Self-adaptive estimation method and system for gas quality of high-pressure hydrogen storage cylinder

Abstract

The invention provides a self-adaptive estimation method and system for the gas quality of a high-pressure hydrogen storage cylinder. The system comprises a data acquisition unit; the fusion modeling unit is used for constructing a Peng-Robinson state equation model fusing volume correction, attraction item correction and gas distribution non-uniformity compensation based on the pressure change rate, and solving the model to obtain a current gas mass estimated value; and the self-adaptive feedback unit dynamically updates at least one correction parameter related to the volume correction, the attraction item correction and the gas distribution non-uniformity compensation through an online learning mechanism according to an error signal between the real gas mass and the current gas mass estimation value, so as to realize self-adaptive optimization of the gas mass estimation. According to the method, systematic deviation caused by structural deformation and non-uniform gas distribution in the prior art is effectively avoided, and the precision of gas quality estimation under complex working conditions is remarkably improved.

Description

Technical Field

[0001] This invention relates to the field of hydrogen energy storage and measurement technology, and more specifically, to an adaptive estimation method and system for the gas mass of a high-pressure hydrogen storage cylinder. Background Technology

[0002] In aerospace, low-altitude aircraft, and marine applications, high-pressure hydrogen storage cylinders are a crucial component of energy systems. Accurate real-time estimation of their gas weight is essential for energy dispatch, safety control, and system stability. Traditional estimation methods include weighing, flow integral, table lookup, and equation of state methods, with the equation of state method receiving widespread attention due to its strong theoretical foundation and broad applicability. However, the original Peng-Robinson equation of state (PR-EOS) suffers from systematic errors under high pressure and dynamic environments, particularly under conditions of cylinder structural deformation, non-uniform gas distribution, or extreme temperature and pressure, where estimation accuracy significantly decreases. Summary of the Invention

[0003] In view of this, the present invention proposes an adaptive estimation method and system for the gas mass of high-pressure hydrogen storage cylinders, aiming to solve the problem of decreased estimation accuracy of the PR-EOS equation of state under complex working conditions due to structural deformation and non-uniform gas distribution.

[0004] This invention proposes an adaptive estimation method for the gas mass of a high-pressure hydrogen storage cylinder, comprising: Obtain the structural parameters, material properties, and empty cylinder mass of the high-pressure hydrogen storage cylinder; The pressure, temperature, and total mass of the high-pressure hydrogen storage cylinder are collected in real time, and the pressure change rate is determined based on the pressure. Based on the pressure, temperature, structural parameters and material properties, a Peng-Robinson equation of state model is constructed that integrates volume correction, attraction term correction and gas distribution non-uniformity compensation based on the pressure change rate, and the model is solved to obtain the current gas mass estimate. The actual gas mass is determined based on the difference between the total mass of the gas cylinder and the mass of the empty cylinder. Based on the error signal between the actual gas mass and the current gas mass estimate, at least one correction parameter related to the volume correction, attraction term correction, and gas distribution non-uniformity compensation is dynamically updated through an online learning mechanism to achieve adaptive optimization of gas mass estimation.

[0005] Furthermore, in the aforementioned adaptive estimation method for the gas mass of high-pressure hydrogen storage cylinders, the volume correction is based on a thin-walled cylindrical elastic mechanical model. Combining the yield strain, elastic modulus, Poisson's ratio, wall thickness, and current internal pressure of the cylinder material, the radial expansion of the cylinder is calculated, and the volume change of the cylinder is derived accordingly. The original nominal volume is replaced with the corrected volume to achieve dynamic correction of the volume term in the Peng-Robinson equation of state.

[0006] Furthermore, in the above adaptive estimation method for the gas mass of high-pressure hydrogen storage cylinders, the attraction term correction is achieved by introducing a temperature-dependent correction function, which is: a corr = a 0 · (1+) a·ΔT / T ),in, a 0 represents the attraction term coefficient in the PR-EOS standard form. ΔT This indicates the deviation of the actual temperature of hydrogen from its ideal state. α This is a correction factor for the intermolecular interaction potential of hydrogen gas.

[0007] Furthermore, in the aforementioned adaptive estimation method for the gas mass of high-pressure hydrogen storage cylinders, the gas distribution non-uniformity compensation based on the pressure change rate is achieved through a dynamic mixing coefficient. m Implementation, including: m =1− e −kt / τ in, k These are the empirical fitting coefficients. t For the duration of filling, t This is the mixing time constant.

[0008] Furthermore, in the above adaptive estimation method for the gas mass of high-pressure hydrogen storage cylinders, the step of dynamically updating at least one correction parameter in the model through an online learning mechanism includes: The total mass of the gas cylinder is periodically obtained by weighing sensors, and the actual gas mass is determined by combining the mass of the empty cylinder. The actual gas mass is compared with the current gas mass estimate output by the model to generate an error signal; Based on the error signal, at least one of the volume correction amount, attraction term correction coefficient, and dynamic mixing coefficient in gas distribution non-uniformity compensation is iteratively updated using an incremental machine learning model.

[0009] Furthermore, in the above-mentioned adaptive estimation method for the gas mass of high-pressure hydrogen storage cylinders, the online learning mechanism adopts an incremental machine learning model and iteratively updates the volume correction, attraction term correction coefficient, and / or dynamic mixing coefficient based on the error signal between the actual gas mass and the current gas mass estimation value.

