure, flow, temperature and current; Collecting and clock aligning according to the time-aligned sampling configuration, combining missing and abnormal annotations to generate traceable original sequences to obtain time-aligned original multi-source data; Performing online bias estimation and drift correction based on physical constraints and redundancy consistency, and recursively updating bias and proportionality coefficients using redundant channels to obtain bias-corrected multi-source data; According to the bias-corrected multi-source data and using electromagnetic interference and retaining transmembrane differential pressure related dynamics to obtain filter-smoothed multi-source data; Performing resampling and physical constraint interpolation consistent with the target estimation period to obtain resampling-consistent multi-source data; Developing cross-channel confidence weighted fusion, solving conflict measurements according to physical coupling relationships and outputting channel-level confidence to obtain fusion-consistent multi-source data; 3. The AEM anode and cathode safe release control method based on differential pressure estimation according to claim 1, characterized in that, Packaging fusion-consistent multi-source data and corresponding confidence and processing metadata as a standard input set as input for subsequent differential pressure estimation to obtain compensated multi-source data. The method comprises the following steps: Building a differential pressure estimation model integrating gas production, two-phase resistance, loop pressure loss and membrane support effect based on the compensated multi-source data and performing state observation to output transmembrane differential pressure estimation, comprising: Decomposing transmembrane differential pressure into gas phase content rate effect, two-phase resistance, loop pressure loss and membrane support feedback based on the compensated multi-source data and stack structure parameters and abstracting into a set of identifiable parameters to obtain a mechanism decomposition framework; Based on the mechanism decomposition framework, the gas production-phase holdup, two-phase resistance, loop pressure loss, and membrane support effect sub-models are established respectively and are unified in dimension, time base, and interface variable, and the coupled mechanism model is obtained; On the coupled mechanism model, the state vector and observation vector are defined, and the robust observer with the trade-off of process and measurement uncertainty is constructed to realize recursive estimation, and the initial transmembrane pressure estimation and uncertainty are obtained; The recursive correction and weight redistribution of key mechanism parameters are performed by online learning driven by estimation residual and uncertainty, so that the model is self-adaptive to the working condition, and the updated mechanism parameters are obtained; The updated mechanism parameters are fed back to the coupled mechanism model, and the robust transmembrane pressure estimation is output as the subsequent criterion input, and the transmembrane pressure estimation is obtained.

4. The AEM anode and cathode safe release control method based on differential pressure estimation according to claim 3, characterized in that, The coupled mechanism model is obtained by establishing the gas production-phase holdup, two-phase resistance, loop pressure loss, and membrane support effect sub-models respectively and unifying the dimension, time base, and interface variable, including: Based on the compensated current and temperature in the multi-source data, the phase holdup sub-model driven by gas production rate is established, and the influence of the phase holdup sub-model on the effective cross section and flow state is abstracted as a set of identifiable parameters, and the gas production-phase holdup sub-model is obtained; Under the driving of the phase holdup, the two-phase resistance and loop pressure loss sub-models are jointly established, and the resistance-pressure loss combined sub-model is obtained; The mechanical response of the membrane and support structure to the transmembrane pressure difference is equivalent to the pressure difference, deformation, and reverse feedback term, and the stiffness and damping are allowed to be self-adaptive to the temperature and aging, and the membrane support effect sub-model is obtained; The membrane support effect sub-model, gas production-phase holdup sub-model, and resistance-pressure loss combined sub-model are executed for dimension unification and time base consistency, the interface variable and directionality specification are formulated, and the mechanism sub-model set with unified interface is obtained; According to the unified interface, the consistency of each sub-model is coupled, the overall mechanism model for state observation is constructed, and the coupled mechanism model is obtained; The expression of the gas production-phase holdup sub-model is: The expression of the resistance-pressure loss combined sub-model is: The expression of the membrane support effect sub-model is: The expression of the coupled mechanism model is: wherein, α g (t) is the gas volume fraction in the channel; α g,max is the upper clipping value of phase holdup; ∈ is the equivalent porosity; ∈ g = 1 - α g (t) is the available porosity caused by gas phase; μ l is the liquid dynamic viscosity; μ g is the gas dynamic viscosity; ρ l is the liquid density; ρ g is the gas density; ρ m (t) = α g (t) ρ g + (1 - α g (t)) ρ l is the mixed phase density; ν g is the gas volume equivalent coefficient corresponding to one electron transfer; n is the number of reaction electrons; F is the Faraday constant; η b is the effective utilization coefficient of bubble nucleation, coalescence and removal; φ deg (T(t), p(t)) is the thermophysical correction factor of temperature and pressure on gas volume flow rate; I(t) is the stack current; T(t) is the representative temperature of fluid or stack; p(t) is the average pressure in the channel; is the gas volume flow rate along the upward direction of the channel; q l (t) is the circulating liquid volume flow rate; is the equivalent liquid volume flow rate reduced by cross-section obstruction due to the presence of bubbles; κ α is the coefficient of effective flow cross-section reduction caused by gas phase obstruction; τ α is the time constant of phase holdup on the comprehensive formation of convection and local lag; clip(·) is the mathematical clipping operator; Δp tp (t) is the frictional pressure drop of two-phase flow over the characteristic channel length; φ 2 is the two-phase friction amplification factor; C χ is the Chisholm correlation coefficient; X tt is the Martinelli parameter; is the mixed phase superficial velocity; A ch is the flow passage cross-sectional area; d p is the equivalent hydraulic characteristic dimension; L ch is the characteristic channel length; Δp mem (t) is the equivalent reverse feedback pressure difference of membrane-supporting structure on the transmembrane pressure difference; ξ(t) is the equivalent small deformation variable of membrane; is the time derivative of deformation variable; k m (T, λ) is the equivalent membrane-supporting stiffness related to temperature T and membrane moisture content λ; c m (T, λ) is the equivalent damping associated with T, λ; k fb is the additional weak feedback coefficient formed by hysteresis and spring-back effect; τ m is the membrane mechanical response hysteresis time constant; ζ m is the proportional coefficient to unify the pressure difference and deformation dynamics; Δp act (t) is the actual fluid pressure difference input acting on both sides of the membrane; λ is the membrane water content index; Δp across (t) is the transmembrane pressure difference estimation value; Δp loop (t) is the circuit level comprehensive pressure loss; R loop is the circuit equivalent linear resistance coefficient; is the circuit mixed phase volumetric flow rate; J valve (u c (t), u a (t)) is the equivalent valve pressure loss function determined by the cathode valve opening u c (t) and the anode valve opening u a (t); u c (t) is the cathode release valve opening control input; u a (t) is the anode release valve opening control input.