[0010] Furthermore, in the above adaptive estimation method for the gas mass of high-pressure hydrogen storage cylinders, the incremental machine learning model is an incremental support vector machine or a recurrent neural network.

[0011] Furthermore, in the above-mentioned adaptive estimation method for the gas mass of high-pressure hydrogen storage cylinders, the solution of the modified Peng-Robinson equation of state model adopts a numerical iteration method. After obtaining the number of gas moles, the current gas mass estimate is calculated by combining the hydrogen mole mass.

[0012] The adaptive estimation method for gas mass of high-pressure hydrogen storage cylinders in this invention significantly improves the accuracy of gas mass estimation during actual filling and discharging processes by integrating volume correction, attraction term correction, and gas distribution non-uniformity compensation based on the pressure change rate, and dynamically updating each correction parameter through an online learning mechanism. It effectively overcomes the problem of decreased gas mass estimation accuracy caused by structural deformation and non-uniform gas distribution in the PR-EOS equation of state under complex operating conditions.

[0013] This invention also provides an adaptive estimation system for the gas mass of a high-pressure hydrogen storage cylinder, comprising: Storage unit, used to store the structural parameters, material properties and empty cylinder mass of high-pressure hydrogen storage cylinder; The data acquisition unit is used to collect the pressure, temperature and total mass of the high-pressure hydrogen storage cylinder in real time. The fusion modeling unit is used to determine the pressure change rate based on the pressure; and to construct a Peng-Robinson equation of state model that integrates volume correction, attraction term correction and gas distribution non-uniformity compensation based on the pressure change rate, according to the pressure, temperature, structural parameters and material properties, and solve the model to obtain the current gas mass estimate. An adaptive feedback unit is used to determine the actual gas mass based on the difference between the total mass of the gas cylinder and the mass of the empty cylinder, and to dynamically update at least one correction parameter related to the volume correction, attraction term correction and gas distribution non-uniformity compensation through an online learning mechanism based on the error signal between the actual gas mass and the current gas mass estimate, thereby achieving adaptive optimization of gas mass estimation.

[0014] Furthermore, in the aforementioned adaptive estimation system for the gas mass of high-pressure hydrogen storage cylinders, the adaptive feedback unit employs an incremental machine learning model and iteratively updates the volume correction, attraction term correction coefficient, and / or dynamic mixing coefficient based on the error signal between the actual gas mass and the current gas mass estimation value.

[0015] The adaptive estimation system for gas mass in high-pressure hydrogen storage cylinders of the present invention integrates volume correction, attraction term correction and gas distribution non-uniformity compensation through a fusion modeling unit, and updates relevant parameters by combining an adaptive feedback unit. This effectively avoids the systematic deviation caused by structural deformation and non-uniform gas distribution in existing technologies, and significantly improves the accuracy of gas mass estimation under complex working conditions. It is especially suitable for scenarios with extremely high requirements for gas mass monitoring, such as aerospace and low-altitude aircraft. Attached Figure Description

[0016] Various other advantages and benefits will become apparent to those skilled in the art upon reading the following detailed description of preferred embodiments. The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. Furthermore, the same reference numerals denote the same parts throughout the drawings. In the drawings: Figure 1 A flowchart illustrating the adaptive estimation method for the gas mass of a high-pressure hydrogen storage cylinder provided in an embodiment of the present invention. Detailed Implementation

[0017] Exemplary embodiments of the present disclosure will now be described in more detail with reference to the accompanying drawings. While exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure may be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided to enable a more thorough understanding of the present disclosure and to fully convey the scope of the disclosure to those skilled in the art. It should be noted that, unless otherwise specified, the embodiments and features described herein can be combined with each other. The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0018] Method Implementation Examples: See Figure 1 The adaptive estimation method for the gas mass of a high-pressure hydrogen storage cylinder according to embodiments of the present invention includes: Step S1: Obtain the structural parameters, material properties, and empty cylinder mass of the high-pressure hydrogen storage cylinder.

[0019] Specifically, in the embodiments of the present invention, the high-pressure hydrogen storage cylinder refers to a gaseous hydrogen storage container with a working pressure of 10~70MPa.

[0020] The structural parameters of a high-pressure hydrogen storage cylinder may include geometric parameters such as the cylinder's nominal volume, wall thickness, inner diameter, and outer diameter; material properties may include the material's yield strain, elastic modulus, and Poisson's ratio, which are used to calculate the deformation of the cylinder's sidewall under internal pressure, thereby supporting the construction of the volume correction term.

[0021] The empty cylinder mass is the net weight of the cylinder when it is not storing hydrogen, and it serves as the benchmark for subsequent calculations of the actual gas mass.

[0022] Step S2: Real-time acquisition of pressure, temperature and total mass of the high-pressure hydrogen storage cylinder, and determination of pressure change rate based on the pressure.

[0023] Specifically, the instantaneous pressure inside the gas cylinder is obtained through a high-precision pressure sensor. P The temperature inside the gas cylinder is obtained through a temperature sensor. T The total mass of the gas cylinder is collected by a weighing sensor, and the current pressure change rate is calculated based on continuously collected pressure data. dP / dt .

[0024] Step S3: Based on the pressure, temperature, structural parameters, and material properties, construct a Peng-Robinson equation of state model that integrates volume correction, attraction term correction, and gas distribution non-uniformity compensation based on the pressure change rate, and solve the model to obtain the current gas mass estimate.

[0025] In this embodiment, the volume correction is based on the thin-walled cylindrical elastic mechanical model. Combining the yield strain, elastic modulus, Poisson's ratio, wall thickness and current internal pressure of the gas cylinder material, the radial expansion of the gas cylinder is calculated, and the volume change of the gas cylinder is derived accordingly. The original nominal volume is replaced with the corrected volume to achieve dynamic correction of the volume term in the Peng-Robinson equation of state, thereby improving the accuracy of volume modeling under high pressure deformation conditions.

[0026] The modified Peng-Robinson equation of state model is solved using a numerical iteration method. After obtaining the number of gas moles, the current gas mass is estimated by combining the molar mass of hydrogen.

[0027] Specifically, the volume correction is based on the elastic mechanical model of a thin-walled cylinder, combined with the yield strain of the gas cylinder material. d Elastic modulus E Poisson's ratio n and wall thickness t and current pressure P The radial expansion amount is calculated, and the volume translation correction amount is derived from it. ΔV Volume translation correction amount ΔV This indicates the volume expansion of a gas cylinder under high pressure due to internal pressure; its size is related to the pressure.P Positively correlated and subject to material yield strain d Elastic modulus E Poisson's ratio n and wall thickness t The influence of elastic modulus; among them, elastic modulus E Poisson's ratio n and wall thickness t The correction calculation is involved when the gas cylinder undergoes elastic deformation; while the material yield strain δ is only used as a correction for volume translation when the gas cylinder undergoes plastic deformation. ΔV The effect is that, under normal conditions, the gas cylinder does not undergo plastic deformation; therefore, the material's yield strain δ does not participate in the volume shift correction. ΔV Correction.

[0028] radial expansion of gas cylinder Δr Due to internal pressure P Determined by material properties: in: The inner radius of the gas cylinder (obtained from structural parameters); P Due to current internal pressures; E The elastic modulus of the material; n Poisson's ratio of the material; t For wall thickness; volume translation correction amount ΔV By integrating the radial expansion using the formula for the volume of a cylinder, the change in volume is derived: in: L The length of the gas cylinder (obtained from structural parameters).

[0029] Substitution Δr The complete expression is obtained after applying the calculation formula: The original nominal volume of the gas cylinder V 0 Updated to take into account the actual effective volume after deformation. V' = V 0+ ΔV Substituting this into the volume term of the Peng-Robinson equation of state more accurately reflects the true volume of the gas cylinder. By solving the Peng-Robinson equation of state, the number of moles of hydrogen in the gas cylinder can be obtained. n Then, based on the molar mass of hydrogen... M The estimated value of the current gas mass is calculated. m est = n · M Due to the effective volume V'It already includes the expansion effect caused by the deformation of the gas cylinder under high pressure, thus overcoming the estimation error caused by the traditional model ignoring the deformation of the container structure.

[0030] In this embodiment, the attraction correction term is introduced to address the underestimation of the attraction of hydrogen in the existing Peng-Robinson equation of state under extreme conditions of low temperature or high pressure. To improve the accuracy of the PR-EOS in characterizing the intermolecular interaction potential under these conditions, this embodiment introduces a temperature- and quantum effect coupled attraction correction term to dynamically adjust the attraction parameters in the Peng-Robinson equation of state. a Specifically, the attraction term correction is achieved by introducing a correction function that couples temperature with quantum effects. a ( T , ΔT , α To dynamically adjust the attraction parameters in the Peng-Robinson equation of state. a ,in, T This represents the current measured gas temperature. ΔT This represents the deviation of the actual temperature of the gas from its ideal state. α This is a correction factor for the intermolecular potential of hydrogen. The ideal state temperature refers to the reference temperature at which hydrogen, under current pressure, best conforms to the classical Peng-Robinson equation of state (PR-EOS) theory. This temperature is determined experimentally by fitting the second virial coefficient of hydrogen to reflect the thermodynamic equilibrium point where quantum effects are negligible. The deviation between the actual temperature and the ideal state temperature is... ΔT Through the formula: Calculations, for example, when the measured temperature ( And the fitting yields ( )hour,( This offset is used to correct the attraction term coefficient to compensate for the quantum behavior deviation of hydrogen under low temperature and high pressure, thereby reducing the mass estimation error from more than 3% in the traditional method to less than 0.8%.

[0031] Because hydrogen exhibits significant quantum deviation behavior under high pressure and low temperature conditions, the above-mentioned correction mechanism effectively compensates for the systematic deviation of the traditional PR-EOS equation under such conditions.

[0032] The corrected attraction parameters a Substituting the values ​​into the Peng-Robinson equation of state can significantly improve the accuracy of estimating the density and number of moles of a gas under extreme conditions such as low temperature or high pressure.

[0033] In this embodiment, the correction function is: a ( T , ΔT ,α The specific form of ) is: a corr = a 0 · (1+) a·ΔT / T ) in, a 0 represents the attraction term coefficient in the PR-EOS standard form; a corr The corrected attraction term coefficient, α This is a correction factor for the intermolecular interaction potential of hydrogen gas.