5. The AEM anode and cathode safe release control method based on differential pressure estimation according to claim 3, characterized in that, The recursive correction and weight redistribution of key mechanism parameters are performed by online learning driven by estimation residual and uncertainty, so that the model is self-adaptive to the working condition, and the updated mechanism parameters are obtained, including: The normalized residual and consistency index are calculated by aligning the prediction and measurement of each sub-model, and a single diagnostic input that can be compared across channels is formed; Based on the decomposition of process side and measurement side uncertainty based on the unified diagnostic input, combined with the channel credibility, the scheduling parameters for controlling the learning step and gain are automatically generated, and the learning scheduling set is obtained; In the current observation period, the sensitivity matrix of each sub-model output to the parameters to be updated is calculated based on the unified diagnostic input, and is projected according to the physically feasible boundary, the stable and identifiable update direction is selected, and the calculation priority is assigned to different channels according to the learning scheduling set, and the parameter sensitivity is obtained; Based on the unified diagnostic input, learning scheduling set, parameter sensitivity and adopting the closed-form update of weighted least squares, the parameter increment is obtained and the step and boundary constraints are applied, the normalization redistribution of the weight of each mechanism channel is driven synchronously, and the adaptive updated mechanism parameters are obtained.

6. The AEM anode and cathode safe release control method based on differential pressure estimation according to claim 1, characterized in that, The adaptive hierarchical threshold and differential pressure change rate limit value are set and predicted according to the estimation of the transmembrane differential pressure, combined with the membrane and stack tolerance curve, the current hierarchical level and triggering reason are determined, and the hierarchical triggering decision is obtained, including: The estimation value of the transmembrane differential pressure is obtained, smoothed, denoised and uniformly checked, and the available data sequence and interval range are formed, and the effective differential pressure data are obtained; The tolerance curve of the membrane and the stack is read, the dimension and the working condition are unified, the boundary function and the margin parameter of safety, early warning and risk are extracted, and the tolerance boundary parameter is obtained; Based on the distance and uncertainty of the effective differential pressure data relative to the tolerance boundary parameter, multi-level differential pressure threshold and differential pressure change rate limit value are generated, and hysteresis and smoothing are added, and the threshold and rate limit value set are obtained; The current and short-term extrapolation are evaluated, the criterion is constructed according to static over threshold and dynamic overspeed, the priority is determined, and the current level and triggering reason are determined, and the hierarchical decision and triggering reason are obtained; The executable triggering decision and disposal suggestion are output, and the current data are recorded, which are used for adaptive adjustment of the threshold and rate limit value in the next cycle, and the hierarchical triggering decision and update record are obtained.