[0034] α The empirical correction coefficients, which need to be fitted experimentally, are obtained as follows: Under a fixed pressure, by comparing the deviations between the actual measured values ​​of hydrogen density and the classical PR-EOS predicted values ​​under different temperature conditions, the least squares method is used to optimize the corrected equation of state. Minimize the prediction error, thereby calibrating α Value; in the embodiments of the present invention α The value range is from 0.15 to 0.25 (e.g., when...). P=60 Fitted at MPa α =0.18), the specific value depends on the purity of hydrogen and the pressure range.

[0035] This embodiment takes α =0.98; ΔT This represents the deviation between the measured temperature and the ideal temperature. Taking a specific low-temperature flight condition as an example, when... T =270K ΔT When =−5K, substituting into the above formula yields: a corr =0.1044 Pa•pm 6 / mole ² Calculation results show that under these conditions a corr The value is reduced by about 3.2% compared to the uncorrected value, which more accurately reflects the actual attraction between hydrogen molecules at low temperatures and helps to improve the accuracy of hydrogen density and molar number estimation.

[0036] During unsteady gas filling and discharging processes, uneven gas distribution can occur inside high-pressure hydrogen storage cylinders, leading to local density errors and consequently affecting the accuracy of mass estimation based on equations of state.

[0037] To characterize this type of non-uniformity, this embodiment introduces a dynamic mixing coefficient. m This coefficient is based on the real-time monitored rate of pressure change. dP / dt and filling duration t Construction. Furthermore, by introducing a time lag factor... t The transient distribution of gas is modeled, and a compensation term is introduced in the process of solving the state equation to correct the local density error caused by uneven gas distribution and improve the consistency of mass estimation under unsteady operating conditions.

[0038] Prioritize monitoring the rate of pressure change during rapid filling. This is because its real-time measurement is simple and directly related to gas flow dynamics and mixing efficiency, effectively reflecting distribution non-uniformity; while temperature gradient and concentration gradient are difficult to capture accurately in real time during high-speed filling due to sensor response lag, spatial distribution complexity, and measurement noise interference. Therefore, this embodiment of the invention only drives the dynamic mixing coefficient through the pressure change rate. A compensation model is proposed to simplify system implementation.

[0039] In this embodiment, the gas distribution non-uniformity compensation based on the pressure change rate is achieved through a dynamic mixing coefficient. m Implementation, including: m =1− e −kt / τ in, k These are the empirical fitting coefficients. t For the duration of filling, t This is the mixing time constant.

[0040] Empirical fit coefficient k The data is obtained through pressure change rate data from filling experiments (e.g., different...). (Pressure gradient measurement), and optimization of dynamic mixing coefficient using the least squares method. The predicted value minimizes the error in the compensated gas mass estimation; the value range in the embodiment is 0.12~0.28 (e.g., when...). The fitting result at =15s is obtained k =0.18), the specific value depends on the filling flow rate and the tank size.

[0041] Dynamic mixing coefficient m This reflects the degree of uniformity of gas mixing within the cylinder; its value approaches 1 when the gas distribution becomes relatively uniform. This dynamic mixing coefficient... m This is used to introduce non-uniformity in the solution of the Peng-Robinson equation of state to correct local density errors caused by insufficient gas mixing, thereby improving the consistency of mass estimation under unsteady operating conditions.

[0042] For example, during ground-based or intermediate hydrogen replenishment, hydrogen is injected at high speed from the cylinder opening, creating a significant concentration and temperature gradient within the cylinder over a period of time. In this case, the aforementioned dynamic mixing coefficient correction mechanism can reflect the hysteresis characteristics of the gas mixing process, thereby improving the stability of mass estimation under unsteady conditions. Taking a rapid filling process as an example, the measured pressure change rate... dP / dt =2.5 MPa / s, combined with historical data to estimate the mixed time constant τ= 10.5s k Using design experience values ​​(experience range 0.12 to 0.28), practical applications require consideration of sensor accuracy and dynamic fine-tuning during filling. The dynamic mixing coefficient is then calculated at the current moment. m The value ≈0.78 indicates that the gas inside the cylinder has not yet achieved a completely uniform distribution. Based on this, a weighted correction is applied to the instantaneously estimated hydrogen density using a dynamic mixing coefficient. Sensor measured value of hydrogen density Compared with model calculated values Perform dynamic fusion: Corrected density in As the filling time Increment (initial) Time depends on sensor values, later (Time-dependent model values).

[0043] The design is achieved through The exponential characteristic gradually suppresses local measurement errors in the sensor caused by uneven gas distribution (such as concentration gradients at the tank edge), while the model value... Integral flow rate from inlet and ideal gas law Generated through temperature compensation.

[0044] Multiplying the corrected hydrogen density by the volume-corrected effective volume of the cylinder yields an estimated hydrogen mass. By introducing a non-uniformity compensation term into the PR-EOS solution, the accuracy of mass estimation under unsteady conditions such as rapid filling is significantly improved.

[0045] Step S4: Determine the actual gas mass based on the difference between the total mass of the gas cylinder and the mass of the empty cylinder, and dynamically update at least one correction parameter related to the volume correction, attraction term correction, and gas distribution non-uniformity compensation through an online learning mechanism based on the error signal between the actual gas mass and the current gas mass estimate, thereby achieving adaptive optimization of gas mass estimation.

[0046] Specifically, at least one correction parameter in the model is dynamically updated through an online learning mechanism, including: The total mass of the gas cylinder is periodically obtained by weighing sensors, and the actual gas mass is determined by combining the mass of the empty cylinder. The actual gas mass is compared with the current gas mass estimate output by the model to generate an error signal; Based on the error signal, at least one of the volume correction amount, attraction term correction coefficient, and dynamic mixing coefficient in gas distribution non-uniformity compensation is iteratively updated using an incremental machine learning model.

[0047] In one specific embodiment of the present invention, the incremental machine learning model is an incremental support vector machine, which updates the volume correction, attraction term correction coefficient and / or dynamic mixing coefficient in real time based on the error signal between the actual gas mass and the estimated value; in another specific embodiment, the incremental machine learning model is a recurrent neural network, which dynamically adjusts the above correction parameters through continuously collected error signals.

[0048] Specifically, the correction parameters include: volume translation correction for compensating for gas cylinder structural deformation; attraction term correction coefficient for compensating for deviations in modeling intermolecular attraction under unsteady conditions in the equation of state; and dynamic mixing coefficient for characterizing gas mixing homogeneity and introducing non-homogeneity compensation during the solution of the equation of state.

[0049] The model in this embodiment refers to a comprehensive thermodynamic model formed by correcting the volume, attraction terms, and gas distribution non-uniformity based on the Peng-Robinson equation of state.

[0050] In this embodiment, the current actual gas mass is determined based on the difference between the total mass of the gas cylinder and the mass of the empty cylinder collected by the weighing sensor. The error signal between the actual gas mass and the gas mass currently estimated by the model is input into the online learning model. Based on the error feedback, the model optimizes the volume translation correction, the attraction term correction coefficient, and the dynamic mixing coefficient in the gas distribution non-uniformity compensation.

[0051] Substituting the modified volume and attraction terms into the Peng-Robinson equation of state, we obtain the modified equation of state: P = RT / [( V m - b )- a corr / V m ( V m + b )+ b ( V m -b )] in, V m The molar volume of hydrogen is given by the corrected effective volume. V′ With the number of gas moles n Relationship V m = V′ / n get; b For the exclusion term parameter.

[0052] When solving this equation, the number of moles of gas can be obtained through numerical iteration methods (such as the Newton-Raphson method). n Then, combined with the molar mass of hydrogen gas M (Approximately 2.016 g / mol), combined with the dynamic mixing coefficient calculated in the mixing non-uniformity compensation mechanism. m The equivalent density calculated using the Peng-Robinson equation of state is adjusted to obtain the current gas mass estimate. m est = n × M。

[0053] In the quality estimation formula There is no need to explicitly introduce dynamic mixing coefficients. This is because A weighted mechanism has been applied during the density correction stage to the equivalent density calculated based on the Peng-Robinson equation of state (e.g., based on , (and component parameter calculations). Corrected density. Used to deduce the amount of substance ( (for the tank volume), final Equivalent to , The impact is already indirectly included in In this case, there is no need to handle it separately in the quality calculation.

[0054] By combining the molar mass of hydrogen with the corrected number of moles, the gas mass under the current condition is calculated. This improves the accuracy of volumetric modeling of the equation of state under high-pressure conditions, thereby enhancing the accuracy of gas weight estimation. It is particularly suitable for scenarios with extremely high requirements for gas mass monitoring, such as aerospace and low-altitude aircraft.

[0055] Furthermore, the mass of real gas m true Compared with current gas mass estimates m est Comparison to generate error signals e=m true －m est Based on this error signal, an incremental machine learning model is used to iteratively update at least one of the volume correction, attraction term correction coefficient, and dynamic mixing coefficient in gas distribution non-uniformity compensation.

[0056] It is evident from the above that the adaptive estimation method for the gas mass of high-pressure hydrogen storage cylinders provided in this embodiment significantly improves the accuracy of gas mass estimation during the actual filling and discharging process of high-pressure hydrogen storage cylinders by integrating volume correction, attraction term correction, and gas distribution non-uniformity compensation based on the pressure change rate, and dynamically updating each correction parameter through an online learning mechanism. This effectively overcomes the problem of decreased gas mass estimation accuracy caused by structural deformation and non-uniform gas distribution under complex operating conditions in the PR-EOS equation of state.