7. The AEM anode and cathode safe release control method based on differential pressure estimation according to claim 1, characterized in that, According to the hierarchical triggering decision, the release valve opening degree and duration of the cathode and anode are controlled in linkage with the minimum transmembrane differential pressure gradient, and the unilateral transition is limited, the transmembrane differential pressure estimation and uncertainty are updated in real time to meet the safety band and hysteresis requirements, and the cooperative release execution result is obtained, including: Based on the hierarchical triggering decision, the current control target is determined to be the minimum transmembrane differential pressure gradient, the safety band and hysteresis range are set, the unilateral transition limit and maximum change rate constraint are given, and the control target and constraint set are obtained. According to the control target and constraint set, the linkage combination of the opening degree and duration of the cathode and anode release valves is calculated, the rate and amplitude limit is added to the opening degree change, and the valve linkage control instruction is obtained. The valve linkage control instruction is sent to the actuator for control according to the set opening degree and time window; the pressure, flow and related state are collected at high frequency within the control window to detect whether the safety band boundary is touched or mutation signs appear, and the execution feedback and process data are obtained. Based on the execution feedback and process data, the transmembrane differential pressure estimation and uncertainty are updated in real time, the abnormal points are smoothed and removed, and whether the safety band and hysteresis requirements are met is checked, and the updated differential pressure estimation and uncertainty are obtained. Whether the transmembrane differential pressure gradient reaches the minimum target and remains within the safety band is evaluated, the valve opening degree, duration, adjustment times and final state are recorded, the reset condition and next cycle initial value are given, and the cooperative release execution result is obtained.

8. The AEM anode and cathode safe release control method based on differential pressure estimation according to claim 7, characterized in that, The cooperative release execution result includes: Control trajectory, final differential pressure, stability determination and reset condition.

9. The AEM anode and cathode safe release control method based on differential pressure estimation according to claim 1, characterized in that, When the valve is stuck, the valve position is abnormal, or the key sensor drifts, the cross-membrane differential pressure estimation and the hierarchical trigger decision trigger the opposite side enhanced release to implement the derating operation and forced equalization, and the failure safety disposal result is obtained, including: The valve response, valve position readback, key sensor consistency, and cooperative release execution result are monitored to identify valve sticking, abnormal valve position, or sensor drift, determine the target deviation of the cross-membrane differential pressure and the safety band and hysteresis violation, and obtain the abnormality determination and deviation level; According to the cross-membrane differential pressure estimation and the hierarchical trigger decision, the opposite side enhanced release is triggered under the corresponding level, and the derating operation constraints are set, including power, flow or load upper limit reduction and change rate limitation, and the forced equalization target interval is determined, and the opposite side enhanced release and derating constraint set are obtained; According to the derating constraint set, enhanced release is performed on the non-failed side to improve the opening and duration, limit unilateral transition, and simultaneously implement derating operation, and execution instructions and process feedback are obtained; Based on the process feedback closed loop, the cross-membrane differential pressure estimation and uncertainty are updated, and whether the equalization target interval is entered and the safety band and hysteresis requirements are met are checked; if not, the opposite side release is stepped or further derated, and sensor and actuator retest suggestions are given, and the updated differential pressure state and compliance conclusion are obtained; According to the updated differential pressure state and compliance conclusion, the failure safety disposal result is generated; wherein the failure safety disposal result includes: execution trajectory, equalization state, derating configuration and reset condition.

10. The AEM anode and cathode safe release control method based on differential pressure estimation according to claim 1, characterized in that, When the cooperative release execution result and the failure safety disposal result both indicate that the cross-membrane differential pressure is stably within the safety band, the model parameters, thresholds and control gains are updated using the compensated multi-source data and the historical record of the cross-membrane differential pressure estimation, and the event is archived, and the adaptive reset and online optimization result is obtained, including: The consistency of the cooperative release execution result and the failure safety disposal result is checked, it is confirmed that the cross-membrane differential pressure is stably within the set safety band and meets the hysteresis requirement, and it is judged whether the conditions for entering the reset and optimization phase are met, and the stability confirmation conclusion is obtained; The compensated multi-source data is aggregated to obtain a standardized training data set; Based on the standardized training data set and the stability confirmation conclusion, the model parameters, hierarchical thresholds and control gains are updated online to obtain updated model parameters, thresholds and control gains; The updated model parameters, thresholds and control gains are offline checked and online sampled verified, and after it is confirmed that they remain stable within the safety band and hysteresis conditions, they are solidified as snapshots and set as the initialization of the next period, and the solidified snapshot and initialization configuration are obtained; The input, update process and verification result of the current process are event archived, version information and recovery strategy are recorded, reset operation is performed and restored to normal operation mode, and the adaptive reset and online optimization result is obtained, including: snapshot version, parameter and threshold list, control gain, verification record and reset state.

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