[0057] Example: The invention will be described in detail using the high-pressure hydrogen storage cylinder in the fuel cell hydrogen supply system of a certain type of drone as an example: To ensure coordinated decision-making between the flight control system and the energy management module, the system needs to estimate the hydrogen mass in the cylinder in real time throughout the flight. The cylinder is made of high-strength aluminum alloy and has a nominal volume of... V 0 =20L, rated working pressure is 70MPa. Due to the periodic acceleration, ambient temperature fluctuations, and frequent filling and discharging conditions experienced by the gas cylinder during flight, traditional mass estimation based on uncorrected PR-EOS has significant errors. Therefore, this embodiment adopts the estimation method based on dynamic correction of the Peng-Robinson equation of state proposed in this invention, as detailed below: During flight, the pressure inside the gas cylinder P The yield strain varies within the range of 10MPa to 70MPa. Based on the material and structural parameters, the yield strain of this aluminum alloy gas cylinder is... d =0.15%, elastic modulus E =70 GPa, Poisson's ratio n =0.33, wall thickness t =12 mm. Based on the elastic mechanical model of a thick-walled cylinder, under a given internal pressure... P Calculate the inner and outer radii of the gas cylinder under the following conditions rᵢ , r o Corresponding radial expansion Δr (r) The volume change is obtained by integrating the volume of the shell. ΔV .

[0058] In this embodiment, when P When the pressure is 60 MPa, the calculated increase in cylinder volume is... ΔV≈0.38 L, therefore the effective volume used for PR-EOS calculation is determined by the nominal value. V 0 =20L is corrected to: V′ = V 0 + ΔV =20.38L, thus eliminating the systematic underestimation of the volume term in the equation of state due to the elastic expansion of the gas cylinder under high pressure.

[0059] Hydrogen exhibits significant quantum deviation behavior under high pressure and low temperature conditions. To improve the characterization accuracy of intermolecular interaction potentials by PR-EOS under these conditions, this embodiment introduces an attraction term correction function. a ( T , ΔT , α ): a corr = a 0 · (1+) a·ΔT / T )in, a 0 represents the attraction term coefficient in the PR-EOS standard form. α As the correction factor for the interaction potential of hydrogen molecules, this embodiment takes... α =0.98; ΔT This represents the deviation between the measured temperature and the ideal temperature. Taking a specific low-temperature flight condition as an example, when... T =270K ΔT When =−5K, substituting into the above relationship, we get: a corr =0.1044 Pa•pm 6 / mole ² Calculation results show that under these conditions a corr The value is reduced by about 3.2% compared to the uncorrected value, which more accurately reflects the actual attraction between hydrogen molecules at low temperatures and helps to improve the accuracy of density and mole number estimation.

[0060] During ground-based or en route hydrogen replenishment, hydrogen is injected at high speed from the cylinder opening, creating a significant concentration and temperature gradient within the cylinder over a period of time. To characterize this non-uniformity, this embodiment uses real-time monitoring of the pressure change rate. dP / dt and filling duration t Constructing dynamic mixing coefficients m Implementation, including: m =1− e −kt / τ in, kThese are the empirical fitting coefficients. t For the duration of filling, t This is the mixing time constant.

[0061] Taking a rapid inflation process as an example, the actual test... dP / dt =2.5 MPa / s, combined with historical data to estimate the mixed time constant τ= 10.5s k By taking the design experience value, the dynamic mixing coefficient can be calculated at the current moment. m The value ≈0.78 indicates that the gas inside the cylinder has not yet achieved a completely uniform distribution. Based on this, a weighted correction is applied to the instantaneously estimated hydrogen density. Multiplying the corrected hydrogen density by the volume-corrected effective volume of the cylinder yields the estimated hydrogen mass. By introducing a non-uniformity compensation term into the PR-EOS solution, the accuracy of mass estimation under unsteady-state conditions such as rapid filling is significantly improved.

[0062] To suppress model drift during long-term operation, this embodiment periodically (e.g., collecting weighing data every 5 minutes) obtains the total mass of the gas cylinder. m rue As a calibration "true value" (e.g., by placing a small weighing sensor near the drone's landing gear), and compared with the current model to estimate the mass. m est By comparison, the relative error sequence is obtained. e The error sequence is input into an incremental support vector machine (SVM) online learning model to automatically output volume translation corrections based on the error trend. ΔV The system adjusts the attraction term correction coefficient and updates the corresponding parameters of the thermodynamic estimation model. Through this adaptive mechanism, the system can maintain the accuracy of gas mass estimation under operating conditions such as cylinder aging and temperature changes.

[0063] For example, in three consecutive estimations at a certain stage, the model errors were +2.1%, +2.4%, and +2.7%, respectively. The SVM model judges the existing... ΔV The value is too small, so the volume translation correction amount is adaptively adjusted to make... ΔV The value was corrected from 0.38L to 0.41L. After the update, the relative error of mass estimation in subsequent flight cycles was stably controlled within ±0.5%, significantly improving the long-term stability and robustness of the method.

[0064] At a certain moment, the system measured the internal pressure of the gas cylinder. P =60MPa, temperature T =270K. The controller first calls the volume translation module and the attraction term correction module to obtain the translation-corrected volume. V′ =20.38L and the corrected attraction term coefficienta corr =0.1044 Pa•pm 6 / mole ²; Exclusion parameter b The standard value of hydrogen is taken, and the dynamic mixing coefficient is calculated in conjunction with the mixing non-uniformity compensation module. m The equivalent density is adjusted.

[0065] Based on this, substituting the modified volume and attraction terms into the Peng-Robinson equation of state, we obtain the modified equation of state: P = RT / [( V m - b )- a corr / V m ( V m + b )+ b ( V m - b )] in, V m The molar volume of hydrogen is given by the corrected effective volume. V′ With the number of gas moles n Relationship V m = V′ / n get; b For the exclusion term parameter.

[0066] When solving this equation, the number of moles of gas, n, can be obtained through numerical iteration methods (such as the Newton-Raphson method). This is then combined with the molar mass of hydrogen, M (approximately 2.016 g / mol), and the dynamic mixing coefficient calculated in the mixing inhomogeneity compensation mechanism. m The equivalent density calculated using the Peng-Robinson equation of state is adjusted to obtain the current gas mass estimate. m est = n × M .

[0067] Extensive flight and ground tests have verified that, under typical mission profiles (including takeoff, cruise, maneuvering, and return phases), the method in this embodiment can control the mean absolute error (AAD) of hydrogen mass in the cylinder to below 0.8%, which is significantly better than the traditional lookup table method and the uncorrected PR-EOS method, providing a reliable data foundation for energy management and safety control of UAV fuel cell hydrogen supply systems.

[0068] System Implementation Example: The adaptive estimation system for the gas mass of the high-pressure hydrogen storage cylinder of the present invention includes: Storage unit, used to store the structural parameters, material properties and empty cylinder mass of high-pressure hydrogen storage cylinder; The data acquisition unit is used to collect the pressure, temperature and total mass of the high-pressure hydrogen storage cylinder in real time. A fusion modeling unit is used to determine the pressure change rate based on the pressure; and to construct a Peng-Robinson equation of state model that integrates volume correction, attraction term correction, and gas distribution non-uniformity compensation based on the pressure change rate, according to the pressure, temperature, structural parameters, and material properties, and solve the model to obtain the current gas mass estimate; wherein, the fusion modeling unit further includes: The volume shift correction module is used to determine the volume shift correction amount based on the measured pressure and the structural parameters and material properties of the high-pressure hydrogen storage cylinder. ΔV, To compensate for the change in effective volume caused by deformation of the gas cylinder structure; The attraction term correction module is used to calculate the attraction term correction coefficient based on the measured temperature, and to perform temperature-related compensation on the intermolecular attraction term in the Peng-Robinson equation of state in order to correct the modeling bias under unsteady conditions. The non-uniformity compensation module is used to output a dynamic mixing coefficient based on the pressure change rate and continuous filling time, and introduces a non-uniformity compensation term in the solution of the Peng-Robinson equation of state to correct local density errors caused by uneven gas distribution.

[0069] The equation-of-state solution module receives pressure, temperature, volume shift correction, attraction term correction coefficient, and dynamic mixing coefficient, constructs the corrected Peng-Robinson equation of state, and uses an iterative numerical solution method to solve for the number of gas moles. Combined with the gas molar mass, it calculates the current gas mass estimate. The Newton-Raphson iterative numerical solution method is used to improve the solution efficiency and convergence, ensuring real-time operation in embedded systems.

[0070] An adaptive feedback unit is used to determine the actual gas mass based on the difference between the total mass of the gas cylinder and the mass of the empty cylinder, and to dynamically update at least one correction parameter related to the volume correction, attraction term correction and gas distribution non-uniformity compensation through an online learning mechanism based on the error signal between the actual gas mass and the current gas mass estimate, thereby achieving adaptive optimization of gas mass estimation.

[0071] The adaptive feedback unit employs an incremental machine learning model and iteratively updates the volume correction, attraction term correction coefficient, and / or dynamic mixing coefficient based on the error signal between the actual gas mass and the current gas mass estimate. This unit uses a lightweight machine learning algorithm (such as an incremental support vector machine or a recurrent neural network), taking the measured weighing data as the "true value" input, performing residual analysis with the model estimation results, and dynamically adjusting the volume shift term. D V Attraction term correction coefficient a Key parameters, etc. This module supports online learning and parameter updates, enabling adaptive optimization of the model during operation and improving long-term estimation stability and robustness.

[0072] The functions and workflows of each unit in the system embodiment can be referred to the relevant descriptions in the above method embodiment, and will not be repeated here.

[0073] In one specific embodiment, the data acquisition unit includes a pressure sensor, a temperature sensor, and a weighing sensor, which are used to collect the pressure, temperature, and total mass of the high-pressure hydrogen storage cylinder in real time.

[0074] The fusion modeling unit and adaptive feedback unit can be integrated into embedded edge computing devices or deployed on general-purpose servers. The entire system implements the operations of the aforementioned units by the processor executing computer programs stored in memory.

[0075] The incremental support vector machine in this embodiment is a well-known online machine learning method in the art. It can adopt any incremental learning algorithm in the prior art that is suitable for small sample regression tasks, and can select an appropriate configuration according to actual needs to achieve the above parameter update function.

[0076] In summary, the adaptive estimation system for the gas mass of high-pressure hydrogen storage cylinders of the present invention integrates volume correction, attraction term correction, and gas distribution non-uniformity compensation through a fusion modeling unit, and updates relevant parameters in conjunction with an adaptive feedback unit. This effectively avoids the systematic deviations caused by structural deformation and non-uniform gas distribution in existing technologies, significantly improving the accuracy of gas mass estimation under complex operating conditions. It is particularly suitable for scenarios with extremely high requirements for gas mass monitoring, such as aerospace and low-altitude aircraft.

[0077] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims of this invention and their equivalents, this invention also intends to include these modifications and variations.

Claims

1. An adaptive estimation method for the gas mass of a high-pressure hydrogen storage cylinder. The adaptive estimation method for the gas mass of a high-pressure hydrogen storage cylinder is characterized by, include: Obtain the structural parameters, material properties, and empty cylinder mass of the high-pressure hydrogen storage cylinder; The pressure, temperature, and total mass of the high-pressure hydrogen storage cylinder are collected in real time, and the pressure change rate is determined based on the pressure. Based on the pressure, temperature, structural parameters and material properties, a Peng-Robinson equation of state model is constructed that integrates volume correction, attraction term correction and gas distribution non-uniformity compensation based on the pressure change rate, and the model is solved to obtain the current gas mass estimate. The actual gas mass is determined based on the difference between the total mass of the gas cylinder and the mass of the empty cylinder. Based on the error signal between the actual gas mass and the current gas mass estimate, at least one correction parameter related to the volume correction, attraction term correction, and gas distribution non-uniformity compensation is dynamically updated through an online learning mechanism to achieve adaptive optimization of gas mass estimation.

2. The adaptive estimation method for the gas mass of a high-pressure hydrogen storage cylinder according to claim 1, characterized in that, The volume correction is based on the thin-walled cylindrical elastic mechanical model, combined with the yield strain, elastic modulus, Poisson's ratio, wall thickness and current internal pressure of the gas cylinder material, to calculate the radial expansion of the gas cylinder, and derive the change in gas cylinder volume accordingly. The original nominal volume is replaced with the corrected volume to achieve dynamic correction of the volume term in the Peng-Robinson equation of state.

3. The adaptive estimation method for the gas mass of a high-pressure hydrogen storage cylinder according to claim 1, characterized in that, The attraction term correction is achieved by introducing a temperature-dependent correction function, which is: a corr = a 0 · (1+ α·ΔT / T ),in, a 0 represents the attraction term coefficient in the PR-EOS standard form. ΔT This indicates the deviation between the actual temperature of hydrogen and its ideal state. α This is a correction factor for the intermolecular interaction potential of hydrogen gas.

4. The adaptive estimation method for the gas mass of a high-pressure hydrogen storage cylinder according to claim 1, characterized in that, The gas distribution non-uniformity compensation based on pressure change rate is achieved through a dynamic mixing coefficient. μ Implementation, in which: μ =1− e −kt / τ in, k These are the empirical fitting coefficients. t For the duration of filling, τ This is the mixing time constant.

5. The adaptive estimation method for the gas mass of a high-pressure hydrogen storage cylinder according to claim 1, characterized in that, The step of dynamically updating at least one correction parameter in the model through an online learning mechanism includes: The total mass of the gas cylinder is periodically obtained by weighing sensors, and the actual gas mass is determined by combining the mass of the empty cylinder. The actual gas mass is compared with the current gas mass estimate output by the model to generate an error signal; Based on the error signal, at least one of the volume correction amount, attraction term correction coefficient, and dynamic mixing coefficient in gas distribution non-uniformity compensation is iteratively updated using an incremental machine learning model.

6. The adaptive estimation method for the gas mass of a high-pressure hydrogen storage cylinder according to claim 1, characterized in that, The online learning mechanism employs an incremental machine learning model and iteratively updates the volume correction, attraction term correction coefficient, and / or dynamic mixing coefficient based on the error signal between the actual gas mass and the current gas mass estimate.

7. The adaptive estimation method for the gas mass of a high-pressure hydrogen storage cylinder according to claim 6, characterized in that, The incremental machine learning model is an incremental support vector machine or a recurrent neural network.

8. The adaptive estimation method for the gas mass of a high-pressure hydrogen storage cylinder according to claim 1, characterized in that, The modified Peng-Robinson equation of state model is solved using a numerical iteration method. After obtaining the number of gas moles, the current gas mass is estimated by combining the molar mass of hydrogen.

9. An adaptive estimation system for the gas mass of a high-pressure hydrogen storage cylinder, characterized in that, include: Storage unit, used to store the structural parameters, material properties and empty cylinder mass of high-pressure hydrogen storage cylinder; The data acquisition unit is used to collect the pressure, temperature and total mass of the high-pressure hydrogen storage cylinder in real time. The fusion modeling unit is used to determine the pressure change rate based on the pressure; and to construct a Peng-Robinson equation of state model that integrates volume correction, attraction term correction and gas distribution non-uniformity compensation based on the pressure change rate, according to the pressure, temperature, structural parameters and material properties, and solve the model to obtain the current gas mass estimate. An adaptive feedback unit is used to determine the actual gas mass based on the difference between the total mass of the gas cylinder and the mass of the empty cylinder, and to dynamically update at least one correction parameter related to the volume correction, attraction term correction and gas distribution non-uniformity compensation through an online learning mechanism based on the error signal between the actual gas mass and the current gas mass estimate, thereby achieving adaptive optimization of gas mass estimation.

10. The adaptive estimation system for the gas mass of a high-pressure hydrogen storage cylinder according to claim 9, characterized in that, The adaptive feedback unit employs an incremental machine learning model and iteratively updates the volume correction, attraction term correction coefficient, and / or dynamic mixing coefficient based on the error signal between the actual gas mass and the current gas mass estimate.

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